Astrometric Detection of Exo-EarthsAstrophysical noise in astrometry and RV

M. Shao, G. Marcy, C. Beichman, J. Catanzarite, N. Law,

V. Makarov, W. Traub

Topics

• SIM-Lite Introduction, detection of 1 Mearth planets in the habitable zone.

• Double blind test, astrometric and RV detection of planets (random noise assumed 0.82uas, 1m/s at each epoch, 5yrs astrometry, 15yrs RV)

• Star spots and their effect on astrometric and RV measurements, using our Sun as a target star. (making a quantitative connection between photometric variability and Astrometric and RV variability)

• Is our Sun a typical star? A comparative look at Corot data and SOHO/Virgo data.

• A double blind test, RV, and astrometry with star spot noise

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SIM Will Test Theories of Planet FormationSIM Will Test Theories of Planet Formation

Terrestrial planets in Habitable Zone

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Double Blind Study• 5 “theory” teams to generate multiple planet systems (provides a

list of planets (mass, period, eccentricity, coplanarity etc.)• Data generation team. Introduces randomized Euler rotations and

orbital phases, pm and prlx, and generated the Astrometric and RV observables. 5 yrs of astrometric data (consistent with SIM), 15 years of RV data 1m/s (~8 obs/yr). Time sampling was “randomized” and included Sun avoidance for both SIM and RV measurements.

• ~400 fake planetary systems were generate, 48 systems were selected randomly to be solved by the “Analysis teams”.

• In addition to the “random” planetary system there were several solar system clones (with randomized orbital parameters).

• 5 Analysis teams (4 produced solutions)– Casertano, Sozzetti et al (STScI, INAF/CFA)– Fischer et al (SFSU)– Kasdin et al (Princeton)– Muterspaugh et al (Berkeley)– Internal SIM team (JPL, Cornell, U Texas)

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Asteroids

Earths

Neptunes

Saturns

Jupiters

Fig 2 Mass Distribution of 581 Objects

Planet Population in Study (48 stars)Huge number of asteroids were include, could not be detected, did not interfere with detection of planets.

There were 95 planets with orbital period < 5 yrs, mass > 0.1 Mearth.

Previously, we knew that an SNR= 5.8 was needed to detect a planet (with 1% FAP)

SNR = a / ( * sqrt(N_obs))a = semi-major axis = single epoch noise

52 of the 95 planets had SNR > 5.8 ,theoretically detectable in “solo” systems.

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Results of Double Blind Test

• Completeness. (what fraction of planets with SNR>5.8 were detected in a multiplanet environment)?

• Confidence. (If we made a “claim” that we found a planet, how often were we right?)

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Impact of Star Spots on Astrometry and RV

• We apply a dynamic starspot model to estimate the impact of starspot noise on the detection of Earth via astrometric and radial velocity techniques.

• We find that for the Earth-Sun system, starspots – do not appreciably interfere with astrometric detection.– impose severe requirements on the number of measurements

and duration of an observing campaign needed for radial velocity detection.

Example:Spot area 10-3, Sun @ 10pc Astrometry RVSpot bias 0.25 uas 1 m/sEarth @1AU amp 0.3 uas 0.1m/s

Total_noise2 =Instrument 2 + Photon2 + Stellar_N2 Time scale: Instrument sqrt(T) till systematic Photon sqrt(T) Stellar sqrt(T/ ~1 week)

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Dynamic starspot model

• Assumptions– All of the Sun’s visible flux variation is due to dark starspots.– On average there are three starspots of equal area on the Sun’s surface

at any time.– The birth of starspots is a Poisson process in time.

• Adjustable parameters:– Lognormal distribution of starspot lifetimes (2 parameters)– Starspot area (1 parameter)

• Model includes effects of– Area projection and limb-darkening– Systematic latitude drift with solar cycle “Maunder Butterfly pattern”– Inclination of stellar rotation axis with respect to the line of sight.

• Each starspot is specified by its creation date, lifetime, latitude, and area.• Each starspot is propagated in time as the star rotates.• Drive the total daily starspot area with the 30-year record of sunspot

numbers, that overlaps the space-based TSI (total solar irradiance) record.• Tune the model parameters to approximately match the Sun’s observed flux

variations.

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Flux jitter in the time domain

Simulation

RMS = 4.7x10-4

Observation

RMS = 4.2x10-4

5 yr

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Maunder Butterfly Pattern

• An 11-year sunspot cycle is included in the simulation.

• Sunspots occur at higher latitudes at the beginning of the cycle.

• As the cycle progresses sunspots become more likely to appear at lower latitudes.

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Flux jitter in the frequency domain

Construct a star spot model, that matches the power spectrum of photometric fluctuations.

Use that model to calculate the astrometric and RV noise caused by the star spots.

Goal is to be able to estimate Astrometric and RV noise from photometric noise

Note that photometric noise at high freq (5 min ~ 3x10-3 hz) are orders of magnitude smaller than at 10-6 hz. It’s much easier to find a planet with a 1 day period than with a 10 day period.

