The masses and shapes of dark matter halos from galaxy- galaxy lensing in the CFHTLS Henk Hoekstra Mike Hudson Ludo van Waerbeke Yannick Mellier Laura Parker

CFHTLS Galaxy-Galaxy Lensing 5 year, 3 component imaging survey 5 year, 3 component imaging survey Deep – SN, dark energy Deep – SN, dark energy Wide – weak lensing Wide – weak lensing Very wide - KBOs Very wide - KBOs Galaxy masses Galaxy masses Halo profiles (beyond rotation curves, strong lensing) Halo profiles (beyond rotation curves, strong lensing) Galaxy extents (as a function of environment) Galaxy extents (as a function of environment) Halo shapes (flattening?) Halo shapes (flattening?) Biasing (as a function of scale) Biasing (as a function of scale) Link galaxies to their host halos Link galaxies to their host halos divide lens sample by redshift, morphology, luminosity, environment divide lens sample by redshift, morphology, luminosity, environment Parker et al, 2007

Data Early CFHTLS i’ wide data Early CFHTLS i’ wide data ~20 sq degrees ~20 sq degrees no colours / redshifts no colours / redshifts Lenses and sources divided based on their observed magnitudes Lenses and sources divided based on their observed magnitudes Working on photometric redshifts for every lens and source (see Hudson talk) Working on photometric redshifts for every lens and source (see Hudson talk) Magnitude distribution – used to estimate redshifts (  ) N gal i’  =D LS /D S

'basic' weak lensing Measure tangential component of shape in bins Measure tangential component of shape in bins Need to stack signal around MANY foreground lenses Need to stack signal around MANY foreground lenses Correct galaxy shapes using KSB+ (KSB, Hoekstra et al 1998, etc) Correct galaxy shapes using KSB+ (KSB, Hoekstra et al 1998, etc) ForegroundLens expected signal Alternative to maximum likelihood technique fit signal with your favourite mass profile

Redshift Distribution varies for different samples (dashed = HDF, solid llbert et al. CFHTLS-DEEP photo-zs) varies for different samples (dashed = HDF, solid llbert et al. CFHTLS-DEEP photo-zs) Photo-zs critical (even more so for cosmic shear) Photo-zs critical (even more so for cosmic shear) Mass, M/L etc all scale with  Mass, M/L etc all scale with  lenses sources  =D LS /D S

Shear Results start to see “two-halo” term unless galaxies are truly isolated start to see “two-halo” term unless galaxies are truly isolated Velocity dispersion depends on the lens sample. Velocity dispersion depends on the lens sample. Must scale to some typical L* galaxy, based on an assumed relation between L and velocity Must scale to some typical L* galaxy, based on an assumed relation between L and velocity  prop.to L 0.25, for example Use  * to estimate the total mass of the halo assuming a cut-off radius Use  * to estimate the total mass of the halo assuming a cut-off radius 132+/ / e12 Masstotal <M/L>R-band 170+/-30 km/s * *km/s Mass at r e12 well-fit with a singular isothermal sphere with a velocity dispersion of 132 +/- 10 km/s no evidence of systematics (cross-shear is consistent with 0) best fit NFW (dashed) has r 200 = 150 h -1 kpc  2 

Evolution? Generate two lens catalogues divided by observed magnitude Generate two lens catalogues divided by observed magnitude different average redshifts different average redshifts Shear profiles vary, but so do the lens redshifts (and thus  ) Shear profiles vary, but so do the lens redshifts (and thus  ) This measurement will be greatly improved by having photometric redshifts for all lenses and sources This measurement will be greatly improved by having photometric redshifts for all lenses and sources Result: Faint lenses: *= 134+/-12 km/s (high z) Bright lenses: *= 142+/- 18 km/s (low z) Doing this now with CFHTLS-DEEP data with photo-zs

Halo Shapes Halo shapes can constrain alternative gravity theories. Halo shapes can constrain alternative gravity theories. Look for non-spherical halo shapes by comparing the tangential shear from sources near the major axis to those near the minor Look for non-spherical halo shapes by comparing the tangential shear from sources near the major axis to those near the minor Halo flattening was observed in a weak lensing analysis of RCS data (Hoekstra et al., 2004), but not in SDSS by Mandelbaum et al. (2005 ) Results not totally inconsistent -- low significance measurement of flattening in SDSS for gals with same luminosities as the RCS

Halo Shapes Brainerd & Wright, 2000 ~2  detection of non-spherical halo shape Our results favour a halo ellipticity of ~0.3. This is roughly in agreement with simulations of CDM halos (eg Dunbinski & Carlberg, 1991) Without any redshift information there may be contamination from satellites (we don’t have isolated galaxies) minor/major shear ratio radius Targeting early types by looking at 0.5< b/a <0.8

In alternative theories of gravity (without dark matter) the lensing signal is coming from the observed luminous material (plus massive neutrinos?) The lensing signal is measured at large radii The lensing signal is measured at large radii Quadrupole term from baryon distribution decays rapidly Quadrupole term from baryon distribution decays rapidly such theories predict an isotropic lensing signal such theories predict an isotropic lensing signal To test need to use isolated galaxies in g-g analysis, must assume halo aligned with light distribution To test need to use isolated galaxies in g-g analysis, must assume halo aligned with light distribution Dark matter halo shapes can be used to place constraints on alternative gravity theories Alternative Theories of gravity?

