Constraining photometric redshift errors with galaxy two-point correlation functions
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Transcript of Constraining photometric redshift errors with galaxy two-point correlation functions
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8/14/2019 Constraining photometric redshift errors with galaxy two-point correlation functions
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Constraining photometric redshift errors
with galaxy two-point correlations
Michael Schneider
UC Davis
Collaborators: Andy Connolly, Lloyd Knox, Hu Zhan
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Outline
The basic idea
Cross-correlating the photometricsample with itself
Cross-correlating with an overlapping
spectroscopic sample (J. Newman)
Challenges and future directions
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Motivation
Future dark energy surveys (DES, Pan-STARRS, LSST, EUCLID, JDEM)
plan to usephotometric redshifts to measure cosmic shear and
galaxy correlations
Hard to getfair spectroscopic training samples to the depth of the
photometric sample
Conventional photo-z estimation methods may leave intolerably
large errors
Can other calibration methods reduce the size of the fair
spectroscopic training sample needed for a given photo-z
error target?
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Cross correlating galaxies binned
by photometric redshift
astro-ph/0606098
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Photo-z errors induce cross-correlations
bin
Z
Scatter Catastrophic
n(z) A. Schulz
z
n(z)
overlap causes
correlation
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Sensitivity of galaxy power spectrum
10-7
10-6
10-5
10-4
10-3
10-2
10-1
50 100 200 400 800
l2
P(l)/(2)
l
bins (1,1)bins (1,3), var. a13bins (1,3), var. a31
Auto and cross angular
galaxy power spectra
for: 0 < zp < 0.5and 1 < zp < 1.5
Points with errors:
fiducial values (with
photo-z errors)
Lines:1- variation
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Model for photo-z errors
Bin galaxy number density in z and mix values between bins:
dNai
dzd(z, ) =
Nai
1
Na
dNa
dzd(z, )(z)
mean number of galaxies of spectral-type a in photo-z bini that come from true-z bin
Nai
0.01
0.1
1
10
photometric z
spectroscop
ic
z
0 0.5 1 1.5 2 2.5 3
0
0.5
1
1.5
2
2.5
3
Fiducial model:
- Estimate photo-z of 105 simulated galaxy
colors in ugrizy filters (limited in i-band at i
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Model for galaxy correlations
UseLimber approximation to compute linear
angular galaxy power spectrum:
constrain linear galaxy bias jointly with photo-z errorparameters
truncate range to justify Gaussian and Limber
approximationsWith photo-z errors:
C() = NN = NN bb PDM
()
Cij() =
NiNjC()
NN+ Cshotij ()
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- Fractional constraints on
- 10% prior on the galaxy bias
Ni N1
i+ N
2
i
10-3
10-2
10-1
100
0 0.5 1 1.5 2 2.5 3
!
/dN/dz
z
photo-z bin 1
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 2
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 3
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
!
/dN/dz
z
photo-z bin 4
10-3
10-2
10-1
100
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 5
10-3
10-2
10-1
100
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 6
Parameter constraint forecasts
Filled:
full sample
Open:
red/blue split
sample
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Bias and red and blue population
constraints
Galaxy bias constraints
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3
!((b
gal
(z))/b
gal
(z)
z
redblue
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
!
/dN/dz
z
photo-z bin 1
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 2
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 3
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
!
/dN/dz
z
photo-z bin 4
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 5
10-3
10-2
10-1
100
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 6
Red & Blue sub-populations
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Cross correlating with an
overlapping spectroscopic sample
See J. Newman paper:http://astron.berkeley.edu/~jnewman/xcorr/xcorr.pdf
http://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdfhttp://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdfhttp://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdfhttp://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdf -
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Model for galaxy correlations
2DAngular
cross-corr
elation
3Dcross-c
orrelation
function
Photometr
icselection
function
At large (linear) scales assume:
In previous notation: Now observable
From A. Schulz Moriond talk
Ci() =
Nib
p ot
bspec
Cspec
()
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Monte Carlo tests (J. Newman)
Assumptions:
Gaussian photo-z errors (fit for 2 parameters)
No bias evolution (so no degeneracy)
25k spec. galaxies per unit z
10 phot. galaxies per arcmin^2clustering of photometric sample independent of z
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How many spectra do we need?
