A Technique to Derive Improved Proper Motions for Kepler Objects ...
Transcript of A Technique to Derive Improved Proper Motions for Kepler Objects ...
A Technique to Derive Improved Proper Motions for Kepler
Objects of Interest1
G. Fritz Benedict2,
Angelle M. Tanner3, Phillip A. Cargile4, and David R. Ciardi5
ABSTRACT
We outline an approach yielding proper motions with higher precision than
exists in present catalogs for a sample of stars in the Kepler field. To increase
proper motion precision we combine first moment centroids of Kepler pixel data
from a single Season with existing catalog positions and proper motions. We
use this astrometry to produce improved reduced proper motion diagrams, anal-
ogous to a Hertzsprung-Russell diagram, for stars identified as Kepler Objects of
Interest. The more precise the relative proper motions, the better the discrimi-
nation between stellar luminosity classes. With UCAC4 and PPMXL epoch 2000
positions (and proper motions from those catalogs as quasi-bayesian priors) as-
trometry for a single test Channel (21) and Season (0) spanning two years yields
proper motions with an average per-coordinate proper motion error of 1.0 mas
yr−1, over a factor of three better than existing catalogs. We apply a mapping
between a reduced proper motion diagram and an HR diagram, both constructed
using HST parallaxes and proper motions, to estimate Kepler Object of Inter-
est K-band absolute magnitudes. The techniques discussed apply to any future
small-field astrometry as well as the rest of the Kepler field.
Subject headings: astrometry — stars: distances — stars: proper motions —
stars: exoplanet hosts
2McDonald Observatory, University of Texas, Austin, TX 78712
3Department of Physics and Astronomy, Mississippi State University, Starkville, MS 39762
4Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235
5NASA Exoplanet Science Institute, Caltech, Pasadena, CA 91125
1Based on observations made with the NASA Kepler Telescope
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1. Introduction
Astrometric precision, ε, in the absence of systematic error is proportional to N−1/2,
where N is the number of observations (van Altena 2013). Theoretically, averaging the
existing vast quantity of Kepler data might permit one to approach HST /FGS astrometric
precision, 1 millisecond of arc per observation. While Kepler was never designed to be an
astrometric instrument, and despite significant astrometric systematics and the challenge of
fat pixels (3.′′9757/pixel), one can reach a particular goal; higher precision proper motions
for Kepler Objects of Interest (KOIs) from Kepler data. Additionally, these techniques
may find utility when future astrometric users of, for example, the Large Synoptic Survey
Telescope (Ivezic et al. 2008) require the highest possible astrometric precision for targets of
interest contained on a single CCD in the focal plane. Finally, proper motion measures from
any Kepler extended mission might benefit from the application of these techniques.
In transit work it is useful to know the luminosity class of a host star when estimating the
size of the companion. This requires a distance, ideally provided by a measurement of par-
allax. With simple centroiding unaware of point spread function (PSF) structure the season
to season Kepler astrometry required for parallaxes presently yields positions with average
errors exceeding 100 milliseconds of arc (mas), insufficient for parallaxes (Section 4.3). Yet
distance is a desirable piece of information. Reduced proper motion (RPM) diagrams may
provide an alternative distance estimate. The concept is simple: proper motion becomes a
proxy for distance (Stromberg 1939; Gould & Morgan 2003; Gould 2004). Statistically, the
nearer any star is to us, the more likely it is to have a larger proper motion. The RPM dia-
gram consists of the proper motion converted to a magnitude-like parameter plotted against
color. The RPM diagram is thus analogous to a Hertzsprung-Russell (HR) diagram. While
some nearby stars might have low proper motions, typically giant and dwarf stars are sep-
arable. The more precise the proper motions, the better the discrimination between stellar
luminosity classes.
In the following sections we describe our approach yielding improved placement within
an RPM for any Kepler target of interest. We outline in Section 2 the utility of RPM dia-
grams, including a calibration to absolute magnitude derived from HST astrometry; discuss
in Section 3 Kepler data acquisition and reduction; present the results of a number of tests
providing insight into the many difficulties associated with Kepler astrometry (Section 4);
describe the modeling and the proper motion results for our selected Kepler test field, (Sec-
tion 5); compare our improved RPM with that previously derived from existing astrometric
catalogs (Section 5.8); and discuss the astrophysical ramifications of our estimated absolute
magnitudes for the over 60 KOI’s in our test field (Section 6). We summarize our findings
in Section 7.
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2. A Calibrated RPM Diagram
In past HST astrometric investigations (e.g. Benedict et al. 2011, McArthur et al.
2010) the RPM was used to confirm the spectrophotometric stellar spectral types and lumi-
nosity classes of reference stars. Their estimated parallaxes are entered into the modeling
as observations with associated errors. To minimize absorption effects HST astrometric in-
vestigations use for the magnitude-like parameter HK(0) = K(0) + 5log(µ), and for a color,
(J−K)0, where K magnitudes and (J−K) colors (from 2MASS, Skrutskie et al. 2006) have
been corrected for interstellar extinction. For all of our RPMs we use the vector length
proper motion, µ = (µ2RA + µ2
DEC)1/2.
Compared to Hipparcos, HST has produced only a small number of parallaxes and
proper motions (Benedict et al. 1999, 2000a, 2000b, 2002, 2006, 2007, 2009, 2011; Harrison
et al. 2013; McArthur et al. 2001, 2010, 2011, 2013; Roelofs et al. 2007), but with higher
precision. Parallax and proper motion results for forty-two stars with HST proper motion
and parallax measures are collected in Table 1. Average parallax errors are 0.2 mas. Average
proper motion errors are 0.4 mas yr−1. Compared in Figure 1 are an HR diagram and an
RPM diagram constructed with HST parallax and proper motion results for the targets
listed in Table 1. Conspicuously absent from the RPM diagram are the RR Lyr results from
Benedict et al. (2011) with their large proper motions due to their Halo Pop II identification.
Lines plotted on the HR diagram show predicted loci for 10 Gyr age solar metallicity stars
and 3Gyr age metal-poor stars from Dartmouth Stellar Evolution models (Dotter et al.
2008). These ages and metallicities encompass the majority of what might be expected from
a random sampling of stars in our Galaxy.
Even though these targets are scattered all over the sky and range from PN central
stars to Cepheid variables, the similarity between the HR and RPM diagrams is striking. In
Figure 2 we plot the extinction corrected K-band absolute magnitude derived from HST par-
allaxes against the magnitude-like parameter HK(0). The resulting scatter, 0.7 mag RMS,
suggests that precise proper motion is a good enough proxy for distance to allow the assign-
ment of luminosity class.
Note that while this calibration is produced with proper motions sampling much of the
celestial sphere, the HR diagram and RPM main sequences are defined almost exclusively
by stars belonging to the Hyades and Pleiades clusters. This may become an issue when we
attempt to apply the calibration to a small piece of the sky in a different location. Both
the calibration sources and a random Kepler field have systematic proper motions due to
galactic rotation (c.f. van Leeuwen 2007, section 6.1.5), possibly requiring some correction.
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3. Kepler Observations and Data Reduction
The primary mission of the Kepler spacecraft is high-precision photometry with which
to discover transiting planets. Kepler rotates about the boresight once each 90 days to
maximize solar panel illumination. Each such pointing is identified by a Season number; 0–
3. Each 90 day span is identified by a Quarter number; 1–17. The CCDs in the Kepler focal
plane are identified by Channel number; 1-84. Our goal is to produce an astrometric reference
frame across a given Kepler channel containing KOIs of interest, the end product being KOI
proper motions with which to populate an RPM.
3.1. Star Data
The Kepler telescope trails the Earth in Sun-centered orbit. Details on the photometric
performance and focal plane array can be found in Borucki et al. (2010) and Caldwell et al.
(2010a). The following explorations restrict themselves to the so-called long-cadence data,
where each subsection containing a star of interest in the array is read out once every 30
minutes. These subsections of the Kepler FOV (hereafter, postage stamps) range from 4x5
pixels for fainter stars to larger than 8x8 pixels for brighter stars. Kepler pixels are a little
less than 4 arc sec on a side. Targets observed with long-cadence generate approximately
4700 postage stamps per star per Quarter.
We obtain Kepler data from the Space Telescope Science Institute Multimission Archive
(MAST). These data include both pipelined positions ( the * llc.fits files, where ‘*’ is a
global replacement marker) and postage stamp image data (the * lpd-targ.fits files). The
Kepler Archive Manual (Fraquelli & Thompson 2012) greatly assisted us with any access
issues.
3.2. Positions from Kepler image data
Positions used in this paper are generated from the Kepler postage stamp image data,
using a simple first-moment centering algorithm. We calculate
MOM CENTR X =∑
i ∗ z/∑
i (1)
MOM CENTR Y =∑
j ∗ z/∑
j (2)
where z = flux(i,j) are the flux count values for each Kepler pixel within the postage stamp.
To generate positions from the optimal aperture, any z value not in the optimal aperture is
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set to zero. To reduce the computational load and to smooth out high frequency positional
variations, normal points (NP) are formed by averaging the x and y positions for a specified
time span. The tests and results reported herein are based on nine day normal points. We
also use only data within an optimal aperture for each star defined by the Kepler team.
We provide an example of an optimal aperture for a star with Kepler identification number
KID = 7031732 in Figure 3. There are positional corrections tabulated in the MAST data
products, e.g. POS CORR1. These report the size of the differential velocity aberration
(DVA), pointing drift, and thermal effects applicable to the region of sky recorded in the file.
These corrections are applied to our derived centroids. Final positions used in the test are
corrected using the MAST position correction values, e.g., XY CORR = MOM CENTR XY
- POS CORR XY. The standard deviation of each normal point along each axis for each
star is calculated. The average standard deviation of these NP is typically on order one mas,
demonstrating exceptional astrometric stability within each postage stamp. However. this
small formal random error is a significant underestimation of the total star-to-star astrometric
quality, as we shall see below in Section 4.1.
We explored utilizing PSF fitting methods to extract positions. That approach did not
resolve the issue of poor astrometric performance over multiple quarters (see Section 4.3
below). PSF fitting is computationally intensive and complicated given the Kepler FOV
crowded stellar field and the significant PSF variations over that field (Bryson et al. 2010).
4. Kepler Astrometric Tests
These tests highlight several systematic errors and motivate our simple strategy for
dealing with them. For all astrometric modeling we employ GaussFit (Jefferys et al. 1988)
to minimize χ2.
4.1. Single Channel, Single Season, Single Quarter
These tests use 95 stars located in Channel 21, Season 0, Quarter 10 and identified as
red giants in the Kepler Input Catalog (KIC). This initial filtering by star type potentially
minimizes any effects of proper motion over the span of one or even two Quarters. The
normal point generator, run on each star selected from test Channel 21, effectively reduces
the number of discrete data sets per star from on order 4500 down to nine. We assign the
nine normal points for each of the 95 stars in the test to the nine ‘plates’. Each plate now
contains 95 stars whose epochs are now separated in time by approximately nine days. With
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the positions and positional errors generated by the normal point code (now organized as nine
‘plates’ each containing 95 star positions and associated errors) we determine scale, rotation,
and offset “plate constants” relative to an arbitrarily adopted constraint epoch (the so-called
“master plate”) for each observation set (the positions generated for each star within each
‘plate’ at each of the nine normal point epochs). The solved equations of condition are:
ξ = Ax+By + C (3)
η = −Bx+ Ay + F (4)
where x and y are the measured normal point coordinates from the Kepler postage stamps.
A and B are scale and rotation plate constants, C and F are offsets. For this test spanning
only one 90 day Quarter we ignore proper motions. When modeling these positions, in
order to approach a near unity χ2/DOF (DOF=degrees of freedom), the input positional
errors, standard deviations from the normal point averaging process, had to be increased by
a factor of four. The final catalog of (ξ, η) positions have average < σξ >= 0.31 millipixel
and < ση >= 0.64 millipixel (1.23 and 2.54 mas), seemingly quite encouraging if one’s goal
is precision astrometry with Kepler.
However, the results of this modeling, shown in Figure 4, exhibit large systematic effects,
well-correlated with time. The constraint epoch for this reduction is JD-24400000=15785.2,
the middle epoch of the nine plotted. We tentatively blame the typically larger y residuals
(y larger than x within each epoch) in Figure 4 with charge transfer smearing along the
CCD column readout direction (Kozhurina-Platais et al. 2008; Quintana et al. 2010). Our
ultimate goal is to tease out stellar positional behavior similarly correlated with time; proper
motion. Among the largest and most strikingly systematic residual patterns we find stars 9
(=KID 6363534) and 27 (=KID 6606001). Figure 5 provides an explanation for the behavior
of star 27 (a close companion that perturbed the simple first moment centering algorithm),
and presents a puzzle regarding Star 9. It has no bright companions, yet is a poorly behaved
component of our astrometric reference frame. We suspect the CCD channel-to-channel
cross-talk discussed in Caldwell et al. (2010b). Four CCDs share common readout electronics.
A bright star on one CCD can affect measured charge in another.
To determine if there might be unmodeled - but possibly correctable - systematic effects
at the 10 millipixel level, we plotted the reference frame x and y residuals against a number
of parameters. These included x, y position within the channel; radial distance from the
channel center; reference star magnitude and color; and epoch of observation. We saw no
obvious trends, other than an expected increase in positional uncertainty with reference star
magnitude. Models with separate x and y scales (6 parameters; in Equation 2 above, where
-B and A are replaced by D and E) or color terms (8 parameters) provided no improvement
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in χ2/DOF.
Given that the pipelined positions available in the llc.fits files are also first moment
centroids calculated from the optimal apertures, we developed the capability to generate
these independently as a further test of Kepler astrometry. The code used to generate the
positions whose residuals are plotted in Figure 4 can also produce first moment centroid data
using the entire postage stamp (e.g., all the flux values in the middle panel in Figure 3).
Comparing positions extracted from the entire postage stamp against the optimal subset of
the postage stamp for Channel 21, the average absolute value residual is reduced by 30% when
using the optimal apertures. However tests carried out on Channel 41 (Season 0, Quarter
10), near the Kepler field of view center result in a much less significant improvement, only
12%. This can be explained by considering the degradation in the point spread function
(PSF) from the center to the edge of the entire Kepler field of view (Bryson et al. 2010;
Tenenbaum & Jenkins 2010).
4.2. Other Single Channel Tests
4.2.1. Same Stars - Multiple Seasons and Quarters
To test whether or not the peculiar fan pattern in the residuals against time seen in
Figure 4 is Channel-specific, we carried out similar tests for Channels 41, 42, 43, and 44,
the central four CCDs in the Kepler focal plane. We sampled Quarter 3 through Quarter
14, using the same ∼75 stars in each channel. The results of this 4 parameter modeling are
given in Figure 6. Every Quarter exhibits time-depends residual behavior. The patterns
often repeat within the same season. For example, in Season 1 the x residuals for star 5
(=KID 8949862) start out large and positive and move down to large negative over ∼ 90
days. Yet star 5 is relatively well-behaved for any other Season. A comparison of Figure 6
with figure 5 in Barclay (2011)2 is convincing evidence that astrometry quality and primary
mirror temperature changes are correlated. Stable temperatures at any level yield better
astrometry (smaller residuals).
2http://archive.stsci.edu/kepler/release notes/release notes12/
DataRelease 12 2011113017.pdf
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4.2.2. An External Check of Single Channel, Single Season Data
We carried out a four parameter modeling of 127 stars randomly chosen (a mix of dwarfs
and giants according to the KIC) in Channel 26 from Season 3, Quarter 5 and found residual
patterns similar to that for Season 3, Quarter 5, Channel 44 shown in Figure 6. We then
extracted a subset of ten stars, five with relatively well-behaved x residuals (stars 4–62), five
with x residuals not constant with time (stars 67–106 in Figure 7). We list these in Table 2.
To explore the hypothesis that astrophysical effects (i.e., companions undetectable at the
resolution of the Kepler detectors) cause the observed residual behavior, these ten stars were
observed with the Keck NIRC2-AO system (Wizinowich et al. 2004; Johansson et al. 2008)
on the nights of 19-21 August 2013 UT with the NIRC2 instrument on Keck II. The targets
themselves were used as natural guide stars and observations were made in the K’ filter or
the Br-γ filter, if the star was too bright for the broader K’ filter. The native seeing on the
three nights (before AO) was approximately 0.′′6 at 2µm. The NIRC2 instrument was in the
narrow field mode with a pixel scale of approximately 0.′′009942 pixel−1 and a field of view
of approximately 10.′′1 on a side. Each dataset was collected with a 3-point dither pattern,
avoiding the lower left quadrant of the NIRC2 array, with 5 images per dither position,
each shifted 1” from the previous. Each frame was dark subtracted and flat fielded. The
sky frames were constructed for each target from the target frames themselves by median
filtering and coadding the 15 dithered frames. Individual exposure times varied depending
on the brightness of the target but typically were 10 - 30 seconds per frame. Data reduction
was performed with a custom set of IDL routines.
