Constraining Source Redshift Distributions with Angular Cross Correlations

Transcription

1 Constraining Source Redshift Distributions with Angular Cross Correlations Matt McQuinn (UC Berkeley) in collaboration w/ Martin White arxiv:

2 Technique: Using spatial clustering to measure source redshifts Let s say you know the redshift of this galaxy Picture shows the CFHTLS wide field over 155 sq deg. 1st reference to a similar technique: Selder & Peebles 79

3 Technique: Using spatial clustering to measure source redshifts It is more likely that this galaxy is coeval with it than this one Let s say you know the redshift of this galaxy Picture shows the CFHTLS wide field over 155 sq deg. 1st reference to a similar technique: Selder & Peebles 79

4 Possible applications Studies of galaxy evolution redshift identification of diffuse backgrounds statistically cleaning correlated anisotropies from maps photo-z calibration (essential for e.g. weak lensing studies)

5 Background: large-scale structure theory Overdensity angle At > 10 Mpc scales, δgalaxy = b δdensity+ var[(vpixel n) -1 ] 1/2 where b is an order unity constant called the linear bias δgalaxy (l) 2 Plot for z=1, dz =0.1, b = 1

6 Background: large-scale structure theory Overdensity angle At > 10 Mpc scales, δgalaxy = b δdensity+ var[(vpixel n) -1 ] 1/2 where b is an order unity constant called the linear bias δgalaxy (l) 2 Plot for z=1, dz =0.1, b = 1

7 Background: large-scale structure theory Overdensity angle At > 10 Mpc scales, δgalaxy = b δdensity+ var[(vpixel n) -1 ] 1/2 where b is an order unity constant called the linear bias δgalaxy (l) 2 Plot for z=1, dz =0.1, b = 1

8 Optimal Estimator Even though the above is written in harmonic space, can trivially write in configuration space

9 This results of this estimator can be expressed analytically: Figure shows validity of Limber approximation for dz=0.1 (contours are log of error) (in the limber approximation) In the limit where there are <~10 3 spectra per square degree: (Fii -1/2 is also the estimator error)

10 Configuration Space where x = cos(θ) and vi is Hankel transform of Fourier space weights

11 What number densities are relevant Critical density for cosmic fluctuations to be dominate at any scale

12 Spectroscopic Survey Optimizations All panels are error in bins of dz = 0.05 and unknown sample complete to i<23. Left panel assumes 100 deg 2 and right assumes 10 5 spectroscopic galaxies. Many-Many: Many-Rare: Rare-Rare:

13 Examples Fractional error in number in z-bin dashed = no nonlinear cutoff over 1600 deg 2 over 40 deg 2 over 1 deg 2 solid = cutoff at lnl ``Newman-like curves are previous estimator in literature; Newman (2008) (assumes errors in bins of dz = 0.05)

14 Fractional error in number in z-bin Photo-z calibration (assumes errors in bins of dz = 0.05) Rare spectra: Abundant spectra: Photo-z bin centered at z = 1.4 with σz = 0.05

15 What scales are relevant? known-unknown known-unknown Angular Space Both plots are for z=0.7

16 Questions answered in this work Q: What is the minimum number of spectra required to even bother? A: ~1000 (It generally doesn t depend on their density) Q: How well can the redshift distribution of an unknown population be measured? A: Potentially to percent level with future large spectroscopic surveys, especially for photo-z s Q: When are the approximations of ignoring RSDs, magnification, using Limber, & linear theory accurate? A: Often, but magnification (and maybe dust) is most worrisome

17 Conclusions There is a simple and optimal algorithm for estimating the redshift distribution of an unknown population This estimator has 1-2 orders of magnitude reduced variance over previous estimators We have demonstrated estimator on mocks and are planning to apply it to real data

18 Magnification Rare quasar-like α (=-1) ratio of magnification to the term we considered