J. Newman
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Near-term spec. samples
Blue: SDSS +
AGES + VVDS +
DEEP2+1700
galaxies/unit z at
high zRed: add
zCOSMOS +
PRIMUS + WiggleZ
+ 5000 galaxies/unit
z at high z
J. Newman
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Test with N-body simulations (A. Schulz)
Boxside (Gpc/h) Boxside (Gpc/h)
Populate 1 (Gpc/h)^3 box with galaxies using HOD
No z evolution of correlations or bias
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Complications
Galaxy bias:
redshift evolution
nonlinear biasMagnification bias
Intrinsic l.o.s. correlations between narrow z-bins
Sample variance
Cosmology dependence
Practical method for reconstruction
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Restricting the number of parameters
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
!
/dN/dz
z
photo-z bin 1
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 2
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 3
10-3
10-2
10-1
0 0.5 1 1.5 2 2.5 3
!
/dN/dz
z
photo-z bin 4
10-3
10-2
10
-1
100
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 5
10-3
10-2
10
-1
100
0 0.5 1 1.5 2 2.5 3
z
photo-z bin 6
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PC decomposition of error distributions
0.0 0.5 1.0 1.5 2.0
0.
0
0.
5
1.
0
1.
5
2.
0
spec. z
ph
ot.z
0.0 0.5 1.0 1.5 2.0
!0.
4
!0.
2
0.0
0.
2
0.
4
z
eigenfunctions
!
!
!
!
!!!!
!!!!!!!!!!! !! !!!!!!!!!!!!!!!!!!!
0 10 20 30 40
0.5
0.6
0.7
0.8
0.9
1.0
Mode number
Cum.prop.ofvarianceSims. from M. Banerji website
(Collister & Lahav 2004, Banerji et al. 2007)
grizY, i < 24.3
Effect on DE
constraints?
http://zuserver2.star.ucl.ac.uk/~mbanerji/DESdata/
Cum.proportionofvariance
Eigenfunctions
http://zuserver2.star.ucl.ac.uk/~mbanerji/DESdata/http://zuserver2.star.ucl.ac.uk/~mbanerji/DESdata/ -
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Constraints on bias?
Add weak lensing measurementsFit with HOD model(Blake, Collister, & Lahav)
Add 3-point correlations (McBride &Connolly, Ashley & Brunner)
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Conclusions
Amount ofleakage of galaxies between photo-z bins due to catastrophic
errors can be constrained to ~10% of the number of galaxies in each bin if
galaxy bias is known.
Priors on the galaxy bias are necessary to constrain the photo-z error
parameters.
Separation of the galaxy sample according to spectral type may significantly
improve the photo-z errorparameter constraints.
Cross-correlating with a spatially overlapping spectroscopic sample may
provide even tighter constraints on the photo-z errors.
The sizes of the required spectroscopic training samples are not yet
determined.
Might be able tojointly constrain galaxy bias.
Need to test with realistic mocks or data!
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Multipole ranges in galaxy power spectra
photo-z range
0.0 - 0.5 7 114
0.5 - 1.0 23 458
1.0 - 1.5 45 1018
1.5 - 2.0 71 1875
2.0 - 2.5 103 3195
2.5 - 3.0 140 5186
max(z)min(z)
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Fiducial model for red and blue
galaxy spectral types
Total dN/dz normalized to
65 galaxies per sq.
arcmin.
Red and blue dN/dzs are
ad-hoc
Use Cooray 2006 CLFmodels for red and blue
biases
0
5
10
15
20
25
30
0 0.5 1 1.5 2 2.5 3
dN/dzd!
z
total
red
blue