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Starspots cause systematic variation of stellar flux, astrometric centroid and RV

• The effect depends on inclination and latitude.

• In the tangent plane: X is along the direction of the line of nodes, Y is along the projected direction of the star’s rotation axis.

• In general, the jitter in the X centroid and RV are zero-mean, but the jitter in the Y centroid is not.

• The bias in the Y centroid is worst for the case of 45° inclination.

• Typical starspot lifetimes* are about a week so (roughly speaking) starspot noise

– Is correlated for measurements separated by less than a week.

– Is independent for measurements separated by over a week.

*The starspot represented in the figure above is persistent, for the purpose of illustration only.

Astrometric jitter due to starspots

Mean of 80 periodograms sampled 100 times over 5 years, as in a typical observing campaign.

Captures noise in the astrometric centroid as a function of frequency

The noise power at 1 year period is 0.006 uAU2

Noise is 0.08 uAU for the ensemble of 100 measurements, or 0.8 uAU per measurement

At 10 pc, astrometric jitter is 0.08 uas per measurement

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Astrometric detection of Earth at 3 pc in sunspot noise, 45° inclination

• At distances of 3 pc and beyond, instrument noise dominates starspot noise, so that

– Starspot noise doesn’t interfere with astrometric detection of Earth (see periodogram, above).

– Even correlated starspot noise is generally not problematic: the noise average for groups of 10 or so measurements taken within a week is well above the starspot noise.

• SIM PlanetQuest (or SIM PlanetQuest Light) could detect a 0.3 Earth mass planet in the habitable zone at 3 pc, with the 1000 measurements allowed by the noise floor.

• Earth’s signal is 3 μAU• Starspot noise is 0.7 μAU per measurement.• Instrument noise is 3 μAU per measurement, at 3 pc.• Instrument noise floor

– SIM PlanetQuest: 0.025 μas, or 0.075 μAU at 3 pc

– SIM PlanetQuest Light:0.038 μas, or 0.113 μAU at 3 pc

• SNR = 3*sqrt(100)/4.2 ~ 7

RV jitter due to starspots

Mean of 80 periodograms sampled 100 times over 5 years, as in a typical observing campaign.

Captures RV jitter due to starspots as a function of frequency

The noise power at 1 year period is 0.002 (m/s)2

Noise is 0.045 m/s for the ensemble of 100 measurements

RV jitter is 0.45 m/s per measurement

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RV and Ast Sun @10pc Summary

• Equiv ast noise ~0.08 uas 0.3uas signature

• Equiv RV noise ~0.45m/s 0.09m/s signature

How Quiet is the Sun, How Quiet are most stars?

• 12 years of total solar irradiance (SOHO/Virgo) to measure the photometric stability of the sun

• Looked at ~104 stars from Corot, 140 days of photometric data.

• Removed obvious artifacts and calculated the rms fluctuations for each star.– Slope removal, median filter (for spikes)

• Looked at distribution of rms fluctuations• Tried to estimate instrumental effects by looking at the

quietest stars. (this limits what we can say about how quiet stars in the field are relative to the Sun.)

• Given instrumental limitations, and reasonable assumptions on the distribution of stellar variability, what can we say about how stable the Sun is relative to most stars?

Our Sun from SOHO/Virgo

Total Solar irradianceOver ~12.3 years

5 yr time span

Rms over 12.3 yrs4.2e-4

RMS over ~75 days~2e-4.

Any astrometric or RV campaign to look for Earths (~1AU) will have an observing campaign lasting 5 yrs or longer. There are short (1~2) year periods during the sun spot cycle when the sun in very quiet, but a 5~15 year, astrometric or RV campaign will see the “average” sun.

Corot Data (flux vs time) Had a Slope

• The slope is instrumental, not from the star

• Also, there are numerous jumps from “hot” pixels, higher dark current due to cosmic ray events at “edges” of pixels.

Light Curves for 70 of 104 Stars (common slope evident)

Remove Slope, Median Filter

Common slope across all 104 light curves were removed.

Median filter (in green) removed most of the single point glitches. (Cosmic ray hits in pixels adjacent to area used for photometry?) Median filter does not remove the steps.

Steps attributed to “Hot” pixels, also seen on HST and other spacecraft. Increased dark current from cosmic ray damage at edges of pixels. Did not try to “fix” hot pixels, this noise limited the photometric precision and ultimately what we can say about our Sun versus other stars.

Data in 2nd ½ also much noisier and omitted in calculated rms.

RMS of all 104 stars

0.01% 0.1% 1% 10%

SUN

The RMS of all 104 stars is larger than the sun (over ~100 day period). But much of this may be due to hot pixels and other instrumental effects.

How can we separate instrumental vs astrophysical fluctuations? (or rather how well can we separate the two?

The Quietest (29) StarsIf we look at the distribution of rms fluctuations for stars that are perfectly stable, we will find the distribution of instrumental noise.

The quietest stars are NOT perfectly quiet, so this distribution represents a pessimistic assesment of the stability of the Corot data.

