The masses and shapes of The masses and shapes of dark matter halos from dark matter halos from

galaxy-galaxy lensing in the galaxy-galaxy lensing in the CFHTLSCFHTLS

Henk Hoekstra Henk Hoekstra Mike Hudson Mike Hudson

Ludo van Waerbeke Ludo van Waerbeke Yannick Mellier Yannick Mellier

Laura ParkerLaura Parker

CFHTLS Galaxy-GalaxyCFHTLS Galaxy-GalaxyLensingLensing

5 year, 3 component 5 year, 3 component imaging surveyimaging survey

Deep – SN, dark Deep – SN, dark energyenergy

Wide – weak lensingWide – weak lensing

Very wide - KBOsVery wide - KBOs

Galaxy masses Galaxy masses

Halo profiles (beyond Halo profiles (beyond rotation rotation curves, strong curves, strong lensing)lensing)

Galaxy extents (as a function Galaxy extents (as a function of environment)of environment)

Halo shapes (flattening?)Halo shapes (flattening?)

Biasing (as a function of Biasing (as a function of scale)scale)

Link galaxies to their host Link galaxies to their host haloshalos

divide lens sample by divide lens sample by redshift, morphology, redshift, morphology, luminosity, luminosity, environmentenvironment

Parker et al, 2007Parker et al, 2007

DataData Early CFHTLS i’ wide dataEarly CFHTLS i’ wide data

~20 sq degrees~20 sq degrees

no colours / redshiftsno colours / redshifts

Lenses and sources divided based on Lenses and sources divided based on their observed magnitudestheir observed magnitudes

Working on photometric redshifts for Working on photometric redshifts for every lens and source every lens and source (see Hudson talk)(see Hudson talk)

Magnitude distribution – used to Magnitude distribution – used to estimate redshifts (estimate redshifts () )

Ngal

i’

=D=DLSLS/D/DSS

'basic' weak lensing'basic' weak lensing Measure tangential component Measure tangential component

of shape in bins of shape in bins

Need to stack signal around Need to stack signal around MANY foreground lensesMANY foreground lenses

Correct galaxy shapes using Correct galaxy shapes using KSB+ (KSB, Hoekstra et al 1998, KSB+ (KSB, Hoekstra et al 1998, etc)etc)

ForegroundForegroundLensLens

expected signal Alternative to maximum likelihood technique

fit signal with your favourite mass profile

Redshift DistributionRedshift Distribution

varies for different samples varies for different samples (dashed = HDF, solid llbert et (dashed = HDF, solid llbert et al. CFHTLS-DEEP photo-zs)al. CFHTLS-DEEP photo-zs)

Photo-zs critical (even more Photo-zs critical (even more so for cosmic shear)so for cosmic shear)

Mass, M/L etc all scale with Mass, M/L etc all scale with

lenses

sources

=D=DLSLS/D/DSS

Shear ResultsShear Results

start to see “two-halo” start to see “two-halo” term unless galaxies are term unless galaxies are

truly isolatedtruly isolated

Velocity dispersion depends on Velocity dispersion depends on the lens sample.the lens sample.

Must scale to some typical L* Must scale to some typical L* galaxy, based on an assumed galaxy, based on an assumed relation between L and velocityrelation between L and velocity

prop.to Lprop.to L0.250.25 , for , for exampleexample

Use Use * to estimate the total * to estimate the total mass of the halo assuming a cut-mass of the halo assuming a cut-off radiusoff radius

132+/-132+/-1010

137+/-11137+/-11 2.2e122.2e12

MassMasstotaltotal

<M/L><M/L>R-R-

bandband170+/-30170+/-30

<<>>km/skm/s

<<>>**

km/skm/s

MassMassat rat r

200200

1.1e121.1e12

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 r200 = 150 h-1kpc

<<>>22

Evolution?Evolution? Generate two lens catalogues Generate two lens catalogues

divided by observed magnitudedivided by observed magnitude

different average redshiftsdifferent average redshifts

Shear profiles vary, but so do the Shear profiles vary, but so do the lens redshifts (and thus lens redshifts (and thus ) )