To estimate companion detection limits as a function of distance from the selected
targets we utilized PSF planting and cross correlation (Tanner et al. 2010). The science
target was extracted from the image, sky subtracted, and normalized. Then it was added
at random positions around the image such that an equal number of plant positions occur
in each radius bin of 0.′′1 around the science target. The flux within each planted PSF is
scaled by a random value which ranges from 10−3 to 103 times the original number of counts
in the star. The counts were determined through aperture photometry with a radius of 0.′′2
and a sky annulus of 0.′′2-0.′′3. Once added to the image, the threshold for detection was
established by cross-correlating the planted star with the normalized PSF. A scaled and
random PSF plant was considered detected if the cross correlation value was above 0.5 - a
value determined by a ”by eye” assessment. The location and flux of those PSFs which were
detected were recorded over 5000 PSF plants. In each radius bin the PSF with the smallest
flux was used in the resulting plot of detected minimum magnitude difference (∆Ks) versus
distance from the science target.
We found no companion candidates in these images within a radius of 1.′′2. Figure 8
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contains the contrast curves for star 4 (constant residuals) and star 67 (time-varying resid-
uals), along with a fit to normalized average contrast curves for stars 4–62 (〈Good〉) and
67–106 (〈Bad〉). To fit the average contrast curves we employed an exponential function
(y = K0 +K1 ∗ exp(−(x− x0)/K2)) with offset, x0. The similarity of the average contrast
curves removes small angular separation, fainter companions as the cause of the Figure 7 be-
havior. Finally, the average Season 3 crowding, contamination, and flux fraction parameters
(see Fraquelli and Thompson 2012 for parameter details) of the two groups differed little.
4.2.3. Lessons Learned
With as rich a set of data as produced by Kepler our approach is to exercise extensive
editing to establish the best astrometric reference frame; a reference frame with χ2/DOF∼1,
and Gaussian distribution of residuals. If we model only epochs 3–7 in Figure 4, as shown in
Figure 9, we generate a final catalog of (ξ, η) positions with average < σξ >= 0.22 millipixel
and < ση >= 0.46 millipixel (0.87 and 1.83 mas). The residuals are Gaussian (Figure 10)
and naturally larger than the average catalog errors because of the effective averaging to
produce a catalog. Again, the significantly larger residuals along the y axis are likely due to
CCD read-out issues (Kozhurina-Platais et al. 2008; Quintana et al. 2010).
4.3. Two Channels, Two Contiguous Seasons
Again restricting our test to include only stars identified as red giants to minimize proper
motion effects, we now run a plate overlap model for the same set of stars appearing on two
different Channels (21, 37) for Quarters 10 and 11 respectively. Given that the average
absolute value UCAC4 proper motion for this suite of test stars is 7.5 mas yr−1(less than
2 millipixel yr−1), the roughly 180 day span of these data should exhibit very little scatter
due to unmodeled motions. A four parameter model (with the constraint plate chosen to
be from Channel 21) yielded a final catalog with < σξ >= 2.60 millipixel and < ση >= 6.6
millipixel (10.33 and 26.23 mas), significantly poorer astrometric performance than for a
single Channel and Quarter (Section 4.1). A six parameter model with separate scales along
x and y yielded only a 0.8% reduction in the large value of reduced χ2/DOF.
The Kepler telescope has a Schmidt-Cassegrain design. An effective astrometric model
for such a telescope, used successfully in the past on Palomar Schmidt photographic plates,
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is introduced in Abbot et al. (1975) and used in e.g. Benedict et al. (1978). That model,
ξ = Ax′ +By′ + Cx′y′ +Dx′2 + Ey′2
+Fx′(x′2 + y′2) +G(5)
η = A′x′ +B′y′ + C ′x′y′ +D′x′2 + E ′y′2
+F ′y′(x′2 + y′2) +G′(6)
when applied to the Channels 21 and 37 data provided a 9.1% reduction in reduced χ2/DOF,
but a final catalog with errors almost exactly as found for the four and six parameter models.
The run of residual with time is shown in Figure 11. The residuals from this modeling are
on average eight times larger than for Channel 21 alone. That the residuals remain large
even with a Schmidt model demonstrates that the astrometric effects are not due to the
Schmidt nature of the Kepler telescope. The residuals as a function of position within the
Channel 37 CCD show large variations on extremely small spatial scales (Figure 12). We
have yet to identify the source of these high-frequency spatial defects, but cannot yet rule
out the individual field flatteners atop each module containing four Channels (Tenenbaum &
Jenkins 2010). This inter-Channel behavior effectively prohibits the measurement of precise
parallaxes using only Kepler data.
5. Astrometry of a Kepler Test Field
Our ultimate goal is to produce an RPM diagram including KOIs, permitting an esti-
mate of their luminosity class. This may be feasible by restricting astrometry to a single
Channel and Season. Essentially we may be able to ignore the deficiencies demonstrated in
Figures 11 and 12 because each star in any given Season will be observed by the same pixels,
and the starlight is passing through the exact same region of the field flattener. The seven-
teen available Quarters provide 3–4 same-Season observation sets for any Kepler Channel.
Examination of Figure 6 supports our selection of Season 0 as one of the more stable. Tests
similar to those carried out in Section 4.1 yielded very poor results for Quarter 2, hence it
is unused here.
5.1. Populating an RPM Diagram
To fully populate the HK , (J-K)0 plane of an RPM diagram we extract Channel 21
long-cadence image data (*lpd-targ*) for stars with 14 >KEPMAG > 11.6; Quarters 6, 10,
and 14, all Season 0:
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1. ∼ 100 stars classified as red giants,
2. ∼ 100 stars with Teff > 6500K ,
3. ∼ 100 stars with 6200 > Teff > 5100K ,
4. ∼ 30 stars with Teff <5000K and Total PM ≥ 0.′′24yr−1 with any KEPMAG value,
and
5. all KOIs found in Channel 21; e.g., Planetary candidate and Exoplanet host star con-
dition flag objects. These, too, have unrestricted KEPMAG.
We extract positions and generate 9-day average normal points using only the Kepler team
defined optimal apertures for each star. When including these data in our modeling with
the ground-based catalogs, the Kepler x,y values are re-origined to the center of Channel
21.
5.2. Reference Star Priors
To place our relative astrometry onto a Right Ascension, Declination system we extract
J2000 positions and proper motions from the UCAC4 (Zacharias et al. 2013) and PPMXL
(Roeser et al. 2010) catalogs. The catalog positions scale the Kepler astrometry and provide
approximately a 12 year baseline for proper motion determination. Additionally, the catalog
proper motions with associated errors are entered into the modeling as quasi-Bayesian priors.
These values are not entered as hardwired quantities known to infinite precision. The χ2
minimization is allowed to adjust the parameter values suggested by these data values within
limits defined by the data input errors.
The input positional errors average 19 mas for the UCAC4 and 63 mas for the PPMXL.
The average per axis proper motion errors are 2.6 mas yr−1 for UCAC4 and 3.9 mas yr−1 for
PPMXL. A comparison of the two catalogs yields an average per star absolute value proper
motion disagreement of 5.1 mas yr−1, indicating room for improvement. The RA and Dec
positions from the two catalogs are used to calculate ξ, η standard coordinates transformed
from radians to seconds of arc (van de Kamp 1967), using the center of Channel 21 as the
tangent point.
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5.3. The Proper Motion Astrometric Model
With the central five epochs of positions from Quarter 6, Quarter 10, and Quarter 14
from Kepler Channel 21 (the editing of each Quarter illustrated by comparing Figure 4 to
Figure 9), spanning 2.14 years, standard coordinates from PPMXL, and UCAC4, and proper
motion priors from the latter two catalogs we determine “plate constants” relative to the
UCAC4 catalog (it having smaller formal positional errors). The constraint epoch is thus
2000.0. Our reference frame after pruning out astrometrically misbehaving objects contains
226 stars. For this model we include only those stars with a restricted magnitude range, 14
> KEPMAG > 11.6, samples 1-3 discussed in Section 5.1 above. The average magnitude for
this magnitude-selected reference frame is 〈KEPMAG〉 = 13.3.
Again, we employ GaussFit (Jefferys et al. 1988) to minimize χ2. The solved equations
of condition for the Channel 21 field are now:
ξ = Ax′ +By′ + Cx′y′ +Dx′2 + Ey′2
+Fx′(x′2 + y′2) +G− µ′x∆t(7)
η = A′x′ +B′y′ + C ′x′y′ +D′x′2 + E ′y′2
+F ′y′(x′2 + y′2) +G′ − µ′y∆t(8)
where x ′ = x − 500 and y ′ = y − 500 are the re-origined measured coordinates from
Kepler and the standard coordinates from UCAC4 and PPMXL; µx and µy are proper
motions; and ∆t is the epoch difference from the mean epoch.
From the resulting astrometric parameters we form a plate scale
S = (BA′ − AB′)1/2 (9)
and find for the 15 epochs (five for each of the three Quarters) of Kepler observations 〈S〉=3.′′97664±0.′′000009 pixel−1, close to the nominal Kepler plate scale (van Cleve & Caldwell
2009) and an indication that the Kepler telescope plate scale as sampled in Channel 21 was
quite constant. The scale factor of the PPMXL catalog relative to the UCAC4 catalog was
1.000012.
5.4. Assessing the Reference Frame
Using the UCAC4 catalog as the constraint plate, to achieve a χ2/DOF∼1 theKepler nor-
mal point data errors (normal point standard deviations) had to be increased by a factor of
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sixteen. Histograms of the Kepler normal point residuals were characterized by σx = 3.6
mas, σy = 6.4 mas. The average absolute value residual for Kepler was 4.8 mas; for UCAC4,
24.3 mas; for PPMXL, 61.6 mas. The resulting 226 star reference frame ‘catalog’ in ξ and η
standard coordinates was determined with average positional errors 〈σξ,η〉 = 8.6 mas, a 55%
improvement in relative position over the UCAC4 catalog. The average proper motion error
for the stars comprising the reference frame is 0.8 mas yr−1.
Again, to determine if there might be unmodeled - but possibly correctable - systematic
effects, we plotted reference frame x and y residuals against a number of parameters. These
included x, y position within the channel (Figure 13); radial distance from the channel center;
reference star magnitude and color; and epoch of observation. We saw no obvious trends,
other than an expected increase in positional uncertainty with reference star magnitude.
Plots of x and y residual versus pixel phase also indicated no trends. We calculate pixel
phase; φx = x − int(x + 0.5), where int returns the integer part of the (for example) x
coordinate.
5.5. Applying the Reference Frame
To insure that the typically fainter (hence less valuable contributors to the astrometric
reference frame) stars do not affect our astrometric modeling of the Channel 21 CCD, the
identical model in Section 5.3 is re-run adding normal point positions for the K and M stars
(sample 4) and KOI’s (sample 5) from Section 5.1, holding the equations 7–8 coefficients A–
G’ to the values determined in Section 5.3. Note that we do solve for positions and proper
motions. This yields final catalog positions and proper motions for 301 stars representing
all the categories listed in Section 5.1. The inclusion of fainter stars results in a ‘catalog’
with ξ and η standard coordinates average relative positional errors 〈σξ,η〉 = 11.1 mas, and
an average proper motion error for all stars of 1.0 mas yr−1. The decrease in proper motion
precision relative to that found for the reference frame-only stars is driven by the inclusion
of the typically fainter K, M, and KOI stars with average 〈KEPMAG〉 = 15.1. As shown in
Section 5.7 below, the centroids of fainter stars have lower signal to noise, and, if included,
would degrade our astrometric reference frame.
We present final KOI proper motions and errors in Table 3. These are in a sense absolute
proper motions, because of the use of prior information. To reiterate, we treated the UCAC4
and PPMXL proper motion priors as observations with corresponding errors. The Table 3
KOI proper motion parameters (and those for the entire set of reference stars modeled above)
were adjusted by various amounts depending on the data input errors to arrive at a final
result that minimized χ2.
– 14 –
5.6. Reference Star Photometric Stability
Our normal point generation process (Section 3.2) also produces an average magnitude.
In the case of nine-day normal points, all the measured flux values in each optimum aperture
are averaged over the nine day interval and converted to a magnitude with an arbitrary zero-
point through mf = 25.768− 2.5 ∗ log10(〈flux〉). Because we restricted this test to a single
channel, no background correction is applied. The standard deviation for the 15 average mf
magnitudes is plotted against reference star ID number in Figure 14. Referencing Section 5.1,
stars 1–99 are classified as red giants in the KIC (sample 1) ; stars 100–199 are hotter stars
(sample 2); stars 201–299 are intermediate temperature stars (sample 3); stars 300–350 are
selected to be more likely K and M dwarfs (sample 4); and stars 400 – 452 are the KOI’s
found in Channel 21 (sample 5). Note that all ID numbers are not present in the plot due
to the editing process (Section 5.3) producing the final astrometric reference frame.
Highest maximum variability with a nine-day cadence is found in our sample of suspected
giants, not an unexpected result (Bastien et al. 2013). The KOIs seem to have photometric
variability characteristics most similar to the K,M group. We note the trends to smaller
variation with increasing number within each group (as defined in Section 5.1). This may be
a function of photometric noise characteristics having positional dependence within Channel
21. The selection process populating each group and allocating a running number within
each group, always assigned the lowest numbers nearer (x,y)=(0,1000), the highest nearer
(x,y)=(1000,0).
5.7. Astrometry as a Diagnostic
Figure 15 contains an average absolute value Kepler x residual for each reference star
and KOI (numbering from Table 3) as a function of mf . The residuals are calculated from the
Section 5.3 modeling results. We choose the x residual as a potential diagnostic given that
the y residuals in general are systematically larger (c.f. Figures 10 and 13). The trend line is
a quadratic fit to the x residuals for the reference stars only (samples 1–3 in Section 5.1). The
planet-hosting KOI over-plotted with large font show no extreme astrometric behavior, all
lying within ±3-σ of the relation. However several KOI hosting unconfirmed planetary com-
panions exhibit astrometric peculiarities. Both KOI 426 and 452 were inspected in 2MASS
and Palomar Sky Survey images and showed no nearby stellar companions or image struc-
ture indicative of close stellar companions. In addition KOI 452 is the most photometrically
variable (Figure 14) host candidate star. Unfortunately, given the random eruption of as-
trometric peculiarity (c.f. Figure 5), astrometry alone cannot serve as a reliable indicator of
astrophysically interesting behavior.
– 15 –
5.8. RPM Diagrams; Pre- and Post-Kepler
We now have the proper motions required to generate HK(0) values for an RPM (Sec-
tion 2). K-band magnitudes, J−K colors and interstellar extinction values, AV , E(B − V )
were extracted from the online Kepler target data base at the MAST. We assumed (Schlegel
et al. 1998)extinction-corrected by K(0) = K-AK , (J −K)0 = (J −K)-E(J −K), with AK
= AV /9 and E(J −K)= 0.53*E(B−V ). The left-hand RPM in Figure 16 shows HK(0) and
(J −K)0 for all stars except the KOIs and exhibits a distribution of points that appears to
have a main sequence and an ascending sub-giant branch. The average HK(0) error is 0.43
mag, but is dependent on the value of µvec with an increased error towards bright values of
HK(0).
The scatter in Figure 16, left, can be due to several causes. These include proper motion
accuracy, random motions of stars, and systematic motions of stars. The HK(0) average error
bar in the figure indicates ±0.4 magnitude of scatter due to measurement error. The amount
due to random stellar motions is unknown. Any particular star could have a large radial
component to its random motion and be erroneously placed amongst the giant stars with
typically lower than average proper motions. Those two effects increase the random scatter
in an RPM. That systematic motions can corrupt an RPM is illustrated in Benedict et al.
(2011), figure 3. There the RR Lyr variables all lie below and blueward of the broad main
sequence. These Pop II giant stars have anomalously large proper motions, causing their
erroneous placement in the RPM.
Comparing the HST - derived RPM (Figure 1, right) with the left-hand RPM in Fig-
ure 16 yields a systematic difference. What we identify as the locus of main sequence stars
from Figure 1, right, appears to be substantially offset towards more negative HK(0) values
by ∆HK(0) = -1.0. As a check we produced an RPM by averaging measured proper motions
from the UCAC4 and PPMXL catalogs and obtain the same offset. Averaging the proper
motions from the two catalogs, the typical HK(0) error is 1.58 mag, a factor of three larger
than when we include Kepler astrometry. There is also a far greater increase in error for
brighter values of HK(0).
To bring the main sequence stars into coincidence with the HST main sequence would
require decreasing the average µvec proper motions of the final Table 3 proper motions by
∼ 10 mas yr−1. This proper motion offset is likely not from systematic effects on proper
motion due to the space velocity of the Sun. The Kepler field is very near the Solar Apex
at RA ' 287◦, DEC ' +37◦ (Vityazev & Tsvetkov 2013). With most of the vector of solar
motion in the radial direction, stars near the Solar Apex will exhibit very little systematic
proper motion due to solar motion. From Vityazev & Tsvetkov (2013) the average transverse
velocity of stars in the solar neighborhood towards the Galactic center is U = 9 km s−1 and
– 16 –
the average transverse velocity perpendicular to the Galactic plane W = 6 km s−1 for a
systematic total velocity Vt = 10.8 km s−1. Our sample of F–G dwarfs has 〈K〉 = 11.85
mag with 〈MK〉 ' 3 (Cox 2000), hence an average distance of 500pc. The expected proper
motion can be estimated from
µvec = πVt/4.74 (10)
This yields µvec = 4.6 mas yr−1, which could explain some but not all the positive HK(0)
offset in Figure 16.
