GalaxyGalaxy Lensing: History, Theoretical Expectations

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Galaxy-Galaxy Lensing History, Theoretical
Expectations Simulations

• Tereasa Brainerd
• Boston University, Institute for Astrophysical
  Research

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Outline

• What is galaxy-galaxy lensing?
• How strong is the signal (i.e., the shear)?
• Why should you care about galaxy-galaxy lensing?
• Early literature first detections
• Are satellite galaxies (i.e., misidentified
  sources) a problem?
• What is the net effect of multiple deflections?

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What galaxy-galaxy lensing is not
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What galaxy-galaxy lensing is

• systematically throughout the universe background
  galaxies are weakly lensed by foreground galaxies
• multiple imaging does not occur
• results in extremely mild image distortions (few
  in ellipticity) and a slight preference for
  tangential alignments of background galaxies with
  foreground galaxies
• detectable only in a statistical sense using
  large ensemble averages over many pairs of
  foreground and background galaxies

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Theoretical Expectations

• Approximate lens galaxy as a singular isothermal
  sphere
• Place lens at zl and source at zs
• Average shear within an annulus centered on the
  lens is

Expected shear is small and depends only weakly
upon the cosmography!
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Potential Uses for Galaxy-Galaxy Lensing

• Constrain virial masses and physical extents of
  dark matter galaxy halos (photons as tracers of
  the potential)
• Determine halo density profile (e.g., SIS vs.
  NFW)
• Galaxy mass-to-light ratios (M/L) as a function
  of Hubble type of the lens
• Evolution of M/L over cosmic time
• Evolution of Tully-Fisher/Faber-Jackson relations
  over cosmic time
• Constrain halo shapes (e.g., spherical vs.
  triaxial)
• Investigate truncation of halos in cluster
  environments (e.g., galaxy-galaxy lensing with
  cluster galaxies)
• Determine galaxy-mass cross correlation function

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Galaxy-Galaxy Lensing Pros

• Direct probe of halo potential at large radii (gt
  100 kpc)
• Can apply to all galaxies in principle (dont
  need a dynamical tracer at large radius)
• Virialized halos are not required!

Galaxy-galaxy lensing is not a panacea, however
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Galaxy-Galaxy Lensing Cons

• Signal is very small (E0 source becomes an E0.01
  source)
• Cant detect signal for any one lens have to be
  satisfied with statistical measure
• Signal is weakly dependent on both the shape of
  the potential and the outer halo radius
• Potential contamination of lensing signal due to
  unidentified satellite galaxies (e.g., pure noise
  and/or Newtonian tidal distortions)
• All mass along the line of sight affects the
  final shape of the source
• Inherently a multiple-deflection problem for deep
  data sets

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Multiple Deflections in Galaxy-Galaxy Lensing
Closest foreground galaxy in projection on the
sky is not necessarily the only lens, nor is it
necessarily the strongest lens. Shear computed
around the black centers is not the same as the
shear produced by the black centers WEAK
deflections can be treated as being independent
and add linearly. They are easily handled in
Monte Carlo simulations.
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Tyson et al. 1984, ApJ, 281, L59

• First published attempt to detect galaxy-galaxy
  lensing imaging from scans of photographic
  plates
• 46,959 background galaxies (22.5 lt J lt 23.5 or
  21 lt F lt 22)
• 11,789 foreground galaxies (19 lt J lt 21.5 or
  17.5 lt F lt 20)
• Considered only the nearest neighbor deflector
  in calculating the image distortion parameter
• A proof of concept if nothing else

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Tyson et al. concluded that the typical galaxy
circular velocity was small (lt 170 km/s) Kovner
Milgrom (1987) showed that the signal was
consistent with circular velocities as large as
330 km/s
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Brainerd, Blandford Smail 1996, ApJ, 466, 623
(BBS)

• single, deep CCD image from Palomar 5m complete
  to r26
• seeing 0.87 arcsec FWHM, total area used 72 sq.
  arcmin.
• data obtained by Jeremy Mould in June 1992 using
  COSMIC imaging spectrograph
• 4-sigma detection of galaxy-galaxy lensing, ltpgt
  0.011 /- 0.003 (image polarization 2 times the
  shear)
• 439 bright galaxies (20 lt r lt 23), 511 faint
  galaxies (23 lt r lt 24)
• lens zmed 0.4, source zmed 0.7
• intrigued people sufficiently that they started
  thinking about galaxy-galaxy lensing

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A very simple experiment
Compute the position angles of faint galaxies
with respect to the line that connects faint and
bright galaxies. If the faint galaxies are
systematically lensed by the bright galaxies,
there will be an excess of pairs in which the
faint galaxy is tangentially aligned and a
deficit of pairs in which the faint galaxy is
radially aligned. In the case of lensing, expect
to see
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BBS (1996)
Annulus of inner radius 5 and outer radius 35
used each source is paired with 6
lenses! Chi-squared test rules out a uniform
distribution in a) at the 98.6 confidence
level. KS test rules out a uniform distribution
for a) at the 99.9 confidence level ltpgt 0.011
/- 0.003 in a) Signal goes away for fainter
sources because of circularization.
ltpgt 0.011 /- 0.003
Npairs 3202
ltpgt 0.005 /- 0.002
Npairs 10,870
ltpgt 0.001 /- 0.001
Npairs 26,412
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BBS (1996)
Approximate lens halos as modified isothermal
spheres, assume constant M/L, and scale lens
properties using Tully-Fisher relation
Assign redshifts to the lenses and sources based
upon apparent magnitudes, and find best-fitting
Vc and s using Monte Carlo simulations
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BBS (1996)
Best-fitting halo model Vc 220 /- 80
km/s s gt 100 h-1 kpc M(100 h-1 kpc)
1.01.2-0.5 x 1012 Msun Fit is largely
insensitive to outer scale radius, s
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Fisher et al. 2000 AJ, 120, 1198

