Galaxy-Galaxy Lensing: History, Theoretical Expectations & Simulations

Tereasa Brainerd

Boston University, Institute for Astrophysical Research

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”?

What “galaxy-galaxy” lensing is not…

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

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!

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

Galaxy-Galaxy Lensing “Pros”

• Direct probe of halo potential at large radii (> 100 kpc)

• Can apply to all galaxies in principle (don’t need a dynamical tracer at large radius)

• Virialized halos are not required!

Galaxy-galaxy lensing is not a panacea, however…

Galaxy-Galaxy Lensing “Cons”

• Signal is very small (E0 source becomes an E0.01 source)

• Can’t 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

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.

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 < J’ < 23.5 or 21 < F < 22)

• 11,789 foreground galaxies (19 < J’ < 21.5 or 17.5 < F < 20)

• Considered only the “nearest neighbor” deflector in calculating the image distortion parameter

• A “proof of concept” if nothing else

Tyson et al. concluded that the typical galaxy circular velocity was small (< 170 km/s)

Kovner & Milgrom (1987) showed that the signal was consistent with circular velocities as large as 330 km/s

Brainerd, Blandford & Smail 1996, ApJ, 466, 623 (“BBS”)

• single, deep CCD image from Palomar 5m; complete to r=26

• 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, <p> = 0.011 +/- 0.003 (image polarization ~2 times the “shear”)

• 439 bright galaxies (20 < r < 23), 511 faint galaxies (23 < r < 24)

• lens zmed ~ 0.4, source zmed ~ 0.7

• intrigued people sufficiently that they started thinking about galaxy-galaxy lensing

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:

A very simple experiment…

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

<p> = 0.011 +/- 0.003 in a)

Signal “goes away” for fainter sources because of circularization.

<p> = 0.011 +/- 0.003

<p> = 0.005 +/- 0.002

<p> = 0.001 +/- 0.001

Npairs = 3202

Npairs = 10,870

Npairs = 26,412

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

BBS (1996)

Best-fitting halo model:

Vc* = 220 +/- 80 km/s

s* > 100 h-1 kpc

M*(100 h-1 kpc) =

1.0+1.2-0.5 x 1012 Msun

Fit is largely insensitive to outer scale radius, s*

BBS (1996)

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!!

Fischer et al. (2000)

Fischer et al. (2000)

Control statistic

(Albert Stebbins’ “Twisted Sister” test)

Potential Bugs/Features in GG Lensing Data Sets

• Contamination of lensing signal due to physical satellites of lens galaxies

• Multiple deflections for distant sources

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 < 20% in the SDSS

Satellite Galaxies in the SDSS-DR4(Agustsson & Brainerd 2006, ApJ, 644, L25)

Radial Distortions of SDSS Satellite GalaxiesAgustsson & Brainerd 2006 ApJL

• On scales rp < 250 kpc, SDSS satellites are, on average, radially aligned toward their host

• Averaged over 10 kpc < rp < 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)

Sample of hosts and satellites from the SDSS DR4

Hosts are “isolated” from other bright galaxies

Satellites selected by proximity in radial velocity (< 500 km/s) and projected radius (<250 kpc here)

~4300 satellites

~3200 hosts

~92,500 stars

From SDSS DR4

What is the angle between the major axis of the satellite and the direction vector to the host?

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”

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 < I < 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?

Halo Lens Model (BBS):

Shown is mean shear field from 6500 Monte Carlo realizations of the source distribution for fiducial halo model:

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)

More than 50% of the time, the net shear after multiple-deflections is GREATER than the shear due to the strongest individual lens!

Shear profile with (squares) and without (crosses) multiple deflections

“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

RMS shear in HDF-N due to galaxy-galaxy lensing ALONE

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

all deflections included in calcuation of shear field

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?

L = 1000 h-1 Mpc

Np = 1010

Softening length = 5 h-1 kpc

Volker Springel & the Virgo Consortium

http://www.mpa-garching.mpg.de/galform/virgo/millennium