However as mentioned in Section 2 above, a systematic effect of Galactic rotation on
stellar velocities does exist. Our HST -derived RPM main sequence is composed of stars
belonging to the Hyades and Pleiades star clusters. They have a Galactic longitude, ` ∼ 175◦.
The Kepler field has ` ∼ 74◦. The velocity difference due to Galactic rotation is ∼ 30km
s−1, translating to a proper motion difference, ∆µvec = 12.7 mas yr−1, close to the correction
needed above.
We seek luminosity class differentiation, a relative determination within an RPM. We
ascribe the need for a correction to bring the Channel 21 RPM into closer agreement with
Figure 1, right, to a mix of the random and systematic proper motions just identified. We
add the ∆HK(0) = -1.0 and replot, this time including the KOI, similarly corrected for offset
(right-hand side of Figure 16). Identification number in this plot, KIC numbers, and KOI
numbers are collected in Table 4.
6. Estimated Absolute Magnitudes for Channel 21 KOI
Table 4 contains the HK(0) values (corrected by ∆HK(0) = -1.0) derived from the Table 3
KOI proper motions and K(0) magnitudes. The listed K-band absolute magnitudes, MK(0)
are obtained using the Figure 2 calibration; MK(0) = 1.51±0.12+(0.90±0.02)×HK(0). An
MK(0), (J − K)0 HR diagram is shown in Figure 17. An HR diagram constructed using
HK(0) from the UCAC4, PPMXL average proper motions has a distribution similar to
Figure 17, but with significantly increased scatter. Nine stars in Channel 21 (Season 0)
host confirmed planetary systems. Our number 409 is Kepler-100, hosting three confirmed
planets (Marcy et al. 2014), and our number 441 is Kepler-28, hosting two confirmed planets
(Steffen et al. 2012). Recently Rowe et al. (2014) have statistically confirmed a number
of multi planet systems. All exoplanet host stars and associated companions found in the
Channel 21 field are listed in Table 5. Most of their positions in the Figure 17 HR diagram
lie on or close to a solar-metallicity 10Gyr old main sequence (Dartmouth Stellar Evolution
model, Dotter et al. 2008). Our number 435 = KOI-1359 has a photometrically-determined
(hence, low-precision) lowest metallicity in Table 5, consistent with sub-dwarf location on an
– 17 –
HR diagram, as indicated in Figure 17. The other eight hosts of confirmed planetary systems
have locations in the HR diagram consistent with a main sequence dwarf classification.
Inspection of Figure 17 suggests that a significant number of our astrometric reference
stars (and some of the KOI) appear to be sub-giants. As with any apparent magnitude
limited survey, the stars observed with Kepler will have a Malmquist-like bias, i.e., the
survey will be biased towards the inclusion of the most luminous objects in the field as a
result of the greater volume being surveyed for these intrinsically brighter objects (Malmquist
1922). Therefore, within the Kepler field there is a significant bias towards observing stars
that are more massive and/or more evolved.
The Kepler target selection attempted to mitigate this bias by selecting stars identified
as main-sequence solar-type dwarfs based on their KIC values (Batalha et al. 2010). However,
significant uncertainty in KIC surface gravities make this selection process suspect. Brown
et al. (2011) concluded that uncertainties in KIC log(g) are ∼0.4 dex, and are unreliable
for distinguishing giants/main-sequence stars for Teff & 5400 K. Consequently, a significant
fraction of Kepler target stars are expected to be F and G spectral type subgiant stars
(Farmer et al. 2013; Gaidos & Mann 2013).
Finally, to argue for the added value of carrying out this astrometry, Figure 18 plots
a theoretical HR diagram (log g vs. log T) for the astrometric reference stars (grey dots)
and the Table 4 KOI. The log g and T values are from the Kepler Target Search results
tabulated at the STScI MAST3. There are very few stars in the expected locus of F–G sub
giants. Cargile et al. (in preparation) have re-measured Teff and log g for 850 KOIs using
Keck HiRes archived material and find a sub-giant fraction amongst Kepler targets similar
to that shown in Figure 17. Again, we include on this plot a range of metallicities and ages
from the Dartmouth evolution models.
7. Summary
1. Astrometry carried out on Kepler data yields significant systematics in position. These
systematics correlate with time.
2. Astrometric performance correlates with Kepler telescope temperature variations.
Larger variations result in poorer astrometry.
3. Astrometric modeling with a previously successful Schmidt model of more than one
3http://archive.stsci.edu/kepler/kepler fov/search.php
– 18 –
Kepler Season fails to produce astrometric precision allowing for the measurement of
stellar parallax.
4. Combining Kepler astrometry for a single Season and Channel and three Quarters
with existing catalog positions and proper motions, extends the time baseline to over
12 years. This provides a mapping of the lower-spatial frequency distortions over a
Channel, and improves the precision of measured proper motions to 1.0 mas yr−1, over
a factor of three better than UCAC4 and PPMXL.
5. Applying that astrometric model, Kepler measurements yield absolute proper motions
for a number of KOIs with an average proper motion vector error σµ = 2.3 mas yr−1,
or σµ/µ = 19.4%. In contrast, averaging the UCAC4 and PPMXL catalog proper
motions provide σµ = 5.0 mas yr−1, or σµ/µ = 43.0%.
6. An RPM diagram constructed from the proper motions determined by our method,
when compared to one based on HST proper motions, shows a systematic offset. Much
of the offset can be attributed to the effect of Galactic rotation on proper motions.
7. The corrected RPM parameter, HK(0), transformed to MK(0) through an HK(0) -
MK(0) relation derived from HST proper motions and parallaxes, yields MK(0) for fifty
KOIs, including nine stars with confirmed planetary companions, 8 now confirmed as
dwarfs, one a possible sub-dwarf. Six KOIs are identified as giants or sub-giants.
The next significant improvement in KOI proper motions will come from the space-
based, all-sky astrometry mission Gaia (Lindegren et al. 2008) with ∼ 20 microsecond of arc
precision proper motions and parallaxes for the brighter KOI’s. With parallax there will be
no need for RPM diagrams. Final Gaia results are expected early in the next decade.
This paper includes data collected by the Kepler mission. Funding for Kepler is pro-
vided by the NASA Science Mission directorate. All of the Kepler data presented in this
paper were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space
Telescope Science Institute. STScI is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST
data is provided by the NASA Office of Space Science via grant NNX13AC07G and by
other grants and contracts. Direct support for this work was provided to GFB by NASA
through grant NNX13AC22G. Direct support for this work was provided to AMT by NASA
through grant NNX12AF76G. PAC acknowledges NSF Astronomy and Astrophysics grant
AST-1109612. This publication makes use of data products from the Two Micron All Sky
– 19 –
Survey, which is a joint project of the University of Massachusetts and the Infrared Process-
ing and Analysis Center/California Institute of Technology, funded by NASA and the NSF.
This research has made use of the SIMBAD and Vizier databases and Aladin, operated at
CDS, Strasbourg, France; the NASA/IPAC Extragalactic Database (NED) which is oper-
ated by JPL, California Institute of Technology, under contract with the NASA; and NASA’s
Astrophysics Data System Abstract Service. This research has made use of the NASA Exo-
planet Archive, which is operated by the California Institute of Technology, under contract
with the National Aeronautics and Space Administration under the Exoplanet Exploration
Program. Some of the data presented herein were obtained at the W.M. Keck Observatory,
which is operated as a scientific partnership among the California Institute of Technology,
the University of California and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W.M. Keck Foun-
dation. The authors wish to recognize and acknowledge the very significant cultural role and
reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct observations from
this mountain. GFB thanks Bill Jefferys, Tom Harrison, and Barbara McArthur who over
many years contributed to the techniques reported in this paper. GFB and AMT thank Dave
Monet for several stimulating discussions that should have warned us off from this project,
but didn’t. GFB thanks Debra Winegarten for her able assistance, allowing progress on this
project. We thank an anonymous referee for a thorough, careful, and useful review which
materially improved the final paper.
– 20 –
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Table 1. HST MK(0) and HK(0)
# ID m-M MK(0) SpT µTa K0 (J-K)0 HK(0) Refb
1 HD 213307 7.19 -0.86 B7IV 21.82±0.42 6.32 -0.12 -1.98±0.05 B02
2 υ AND 0.66 2.20 F8 IV-V 419.26 0.14 2.86 0.32 0.97 0.03 M10
3 HD 136118 3.59 2.00 F9V 126.31 1.20 5.60 0.34 1.11 0.03 Mr10
4 HD 33636 2.24 3.32 G0V 220.90 0.40 5.56 0.34 2.28 0.03 Ba07
5 HD 38529 3.00 1.22 G4IV 162.31 0.11 4.22 0.68 0.27 0.03 B10
6 vA 472 3.32 3.69 G5 V 104.69 0.21 7.00 0.50 2.10 0.03 M11
7 55 Cnc 0.49 3.49 G8V 539.24 1.18 3.98 0.70 2.64 0.03 SIMBAD
8 δ Cep 7.19 -4.91 F5Iab: 17.40 0.70 2.28 0.52 -6.51 0.09 B07
9 vA 645 3.79 4.11 K0V 101.81 0.76 7.90 0.77 2.93 0.03 M11
10 HD 128311 1.09 3.99 K1.5V 323.57 0.35 5.08 0.53 2.63 0.03 M13
11 γ Cep 0.67 0.37 K1IV 189.20 0.50 1.04 0.62 -2.58 0.03 B13
12 vA 627 3.31 3.86 K2 V 110.28 0.05 7.17 0.56 2.38 0.03 M11
13 ε Eri -2.47 4.24 K2V 976.54 0.10 1.78 0.45 1.72 0.03 B06
14 vA 310 3.43 4.09 K5 V 114.44 0.27 7.52 0.63 2.82 0.03 M11
15 vA 548 3.39 4.13 K5 V 105.74 0.01 7.52 0.71 2.64 0.03 M11
16 vA 622 3.09 5.13 K7V 107.28 0.05 8.22 0.84 3.38 0.03 M11
17 vA 383 3.35 5.01 M1V 102.60 0.32 8.36 0.91 3.42 0.03 M11
18 Feige 24 4.17 6.38 M2V/WD 71.10 0.60 10.55 0.69 4.81 0.03 B00a
19 GJ 791.2 -0.26 7.57 M4.5V 678.80 0.40 7.31 0.92 6.47 0.03 B00b
20 Barnard -3.68 8.21 M4Ve 10370.00 0.30 4.52 0.72 9.60 0.03 B99
21 Proxima -4.43 8.81 M5Ve 3851.70 0.10 4.38 0.97 7.31 0.03 B99
22 TV Col 7.84 4.84 WD 27.72 0.22 12.68 0.49 4.89 0.03 M01
23 DeHt5 7.69 7.84 WD 21.93 0.12 15.53 -0.07 7.24 0.03 B09
24 N7293 6.67 7.87 WD 38.99 0.24 14.54 -0.23 7.49 0.03 B09
25 N6853 8.04 2.54 WD 8.70 0.11 10.58 1.13 0.27 0.04 B09
26 A31 8.97 6.69 WD 10.49 0.13 15.66 0.25 5.77 0.04 B09
27 V603 Aql 7.20 4.12 CNe 15.71 0.19 11.32 0.31 2.30 0.04 H13
28 DQ Her 8.06 5.00 CNe 13.47 0.32 13.06 0.46 3.70 0.06 H13
29 RR Pic 8.71 3.54 CNe 5.21 0.36 12.25 0.18 0.83 0.15 H13
30 HP Lib 6.47 7.35 WD 33.59 1.54 13.82 -0.12 6.45 0.10 R07
31 CR Boo 7.64 8.59 WD 38.80 1.78 16.23 -1.52 9.17 0.10 R07
– 24 –
Table 1—Continued
# ID m-M MK(0) SpT µTa K0 (J-K)0 HK(0) Refb
32 V803 Cen 7.70 6.12 WD 9.94 2.98 13.82 -0.10 3.81 0.65 R07
33 ` Car 8.56 -7.55 G3Ib 15.20 0.50 0.99 0.55 -8.10 0.08 B07
34 ζ Gem 7.81 -5.73 G0Ibv 6.20 0.50 2.13 0.23 -8.91 0.18 B07
35 β Dor 7.50 -5.62 F6Ia 12.70 0.80 2.06 0.48 -7.42 0.14 B07
36 FF Aql 7.79 -4.39 F6Ib 7.90 0.80 3.45 0.40 -7.06 0.22 B07
37 RT Aur 8.15 -4.25 F8Ibv 15.00 0.40 3.90 0.28 -5.22 0.06 B07
38 κ Pav 6.29 -3.52 F5Ib-II: 18.10 0.10 2.71 0.62 -6.00 0.03 B11
39 VY Pyx 6.00 -0.26 F4III 31.80 0.20 5.63 0.33 -1.86 0.03 B11
40 P3179 5.65 3.02 G0V: 50.36 0.40 8.67 0.35 2.18 0.03 S05
41 P3063 5.65 4.68 K6V: 45.30 0.50 10.33 0.82 3.61 0.04 S05
42 P3030 5.65 4.97 K9V: 43.20 0.50 10.62 0.83 3.79 0.04 S05
aµT = (µ2RA + µ2
DEC)1/2 in mas yr−1
bB99=Benedict et al. (1999), B00a=Benedict et al. (2000a), B00b=Benedict et al. (2000b),
B02=Benedict et al. (2002), B06=Benedict et al. (2006), B07=Benedict et al. (2007), B09=Benedict
et al. (2009), B11=Benedict et al. (2011), Ba07=Bean et al. (2007), H13=Harrison et al.
(2013), Mr10=Martioli et al. (2010), M01=McArthur et al. (2001), M11=McArthur et al. (2011),
R07=Roelofs et al. (2007), S05=Soderblom et al. (2005)
– 25 –
Table 2. Companion Test Stars
#a KID KEPMAG K FluxFracb
4 5698236 15.637 14.243 0.886
5 5698325 12.264 10.747 0.920
10 5698466 13.113 11.561 0.921
34 5783576 14.135 12.656 0.874
62 5784222 15.475 13.885 0.881
67 5784291 13.148 11.074 0.936
77 5869153 15.596 13.537 0.706
96 5869586 15.466 13.672 0.886
103 5869826 15.768 13.473 0.774
106 5870047 11.747 6.328 0.962
aNumbering in Figure 7
bFraction of target flux in the Kepler project-defined optimum aper-
ture.
