Photo-z Requirements for Self-Calibration of Cluster Dark Energy Studies

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1 Photo-z Requirements for Self-Calibration of Cluster Dark Energy Studies Marcos Lima Department of Physics Kavli Institute for Cosmological Physics University of Chicago DES Collaboration Meeting Barcelona - May 18, 2006

Kavli Institute for Cosmological Physics University of

2 Collaborators Wayne Hu Huan Lin Josh Frieman Carlos Cunha Hiroaki Oyaizu Ofer Lahav University of Chicago Fermilab Fermilab, University of Chicago University of Chicago University of Chicago University College London

Fermilab Fermilab, University of Chicago University

3 Outline Cluster mass function Number counts and Covariance Mass-Observable relation Self-Calibration Results

4 Mass function Cluster mass-function exponentially sensitive to linear density perturbations " dn d ln M = 0.3 " m M d ln# $1 d ln M exp $ln# $ [ ] Jenkins et al. 2001!! " Cluster number counts sensitive to DE parameters.

3 " m M d ln# $1 d ln M exp $ln# $1 + 0.64 3.

5 Number Density Number density in bin i (z, M, angle, etc...) n i = where obs M i+1 " d ln M obs " d ln M dn d ln M p(m obs M) M i obs!! p(m obs M) = 1 2 2"# ln M (z) + % ln M obs $ ln M $ ln M bias ( (z) exp - $ - ' 2 & 2# ln M (z) *, ) /

6 Number Counts Volume element Number counts dv = D 2 A (z) H(z) dzd"! where phot z i+1 N i = "# $ dz phot dz D A! $ H n i(z)p(z phot p(z phot z) = z i phot 2 z) + % 1 2"# 2 z (z) exp $ z phot $ z $ z bias ( - (z) - ' & 2# 2 z (z) *, ) /

7 Sample Covariance S ij = (N i " N i )(N j " N j )! = b i b j n in j where the window W i (k) the photo-z distribution. $ d 3 k (2#) W * 3 i (k)w j (k)p(k) is convolved with!

8 Mass-Observable Relation: Redshift Evolution Arbitrary (2 mass parameters per bin) Mean relation: Power law M(z i ) " O = e A (1+ z i ) n M $ fid # O fid Assume is known. Scatter: Polynomial (cubic)!! p 2 " ln M 2 (z i ) = " ln M 3 # k= 0 % ' & (z i ) fid + B k z i k p

z i ) n M $ fid # O fid Assume is known.

9 Uncertainties Mass and redshift uncertainties change the observed number counts and are degenerate with DE. Lima & Hu 2004

10 Self-Calibration Self-calibration of mass-observable parameters: consistency between number counts and 1) clustering Majumdar & Mohr 2004; Lima & Hu ) shape of observed mass function Hu 2003; Lima & Hu ) follow up Majumdar & Mohr 2003, 2004

clustering Majumdar & Mohr 2004; Lima & Hu 2004 2) shape of

11 Self-Calibration Clustering: Requiring consistency between counts and sample variance breaks degeneracy between shifts in mass and DE variations.

12 Self-Calibration Shape: Measuring number counts as a function of mass provides observed mass function. Consistency breaks degeneracy of DE with scatter in mass-observable. Lima & Hu 2005

13 Previous studies Fixed mass-observable. No z scatter. Priored z bias. Counts only Huterer et al. 2004

14 Number Counts SPT like 4000 deg 2 "z = 0.1 bins WMAP 1yr

15 Number Counts SPT like 4000 deg 2 "z = 0.1 bins WMAP 1yr WMAP 3yr (4 x less!)

16 Baseline constraints Fixed Mass, Redshifts. WMAP 1yr

17 Baseline constraints Fixed Mass, Redshifts. WMAP 1yr WMAP 3yr

18 Cluster Photo-z s Huan Lin s catalog. Template Fitting photo-z s

19 Cluster Photo-zs Huan Lin s catalog. Template Fitting photo-z s

20 Constraints SPT like, 4000 deg 2, z max = 2, "z = 0.1 M th = solar masses Flat universe WMAP! 3yr cosmology!! Other cosmological parameters (not DE): priors of ~1% Constant w

21 Fixed Mass-Observable Fixed z bias Fixed z scatter Counts

22 Fixed Mass-Observable Priored z bias Priored z scatter Counts

23 Fixed Mass-Observable: Degradation in w

24 Self-Calibration: Mean + Scatter in Mass-Observable Fixed z bias Fixed z scatter Fixed M bias Fixed M scatter Counts

25 Self-Calibration: Mean + Scatter in Mass-Observable Fixed z bias Fixed z scatter Power Law M bias Cubic M scatter Counts + Clustering

26 Self-Calibration: Mean + Scatter in Mass-Observable Fixed z bias Fixed z scatter Power Law M bias Cubic M scatter Counts + Clustering + Shape

27 Self-Calibration: Mean + Scatter in Mass-Observable Priored z bias Priored z scatter Power Law M bias Cubic M scatter Counts + Clustering + Shape

28 Mean + Scatter in Mass-Observable: Degradation in w

29 Another case: n fixed Mean relation: Power law M(z i ) " O = e A (1+ z i ) n M $ fid # O fid % ' & p Assume Assume! p n fixed. fixed.!!

30 Another case: n fixed Fixed z bias Fixed z scatter Power Law M bias Cubic M scatter Counts + Clustering + Shape

31 Another case: n fixed Fixed z bias Fixed z scatter Power Law M bias Cubic M scatter Counts + Clustering + Shape + n fixed

32 Another case: n fixed Priored z bias Priored z scatter Power Law M bias Cubic M scatter Counts + Clustering + Shape + n fixed

33 Another case: n fixed

34 Summary WMAP 3yr: 4 times less clusters ~ 40% degradation in baseline. Up to ~ 100% in self-calibration. Photo-z requirements: ~ for z bias, ~ 0.05 for z scatter. Future: - Improve uncertainty in z bias and scatter requirement to be a function of z. - Calculations with CatSim1 cluster catalog.

Self Calibration of Cluster Counts: Observable-Mass Distribution. Wayne Hu Kona, March 2005

Self Calibration of Cluster Counts: Observable-Mass Distribution Wayne Hu Kona, March 2005 Self Calibration of Cluster Counts: Observable-Mass Distribution Wayne Hu Kona, August 2004 Scattered Forecasts