This measurement will be greatly This measurement will be greatly improved by having photometric improved by having photometric redshifts for all lenses and sourcesredshifts for all lenses and sources

Result:Result:Faint lenses: <Faint lenses: <>*= 134+/-12 km/s >*= 134+/-12 km/s (high z)(high z)

Bright lenses: <Bright lenses: <>*= 142+/- 18 >*= 142+/- 18 km/skm/s(low z)(low z) Doing this now with CFHTLS-DEEP Doing this now with CFHTLS-DEEP

data with photo-zs data with photo-zs

Halo ShapesHalo Shapes Halo shapes can constrain Halo shapes can constrain

alternative gravity theories.alternative gravity theories. Look for non-spherical halo shapes Look for non-spherical halo shapes

by comparing the tangential shear by comparing the tangential shear from sources near the major axis to from sources near the major axis to those near the minorthose near the minor

Halo flattening was observed in a Halo flattening was observed in a weak lensing analysis of RCS data weak lensing analysis of RCS data (Hoekstra et al., 2004), but not in (Hoekstra et al., 2004), but not in SDSS by Mandelbaum et al. (2005SDSS by Mandelbaum et al. (2005))

Results not totally inconsistent -- Results not totally inconsistent -- low significance measurement of low significance measurement of flattening in SDSS for gals with flattening in SDSS for gals with same luminosities as the RCSsame luminosities as the RCS

Halo ShapesHalo Shapes

Brainerd & Wright, 2000Brainerd & Wright, 2000

~2~2 detection of non- detection of non-spherical halo shapespherical halo shape

Our results favour a halo ellipticity of ~0.3. Our results favour a halo ellipticity of ~0.3. This is roughly in agreement with This is roughly in agreement with simulations of CDM halos simulations of CDM halos (eg Dunbinski & Carlberg, (eg Dunbinski & Carlberg, 1991)1991)

Without any redshift information there may be contamination from satellitesWithout any redshift information there may be contamination from satellites(we don’t have isolated galaxies)(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 gravityIn alternative theories of gravity (without dark matter)(without dark matter) the the lensing signal is coming from the observed luminous lensing signal is coming from the observed luminous material material (plus massive neutrinos?)(plus massive neutrinos?)

The lensing signal is measured at large radiiThe lensing signal is measured at large radii

Quadrupole term from baryon distribution decays rapidlyQuadrupole term from baryon distribution decays rapidly

such theories predict ansuch theories predict an isotropicisotropic lensing signal lensing signal

To test need to use To test need to use isolatedisolated galaxies in g-g analysis, must galaxies in g-g analysis, must assume halo aligned with light distributionassume halo aligned with light distribution

Dark matter halo shapes can be used to Dark matter halo shapes can be used to place constraints on alternative gravity place constraints on alternative gravity

theoriestheories

Alternative Theories of Alternative Theories of gravity?gravity?

Systematics G-G lensingSystematics G-G lensing

LensLens√ 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)

SatellitesSatellites?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. 2007 (astroph/0706.1350)

? 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

SummarySummary

Using early single-band data we measure a galaxy-Using early single-band data we measure a galaxy-galaxy lensing signal at very high significancegalaxy lensing signal at very high significance

Estimate the mass, M/L and shape of dark matter Estimate the mass, M/L and shape of dark matter halos for an L* galaxyhalos for an L* galaxy

Stay tunedStay tuned - g-g lensing with CFHTLS data (Deep - g-g lensing with CFHTLS data (Deep and Wide) using photo-zs is coming soon! and Wide) using photo-zs is coming soon!