– 26 –
Table 3. Channel 21 KOI Proper Motions (µ)
ID KID KOI mf µRAa µDEC
b µT
401 6362874 1128 13.51 -0.0063±0.0008 -0.0307±0.0008 0.0314±0.0011
402 6364215 2404 15.66 0.0005 0.0015 -0.0056 0.0019 0.0056 0.0024
403 6364582 3456 12.99 0.0022 0.0011 0.0029 0.0005 0.0036 0.0012
404 6441738 1246 14.90 -0.0038 0.0013 0.0158 0.0012 0.0163 0.0017
405 6442340 664 13.48 0.0090 0.0009 -0.0103 0.0011 0.0137 0.0015
406 6442377 176 13.43 0.0079 0.0009 0.0096 0.0012 0.0124 0.0015
407 6520519 4749 15.61 0.0026 0.0017 -0.0061 0.0019 0.0067 0.0025
408 6520753 4504 11.20 0.0046 0.0087 -0.0535 0.0061 0.0537 0.0106
409 6521045 41 15.20 0.0205 0.0003 -0.0275 0.0006 0.0343 0.0007
410 6522242 855 15.98 0.0025 0.0037 0.0128 0.0029 0.0130 0.0047
411 6523058 4549 13.16 0.0041 0.0019 0.0024 0.0017 0.0048 0.0025
412 6523351 3117 11.38 0.0052 0.0006 -0.0021 0.0006 0.0056 0.0009
413 6603043 368 15.90 -0.0029 0.0005 -0.0018 0.0004 0.0034 0.0006
414 6604328 1736 13.80 0.0033 0.0026 0.0026 0.0021 0.0042 0.0034
415 6605493 2559 15.55 -0.0052 0.0011 -0.0076 0.0012 0.0092 0.0016
416 6606438 2860 13.42 0.0044 0.0025 0.0051 0.0020 0.0068 0.0032
419 6607447 1242 13.75 0.0087 0.0009 0.0002 0.0014 0.0087 0.0017
420 6607644 4159 14.50 -0.0070 0.0017 0.0395 0.0018 0.0402 0.0025
421 6690082 1240 14.47 -0.0027 0.0010 -0.0130 0.0012 0.0133 0.0015
422 6690171 3320 15.95 0.0060 0.0021 -0.0027 0.0015 0.0066 0.0026
423 6690836 2699 15.23 -0.0081 0.0031 -0.0026 0.0019 0.0085 0.0036
424 6691169 4890 15.77 -0.0006 0.0016 -0.0105 0.0021 0.0106 0.0026
425 6693640 1245 14.20 0.0098 0.0012 0.0059 0.0013 0.0115 0.0018
426 6773862 1868 15.22 -0.0089 0.0024 -0.0014 0.0020 0.0091 0.0031
427 6774537 2146 15.33 -0.0023 0.0014 0.0026 0.0013 0.0035 0.0019
428 6774880 2062 15.00 0.0024 0.0019 -0.0019 0.0016 0.0031 0.0025
429 6776401 1847 14.81 -0.0031 0.0014 -0.0295 0.0015 0.0297 0.0020
430 6779260 2678 11.80 0.0000 0.0006 0.0063 0.0004 0.0063 0.0007
431 6779726 3375 15.70 0.0011 0.0031 -0.0084 0.0024 0.0085 0.0040
432 6862721 1982 15.77 0.0026 0.0017 0.0051 0.0022 0.0057 0.0027
433 6863998 867 15.22 0.0076 0.0014 0.0054 0.0012 0.0093 0.0019
– 27 –
Table 3—Continued
ID KID KOI mf µRAa µDEC
b µT
434 6945786 3136 15.74 0.0088 0.0018 0.0010 0.0019 0.0089 0.0026
435 6946199 1359 15.23 0.0291 0.0032 -0.0082 0.0023 0.0303 0.0040
436 6947164 3531 14.62 -0.0002 0.0009 0.0010 0.0013 0.0011 0.0016
437 6947668 3455 15.80 -0.0027 0.0015 -0.0046 0.0017 0.0054 0.0023
438 6948054 869 15.60 0.0112 0.0023 0.0097 0.0020 0.0148 0.0031
439 6948480 2975 15.31 -0.0030 0.0013 -0.0004 0.0013 0.0030 0.0018
440 6949061 1960 14.13 0.0050 0.0012 -0.0022 0.0010 0.0055 0.0015
441 6949607 870 15.04 -0.0003 0.0017 0.0216 0.0019 0.0216 0.0026
442 6949898 3031 15.27 -0.0020 0.0021 -0.0021 0.0015 0.0029 0.0026
443 7031517 871 15.22 0.0066 0.0021 -0.0072 0.0014 0.0097 0.0025
444 7032421 1747 14.79 0.0088 0.0020 0.0160 0.0026 0.0182 0.0033
445 7033233 2339 15.13 0.0102 0.0016 0.0072 0.0017 0.0125 0.0023
446 7033671 670 13.77 0.0034 0.0008 -0.0076 0.0007 0.0083 0.0011
447 7115291 3357 15.19 0.0030 0.0018 -0.0014 0.0013 0.0034 0.0023
448 7115785 672 14.00 -0.0078 0.0011 -0.0117 0.0012 0.0141 0.0016
449 7118364 873 15.02 0.0072 0.0018 -0.0040 0.0015 0.0083 0.0023
450 7199060 4152 12.97 -0.0047 0.0010 -0.0028 0.0005 0.0054 0.0011
451 7199397 75 10.78 -0.0019 0.0007 0.0265 0.0006 0.0266 0.0009
452 7199906 1739 15.13 0.0029 0.0014 0.0041 0.0018 0.0050 0.0022
aProper motions in seconds of arc per year.
bCorrected for cosδ declination.
– 28 –
Table 4. Channel 21 KOI Absolute Magnitude
ID KID KOI K0 (J-K)0 HK(0)a MKb Statusc
401 6362874 1128 11.75 0.41 3.23±0.08 4.4±0.1 PC
402 6364215 2404 14.02 0.14 1.73 0.96 3.1 0.4 PC
403 6364582 3456 11.38 0.38 -1.76 0.71 -0.1 0.9 PC
404 6441738 1246 13.34 0.31 3.39 0.23 4.6 0.1 PC
405 6442340 664 11.96 0.27 1.65 0.23 3.0 0.1 Kepler-206b,c,d
406 6442377 176 12.18 0.24 1.65 0.26 3.0 0.1 PC
407 6520519 4749 13.77 0.39 1.90 0.81 3.2 0.3 PC
408 6520753 4504 13.94 0.43 6.59 0.43 7.4 0.1 PC
409 6521045 41 9.76 0.29 1.43 0.05 2.8 0.1 Kepler-100b,c,d
410 6522242 855 13.27 0.43 2.83 0.78 4.1 0.2 PC
411 6523058 4549 14.24 0.32 1.64 1.14 3.0 0.4 PC
412 6523351 3117 11.47 0.40 -0.80 0.34 0.8 1.7 PC
413 6603043 368 11.03 -0.05 -2.22 0.39 -0.5 0.3 PC
414 6604328 1736 14.24 0.38 1.37 1.73 2.7 0.7 PC
415 6605493 2559 12.30 0.27 1.12 0.38 2.5 0.2 PC
416 6606438 2860 14.04 0.23 2.19 1.03 3.5 0.3 PC
419 6607447 1242 12.43 0.20 1.14 0.42 2.5 0.2 PC
420 6607644 4159 12.60 0.47 4.62 0.14 5.7 0.1 PC
421 6690082 1240 12.81 0.39 2.41 0.26 3.7 0.1 PC
422 6690171 3320 13.79 0.53 1.88 0.85 3.2 0.3 EB; PC
423 6690836 2699 13.27 0.46 1.91 0.92 3.2 0.3 PC
424 6691169 4890 14.41 0.18 3.53 0.54 4.7 0.1 PC
425 6693640 1245 12.79 0.24 2.12 0.33 3.4 0.1 PC
426 6773862 1868 12.27 0.82 1.12 0.70 2.5 0.4 PC
427 6774537 2146 13.13 0.56 -0.15 1.16 1.4 1.3 PC
428 6774880 2062 13.45 0.26 -0.12 1.75 1.4 2.0 PC
429 6776401 1847 12.88 0.45 4.23 0.15 5.3 0.1 PC
430 6779260 2678 10.07 0.41 -1.96 0.23 -0.3 0.3 PC
431 6779726 3375 14.00 0.28 2.65 1.01 3.9 0.3 PC
432 6862721 1982 13.97 0.31 1.76 1.03 3.1 0.4 PC
433 6863998 867 13.11 0.55 1.94 0.44 3.3 0.2 PC
– 29 –
Table 4—Continued
ID KID KOI K0 (J-K)0 HK(0)a MKb Statusc
434 6945786 3136 13.52 0.61 2.24 0.63 3.5 0.2 PC
435 6946199 1359 13.48 0.40 4.88 0.28 5.9 0.1 R14
436 6947164 3531 13.06 0.34 -2.39 2.66 -0.6 1.8 EB; PC
437 6947668 3455 13.93 0.39 1.56 0.92 2.9 0.4 PC
438 6948054 869 13.59 0.41 3.45 0.45 4.6 0.1 Kepler-245b,c,d
439 6948480 2975 13.69 0.31 0.12 1.28 1.6 1.2 PC
440 6949061 1960 12.64 0.29 0.30 0.62 1.8 0.5 Kepler-343b,c
441 6949607 870 12.68 0.56 3.35 0.26 4.5 0.1 Kepler-28b,c
442 6949898 3031 13.61 0.28 0.02 1.83 1.5 2.1 PC
443 7031517 871 13.60 0.40 2.53 0.56 3.8 0.2 PC
444 7032421 1747 13.10 0.39 3.43 0.39 4.6 0.1 R14
445 7033233 2339 12.78 0.61 2.27 0.40 3.6 0.1 R14
446 7033671 670 12.15 0.33 0.72 0.28 2.2 0.2 PC
447 7115291 3357 13.49 0.32 0.11 1.45 1.6 1.3 EB; PC
448 7115785 672 12.32 0.37 2.04 0.25 3.3 0.1 Kepler-209b,c
449 7118364 873 13.34 0.37 1.91 0.62 3.2 0.2 PC
450 7199060 4152 11.84 0.10 -0.49 0.43 1.1 0.8 PC
451 7199397 75 9.37 0.29 0.50 0.08 2.0 0.1 PC
452 7199906 1739 13.43 0.36 1.01 0.93 2.4 0.5 PC
aHK(0) = K(0) + 5log(µT) with ∆HK(0)=-1.0 correction.
bMK(0) = 1.51±0.12 + (0.90±0.02)×HK(0) from the Figure 2 calibration.
cPC = Planetary candidate, EB = Eclipsing Binary, FP = False Positive, Kepler = designated
exoplanets have been confirmed, R14 = statistical multi-exoplanet confirmation (Rowe et al. 2014).
– 30 –
Tab
le5.
Chan
nel
21,
Sea
son
0P
lanet
ary
Syst
ems
IDK
IDK
OI
Pla
net
aP
(day
s)re
f.b
Teff
R�
log
g[F
e/H
](J
-K) 0
MK
(0)
405
6442
340
664.
0120
6c13
.137
5R
1457
641.
194.
24-0
.15
0.27
3.0±
0.1
664.
0220
6b7.
7820
664.
0320
6d23
.442
8
409
6521
045
41.0
110
0b12
.816
Mar
1458
251.
494.
13+
0.02
0.29
2.8
0.1
41.0
210
0c6.
887
41.0
310
0d35
.333
435
6946
199
1359
.01
37.1
01R
1459
850.
854.
53-0
.51
0.4
5.9
0.1
1359
.02
104.
8202
438
6948
054
869.
0124
5b7.
4902
R14
5100
0.80
4.56
-0.0
30.
414.
60.
1
869.
0224
5d36
.277
1
869.
0324
5c17
.460
8
440
6949
061
1960
.01
343b
8.96
86R
1458
071.
434.
18-0
.14
0.29
1.8
0.5
1960
.02
343c
23.2
218
441
6949
607
870.
0128
b5.
9123
R14
4633
0.67
4.65
+0.
340.
564.
50.
1
870.
0228
c8.
9858
Ste
12
444
7032
421
1747
.01
20.5
585
R14
5658
0.89
4.54
+0.
070.
394.
60.
1
1747
.02
0.56
73
445
7033
233
2339
.01
2.03
23R
1446
660.
684.
64+
0.38
0.61
3.5
0.1
2339
.02
65.1
900
448
7115
785
672.
0120
9b41
.749
9R
1455
130.
944.
47+
0.01
0.37
3.4
0.1
– 31 –aA
ssig
ned
num
ber
inth
eK
eple
rco
nfirm
edpla
net
sequen
ce,
e.g.
,K
eple
r-20
6c.
aM
ar14
=M
arcy
etal
.(2
014)
,Ste
12=
Ste
ffen
etal
.(2
012)
,R
14=
Row
eet
al.
(201
4).
– 32 –
10
5
0
-5
Red
uced
Pro
per M
otio
n (H
K(0
) = K
0 + 5
log(µ
) )
1.20.80.40.0-0.4(J-K)0
1
23
4
5
67
8
910
11
1213
14151617
18
19
20
21
22
2324
25
26
27
28
29
30
32
3334
3536
3738
39
40
4142
10
5
0
-5
MK
1.20.80.40.0-0.4(J-K)0
1
23
4
5
6 7
8
910
11
1213 1415
1617
18
1920
21
22
2324
25
26
2728
29
30
32
33
34 35
363738
39
40
4142
Fig. 1.— Left: Hertzsprung-Russell (HR) diagram absolute magnitude MK(0) vs (J-K)0,
both corrected for interstellar extinction. Plotted lines show predicted loci for 10Gyr age
solar metallicity stars (- - -) and 3Gyr age metal-poor ([Fe/H]=-2.5) stars (-··-) from Dart-
mouth Stellar Evolution models (Dotter et al. 2008). Right: RPM diagram, same targets
plotted. Horizontal line separates main sequence and sub-giants, giants and super-giants.
Star numbers are from Table 1. Color coding denotes main sequence (red), white dwarfs
(blue), super-giants (black).
– 33 –
10
5
0
-5
MK(0
)
10 5 0 -5 -10Reduced Proper Motion (HK(0) = K(0) + 5log(µ) )
-2
-1
0
1
2
Resid
ual (
mag
nitu
de)
1
234
5
67
8
910
11
121314151617
1819
2021
22
2324
25
26
2728
29
3031
32
33
34353637
38
39
40
4142
123
45
6
7 8910
11
12
13
1415161718
19
20
21
22
2324
25
2627
28
29
30
31
32
33
34
35
36
37
3839
404142
a = 1.51 ± 0.12b = 0.90 ± 0.02
Fig. 2.— A linear mapping between MK(0) and HK(0) using HST parallaxes and proper
motions for targets scattered over the entire sky. RMS residual is 0.7 mag. The linear fit
(MK(0) = a + b HK(0)) coefficient errors are 1-σ. Stellar classifications range from white
dwarfs to Cepheids, as listed in Table 1.
– 34 –
Kepler ID = 7031732
Fig. 3.— Left: KID 7031732 in a crowded field. Image from Digital Sky Survey via Aladin.
Middle: Postage stamp for KID 7031732. Right: Optimum aperture for KID 7031732.
– 35 –
-20
-10
0
10
20
mill
ipix
el
158401582015800157801576015740JD -2440000
1
2
3
45
6
7
8
9
10
1112
13
14
151617
1819
2021
22
23
2425
262829
30
313233
34
35
36
3738
3940
41
42
4344
4546
47
48
4950
51
52
535455
56
57
5859
60
61
62
63
64
656667686970
7172
737475
7677
7879
8081
82
838485868788899091929394
9596
97
1
2
3
456
78
9
10
11121314
151617
1819
2021
22
23
2425
26
27
282930313233
34
35
36
37383940
41
42
43444546
47
48
4950
51
52
535455
56
57
5859
60
61
62
63
64
656667686970
7172
737475
7677
7879
8081
82
838485868788899091929394
959697
1
2
3456
78
9
10
11121314
151617
1819202122
23
2425
26
27
282930313233
34
353637383940
4142
43444546
47
48
495051
52
535455
56
575859
6061
62
6364
6566676869707172
737475
7677
7879808182838485868788899091929394
959697
12345678
9
1011121314151617181920212223242526
27
28293031323334353637383940414243444546
47
48
49505152
535455565758596061
62
6364
6566676869707172
737475
7677
7879808182838485868788899091929394959697 12345
678
9
1011121314
1516171819202122232425262728
2930313233343536373839404142
4344454647
484950515253545556575859
6061
626364
656667686970717273747576777879808182838485868788899091929394959697 1
2345678
9
1011121314
151617
1819202122
23242526
27
28
29303132333435363738394041424344454647
4849505152535455
565758596061626364656667686970717273747576777879808182838485868788899091929394959697 1
2345
6789
101112
1314
15
1617
18192021
22
232425
26
27
28
29303132
33343536373839404142
43444546474849505152535455
56
5758596061626364656667686970717273
747576777879808182838485
8687888990919293
94959697
12
3
45
6789
10
1112
13
14
15
1617
181920
21
22
23
2425
26
27
28
29303132
33
343536373839404142
43444546474849505152535455
56
5758596061626364
65666768
6970717273
747576777879808182838485
86 8788899091
9293
94
95
9697
12
3
45
67
8
910
111213
14
15
1617
181920
21
22
23
2425
26
27
28
29
303132
33
34353637383940
4142
4344454647
4849505152
535455
56
5758596061
62
636465666768
697071727374
75767778798081
82838485
86 878889
90
9192
93
94
95
9697
Y
-20
-10
0
10
20
mill
ipix
el
12
3
456789
10
111213141516
17
1819
20
21
22
23
2425262728
2930
313233
3435
363738
39
40
41
4243
44
45
46
474849505152535455
56
57
58
59
60
6162
63
64
6566676869707172
73
74757677787980818283
84
8586
87
88899091929394959697
123456789
10
111213141516171819
20
2122
2324252627282930
3132333435
363738
39
40
414243
44
4546
474849505152535455
56
57
58
59
606162
63
64656667686970717273
74757677787980818283
84858687
88899091929394959697
123456789
101112131415161718192021222324252627282930
3132333435
363738
39
40
414243
444546474849505152535455
565758
59606162
63
64656667686970717273747576777879808182838485868788899091929394959697 123456789
1011121314151617181920212223242526272829303132333435
363738394041424344
4546474849505152535455
56575859606162
63
646566676869707172737475767778798081828384
85868788899091929394959697 123456789101112131415161718192021222324
25262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697
123456789101112
131415161718192021222324
2526
2728293031323334353637383940414243444546474849505152535455565758596061626364
65
6667686970717273747576777879808182838485868788899091929394959697
1234567
8
9101112131415161718192021222324
25
2627
28293031323334353637383940414243444546474849505152535455
565758596061626364
65
666768
69707172737475767778798081828384
85868788899091929394959697
1234
567
8
910111213
14151617181920
21222324
25
26
2728
2930313233343536373839
40
414243444546
47
4849505152535455
56575859
6061626364
65
666768697071
72
737475767778798081828384
85
86 8788899091929394959697
1
234
5
67
8
9101112
13
14151617181920
21222324
25
26
27
282930313233343536373839
40
4142434445
4647484950
5152535455
565758
596061626364
65
666768
697071
72
737475767778798081828384
85
86 8788899091929394959697
X
Fig. 4.— x and y residuals as a function of time for the Q10-only four parameter modeling
from Section 4.1. The residual clumps from left to right are ’plates’ 1–9, the epochs of the
averaged normal points. Stars are labeled with a running number from 1 to 97. The residuals
exhibit significant time-dependency. Regarding two of the stars with more extreme behavior,
neither star 9 (=KID 6363534) nor star 27 (=KID 6606001) is a high-proper motion object.
