Testing the Shear Ratio Test: (More) Cosmology from Lensing in the COSMOS Field James Taylor University of Waterloo (Waterloo, Ontario, Canada) DUEL Edinburgh, Summer Conference July

The COSMOS Survey P.I. Nick Scoville

The COSMOS Survey  2 square degree ACS mosaic  lensing results from 1.64 square degrees (~600 pointings)  2-3 million galaxies down to F814W AB = 26.6 (0.6M to 26)  30-band photometry, photo-zs with dz ~ 0.012(1+z) to z = 1.25 and I F814W = 24  follow-up in X-ray, radio, IR, UV, Sub-mm, …

WL Convergence Maps (cf. Rhodes et al. 2007; Massey et al. 2007; Leauthaud et al 2007)  cut catalogue down to 40 galaxies/arcmin 2 to remove bad zs  correct for PSF variations, CTE  Get lensing maps, low-resolution 3D maps, various measures of power in 2D and restricted 3D  results compare well with baryonic distributions (e.g. galaxy distribution)

The Final Result: E-modes (left) versus B-modes (right)

recent updates: - improved photo-zs - improved CTE correction in images - new shear calibration underway + updated group catalog(s) so expect stronger signal around peaks in lensing map, and cleaner dependence on source and lens redshift  time for some 2nd generation tests of the lensing signal The Final Result: 3-D constraints on the amplitude of fluctuations: Massey et al 2007

Measuring Geometry: Shear Ratio Test (Jain & Taylor 2003, Bernstein & Jain 2004, Taylor et al. 2007) Bartelmann & Schneider 1999 Relative Lensing Strength Z(z) Your cluster goes here Take ratio of shear of objects behind a particular cluster, as a function of redshift Details of mass distribution & overall calibration cancel  clean geometric test Can extend this to continuous result by fitting to all redshifts Z(z)  D LS /D S

But how big is the signal? Use strength of signal behind cluster as a function of redshift to measure D A (z): Base: h = 0.73,  m = 0.27 (  or X = 1 -  m ) Variants (different curves):  m = 0.25,0.30,0.32 w 0 = -1,-0.95,-0.9,-0.85,-0.8 w(z) = w 0 + w a (1-a) with w 0 = -1, w a = 0.05, 0.1 h = 0.7, 0.75

Use strength of signal behind cluster as a function of redshift to measure D A (z): weak but distinctive signal; relative change (change in distance ratio) is only 0.5% Lens at z = % relative change Base: h = 0.73,  m = 0.27 (  or X = 1 -  m ) Variants (different curves):  m = 0.25,0.30,0.32 w 0 = -1,-0.95,-0.9,-0.85,-0.8 w(z) = w 0 + w a (1-a) with w 0 = -1, w a = 0.05, 0.1 h = 0.7, 0.75 How big is the signal?

Use strength of signal behind cluster as a function of redshift to measure D A (z): weak but distinctive signal; relative change (change in distance ratio) is only 0.5% Lens at z = % relative change Base: h = 0.73,  m = 0.27 (  or X = 1 -  m ) Variants (different curves):  m = 0.25,0.30,0.32 w 0 = -1,-0.95,-0.9,-0.85,-0.8 w(z) = w 0 + w a (1-a) with w 0 = -1, w a = 0.05, 0.1 h = 0.7, 0.75 How big is the signal?

Use strength of signal behind cluster as a function of redshift to measure D A (z): weak but distinctive signal; relative change (change in distance ratio) is only 0.5% Lens at z = % relative change Base: h = 0.73,  m = 0.27 (  or X = 1 -  m ) Variants (different curves):  m = 0.25,0.30,0.32 w 0 = -1,-0.95,-0.9,-0.85,-0.8 w(z) = w 0 + w a (1-a) with w 0 = -1, w a = 0.05, 0.1 h = 0.7, 0.75 How big is the signal?

Use strength of signal behind cluster as a function of redshift to measure D A (z): weak but distinctive signal; relative change (change in distance ratio) is only 0.5% Lens at z = % relative change Base: h = 0.73,  m = 0.27 (  or X = 1 -  m ) Variants (different curves):  m = 0.25,0.30,0.32 w 0 = -1,-0.95,-0.9,-0.85,-0.8 w(z) = w 0 + w a (1-a) with w 0 = -1, w a = 0.05, 0.1 h = 0.7, 0.75 How big is the signal?

Use strength of signal behind cluster as a function of redshift to measure D A (z): weak but distinctive signal; relative change (change in distance ratio) is only 0.5% Lens at z = % relative change Base: h = 0.73,  m = 0.27 (  or X = 1 -  m ) Variants (different curves):  m = 0.25,0.30,0.32 w 0 = -1,-0.95,-0.9,-0.85,-0.8 w(z) = w 0 + w a (1-a) with w 0 = -1, w a = 0.05, 0.1 h = 0.7, 0.75 Signal weak but distinctive How big is the signal?

Previous detections with massive clusters Signal has been seen previously behind a few clusters: e.g. Wittman et al ~3e14 M o cluster in DLS; detection, mass and redshift all from weak lensing (source photo-zs from 4 bands)

Previous detections with massive clusters Signal has been seen previously behind a few clusters: e.g. Gavazzi & Soucail (2008): cluster Cl-02 in CFHTLS-Deep (cf. also Medezinski et al. submitted: 1.25 M galaxies behind 25 massive clusters, in a few bands)

So why try this in COSMOS ? Less signal (groups only, no truly massive clusters), but far better photo-zs can push techniques down to group or galaxy scales nice test of systematics in catalogue selection, effect of photo-z errors test/confirm error forecasts for future surveys Percival et al.2007: interesting indication of possible mismatch in distance scales in BAO?

Log(volume) The sample of COSMOS Groups and Clusters (plot from Leauthaud et al. 2009) (X-ray derived Mass)

Log(volume) The sample of COSMOS Groups and Clusters (plot from Leauthaud et al. 2009) (X-ray derived Mass) ~67  in top 14 objects?

Log(volume) The sample of COSMOS Groups and Clusters (plot from Leauthaud et al. 2009) (X-ray derived Mass) could get another ~60  from less massive groups?

Shear vs. photo-z around peaks, along promising lines of sight

How to stack clusters? Tangential shear goes as: so redshift dependence enters via critical surface density: Thus if we define(assumes flat models) and then independent of cosmology

We see the signal! Stack of regions within 6’ of ~200+ x-ray groups good fit in front of/behind cluster significance still unclear; seems less than expected effect of other structures along the line of sight decreases chi 2, but hard to quantify

A Caveat In a field this small, a few redshifts dominate the distribution of structure  systematics in shear ratio

Prospects ¶ Signal detected, well behaved, significance slightly lower than expected? ¶ Still studying noise versus radial weighting, catalogue cuts, path weighting ¶ Results roughly consistent with w 0 ~ /- 1.0 ¶ Future predictions for large surveys + CMB + BAO (Taylor et al. 2007):  w 0 = 0.047,  w a = and 2% measurement of dark energy at z ~ 0.6 Or use CMB as an extra slice? (cf. Hu, Holz & Vale 2007; Das & Spergel 2009) error forecasts from 20,000 deg 2 survey (Taylor et al. 2007)