See talk by HudsonSee talk by Hudson

Goal:Goal: g-g lensing for galaxies segregated by g-g lensing for galaxies segregated by luminosity, morphology, environment, redshift, luminosity, morphology, environment, redshift, colour etccolour etc

The EndThe End

Extent of HalosExtent of Halos Maximum likelihood technique to fit for halo modelMaximum likelihood technique to fit for halo model

For each source you determine the influence from all For each source you determine the influence from all nearby foreground lenses with a parameterised lens nearby foreground lenses with a parameterised lens modelmodel

Need redshifts (see Kleinheinrich et al. 2005)Need redshifts (see Kleinheinrich et al. 2005)

(r) 2s2

2Gr2(r2 s2)

p(r) cc

(r /rs)(1 r /r

s)2

Hoekstra et al., 2004Hoekstra et al., 2004

NFWNFW

Link with galaxy formation Link with galaxy formation studies:studies:• The relation between galaxies and the underlying mass The relation between galaxies and the underlying mass distribution can provide important information about the distribution can provide important information about the way galaxies form (constraints on cooling & feedback). way galaxies form (constraints on cooling & feedback).

• Weak lensing provides a unique way to study the biasing Weak lensing provides a unique way to study the biasing relations as a function of scalerelations as a function of scale

• G-G lensing probes dark matter halos to large radii, G-G lensing probes dark matter halos to large radii, beyond rotation curves, strong lensingbeyond rotation curves, strong lensing

Why study G-G Why study G-G Lensing?Lensing?

bb2 2 = = gggg//mmmm

r = r = gmgm/(/(mmmmgggg))1/21/2

gggg//gm gm = b/r= b/rUse lensing to estimate b – important input for galaxy formation modelsUse lensing to estimate b – important input for galaxy formation models

Measuring the clustering of galaxies is an indirect probe of Measuring the clustering of galaxies is an indirect probe of mass distribution (subject to bias parameter)mass distribution (subject to bias parameter)

Can see galaxies very well. Can simulate DM very Can see galaxies very well. Can simulate DM very well. Do galaxies trace DM?well. Do galaxies trace DM?

Why study G-G Lensing?Why study G-G Lensing?

SDSS (Sheldon et al.) and RCS (Hoekstra et al.) show b/r SDSS (Sheldon et al.) and RCS (Hoekstra et al.) show b/r (from lensing) is scale invariant out to ~10 Mpc (low-z)(from lensing) is scale invariant out to ~10 Mpc (low-z)

Depends on gal colour & LDepends on gal colour & L

eehalohalo= = ff eelenslens

Spherical halos excluded Spherical halos excluded with 99.5% confidencewith 99.5% confidenceGood agreement with CDM Good agreement with CDM predictionspredictionsIf halos are not aligned with If halos are not aligned with galaxy then the flattening is galaxy then the flattening is underestimatedunderestimated

Simple model:Simple model:

and determineand determine ff

Found f = Found f = 0.77 +/- 0.200.77 +/- 0.20

Hoekstra et al., 2004Hoekstra et al., 2004

Flattening of dark matter halos from Flattening of dark matter halos from RCSRCS

Targeting galaxies with with Targeting galaxies with with e>0.15 (throw out roundest e>0.15 (throw out roundest

gals.)gals.)

Targeting early types Targeting early types by looking at 0.5<b/a<0.8by looking at 0.5<b/a<0.8

minor/major shear ratio

minor/major shear ratio

Halo Shapes SimulationsHalo Shapes Simulations

Allgood et al., 2005, Flores et al., 2005, Bullock 2001, Allgood et al., 2005, Flores et al., 2005, Bullock 2001, Jing & Suto 2002 Jing & Suto 2002

Mean and scatter of halo shape parameters (axis ratios) Mean and scatter of halo shape parameters (axis ratios) as a function of mass and epochas a function of mass and epoch More massive halos are more triaxialMore massive halos are more triaxial Halos of a given mass are more triaxial at earlier timesHalos of a given mass are more triaxial at earlier times Halos are increasingly round at large radiiHalos are increasingly round at large radii Halos in lower sigma8 cosmologies are more triaxialHalos in lower sigma8 cosmologies are more triaxial Ratio of smallest to largest axis, s, = 0.54 (Mvir/M*) ^(-Ratio of smallest to largest axis, s, = 0.54 (Mvir/M*) ^(-

0.05)0.05)