– 36 –
STScI POSS2UKSTU_Red 19:26:34.92 +41:44:27
30" 2.698’ x 2.404’
N
EPowered by Aladin
2MASS.J.980601N_JI0640256
30" 2.675’ x 2.388’
N
EPowered by Aladin
STScI POSS2UKSTU_Blue 19:27:08.16 +42:02:44
30" 2.698’ x 2.404’
N
EPowered by Aladin
Star 9! Star 9!
Star 27! Star 27!
Fig. 5.— Top: Star 27 (POSS-J on left, 2MASS on right) obviously with a close compan-
ion that confused the first moment centering. Bottom: Star 9, similarly illustrated. No
companion to Star 9 is detected. The positional shift is assumed instrumental.
– 37 –
-20
-10
0
10
20
mas
1518015160151401512015100JD -2440000
1
23
4
6791011
12
13
14
16
1718
19
20
21
22
23
24
25
27
28
29
30
31
32
33
34
3536
37
38
39
40
414243
45
46
47
48
49
50
51
52
53
54
55
565759
60
61
62
63
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67
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7172737475767879
8081
82
83
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86
88
89
9091
9293
94
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100
101
102103
104
105
106107
1
23
4
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12
13
14
16
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192021
22
23
24
25
27
28
29
30
31
32
33
34
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37
38
39
40
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44
45
46
47
48
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51
52
53
54
55
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60
61
62
63
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7172737475767879
80
81
82
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105
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1
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63
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68697172737475767879
8081
8283848586
88
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929394959699100101102103
104105106107 1
23
4
5
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12
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161718192021
2223242527
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7678798081828384858688
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1
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20
21
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75767879
80 81
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89
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101102103104
105
106107
1
2345
6 7910
11
1213
1416
1718
19
20
21
22
23
24
25
27
28
29
30
31
32333435
36
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59
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81
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86 88
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101
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105
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1
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67
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11
1213
1416
1718
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20
21
22
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25
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28
29
30
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39
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48
49
50
51
52
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60
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7172737475 76787980
81
82
83
8485
86 88
89
9091
9293
94
959699
100
101
102103104
105
106107
-20
-10
0
10
20
mas
1518015160151401512015100
123
4
5
6
79101112
13
1416
171819
20
2122
2324
25
27
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30
31
32
33
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38
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45464748495051525354
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72
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80
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72
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80
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8384858688
8990919293
94
95
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103
104
105106107
1234
5
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13
1416171819
20
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25
272829
303132
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888990919293
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104
105106107 1234
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1234
5
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17
18
19
20
21
22
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6364
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73
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8081
82
838485868889909192
93
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96
99
100101102
103
104
105
1061071234
5
6
7
9
1011 1213
14
16
17
18
19
20
21
22
2324
25
27
2829
3031
32
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39
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44
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47
48
49
50
51
52
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55
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606162
63
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72
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78
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81
82
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93
94
95
96
99
100101
102
103
104
105
106107
123
4
5
6
7
9
1011 1213
1416
17
18
19
20
21
22
2324
25
27
2829
3031
32
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3738
39
4041
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44
45
46
47
48
49
50
51
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53 54
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63
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7980 81
82
83848586
88
89
909192
93
94
95
96
99
100101
102
103
104
105
106
107
X Residuals
S1Q3 FOVC Residuals
-20
-10
0
10
20
mas
1526015240152201520015180JD -2440000
123
4
5
6
7
8
9
101112
13
15
16
17
18
19
2021
22
23
24
25
2627
28
29
3031
32
33
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37
39
40
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44
45
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48
49
50
5152
53
54
55
5657
58
596061
62
636465
6667
6869
70
72
74
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79
80
82
83
8485
86
87
88
89
90
92
93
9495
96
99
101
102
103
104
105
106
107
123
4
5
6
7
8
9
101112
1315
16
17
18
19
202122
23
24
25
2627
28
29
30
31
32
33343536
37
39
404143
44
45
4647
48
49
50
5152
53
54
55
56
57
58
596061
62
636465
6667
6869
70
72
73
74
757678
79
8082
83
8485
86
87
88
89
90
91
92
93
9495
96
97
99
101
102
103
104
105
106
107123
4
5
67
8
9
101112
1315
16
17
18
19202122
23
24
252627
28
29
3031
32
33343536
37
39
404143
44
45
4647
48
49
50
5152
53
54
55
5657
58
596061626364
65
6667
6869
70
72
73
74757678
798082
83
8485
86
87
88
89
90
91
92
93
9495
96
97
98
99
101
102
103
104
105
106
107123
4
5
67
8
9
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1315
1617
18
19202122
23
24
252627
28
293031
32
33343536
37
39
404143
44
45
4647
48
49
50
515253
54
5556
57
58
59606162636465
6667
6869
70
72
73
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7678
79808283
8485
86
87
88
89
90
91
92
939495
96
97
98
99
101
102
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105
106
107
1 234567
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32
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545556
57
58
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96
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28
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49
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6869
7072737475767879808283848586
878889909192939495 9697
9899101102103104105106107 1
23456 78
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101102103104105106107 1
23
456
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232425
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28
29
3031
323334353637
39404143
4445464748
49
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545556
5758596061
626364
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67
6869
70
727374757678
79
8082838485
86
87
88
89
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939495 969798
99
101102
103104105
106107
-20
-10
0
10
20
mas
1526015240152201520015180
1
23
4
567
8
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15161718192021222324252627
28
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1
23
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567
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1
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7879808283848586
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1
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104105106107 1 23 45
6 789101112
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123
45
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45
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545556 575859606162
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87
88
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106107 123
4
56
7
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15
16
17
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20
2122
2324
25
2627
28293031
32
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545556 5758596061
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68
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75
767879
80
82
83848586
87
88
89
90
91
9293949596
9798
99
101
102103104
105
106107
X Residuals
S2Q4 FOVC Residuals
-20
-10
0
10
20
mas
1536015340153201530015280JD -2440000
1234567891011121314151617181920212223242526272829303132333435363738394041434445464748495051525354555657585960616263646566676869707273747576787980818283848586
87888990919293949596979899100101102103104105106107
12345678910
11121314151617181920212223242526272829303132333435363738394041434445464748495051525354555657585960616263646566676869707273747576787980818283848586
87888990919293949596979899100101102
103104105106107
12345678910
1112131415161718192021222324252627282930313233343536373839404143444546474849505152
535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100101
102103104105106107
1234567891011121314151617181920212223242526272829303132333435363738394041
43444546474849505152
53545556575859606162636465666768697072737475767879
8081
8283848586878889
909192939495969798
99100101102103104105106107 123
4
5678
910
11
1213141516171819202122232425262728293031323334353637383940414344454647484950515253
545556
57
585960616263646566
676869
7072737475767879
80818283848586
87888990919293949596979899100101102103104105106107
1
2
3
4
56
7
8
9
10
1112
13
14
15
16
17
18
19
2021
22
2324
252627
28
29
3031
32
33343536
37
38
3940
41
4344454647
48
49
50
51
52
53
54
5556
57
5859
60616263646566
67
6869
70
72
7374
7576
78
79
80
81
82
83
84
8586
87
88
89
90
91929394
95
96
97
98
99
100101
102
103104
105
106107
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
252627
28
29
30
31
32
33
3435
36
37
38
3940
41
4344
4546
47
48
49
50
51
52
53
54
5556
57
58
59
6061
6263646566
67
6869
70
72
7374
75
76
78
79
80
81
82
83
84
85
86
87
88
89
90
9192
9394
95
96
97
98
99
100101
102
103104
105
106
107
1
2
35
6
7
9
10
11
12
13
14
15
16
18
20
21
22
23
24
25
2627
29
31
32
33
3435
36
37
38
3940
41
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45
46
47
49
50
52
53
54
55
56
58
59
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62
63
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7374
75
76
79
80
81
83
84
85
86
87
88
89
90
9192
9394
95
96
97
98
99
100101
102
103104
106
107
2
35
6
9
10
11
12
13
14
15
18
20
21
22
23
24
25
2627
29
31
32
33
3435
36
37
3940
41
4344
45
46
47
49
50
52
53
55
56
58
59
60
61
62
63
64
65
66
686972
7374
75
76
79
80
81
84
85
86
87
88
90
91
92
95
96
97
98
99
100
101
102
103104
106
107-20
-10
0
10
20
mas
1536015340153201530015280
123456789101112131415
161718
192021222324252627
28293031
32333435363738
39
404143
44
45464748495051525354555657585960616263646566676869
707273747576787980818283848586
87888990919293949596979899100
101
102103104105106107 123
456789
101112131415161718192021222324252627
282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100
101
102103104105106107 123
456789101112131415161718192021222324252627
282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100
101102103104105106107 12345678910111213141516
1718192021222324252627282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100
101102103104105106107 12345678910111213141516
1718192021222324252627282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899
100101102103104105106107 12
3
4
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1112131415161718
192021
22
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28
29
30
31
32
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55
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6263646566676869707273747576787980818283848586878889
90
91
92
93949596
9798
99
100
101
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105106107
1
23
4
56
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53
54
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58
59
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65
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73
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82
83
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89
90
91
92
93
94
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99
100
101
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104
105
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3
4
567
8
9
10
1112
13
14
15
16
17
18
19
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22
23
24
25
2627
28
29
30
31
32
3334
35
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48
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51
52
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55
56
57
58
59
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65
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68
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73
74
75
76
78798081
82
83
84858687
88
89
90
91
92
93
94
95
96
9798
99
100
101
102103
105
106107
X Residuals
S3Q5 FOVC Residuals
-20
-10
0
10
20
mas
1546015440154201540015380JD -2440000
1
2
3
45
6
78910
11
12
131415
16
1718
19
20
2122
232425
2627
28
29
30
31
32
33
34
35
363738
39
4041
42
43
44
45464748
49
5051
52
53
54
55
56
575859
6061
626364
6566
67
6869
707172737475
767778
79
80
81
82838485
86
87
88
89
90
9192
939495
96
9798
99100
101
102103
104105
106107
1
2
3
4
5
6
7
891011121314
1516
171819
20
2122
232425
26272829
30
31
3233
34
35
363738
39
4041
42
43
4445
46474849505152
53
54
55565758
596061
626364
65
66
67
6869
707172737475
767778
79
80
81
82
838485
86
87
88
89909192
93
949596979899
100
101
102103
104
1051061071
2
34
5
6
78910
11121314
1516
171819
20212223242526272829
30
31
32333435363738
39
4041
42
434445
46474849505152
53
5455565758596061
626364
65
66676869707172737475
76777879
80
8182
83848586
87
88
89909192
93
9495969798
99
100
101102103
104
105106107 1
2345
67
891011121314151617181920212223242526272829
30
313233
3435363738
39404142
4344454647484950515253
5455565758596061626364
65
66676869707172737475 7677787980
818283848586
8788
8990919293949596979899
100101
102103104105106107 123 4567891011121314151617181920212223242526272829
3031323334353637383940414243444546474849505152535455565758596061626364
6566676869707172737475 767778798081
828384858687 888990919293
949596979899100101102103104
105106107 123 456789 10111213141516171819202122232425262728
29303132 3334353637383940414243444546474849505152535455565758596061626364656667686970717273
7475 767778798081828384858687 888990919293
949596979899100101102103
104
105106107 1
23 456
789 1011
1213141516171819202122232425262728293031
32 33343536373839404142
4344454647484950515253
545556
57585960616263 6465
6667686970717273
747576777879
80
81828384858687
888990919293
9495 96979899
100101
102103
104
105106107
12
3
456
789 1011
1213141516
1718192021222324252627
2829
3031
3233
3435363738
39
40414243
4445
464748495051
52
53
5455
565758596061
6263 6465
66
67
6869
707172737475
767778
79
80
81828384
8586
87
88
8990
919293 9495
96979899
100
101102103
104
1051061071
23
45
6789 10
11
1213 141516
1718192021222324252627
2829
3031
32
3334
35363738
39
404142
43
4445
464748495051
52
53
5455
56
575859
60616263 64
65
66
67
6869
70717273
7475
76777879
80
81828384
8586
87
88
8990
919293 9495
9697
9899100
101
102103
104
105106107
-20
-10
0
10
20
mas
1546015440154201540015380
12
34
5
6
78910111213141516
1718192021
22232425262728293031
32
33343536
37
38
39
4041424344
454647
48
49
50515253
54
555657
585960616263
64
6566
67
68
69707172
7374757677
7879
80
818283848586
87
888990919293
94
95
96979899100
101
102
103
104
105106107 1234
5678910
11121314
15161718192021
2223242526272829303132
3334353637
38
39
404142434445464748
49
50515253
54
555657
58596061626364
65666768
697071727374757677
7879
80
81828384858687
888990919293
94
9596979899100101
102
103104
10510610712345678910
11121314
151617181920212223242526272829303132
333435363738
39404142434445464748
4950515253
54555657
585960616263
646566
676869707172737475 7677787980
81828384858687
888990919293
949596979899100101
102103104
10510610712345678910
1112131415161718192021
2223242526272829303132333435363738
394041424344454647484950515253
5455565758596061626364
6566676869707172737475 7677787980
81828384858687888990919293949596979899100101102
103104105106107 123 4567891011121314151617181920212223242526272829303132333435363738
39404142434445464748495051525354555657585960616263646566676869707172737475 767778798081828384858687 888990919293949596979899100101102103104105106107 123 456789 1011121314151617181920212223242526272829303132 33343536373839404142434445464748495051525354555657
5859606162636465
66676869707172737475 767778798081828384858687 888990919293949596979899100101102103104105106107 123 456 7
89 1011
121314151617181920212223242526272829303132 33343536373839404142434445464748
4950515253
54555657
585960616263 6465
66676869707172737475 76
77787980
8182838485868788899091929394
95 96979899100101102
103104105106107 12
3 45
67
8910
11 121314
151617181920212223242526272829303132
333435363738
39404142
4344
45464748
4950515253
54
555657
5859
6061626364
65
6667
68
69707172737475
7677
7879
80818283848586
8788899091929394
9596
979899100101
102
103104
105106107 1 2
3 456
789
1011
1213
141516171819202122
23242526272829
303132
333435363738
39
404142
4344
45464748
49
50515253
54
555657
58
5960616263
64
65
66
6768
69707172737475
7677
7879
80
81828384858687
8889
90919293
94
9596
979899100101
102
103104
105106107
X Residuals
S0Q6 FOVC Residuals
-20
-10
0
10
20
mas
1582015800157801576015740JD -2440000
1 1 1 1 1 1 1 1 12 2 2 2 2 2 2 2 233 3 3 3 3 3 3 3
4
4
4 4 4 4 4
4 4
5 5 55
5 5 5 5 56 6 6 6 6 6 6 6 6
77 7 7 7 7 7 7 7
8
88 8 8 8 8
