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)
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