Systematics G-G lensing Lens √ Rotate source images by 45 degrees √ Measure signal around random centres √ Correct for overdensity near lenses (physically associated lens-source pairs) √ Estimate maximum intrinsic alignment contamination from satellites (see papers by Agustsson & Brainerd) √ Alternatively estimate by determining the shear when the lenses stay the same but the sources are divided into diff. mag. bins (the bright ones are likely to be nearby and are more likely to be physically associated with lenses & would decrease shear signal) N(z) distribution? True intrinsic alignment? (in future use photo-zs)

Satellites ? What is the distribution of satellites? ? anisotropic? Cluster near major or minor axes? ? What is their alignment? ? all aligned with major axes? ? does the alignment change with distance from the host? (Agustsson & Brainerd 2007) ? satellites of early types align with major axis? Bailin et al (astroph/ ) ? satellites of late types align with minor axis of host (Holmberg effect, Bailin et al 2007) or isotropically distributed (Agustsson & Brainerd 2007) ? Environmental effects? ? host galaxies in groups versus isolated hosts The sample definition of (isolated) host galaxies is critical The sample definition of (isolated) host galaxies is critical

Summary Using early single-band data we measure a galaxy- galaxy lensing signal at very high significance Using early single-band data we measure a galaxy- galaxy lensing signal at very high significance Estimate the mass, M/L and shape of dark matter halos for an L* galaxy Estimate the mass, M/L and shape of dark matter halos for an L* galaxy Stay tuned - g-g lensing with CFHTLS data (Deep and Wide) using photo-zs is coming soon! Stay tuned - g-g lensing with CFHTLS data (Deep and Wide) using photo-zs is coming soon! See talk by Hudson See talk by Hudson Goal: g-g lensing for galaxies segregated by luminosity, morphology, environment, redshift, colour etc Goal: g-g lensing for galaxies segregated by luminosity, morphology, environment, redshift, colour etc

The End

Extent of Halos Maximum likelihood technique to fit for halo model Maximum likelihood technique to fit for halo model For each source you determine the influence from all nearby foreground lenses with a parameterised lens model For each source you determine the influence from all nearby foreground lenses with a parameterised lens model Need redshifts (see Kleinheinrich et al. 2005) Need redshifts (see Kleinheinrich et al. 2005) Hoekstra et al., 2004  NFW

Link with galaxy formation studies: The relation between galaxies and the underlying mass distribution can provide important information about the way galaxies form (constraints on cooling & feedback). The relation between galaxies and the underlying mass distribution can provide important information about the way galaxies form (constraints on cooling & feedback). Weak lensing provides a unique way to study the biasing relations as a function of scale Weak lensing provides a unique way to study the biasing relations as a function of scale G-G lensing probes dark matter halos to large radii, beyond rotation curves, strong lensing G-G lensing probes dark matter halos to large radii, beyond rotation curves, strong lensing Why study G-G Lensing?

b 2 =  gg /  mm r =  gm /(  mm  gg ) 1/2  gg /  gm = b/r Use lensing to estimate b – important input for galaxy formation models Measuring the clustering of galaxies is an indirect probe of mass distribution (subject to bias parameter) Can see galaxies very well. Can simulate DM very well. Do galaxies trace DM? Why study G-G Lensing? SDSS (Sheldon et al.) and RCS (Hoekstra et al.) show b/r (from lensing) is scale invariant out to ~10 Mpc (low-z) Depends on gal colour & L

e halo = f e lens Spherical halos excluded with 99.5% confidence Good agreement with CDM predictions If halos are not aligned with galaxy then the flattening is underestimated Simple model: and determine f Found f = / Hoekstra et al., 2004 Flattening of dark matter halos from RCS

Targeting galaxies with with e>0.15 (throw out roundest gals.) Targeting early types by looking at 0.5<b/a<0.8 minor/major shear ratio minor/major shear ratio

Halo Shapes Simulations Allgood et al., 2005, Flores et al., 2005, Bullock 2001, Jing & Suto 2002 Allgood et al., 2005, Flores et al., 2005, Bullock 2001, Jing & Suto 2002 Mean and scatter of halo shape parameters (axis ratios) as a function of mass and epoch Mean and scatter of halo shape parameters (axis ratios) as a function of mass and epoch More massive halos are more triaxial More massive halos are more triaxial Halos of a given mass are more triaxial at earlier times Halos of a given mass are more triaxial at earlier times Halos are increasingly round at large radii Halos are increasingly round at large radii Halos in lower sigma8 cosmologies are more triaxial Halos in lower sigma8 cosmologies are more triaxial Ratio of smallest to largest axis, s, = 0.54 (Mvir/M*) ^(-0.05) Ratio of smallest to largest axis, s, = 0.54 (Mvir/M*) ^(-0.05)