8 8
9
99 9 9 9 9
9 910 10 10 10 10 10 10 10 10
11 11 11 11 11 11 11 11 11
12 12 12 12 12 12 12 12 12
13 13 13 13 13 13 13 13 13
1414 14 14 14 14 14 14 14
15
1515 15 15
15 1515 15
16 16 16 16 16 16 16 16 1617 17 17 17 17 17 17 17 1718 18 18 18 18 18 18 18 18
1919
19 19 19 19 19 19 1920
20 20 20 2020
20 20 2021
2121 21 21 21 21 21 21
22 22 22 22 22 22 22 22 2223
23 23 23 23 23 23 23 2324 24 24 24 24 24 24 24 2425
2525 25 25
25 25 25 25
2626
26 26 26 26 26 26 26
27
2727 27 27 27 27 27 27
28
2828 28 28 28 28
28 28
29
2929 29 29 29 29
29 293030 30 30 30 30 30 30 30
31 31 3131 31 31 31 31 31
3232
32 32 32 32 3232 32
33 33 33 33 33 33 33 33 33
3434 34 34 34 34 34 34 3435 35 35 35 35 35 35 35 35
3636
36 36 36 36 36 36 36
37
3737 37 37 37 37 37 37
3838
3838
38 38 38 38 3839
3939 39 39 39 39 39 39
40 40 4040
40 40 40 40 40
41 4141
4141 41 41 41 4142 42 42 42 42 42 42 42 42
43 4343
4343 43 43 43 43
44
4444 44 44 44 44
44 4445 45 45 45 45 45 45 45 4546
4646 46 46
4646 46 4647
4747 47 47
4747 47 47
4848
48 48 48 48 4848 4849 49 49 49 49 49 49 49 49
5050
50 50 50 50 5050 50
51
51 51 51 51 51 5151 5152 52 52 52 52 52 52 52 52
5353
53 53 53 53 5353 53
54
5454
54 54 54 5454 5455 55 55 55 55 55 55 55 55
5656 56 56 56 56 56 56 565757 57 57 57 57 57 57 57
5858 58 58 58 58 58 58 58
59
5959 59 59
5959 59 59
6060 60
60 6060
60 60 6061
61 6161 61
6161 61 6162
62 62 62 62 62 62 62 62
63
6363 63 63 63 63 63 63
64
6464 64 64 64 64
64 64
65
6565
65 6565
65 65 6566 66 66 66 66 66 66 66 6667 67 67 67 67 67 67 67 6768
6868 68 68 68 68 68 68
69
6969 69 69 69 69 69 69
7070 70 70 70 70 70
70 70
71 71 71 71 71 71 71 71 717272 72 72 72 72 72 72 72
7373 73 73 73 73 73
73 73
74 74 74 74 74 74 7474 74
75 75 75 75 75 75 75 75 757676 76 76 76 76 76 76 76
7777 77 77 77 77 77 77 7778 78 78 78 78 78 78 78 78
79
7979 79 79 79 79
79 798080 80
80 8080
80 80 80
8181
8181
81 81 8181 8182
82 8282 82 82 82
82 82
83
8383
83 8383
8383 83
84 84 84 84 84 84 84 84 8485
85 85 85 85 85 85 85 85
86
8686
86 86 86 8686 8687 87 87 87 87 87 87 87 87
88
88
8888
88 88 8888 8889
8989 89 89 89 89
89 899090
90 90 90 90 90 90 9091 91 91 91 91 91 91 91 91
9292 92 92 92 92 92
92 9293
93 9393 93 93 93 93 93
9494 94 94 94 94 94 94 949595 95 95 95 95 95 95 95
96
9696 96 96 96 96
96 9697
97 97 97 97 97 9797 97
9898 98 98 98 98 98
98 98
99
9999 99 99 99 99 99 99
100100
100100
100 100 100 100 100101101 101 101 101 101 101 101 101102 102 102 102 102 102 102 102 102
103 103103 103 103 103 103 103 103
104 104 104104 104
104104 104 104
105105 105
105 105 105 105105 105
106
106106 106 106 106 106 106 106107 107 107 107 107 107 107 107 107
-20
-10
0
10
20
mas
1582015800157801576015740
11 1 1 1 1 1 1 12 2 2 2 2 2 2 2 2
3
33 3 3 3 3
3 3
4
44 4 4 4 4
4 45 5 5 5 5 5 5 5 5
66
6 6 6 6 6 6 67 7 7 7 7 7 7 7 78
8 8 8 88 8 8 8
9 9 9 9 9 9 9 9 910 10 10 10 10 10 10 10 1011
11 11 11 11 11 11 11 11
12 12 12 12 12 12 12 12 12
1313 13 13 13 13 13 13 13
14 14 14 14 14 14 14 14 1415
15 15 15 15 15 15 15 15
16 16 16 16 16 16 16 16 161717 17 17 17 17 17 17 17
1818 18 18 18 18 18 18 1819 19 19 19 19 19 19 19 19
2020 20 20 20 20 20 20 20
2121
21 21 21 21 2121 21
22 22 22 22 22 22 22 22 22
2323
23 23 23 23 23 23 2324 24 24 24 24 24 24 24 2425 25 25 25 25 25 25 25 2526 26 26 26 26 26 26 26 2627 27 27 27 27 27 27 27 2728 28 28 28 28 28 28 28 2829 29 29 29 29 29 29 29 2930
30 30 30 30 30 30 30 3031 31 31 31 31 31 31 31 31
32
3232 32 32 32 32
32 32
33 33 33 33 33 33 33 33 3334 34 34 34 34 34 34 34 3435 35 35 35 35 35 35 35 3536
36 36 36 36 36 36 36 3637
37 37 37 37 37 37 37 37
3838 38 38 38 38 38 38 38
39
3939 39
39 39 3939 39
4040 40 40 40 40 40 40 40
41 41 41 41 41 41 41 41 4142
42 42 42 42 42 42 42 42
4343
43 43 43 43 4343 43
44
4444 44 44 44 44
44 44
45 45 45 45 45 45 45 45 4546 46 46 46 46 46 46 46 46
4747 47 47 47 47 47 47 474848 48 48 48 48 48 48 48
4949
49 4949
4949
49 49
50 50 50 50 50 50 50 50 5051 51 51 51 51 51 51 51 5152 52 52 52 52 52 52 52 5253
53 53 53 5353 53 53 53
5454 54 54 54 54 54 54 5455 55 55 55 55 55 55 55 555656 56 56 56 56 56 56 56
5757 57 57 57 57 57 57 5758 58 58 58 58 58 58 58 58
59 59 59 59 59 59 59 59 5960 60 60 60 60 60 60 60 60
61 61 61 61 61 61 61 61 6162 62 62 62 62 62 62 62 6263 63 63 63 63 63 63 63 6364
64 64 64 64 64 64 64 6465 65 65 65 65 65 65 65 6566 66 66 66 66 66 66 66 6667 67 67 67 67 67 67 67 67
6868
68 68 68 68 6868 68
69 69 69 69 69 69 69 69 6970
70 70 70 70 70 70 70 7071 71 71 71 71 71 71 71 7172
72 72 72 72 72 72 72 7273 73 73 73 73 73 73 73 73
74 74 74 74 74 74 74 74 74
75 75 75 75 75 75 75 75 75
76 7676 76 76
76 76 76 76
77 77 77 77 77 77 77 77 7778
7878 78 78 78 78 78 78
7979
79 79 79 79 79 79 7980 80 80 80 80 80 80 80 8081 81 81 81 81 81 81 81 8182 82 82 82 82 82 82 82 8283 83 83 83 83 83 83 83 8384 84 84 84 84 84 84 84 8485
85 85 85 85 85 85 85 8586 86 86 86 86 86 86 86 86
8787
87 87 87 87 8787 87
88 88 88 88 88 88 88 88 8889 89 89 89 89 89 89 89 8990 90 90 90 90 90 90 90 9091 91 91 91 91 91 91 91 9192
92 92 92 92 92 92 92 929393 93 93 93 93 93 93 93
9494 94 94 94 94 94 94 9495 95 95 95 95 95 95 95 9596 96 96 96 96 96 96 96 96
97 97 97 97 97 97 97 97 979898 98 98 98 98 98 98 98
99 99 99 99 99 99 99 99 99
100 100 100 100 100 100 100 100 100
101101
101 101 101 101 101101 101102 102 102 102 102 102 102 102 102
103 103 103 103 103 103 103103 103
104104
104 104104 104 104
104 104
105 105 105 105 105 105 105 105 105
106106 106 106 106 106 106 106 106
107 107 107 107 107 107 107 107 107
X Residuals
S0Q10 FOVC Residuals
-20
-10
0
10
20 m
as
157401572015700156801566015640JD -2440000
1
25678
910111213141516
171819
202122
23242550
51
52
535455565758596061
6263646566
67
6869
70
7273747578798081
82
8384858687888990
91929394
95979899
100101
102
103104
105
106107 125678910111213141516
17181920212223242550515253545556575859606162636465666768697072737475787980818283848586
878889909192939495979899100101102103104105106107 125678910111213141516171819202122232425505152
53545556575859606162636465666768697072737475787980818283848586
878889909192939495979899100101102103104105106107 125
6789
10111213141516
171819202122232425505152
53545556575859606162636465666768697072737475787980818283848586
878889
909192939495979899100101102103104105106107 125
6789
10111213141516171819
20212223242550515253545556575859606162636465666768697072737475787980818283848586
878889909192939495979899100101102103104105106107
12567
8
9101112
1314
1516
171819202122232425505152535455565758
596061626364656667686970727374757879
80
818283848586878889
909192939495979899100101102103104105106107
1
25
6
7
8
9
10
1112
13
14
15
16
17
18
19
2021
22
23242550
51
52
53
54
5556
57
58
59
60616263646566
67
6869
70
72
7374
75
78
79
80
81
82
83
84
85
86
87
88
89
90
91929394
9597
98
99
100101
102
103104
105
106107
1
25
6
7
9
10
1112
13
14
15
16
17
18
19
20
21
22
23
24
25
50
51
52
53
54
5556
57
58
59
6061
6263
64
6566
67
6869
70
72
7374
75
78
79
80
81
82
83
84
85
86
87
88
89
90
9192
9394
95
97
98
99
100101
102
103104
105
106
10725
6
7
9
10
1112
13
14
15
16
18
20
21
22
23
24
25
50
52
53
54
55
56
57
58
59
6061
62
63
64
6566
686972
7374
7579
80
81
83
84
85
86
87
88
89
90
91
92
93
95
97
98
99
100101
102
103104
106
107
25
6
7
9
10
1112
13
14
15
18
20
21
22
23
24
25
50
52
53
55
56
58
59
6061
62
63
64
6566
686972
7374
7579
80
81
83
84
85
86
87
88
89
90
91
92
95
97
98
99
100
101
102
103104
106
-20
-10
0
10
20
mas
157401572015700156801566015640
1
25
678
910111213141516
1718
19202122232425505152
53
54555657585960616263646566
67
6869
70727374757879
80
818283848586
87
8889909192939495979899
100
101
102103
104
105106107 1
256789
1011121314151617181920212223242550515253545556575859606162636465666768697072737475787980818283848586878889909192939495979899100
101
102103104105106107 12
56789
1011121314151617181920212223242550515253545556575859606162636465666768697072737475787980818283848586878889909192939495979899100
101
102103104105106107 125678910111213141516
17181920212223242550515253545556575859
606162636465666768697072737475787980818283848586878889909192939495979899100101102103104105106107 1
2567891011121314151617181920212223242550515253545556575859
60616263646566676869707273747578798081
82838485868788899091
92939495979899100101102103104
105106107 1256789101112131415
1617181920212223242550515253545556575859606162636465666768697072737475787980818283848586878889909192939495979899100101102103104105106107
12567
89
10111213
1415
161718
192021
22
2324
25
505152
5354
55
565758596061
626364
656667686970727374757879808182
83
8485868788
89
90
91
929394959798
99
100101102103
104
10510610712567
8
9
10
1112
13
14
15
16
1718
19
2021
22
2324
25
5051
52
5354
55
5657
58
59
6061
6263
64
65
6667
6869
7072
73
74757879
80
8182
83
848586
87
88
89
90
91
92
939495
9798
99
100
101
102103
104
105
106107
1
25
67
8
9
10
1112
13
14
15
16
1718
19
2021
22
23
24
25
50
51
52
53
54
55
56
57
58
59
6061
6263
64
65
66
67
68
69
7072
73
74757879
80
8182
83
848586
87
88
89
90
91
92
93
9495
9798
99
100
101
102103
104
105
106107
1
2567
8
9
10
11
12
13
14
15
16
1718
19
2021
22
23
24
25
50
51
52
53
54
55
56
57
58
59
6061
6263
64
65
66
67
68
69
70
72
73
74
75
7879
80
8182
83
848586
87
88
89
90
91
92
93
9495
9798
99
100
101
102103
105
106107
X Residuals
S3Q9 FOVC Residuals
-20
-10
0
10
20
mas
1554015520155001548015460JD -2440000
1
23
4
67
8
91011
12
13
14
15
16
1718
192021
22
23
24
25
2627
28
29
30
31
32
33
3435
36
37
38
39
40
41
43
45
46
47
48
49
50
51
52
53
54
55
5657
58
59
60
61
62
63
64
6566
67
6869
70
7273747576
78
79
8081
82
83
84
8586
87
88
89
9091
9293
94
95
96
97
98
99
100
101
102103
104
105
106107
1
23
4
67
8
910
11
12
13
14
15
16
1718
192021
22
23
24
25
2627
28
29
30
31
32
33
3435
36
37
38
39
40
4143
45
46
47
48
49
50
51
52
53
54
55
5657
58
59
60
61
62
63
64
6566
67
68
69
70
7273747576
78
79
8081
82
83
848586
87
88
89
9091
9293
94
9596
97
98
99
100
101
102103
104
105
106107
1
23
4
67
8
91011
12
1314
15
16
1718
19202122
23
24
25
2627
28
29
30
31
32
33
343536
37
38
39
40
4143
44
45
46
47
48
4950
51
52
53
54
55
5657
58
59
60
61
62
63
646566
67
6869
70
7273747576
78
79
8081
82
83
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87
88
89
9091
929394
9596
97
98
99
100
101102103
104
105
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1
23
4
5
67
8
91011
12
1314
15
16
1718
1920212223
24
25
2627
28
29
30
31
32
33
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37
38
39
40
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44
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48
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58
59606162
63
646566
67
6869
70
7273747576
78
798081
8283848586
87
88
8990
91
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9697
9899
100101102103104
105106107 123
4
5
67
8
91011
12131415
16
17181920212223242526272829
303132
33343536
3738
39404143
44
45464748495051525354555657585960616263
64656667
6869707273747576787980818283848586
87
888990919293949596979899100101102103104105
106107
1
234567891011121314
15
16
1718
192021
22
2324
25
2627
28
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32333435363738
39404143
444546
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48
4950
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52
53
545556575859
60616263
64
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70
72737475 76
78
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81
82
8384858687 88
89
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9293
94959697
98
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105
106107
1
234567891011121314
15
16
1718
1920
21
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2324
25
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32333435363738
39404143444546
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48
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50
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59
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64
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69
70
72737475 76
78
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81
82
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9091
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105
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1
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11
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14
15
16
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192021
22
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25
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28
29
3031
323334
35363738
39404143444546
47
48
4950
51
52
53
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59
60
61
626364
65
66
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69
70
72737475 76
78
7980
81
82
83
848586
87 8889
9091
9293
9495
96
97
98
99100
101
102103104
105
106107
-20
-10
0
10
20
mas
1554015520155001548015460
123
4
5
6
789101112
13
14
15
16
171819
20
2122
2324
25
2627
2829
30
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33
343536
37
38
39
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4445464748495051525354
555657
58
59
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65
66
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72
73
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79
80
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838485868788
8990919293
94
95
96
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102
103
104
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123
4
5
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13
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20
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25
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30
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33
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37
38
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5051525354555657
58
59
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626364
6566
67686970
72
7374757678
79
80
8182
838485868788
8990919293
94
95
96
979899100101
102
103
104
105106107 123
4
5
6
789101112
13
141516
171819
20
21222324
25
26272829
303132
33
343536
37
3839404143444546474849
5051525354555657
58
59
6061626364
6566
676869
70
72
737475
7678
798081
82838485868788
8990919293
94
95
96
979899100101102
103
104
105106107
1234
5
6789101112
13141516171819
2021222324
2526272829
303132
33343536
3738394041434445464748
49505152535455565758596061626364656667686970
72
7374757678
79808182838485868788
89909192939495
96
979899100101102103104105106107
12345
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17181920212223242526272829303132
3334353637383940414344454647484950
51525354555657585960616263646566
676869707273
747576
78798081828384858687
888990919293949596979899100101102
103104105106107
1234
5
678
9
1011121314
1516
1718
19
20
2122
2324
25
2627
2829
303132
33343536373839
404143444546
47
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50
5152
5354
55
56575859606162
6364
6566676869
7072
73
7475 7678
798081
82
8384858687 8889
909192
93
9495
96979899
100101102
103
104
105106107
123
4
5
678
9
10111213
14
1516
1718
19
20
21
22
2324
25
2627
2829
3031
3233343536
3738
394041434445
46
47
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50
51
5253 54
55
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606162
63
646566676869
7072
73
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798081
82
8384858687 8889
909192
93
9495
96
979899
100101102
103
104
105
106107
123
4
5
678
9
10111213
141516
1718
19
20
21
22
2324
25
2627
2829
3031
32
333435363738
394041434445
46
47
48
49
50
51
5253 54
55
565758
59606162
63
64656667
6869
7072
73
7475 7678
7980 81
82
8384858687 88
89
909192
93
94
9596
979899
100101102
103
104
105
106
107
X Residuals
S1Q7 FOVC Residuals
-20
-10
0
10
20
mas
1564015620156001558015560JD -2440000
123
4
5
67
8
9
101112
13
14
15
1617
18
19
20
21
22
2324
25
2627
28
29
3031
32
33
343536
37
38
39
40
4143
44
45
4647
48
49
50
5152
53
54
55
5657
58
596061
62
636465
66
67
6869
70
72
74
757678
7980
8182
83
8485
86
87
88
89
90
92
93
9495
96
97
99
100
101
102
103104
105
106
107
1234
5
67
8
9
101112
13
14
15
1617
18
1920
21
22
2324
25
2627
28
29
3031
32
33
343536
37
38
39
404143
44
45
4647
48
49
50
5152
53
54
55
5657
58
596061
62636465
6667
6869
70
72
73
74757678
79808182
83
8485
86
87
88
89
90
91
92
93
9495
96
97
98
99
100
101
102
103104
105
106
107
1234
5
6 7
8
9
101112
1314
15
1617
18
192021
22
2324
252627
28
29
3031
32
33343536
3738
39
404143
44
454647
48
49
50
5152
53
54555657
58
59606162636465
6667
6869
7072
73
747576787980818283
8485
86
87
88
89
90
91
92
939495
96
9798
99100
101102
103104105
106
107
123456 78910111213141516171819202122
232425262728293031
323334353637383940414344454647484950515253
54555657
5859606162636465666768697072
7374757678798081828384858687
888990919293949596
9798
99100101102103104105
106107
123456 78910111213141516171819
2021
22232425262728
2930313233343536373839404143
444546474849
505152535455565758596061626364656667
686970
7273747576787980818283848586
87888990919293949596979899100101102103104105106107 123
456
7891011 12131415161718
19
2021222324252627
28
29
30313233343536373839404143
4445464748
49
50515253
5455565758596061626364
6566676869
70
727374757678
7980
8182838485
86
8788
89
90919293949596
9798
99100101102103
104105106107
-20
-10
0
10
20
mas
1564015620156001558015560
1
23
45
67
8
91011
121314151617181920212223242526
27
28
29303132333435
3637383940
41
43444546474849
5051
5253
54555657
58
596061626364
65
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70
72737475
76
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82
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87
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96
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104105
106107
1
23
45
67
8
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12131415161718192021222324252627
2829303132333435363738394041434445464748495051
5253
54555657
58
596061626364
65
66676869
70
7273747576
78798081
8283848586
87
88
899091
92939495
96
979899100101102103
104105106107
1
23456 7
8
910111213141516171819202122232425
262728
293031323334353637383940
4143444546474849505152
5354555657
58
596061626364
65
66676869
70
72737475767879808182838485868788
89909192939495
96979899100101102103104105106107 1234
56 7891011121314151617181920212223242526272829303132333435363738394041434445
464748495051525354
55565758596061626364656667
6869707273747576787980818283848586
8788899091929394959697989910010110210310410510610712345
67
891011121314
151617181920
212223242526272829303132333435363738
394041434445
4647484950515253
5455565758596061626364656667
68
69707273747576
78798081
8283848586
87
88
8990919293949596979899
100
101102103104105106107
123
45
6
7
891011
121314
15
16171819
2021222324252627
2829303132
333435363738
394041434445
46474849
50515253545556575859606162
6364
656667
68
6970
72737475
7678798081
8283848586
87
88
8990
9192939495
96979899
100
101
102103104105
106107
X Residuals
S2Q8 FOVC Residuals
-20
-10
0
10
20
mas
162001618016160161401612016100JD -2440000