But it seems that hot pixels will produce ~0.1% fluctuations most of the time. The instrument is never quieter than 3e-4 and rarely noiser than 3e-3.How can we interpret the distribution of

fluctuations of the 104 stars?

What do we want to know? The distribution of variability of stars. (eg 4% of stars will fluctuate by > 1%, 20% of stars fluctuate >0.3% etc.

Discussion

• Because instrumental effects peak at ~0.1% and are non-trivial even at 0.2%, if a star’s rms is <0.2% we can’t say for certain that that is due primarily to astrophysical effects.– 40% of stars have rms > 0.2% – The other 60% are more stable than 0.2%. But can we say

anything about what % of stars are more stable than 0.02%?– We can make some “reasonable assumptions” and see what the

consequences of those assumptions are.• What are reasonable assumptions, on the parent distribution of

stars? (what are unreasonable assumptions?)

Possible Distributions (40% >0.2%)

Rectangular Distribution40% of stars > 0.2% variable0% stars < 0.02%

Stars whose intrinsic variability is < 0.15% may look like 0.15% in this Corot data set.

40% of starsSUN0.02%~100 days

Gaussian distribution(s)~40% of stars > 0.2%~2.5% of stars < 0.02%~7% of stars < 0.02%

60% of stars <0.02% would requirea very unusual distribution (2 hump)

Two Hump (Camel) Distribution• 60% of stars are quieter than ~0.2%. The data does not contradict

the statement that 60% of all stars are quieter than the Sun. But the statement 60% of stars are quieter than 0.2% rms does not imply that 60% of all stars are also quieter than 0.02%.

• For the statement 60% of stars are quieter than the Sun to be true, the parent distribution must have 0% of stars whose variability is between 0.2% and 0.02%. A two humped “camel” distribution.

The red dotted line, which is a distribution consistant with 40% > 0.2% but decreases monotonically would have ~14% stars quieter than the Sun.

Very likely only 10~15% of stars are quieter than the Sun.

Likely ~40% stars < 0.06~0.08%

Must deal with stars ~3 times noisier than the Sun

Is the Other Evidence the Sun is Unusually Quiet?

• Solar like stars obey a relation between chromospheric activity and photometric variability down to a level ~1 mmag. The photometric variability of the Sun measured from space shows that it is the quieter than the ~25 stars in this survey.

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Mayor and Udry, 2008,Phys. Scr. T130, 014010

Keck/HIRESHARPS

Eta-Earth Survey starsGKMChromospherically quiet~10-100 observations each

Photometric Variablity Consistant with Measured RV Variability

RV Precision / Noise

Correlated Noise

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• When measurements are limited by systematic error, increased integration time won’t improve accuracy. Noise that decrease with 1/sqrt(T) has a flat power spectrum.

• Star spots are one example of “non-white noise• The astrometric and RV noise for short period planets is quite

small. Because the RV bias from a star spot is roughly constant over a few days. But when looking for planets with periods of > 1 month, the effect of star spots is much larger.• Photometric variability (on ~10hr time scales for transits) of

the sun is ~2e-5 but is ~5e-4 on time scales of ~1 month• For Sun like stars, spot noise is correlated on time scales of 1~2

weeks. Accuracy of RV/Astrometry measurement improve as• 1/sqrt(T/ 1week)• If the spot noise is ~1m/s detecting a 10cm/s signal at

SNR=5~6 will take 3600 weeks 50~65 years

Summary, Next Steps

• Photometric variations on the surface of a star affect both RV and astrometry in basically the same way.

• Relative to a planet in a 1yr orbit, the star spot noise for RV is ~10X larger than for Astrometry. (short periods favor RV, long periods favor Astrometry)

• For the Sun the astrometric noise is ~0.5m/s and ~0.08uas at each epoch. (This noise becomes “random” for epochs separated by longer than ~ 1 week.)

• Preliminary analysis of ~100 stars observed by Corot shows that ~40% of the stars are ~10X or more variable than the Sun. Most likely only 10~15% of stars are quieter than the Sun. To be able to detect Earth-like planets around a majority of stars, will likely have to deal with star spot noise 2~3 times worse than the sun.

• We’ve extended the data generation codes for our double blind test, to include multiple planet systems with star spot and instrument noise of various levels. Ready to start a double blind study of astrometry and RV detection of exo-Earths in the presence of instrument noise, and star spot noise.

Being Prepared

• Simulation of RV and astrometric observations with both instrument noise and astrophysical noise from star spots/groups.– Simulate data for star spot noise that is 1,3,5X solar levels.– Expected instrument noise for both astrometry and RV. 0.1m/sec (100

min) for RV and 1uas/1000 sec for astrometry– Insert multiplanet system typical of the planet systems in the double blind

study.– Determine which planets could be found with 1,3,5X solar levels of spot

noise• NASA has also asked a double blind study for imaging.

– Imaging of multiple planet systems– Speckle noise, local/exo-zodi, – Inner working angle (planets not observable all the time)– 1st image and orbit determination– Imaging alone, imaging with astrometry

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