• 225 sq. deg. of SDSS commissioning data (imaging
  only no spectra, no photo-z)
• 13x106 pairs in g, 17x106 pairs in r, 16x106
  pairs in i
• shallower than BBS (lens zmed 0.15, source zmed
  0.35)
• stunning detection of galaxy-galaxy lensing,
  proving that systematics are fairly easy to
  control
• similar lens modelling to BBS, and similar
  conclusions
• velocity dispersions of L galaxy halos in the
  range of 150 to 190 km/s (95 confidence bounds),
  and halos extend to of order 250 h-1 kpc
• made galaxy-galaxy lensing a respectable
  endeavor!!

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Fischer et al. (2000)
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Fischer et al. (2000)
Control statistic (Albert Stebbins Twisted
Sister test)
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Potential Bugs/Features in GG Lensing Data Sets

• Contamination of lensing signal due to physical
  satellites of lens galaxies
• Multiple deflections for distant sources

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Satellite Galaxies?

• For typical magnitude selection criteria, 10 to
  15 of faint (i.e., source) galaxies are
  actually satellites of the bright (i.e. lens)
  galaxies
• Could be source of noise (random orientations),
  excess signal (tangential distortions), or
  suppressed signal (radial distortions)
• Contribution of satellites to galaxy-galaxy
  lensing signal thought to be considerably less
  than size of error bars in early studies (e.g.,
  Tyson et al. 1984 BBS) based on clustering
  arguments
• Bernstein Norberg (2002, AJ, 124, 733) found no
  systematic distortion of 2dFGRS satellites,
  averaged over 500 kpc scales, and concluded that
  contribution of satellites to gg lensing shear
  was lt 20 in the SDSS

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Satellite Galaxies in the SDSS-DR4(Agustsson
Brainerd 2006, ApJ, 644, L25)
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Radial Distortions of SDSS Satellite
GalaxiesAgustsson Brainerd 2006 ApJL

• On scales rp lt 250 kpc, SDSS satellites are, on
  average, radially aligned toward their host
• Averaged over 10 kpc lt rp lt 50 kpc, a mean tidal
  shear of -0.045 /- 0.010 is seen
• Causes a reduction in the measured shear due to
  gg lensing of 25 to 40 (for lens-source
  separation based on apparent magnitude alone)

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Sample of hosts and satellites from the SDSS
DR4 Hosts are isolated from other bright
galaxies Satellites selected by proximity in
radial velocity (lt 500 km/s) and projected radius
(lt250 kpc here)
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What is the angle between the major axis of the
satellite and the direction vector to the host?
4300 satellites 3200 hosts 92,500 stars From
SDSS DR4
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If 10 of faint sources are actually
satellites, then radial alignment reduces
gg-lensing shear by 25 to 40 Bottom line use
more than just magnitudes to do lens-source
separation! Need very accurate photo-z (to
within 1000 km/s) or make wide cuts in zphot for
lenses and sources
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Multiple Deflections in GG-Lensing HDF (North)

• Use 427 spectroscopic redshifts and known
  rest-frame LB from Cohen et al. (2000) and Cohen
  (2002) in the HDF-North and flanking fields to
  produce theoretical shear field due to gg lensing
  alone
• Place source galaxies with 19 lt I lt 25 in the
  region with z determined from, e.g., Baugh
  Efstathiou (1993) and relative number counts
  based on deep optical counts (e.g., Smail et al.
  1995)
• How frequent are multiple deflections and how do
  they affect the resulting shear field?
• How large is the gg lensing contribution to
  cosmic shear?

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Halo Lens Model (BBS)
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Shown is mean shear field from 6500 Monte Carlo
realizations of the source distribution for
fiducial halo model
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Probability of multiple deflections with shear
greater than a given minimum value Vertical line
shows ND 2 Multiple deflections only weakly
dependent on cosmography (solid flat,
Lambda-dominated, short dash open, dotted EdS)
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More than 50 of the time, the net shear after
multiple-deflections is GREATER than the shear
due to the strongest individual lens!
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Shear profile with (squares) and without
(crosses) multiple deflections
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Cosmic Shear due to large-k end of the power
spectrum (non-linear regime) Squares multiple
deflections included Crosses single deflections
due to nearest lens only
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RMS shear in HDF-N due to galaxy-galaxy lensing
ALONE
all deflections included in calcuation of shear
field
Solid squares fiducial halo model Solid
triangles 20 increase in fiducial halo
mass Solid circles 20 reduction in fiducial
halo mass RMS shear due to fiducial halo
extrapolates to zero at 0.95 arcmin
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Precision cosmology requires precision
simulations (including the highly non-linear
regime)What will be the results from the
Millennium Run for cosmic shear on sub-arcminute
scales?
Volker Springel the Virgo Consortium
L 1000 h-1 Mpc Np 1010 Softening length 5
h-1 kpc
http//www.mpa-garching.mpg.de/galform/virgo/mille
nnium