1 1 1 1 1 1 1 1 12 2
2 2 2 2 2 2 23 3 3 3 33 3 3 3
4
4
4 4 44
44 4
5 55 5
5 5 5 5 56 6 6 6 66 6 6 6
77
7 7 7 7 7 7 7
88
8 8 88 8 8 8
9
9
9 9 99 9 9 910 10 10 10 10 10 10 10 10
1111 11
11 11 11 11 11 1112 12 12 12 12 12 12 12 12
13 1313 13 13 13 13 13 13
1414
14 14 14 1414 14 14
15
15
15 15 1515 15 15 15
16 16 16 16 16 16 16 16 1617 1717 17 17 17 17 17 17
1818 18 18 18 18 18 18 18
1919
1919 19 19 19 19 19
2020
20 20 2020 20 20 20
2121
21 21 21 21 21 21 2122 22
22 22 22 22 22 22 2223
23 23 23 23 23 23 23 232424 24 24 24 24 24 24 24
2525
25 25 2525 25 25 25
2626
26 26 26 26 26 26 26
27
27
2727 27 27
27 27 2728
28 28 28 28 28 28 28 28
29
29
2929 29
2929 29 2930 30 30 30 30
30 30 30 30
31 3131
31 31 31 31 31 3132
32 32 32 32 32 32 32 3233 33 33 33 33 33 33 33 33
3434
34 34 34 3434 34 34
35 35 35 35 35 35 35 35 35
3636
36 36 36 3636 36 36
37
37
37 37 37 3737 37 37
3838
38 38 38 38 38 38 38
39
3939 39 39 39 39 39 3940 4040 40 40 40 40 40 40
41 4141 41 41 41 41 41 41
43 4343
43 43 43 43 43 43
44
4444 44 44 44 44 44 44
45 45 45 45 45 45 45 45 454646
46 46 4646 46 46 4647
4747 47
4747 47 47 47
48
48 48 48 48 48 48 48 4849 4949 49 49 49 49 49 49
50
50 50 50 50 50 50 50 50
51
51 51 51 51 51 51 51 5152 5252 52 52 52 52 52 52
53
5353
53 53 5353 53 53
54
54
5454 54 54
54 54 545555 55 55 55 55 55 55 55
5656 56 56 56 56 56 56 56
5757
57 57 57 5757 57 57
5858
58 58 5858 58 58 58
59
59
59 5959
59 59 59 596060
60 6060
60 60 60 6061
6161 61
6161 61 61 61
6262
62 62 62 62 62 62 62
6363
63 63 6363 63 63 63
64
64
64 64 6464
64 64 64
65
6565 65
65
65 65 65 6566 66 66 66 66 66 66 66 6667
67 67 67 67 67 67 67 67
6868
6868 68 68
68 68 68
6969
6969 69 69
69 69 6970
70 70 70 70 70 70 70 7072 7272 72 72 72
72 72 7273
73 73 73 73 73 73 73 73
7474 74 74 74 74 74 74 74
7575 75 75 75 75 75 75 75
76 7676 76 76 76
76 76 7678 78 78 78 7878 78 78 78
7979
79 79 7979 79 79 79
80 80 80 8080
80 80 80 80
81
81
8181 81 81
81 81 8182
82 82 82 82 82 82 82 8283
83
83 8383
83 83 83 8384 84 84 84 84 84 84 84 84
8585
85 85 85 8585 85 85
86
86
8686 86 86
86 86 8687
87 87 87 87 87 87 87 87
88
88
8888 88 88
88 88 88
89
8989 89 89 89 89 89 89
9090
90 90 9090 90 90 90
9191 91 91 91 91 91 91 91
92
92 92 92 92 92 92 92 9293
93 93 93 93 93 93 93 9394 94
94 94 94 94 94 94 9495 95 95 95 95 95 95 95 95
96
9696 96 96 96
96 96 9697
97 97 97 97 97 97 97 97
98
98 98 98 98 98 98 98 98
99
99
99 99 9999
99 99 99
100100
100100 100 100
100 100 100101101 101 101 101 101 101 101 101
102 102102 102 102 102 102 102 102
103103
103103 103 103 103 103 103
104 104 104 104104
104 104 104 104105
105 105 105 105 105 105 105 105
106106
106 106 106 106106 106 106
107 107 107 107 107 107 107 107 107
-20
-10
0
10
20
mas
162001618016160161401612016100
11 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2
3
33 3 3 3 3 3 3
44
4 4 4 4 4 4 45 5 5 5 5 5 5 5 5
66
6 6 6 6 6 6 67 7 7 7 7 7 7 7 78
8 8 88
8 8 8 89 9 9 9 9 9 9 9 910 10 10 10 10 10 10 10 1011
11 11 1111
11 11 11 1112
12 12 12 12 12 12 12 12
1313
13 13 13 13 13 13 1314 14 14 14 14 14 14 14 1415 15 15 15 15 15 15 15 15
16 16 16 16 16 16 16 16 1617
17 17 17 17 17 17 17 17
1818 18 18 18 18 18 18 1819 19 19 19 19 19 19 19 19
2020
20 20 20 20 20 20 20
2121
21 21 21 21 21 21 21
22 22 22 22 22 22 22 22 22
2323
23 23 23 23 23 23 23
24 24 24 24 24 24 24 24 2425 25 25 25 25 25 25 25 2526 26 26 26 26 26 26 26 2627 27 27 27 27 27 27 27 2728 28 28 28 28 28 28 28 2829 29 29 29 29 29 29 29 2930
30 30 30 30 30 30 30 303131 31 31 31 31 31 31 31
32
3232 32 32 32
32 32 32
33 33 33 33 33 33 33 33 3334 34 34 34 34 34 34 34 3435 35 35 35 35 35 35 35 35
3636 36 36 36 36 36 36 36
3737
37 37 37 37 37 37 37
3838
38 38 38 38 38 38 38
39
39
39 39 39 3939
3939
4040 40 40 40 40 40 40 40
41 41 41 41 41 41 41 41 41
4343
43 43 43 43 43 43 43
44
4444 44 44 44
44 44 44
45 45 45 45 45 45 45 45 4546 46 46 46 46 46 46 46 46
4747 47 47 47 47 47 47 474848 48 48 48 48 48 48 48
49
4949
4949 49
4949
49
50 50 50 50 50 50 50 50 505151 51 51 51 51 51 51 5152 52 52 52 52 52 52 52 525353 53 53
5353 53 53 53
5454
54 54 54 54 54 54 5455 55 55 55 55 55 55 55 555656 56 56 56
56 56 56 5657
57 57 57 57 57 57 57 5758 58 58 5858
58 58 58 5859 59 59 59 59 59 59 59 5960 60 60 60 60 60 60 60 60
61 61 61 61 61 61 61 61 6162 62 62 62 62 62 62 62 6263 63 63 63 63 63 63 63 6364
64 64 64 64 64 64 64 6465 65 65 6565
65 65 65 6566 66 66 66 66 66 66 66 66
6767
67 67 67 67 67 67 67
6868
68 68 68 6868
6868
69 69 69 69 69 69 69 69 6970
70 70 70 70 70 70 70 7072
72 72 72 72 72 72 72 72
7373
73 73 73 73 73 73 73
74 7474 74 74 74 74 74 74
7575
75 75 75 75 75 75 75
7676
76 76 76 76 76 76 76
7878
78 78 78 78 78 78 78
7979
79 79 79 79 79 79 7980 80 80 80 80 80 80 80 8081 81 81 81 81 81 81 81 8182
82 82 82 82 82 82 82 8283 83 83 83 83 83 83 83 8384 84 84 84 84 84 84 84 8485
85 85 85 85 85 85 85 8586 86 86 86 86 86 86 86 86
8787
87 87 87 8787 87 87
88 88 88 88 88 88 88 88 8889 89 89 89 89 89 89 89 89
90 90 90 90 90 90 90 90 9091 91 91 91 91 91 91 91 9192
92 92 92 92 92 92 92 929393 93 93 93 93 93 93 93
94 94 94 94 94 94 94 94 9495 95 95 95 95 95 95 95 9596 96 96 96 96 96 96 96 9697 97 97 97 97 97 97 97 9798
98 98 98 98 98 98 98 98
99 99 99 99 99 99 99 99 99
100100
100 100 100 100 100 100 100
101
101101 101 101 101
101 101 101102 102 102 102 102 102 102 102 102
103 103103 103
103 103 103 103 103
104
104
104104
104 104104
104104
105 105 105 105 105 105 105 105 105106
106 106 106 106 106 106 106 106107 107 107 107 107 107 107 107 107
X Residuals
S0Q14 FOVC Residuals
-20
-10
0
10
20
mas
16000159801596015940JD -2440000
123
4
5
67
8
9
101112
13
14
15
16
17
18
1920
21
22
24
25
26
27
28
29
3031
33343536
37
38
39
4041
43
44
45
4647
48
49
50
5152
53
54
55
56
57
58
596061
62
636465
66
67
6869
70
72
74757678
79808182
83
8485
86
87
88
89
90
92
93
949596
99
100
101
102
103
104
105
106
107
123
4
5
67
8
9
101112
13
14
15
16
17
18
1920
21
22
23
24
25
2627
28
29
3031
32
333435
36
37
38
39
404143
44
454647
48
49
50
5152
53
54
55
56
57
58
596061
62
636465
6667
6869
70
72
73
74757678
79808182
83
8485
86
8788
89
90
91
92
93
949596
9798
99
100
101
102
103
104
105
106
107
1234
5
67
8
9
101112
1314
15
16
1718
19202122
23
24
252627
28
293031
32
333435
36
3738
39
404143
44
454647
48
49
50
5152
53
54
55
56
57
58
596061
62
636465
6667
6869
70
72
73
74757678
7980818283
8485
868788
89
90
91
92
93949596
9798
99100
101
102
103104
105
106
107
1234567
8
910111213141516171819202122
232425262728293031
32
3334
35
36373839
404143
44
454647484950515253
54555657
58
5960616263646566
67686970
72
73
747576
7879808182838485868788
8990
91
92
939495
96
9798
99100
101102103104105106107
12345678910111213141516171819
2021
222324252627282930313233
34
353637383940414344
45
464748
495051525354555657
585960616263646566
676869707273
7475
76787980818283848586
87888990
9192939495
96
979899100101102103
104105106107
1 234
56 78910111213 14
1516171819
2021
22232425262728
29
3031323334
3536
37383940414344
45464748
49
50515253 54555657585960616263 646566
67
6869
707273
7475
767879
8081
8283848586
87
8889909192939495 9697
98
99100101102103
104105106107
123
4
56
7
8
9
1011
1213 1415161718
19
20
2122
232425
2627
28
29
30
31
32333435 363738
394041
4344
45464748
49
5051 5253
545556
5758
596061
6263 64
6566
67
68
69
70
72
73
74
75
7678
79
80
81
82
83
8485
86
87
88
89
9091
9293 9495 9697
98
99100
101
102103
104105106107
-20
-10
0
10
20
mas
16000159801596015940
1
23
45
67
8
91011
121314
15161718192021222324
2526
27
28
29303132333435363738
394041
43
4445
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50
51525354555657
58
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70
72737475
76
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87
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89909192939495
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101
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12131415161718192021222324252627
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1234567
8
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242526272829303132333435363738394041434445464748495051525354555657
58
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979899100101102103104105106107 1234567
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596061626364656667686970727374757678798081828384858687888990919293949596
9798991001011021031041051061071
2345
67891011
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36373839404143444546474849505152535455565758596061626364656667
6869
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8990919293949596979899100101102103104105106107 1 2
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100
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1 23
4
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910
11 1213
14
15
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27
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82
8384
8586
87
88
8990
91
929394
95
96
9798
99
100
101
102103104
105
106107
X Residuals
S2Q12 FOVC Residuals
-20
-10
0
10
20
mas
1592015900158801586015840JD -2440000
1
23
4
67
8
91011
12
13
14
15
16
1718
192021
22
23
24
25
2627
28
29
30
31
32
33
343536
37
38
39
40
41
43
45
46
47
48
49
50
51
52
53
54
55
5657
58
59
60
6162
63
64
6566
67
6869
70
7273747576
78
79
8081
82
83
84858687
88
89
9091
9293
949596
97
98
99
100
101
102103
104
105
106107
1
23
4
67
8
91011
12
1314
15
16
1718
192021
22
23
24
25
2627
28
29
30
31
32
33
343536
37
38
39
40
4143
45
46
47
48
49
50
51
52
53
54
55
5657
58
59
60
6162
63
64
6566
67
6869
70
7273747576
78
79
8081
82
83
84858687
88
89
9091
9293
949596
97
98
99
100
101
102103
104
105
106107
1
23
4
5
67
8
91011
12
1314
15
16
1718
1920212223
24
25
2627
28
29
30
31
32
33
343536
37
38
39
40
4143
44
45
4647
48
4950
51
52
53
54
55
5657
58
59
60
616263
646566
67
6869
70
7273747576
78
79
8081
82
83848586
87
88
89
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9293949596
97
98
99100101102103
104
105
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45
67
8
91011
121314
15
16
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24
25262728
29
30313233343536
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39
40
4143
44
454647484950515253
5455
5657
58
5960616263646566
67
68697072737475767879
8081
828384858687
88
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9899100101102103104105106107 1
2345
67
8
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2324252627
2829
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3940
4143
44
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64656667
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70
72737475 76787980
81
8283848586878889909192
9394
9596979899100101
102103104105
106107
1
23
4
5
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910
11
12
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15
16
1718
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22
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70
72737475 76
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11
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1718
192021
22
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32333435
36
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48
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51
52
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58
59
60
61
62
63
64
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69
70
72737475 76
78
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81
82
83
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89
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101
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11
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29
30
31
323334
35
36
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58
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61
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63
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72737475 76
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82
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8788
89
9091
9293
94
95 9697
98
99
100
101
102103104
105
106107
-20
-10
0
10
20
mas
1592015900158801586015840
123
4
5
6
789
101112
13
14
15
16
171819
20
2122
2324
252627
2829
30
3132
33
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58
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80
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8990919293
94
95
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102
103
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105106107 123
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13
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94
95
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102
103
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4
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6
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1415
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33
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96979899100101102103104105106107
1234
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949596979899100101102103104105106107
1234
5
678
9
1011121314
1516
1718
19
20
21
22
2324
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303132333435363738
394041434445
46
47
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50
51
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55
56575859606162
63
6465666768697072
73
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80 81
82
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93
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103
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105106107 1
23
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5
678
9
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141516
1718
19
20
21
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4
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9
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19
20
21
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2324
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47
48
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7980 81
82
838485
868788
89
909192
93
94
95
96
979899
100101
102
103
104
105
106
107
X Residuals
S1Q11 FOVC Residuals
-20
-10
0
10
20
mas
1610016080160601604016020JD -2440000
12345678910111213141516
171819
202122232425262728
29
3031323334353637383940414344454647
48
4950
51
525354555657585960616263646566
676869
70727374757678798081
82
8384858687888990
91929394
9596979899100101102103104
105106107
1234567891011121314151617181920212223242526272829303132333435363738394041434445464748495051525354555657585960616263646566676869707273747576787980818283848586
87888990919293949596979899100101102103104105106107 12
345678910111213141516
17181920212223242526272829303132333435363738394041434445464748495051525354555657585960616263646566676869707273747576787980818283848586
87888990919293949596979899100101102103104105106107
12345678910
11121314151617181920212223242526272829303132333435363738394041434445464748495051525354555657585960616263646566676869707273747576787980818283848586
87888990919293949596
979899100101102103104105106107 12
345678910
1112131415161718192021222324252627282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081
8283848586
87888990919293949596
979899100101102103104105106107
1
2
3
456
7
8
910
1112
13
1415
16
171819
2021
22
2324252627
28
29
3031
32333435363738
3940
414344454647
48
4950
51
5253
54
5556
57
5859
60616263646566
67
686970
727374
7576
7879
80
818283
84
85
8687
8889
90
91929394
9596
979899
100101102
103104
105
106107
1
2
3
4
5
6
7
8
9
10
1112
13
14
15
16
17
18
19
20
21
22
2324
252627
28
29
30
31
32
33
343536
37
38
3940
41
43444546
47
48
49
50
51
52
53
54
5556
57
58
59
6061
6263
646566
67
6869
70
72
7374
75
76
78
79
80
81
82
83
84
85
86
87
88
89
90
9192
9394
95
96
97
98
99
100101
102
103104
105
106107 2
3
4
5
6
7
9
10
1112
13
14
15
16
18
20
21
22
23
24
25
2627
29
30
31
32
33
343536
37
38
3940
41
4344
45
46
47
49
50
52
53
54
5556
57
58
59
6061
62
63
646566
67
686972
7374
75
76
79
80
81
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103104
106107
2
3
4
5
6
7
9
10
11
12
13
14
15
18
20
21
22
23
24
25
2627
29
31
32
33
3435
36
37
38
3940
41
4344
45
46
47
49
50
52
53
54
55
56
58
59
6061
62
63
646566
686972
7374
75
76
79
80
81
83
84
85
86
87
88
89
90
91
92
93
95
96
97
98
99
100
101
102
103104
106
107
-20
-10
0
10
20
mas
1610016080160601604016020
123456789
1011121314151617181920212223242526272829
3031
3233343536373839404143444546474849505152535455565758596061626364656667
6869
7072737475767879
80818283848586
87888990919293949596979899
100
101
102103
104105106107 123
456789101112131415161718192021222324252627282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100
101
102103104105106107 123456789101112131415161718192021222324252627
282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100
101102103104105106107
12345678910
1112131415161718192021222324252627282930313233343536373839404143444546474849505152535455565758596061626364656667686970727374757678798081828384858687888990919293949596979899100101102103104
105106107
12345678910
11121314151617181920212223242526272829303132333435363738394041434445464748495051525354555657585960616263646566
6768697072737475767879808182838485868788899091
9293949596979899100101102103104
105106107 12
3
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104
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3
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8
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14
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22
2324
25
2627
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36
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8
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13
14
15
16
1718
19
2021
22
23
24
25
2627
28
29
30
3132
333435
36
37
38
39
40
41434445
4647
48
4950
51
52
53
54
55
56
5758
59
6061
6263
64
65
6667
68
69
7072
73
7475
767879
80
8182
83
848586
87
88
89
90
91
92
93
9495
96
9798
99
100
101102103
104
105
106
107
1
2
3
4
567
8
9
10
11
12
13
14
15
16
1718
19
2021
22
23
24
25
2627
28
29
30
3132
33
34
35
36
37
38
39
40
4143
4445
4647
48
4950
51
52
53
54
55
56
57
58
59
6061
6263
64
65
66
67
68
69
70
72
73
74
75
76
7879
80
8182
83
848586
87
88
89
90
91
92
93
9495
96
9798
99
100101102103
105
106
107
X Residuals
S3Q13 FOVC Residuals
Channel 42 Season 1
Channel 43 Season 2
Channel 44 Season 3
Channel 41 Season 0
Fig. 6.— As in Figure 4, x and y residuals as a function of time for four parameter modeling of
a sample of KIC-identified giants in Channels 41–44, but for 11 Quarters. Top row, Quarters
3–6; middle row, Quarters 7–10; bottom row, Quarters 11–14. Top half of each box contains
x residuals; y below. The y-axis range within each coordinate half-box is ±20 millipixels
with an x-axis range between 80 and 90 days. The residuals exhibit time-dependency within
each Quarter that correlates with focal plane temperature changes. Season 0 appears to have
a larger fraction of stable astrometry.
