The masses and shapes of dark matter halos from galaxygalaxy lensing in the CFHTLS

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The masses and shapes of dark matter halos from
galaxy-galaxy lensing in the CFHTLS
Laura Parker
Henk Hoekstra Mike Hudson Ludo van
Waerbeke Yannick Mellier
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CFHTLS Galaxy-Galaxy Lensing
Parker et al, 2007

• Galaxy masses
• Halo profiles (beyond rotation curves, strong
  lensing)
• Galaxy extents (as a function of environment)
• Halo shapes (flattening?)
• Biasing (as a function of scale)
• Link galaxies to their host halos
• divide lens sample by redshift, morphology,
  luminosity, environment

• 5 year, 3 component imaging survey
• Deep SN, dark energy
• Wide weak lensing
• Very wide - KBOs

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Data

• Early CFHTLS i wide data
• 20 sq degrees
• no colours / redshifts
• Lenses and sources divided based on their
  observed magnitudes
• Working on photometric redshifts for every lens
  and source (see Hudson talk)

Ngal
?DLS/DS
i
Magnitude distribution used to estimate
redshifts (?)
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'basic' weak lensing

• Measure tangential component of shape in bins
• Need to stack signal around MANY foreground
  lenses
• Correct galaxy shapes using KSB (KSB, Hoekstra
  et al 1998, etc)

Foreground Lens
Alternative to maximum likelihood technique fit
signal with your favourite mass profile
expected signal
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Redshift Distribution

• varies for different samples (dashed HDF,
  solid llbert et al. CFHTLS-DEEP photo-zs)
• Photo-zs critical (even more so for cosmic
  shear)
• Mass, M/L etc all scale with ?

lenses
?DLS/DS
sources
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Shear Results

• Velocity dispersion depends on the lens sample.
• Must scale to some typical L galaxy, based on
  an assumed relation between L and velocity
• ??? prop.to L0.25 , for example

? lt?gt2 ?

• Use ? to estimate the total mass of the halo
  assuming a cut-off radius

lt?gt km/s
lt?gt km/s
Mass at r200
Mass total
ltM/Lgt R-band
2.2e12
170/-30
1.1e12
137/-11
132/-10

• 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

start to see two-halo term unless galaxies are
truly isolated
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Evolution?

• Generate two lens catalogues divided by observed
  magnitude
• different average redshifts
• 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

Result Faint lenses lt?gt 134/-12 km/s
(high z) Bright lenses lt?gt 142/- 18
km/s (low z)
Doing this now with CFHTLS-DEEP data with
photo-zs
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Halo Shapes

• 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
• 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
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Halo Shapes
2? detection of non-spherical halo shape
minor/major shear ratio
Our results favour a halo ellipticity of 0.3.
This is roughly in agreement with simulations of
CDM halos (eg Dunbinski Carlberg, 1991)
radius
Brainerd Wright, 2000
Without any redshift information there may be
contamination from satellites (we dont have
isolated galaxies)
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Alternative Theories of gravity?

• 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
• Quadrupole term from baryon distribution decays
  rapidly
• 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

Dark matter halo shapes can be used to place
constraints on alternative gravity theories
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Systematics G-G lensing

• 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)

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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. 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

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Summary

• 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
• Stay tuned - g-g lensing with CFHTLS data (Deep
  and Wide) using photo-zs is coming soon!
• See talk by Hudson
• Goal g-g lensing for galaxies segregated by
  luminosity, morphology, environment, redshift,
  colour etc

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The End
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Extent of Halos

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

NFW
?
Hoekstra et al., 2004
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Why study G-G Lensing?
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).
• 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

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Why study G-G Lensing?
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?
b2 ?gg/?mm r ?gm/(?mm?gg)1/2 ?gg/?gm b/r
Depends on gal colour L
Use lensing to estimate b important input for
galaxy formation models
SDSS (Sheldon et al.) and RCS (Hoekstra et al.)
show b/r (from lensing) is scale invariant out to
10 Mpc (low-z)
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Flattening of dark matter halos from RCS
Simple model and determine f Found f 0.77
/- 0.20
ehalo f elens

• Spherical halos excluded with 99.5 confidence
• Good agreement with CDM predictions
• If halos are not aligned with galaxy then the
  flattening is underestimated

Hoekstra et al., 2004
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minor/major shear ratio
minor/major shear ratio
Targeting early types by looking at 0.5ltb/alt0.8
Targeting galaxies with with egt0.15 (throw out
roundest gals.)
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Halo Shapes Simulations

• 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
• More massive halos are more triaxial
• Halos of a given mass are more triaxial at
  earlier times
• Halos are increasingly round at large radii
• Halos in lower sigma8 cosmologies are more
  triaxial
• Ratio of smallest to largest axis, s, 0.54
  (Mvir/M) (-0.05)