– 38 –
-20
-10
0
10
20
mill
ipix
el
1536015340153201530015280JD-2440000
4
4
4
44
444
45
555
5 5555 10
10101010
1010 10 103434
34 343434 3434
3462
62
62
62
6262
62 62
62
67
67
67
67
67
6767
77
77
77
77
77
7777 77
77
9696
969696
96 9696 96103103
103103
103103103 103
103106
106106
106
106
106
106106
106
X Residuals
Fig. 7.— Selected x residuals as a function of time for a four parameter modeling (Equations
3–4) of 127 stars in Channel 26 from Season 3, Quarter 5. The star numbers are identified
with Kepler IDs in Table 2. Note that stars [4, ..., 62] are more astrometrically stable than
stars [67, ..., 106].
– 39 –
4
3
2
1
0
ΔΚ
s Mag
nitu
de C
ontra
st
1.61.41.21.00.80.60.40.2r [arcsec]
Star 4 Star 67 <Good> <Bad>
Fig. 8.— Normalized K-band contrast curves for stars 4 and 67, along with average contrast
curves for stars 4 through 62 (Good) and 67 through 106 (Bad). Note that while star 4 is
more astrometrically stable than star 67, they have virtually identical contrast curves.
– 40 –
-20
-10
0
10
20
mill
ipix
el
158401582015800157801576015740JD -2440000
1
23456
78
910
11121314
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18192021
22
23
2425
26
27
28
2930313233
34353637383940
4142
4344454647
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5758596061
6263646566676869707172
73747576777879808182838485868788899091929394
959697
12345678910
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9293
94
959697
Y
-20
-10
0
10
20
mill
ipix
el
12345678910
1112131415161718192021222324252627282930
3132333435
3637383940414243444546474849505152535455565758596061626364
656667686970717273747576777879808182838485868788899091929394959697 123456789101112131415161718192021222324252627282930
31323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697 1234567
89101112131415161718192021222324252627282930313233343536373839
40414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697
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131415161718192021222324
25
2627
282930313233343536373839
40
4142434445464748495051525354
55565758596061626364
65666768
69707172737475767778798081828384
85868788899091929394959697
X
Fig. 9.— x and y residuals as a function of time for the Q10-only four parameter modeling
from Section 4.1. The residual clumps from left to right are ’plates’ 3–7 first seen in Figure 4.
Stars are labeled with a running number from 1 to 97. The residuals exhibit far less time-
dependency. Stars 9 and 27 continue to exhibit unmodeled behavior.
– 41 –
200
150
100
50
0
Num
ber
-4 -2 0 2 4Residual (miillipixel)
Y Residualsσ = 0.8 millipixelN = 485
200
150
100
50
0
Num
ber
X Residualsσ = 0.4 millipixelN = 485
Fig. 10.— Histograms of x and y residuals for the Q10-only four parameter modeling of only
plates 3–7 (Figure 9) from Section 4.1. The residuals are well-characterized with Gaussians
with 1-σ dispersions as indicated.
– 42 –
-100
-50
0
50
100
mill
ipix
el
159201590015880158601584015820158001578015760JD -2440000
1 1 1 1 11 1 1 1
1
2 2 2 2 2
2 2 2 22
4 4 4 4 44 4 4 4 4
5 5 5 5 55 5 5 5
56 6 6 6 6
6 6 6 667 7 7 7 7
7 7 7 7 7
9 9 9 9 9 9 9 9 9 910 10 10 10 10
10 10 10 10 10
11 11 11 11 11
11 11 11 1111
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1213 13 13 13 13
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21 21 21 21 21
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24 24 24 24 24
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3233 33 33 33 33
33 33 33 333334 34 34 34 34
34 34 34 3434
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39 39 39 39 39
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65 65 65 65 65
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68 68 68 68 68 68 68 68 68
68
70 70 70 70 70
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90 90 90 90 90
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92 92 92 92 92
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93 93 93 93 9393 93 93 93
93
94 94 94 94 94
94 94 94 9494
95 95 95 95 95
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96 96 96 96 96 96 96 96 9696
97 97 97 97 97
97 97 97 9797
Y
-100
-50
0
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mill
ipix
el
1 1 1 1 1 11
11
12 2 2 2 2
22 2 2
2
4 4 4 4 4
44 4 4
4
5 5 5 5 55 5 5 5
5
6 6 6 6 6
66 6 6
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9 9 9 9 9
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9
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10 10 10
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21 2121
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3132 32 32 32 32 32 32 3232
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68 68 68 68 68 68 68 6868
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70 70 70 70 7070 70 70 70
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7575 75 75 75
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95 95 95 95 9595 95 95
95
95
96 96 96 96 96
96 96 9696
9697 97 97 97 97
97 97 9797
97
X
Fig. 11.— x and y residuals in millipixels as a function of time from the full Schmidt 14
parameter modeling from Section 4.3. The residual clumps on the left hand side (Channel
21) from left to right are ’plates’ 3–7. Stars are labeled with a running number from 1 to 97.
Note the scale change along the y-axis, a range five times larger than that in Figure 9. The
residuals exhibit extreme time-dependency. Star 27 continues to show unmodeled behavior
in both channels. Virtually all stars in Channel 37 (right) exhibit unmodeled behavior.
– 43 –
-600
-400
-200
0
200
400
600
CCD
row
[pix
el]
-600 -400 -200 0 200 400 600CCD column [pixel]
1
2
4
567
910
1112
13
14
151617
18
1921
22
23 2425
262728
29
30
31
32 3334
36
37
394041
42
4647
4849
505152
5355 56
57 5859
60
62
63
6568
7071
7374
757677 78
79
8081
82
8384
85
86
87
88
89
90
9192
9394
959697
100 mas
Fig. 12.— Average vector residuals in milliseconds of arc (scale at lower left) as a function
of position within Channel 37 from the full Schmidt 14 parameter modeling of Channel 21
and Channel 37 described in Section 4.3. All positions have been re-origined to the CCD
center. Note the extreme variation in vector length and position angle over small spatial
scales, for example the grouping consisting of stars 22 through 34 (row∼50, column∼-200).
Comparing Channel 21 with Channel 37 demonstrates serious astrometric sytematics on very
small spatial scales.
– 44 –
600
400
200
0
-200
-400
Y (p
ixel
)
6004002000-200-400 X (pixel)
5 mas
Fig. 13.— Average vector residuals in milliseconds of arc as a function of position within
Channel 21 from the full Schmidt 14 parameter modeling of three Season 0 observation sets
described in Section 5.3. Other than a strong tendency for larger residuals in the y direction,
the pattern is satisfactorily random.
– 45 –
40
30
20
10
0
Mea
sure
d di
sper
sion
[mill
imag
nitu
de]
4561213161718
19
2021
22
232425
26
2930313233
34
36
37
38
394041424344454648
49
50515253555657585960
6162636467686970717273747576
77
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79
80818283848586878889909192939596
97
103105106110112114117
119120
121124126127130131132
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139140141142144145146147148149150153154155157158159160161162163165166168
169
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186188
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190193194195196197198
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422
423
424425426
427428
429430
431
432433434435436
437438
439440441442443444445
446447448449
450
451
452
0! 100! 200! 300! 400!Star Number!
Fig. 14.— Measured photometric dispersion (mf standard deviation) over 2.1 y with a nine-
day cadence for each star modeled in Section 5.3. Giants (1–100) exhibit the highest overall
variability. Other groups are the hot star sample (101–199), mid-range Teff (201–299), K-
M star sample (300–350), and KOI sample (400–452). The trends to smaller photometric
variation with number within each sample group (as defined in Section 5.1) may be a function
of position within Channel 21. Lowest variations are nearer (x,y)=(0,1000), highest nearer
(x,y)=(1000,0).
– 46 –
16
14
12
10
8
6
4
2
0
x re
sidua
l [m
illip
ixel
]
17161514131211<mf>
0
5
10
15
20
25
30
35
40
45
50
55
60
45
61213
16
17
18
1920
212223 24
252629
30
31 32 333436
37
3839
40
41 42 43
44
45
464849
5051
52
5355
565758
59
60
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62
63
6467
68
697071
7273 7475
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777879 8081 82 83
84
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8687
8889 90
91 92
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97 103105
106110112
114117
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139140 141142
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267269270
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287288
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297299
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329334
335401402403
404
405406 407
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415416
418
419420421 422
423
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425
426
427428
429430
431432
433
434
435
436 437438
439440441
442443
444445
446
447
448449
450451
452
mas
Fig. 15.— Average x residual from the Section 5.5 modeling plotted against average mf ,
scale in millipixel on the left, mas on the right. The solid curve is a quadratic fit to average
reference star residuals resulting from the modeling in Section 5.3. Also plotted are upper
and lower bounds within which 99% of the Section 5.3 reference stars are expected to fall.
These stars are plotted with smallest ID numbers. The KOI are plotted with larger symbols.
The nine confirmed planetary system host stars are plotted with large bold symbols. All
KOI ID numbers are from Table 4. Clearly KOI 426 and 452 are astrometrically peculiar,
and the nine planetary system host stars behave as expected.
– 47 –
6
4
2
0
-2
-4
-6
Red
uced
Pro
per M
otio
n (H
K(0
) = K
(0) +
5lo
g(µ
) )
1.20.80.40.0-0.4(J-K)0 (2Mass)
Kepler Ch21 Field6
4
2
0
-2
-4
-6
Redu
ced
Prop
er M
otio
n (H
K(0
) = K
(0) +
5lo
g(µ
) )
1.20.80.40.0-0.4(J-K)0 (2Mass)
401
402
403
404
405406407
409
410
411
412
413
414415
416
419
420
421422423
424
425
426
427428
429
430
431
432 433434
435
436
437
438
439440
441
442
443
444
445
446
447
448449
450
451452
Kepler Ch21 Fieldwith KOI
Fig. 16.— Left: RPM from the results of modeling Kepler, UCAC4, and PPMXL data.
The average HK(0) and (J-K)0 ±1σ errors are indicated in the lower left. That error is
reduced by a factor of three compared to an RPM derived by averaging proper motions
from UCAC4 and PPMXL. The heavy tilted line is the location of the main sequence in the
Figure 1 RPM derived from all sky HST proper motions. Note the vertical offset in HK(0)
discussed in the text. Right: RPM with a ∆HK(0) = -1.0 correction, containing the KOI
also shifted. Plotted numbers are from Table 4. The horizontal dotted line represents a
rough demarkation between giant and dwarf stars.
– 48 –
8
6
4
2
0
-2
-4
-6
MK
(0)
1.21.00.80.60.40.20.0-0.2(J-K)0
401
402
403
404
405406 407409
410
411
412
413
414415
416
419
420
421422423
424
425
426
427428
429
430
431
432 433434
435
436
437
438
439440
441
442
443
444445
446447
448449
450
451452
[Fe/H] =-2.5, Age = 3 Gyr [Fe/H] = 0.0, Age = 10 Gyr
Fig. 17.— An HR diagram for the Section 5.5 reference stars and the Table 4 KOIs. MK(0)
are calculated using the Figure 2 linear mapping between MK(0) and HK(0), after applying
the Section 5.8 systematic correction to HK(0). KOI labeling is the same as in Figure 16,
right. Lines show predicted loci for 10Gyr age solar metallicity stars (- - -) and 3Gyr age
metal-poor stars (-··-) from Dartmouth Stellar Evolution models (Dotter et al. 2008). Note
the large number of KOI sub-giants.
– 49 –
5.0
4.5
4.0
3.5
3.0
2.5
2.0
log
g
4.0 3.9 3.8 3.7 3.6log Teff
4
5
6
12
1316
17
18
19
2021
22
23
24
25
2930313233
3436
37 38
39
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41
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4445
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51
52
53
555657
58
59
60
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62
63
6466
676869
70
71
72
7374
757677
79
80
81
82
8384
85
86
87
88
89
9091
92
93
9596
97
103105
106110
112
114 117
119
120
121124
126127
130
131132
133135136
138139
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142144
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150 153
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173174175
176 177
178179
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227228
229
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239240
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252254
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263 264
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266 267269
270
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286287
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292294
295
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297
299
304
306307
308
309
310
311
312
314
317
318 319320
321
322323
324 325326
327328 331332
333
334
335401
402
403404
405
406407409
410411
412413
414
415
416
419
420
421 422
423424
425426427428
429
430
431
432433 434435436
437
438439
440441
442
443
444
445446
447
448
449
450
451
452
[Fe/H] =-2.5, Age = 3 Gyr [Fe/H] = 0.0, Age = 10 Gyr
Fig. 18.— A theoretical HR diagram for the Section 5.5 astrometric reference stars and the
Table 4 KOI. Data are from the MAST. KOI labeling is the same as in Figure 17. The
main sequence and giant branch are apparent. Lines show predicted loci for 10Gyr age solar
metallicity stars (- - -) and 3Gyr age metal-poor stars (-··-) from Dartmouth Stellar Evolution
models (Dotter et al. 2008). Compared with Figure 17, existing log g values apparently do
not readily identify sub-giants.