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Lessons on galaxy formation from weak gravitational lensing
Rachel Mandelbaum Hubble Fellowship Symposium, 2008


Questions in galaxy formation
If we see a galaxy, at a variety of
wavelengths...
What dark matter, if any, is associated with that galaxy? What is the relationship between the visible and the dark components?

What about "special" galaxy types, such
as active galactic nuclei? Relation to central black hole properties


How did these galaxies arise?

Pictures from Sloan Digital Sky Survey data release 6


The fundamental problem:
Telescopes see baryons (galaxies) Baryon physics is imperfectly understood We need observations to refine models of
the physics of galaxy formation/evolution.

Conclusion: our toolbox needs some new tools!


Outline

Motivation Lensing introduction Theoretical interpretation Application: halo mass and satellite fraction versus optical observables


One (relatively) new tool...
Gravitational lensing:
Sensitive to all matter along line of sight, including dark matter!

Depends on projection along line of sight Weak: small effect, can be treated
perturbatively


The (weak) lensing effect

Caution: magnification not depicted accurately!


The basics


· · · ·

Source galaxy at Observed image at Instead of I(), we see I'[()] We care about the Jacobian:

= convergence;

= shear


Definitions
= projected surface density contrast


Definitions
= projected surface density contrast


Definitions
= projected surface density contrast
(axisymmetric)


Definitions
= projected surface density contrast
(axisymmetric)


Definitions
= projected surface density contrast
(axisymmetric)

= "shear"
(comoving)


Sloan Digital Sky Survey (SDSS)
Imaging,

spectroscopy over ~ 1/4 of the sky Imaging in 5 passbands (ugriz)

(from http://www.sdss.org/)


Our approach: Reglens
Lenses: SDSS spectroscopic sample
(~4x105 galaxies, ~0.1) Sources: SDSS photometric galaxies (~3x107 galaxies, ~0.4) Statistics: Stack 3K-100K lenses Systematics: Random points, 45-degree, and ratio test
Pipeline developed with Uros Seljak, Christopher Hirata


Outline

Motivation Lensing introduction Theoretical interpretation Application: halo mass and satellite fraction versus optical observables


Extracting information from lensing
Small scales (below rvir): halo mass Intermediate scales (rvir - cluster scales):
group/cluster membership Large scales (>~ several Mpc): largescales structure Typically determine simultaneously using halo model


Outline

Motivation Lensing introduction Theoretical interpretation Application: halo mass and satellite fraction versus optical observables

RM, Uros Seljak, Guinevere Kauffmann, Christopher Hirata, et al. (2006) MNRAS 368, 715


Relating mass to light
Questions: baryon conversion efficiency,
satellite fractions Stellar masses (Kauffmann, et. al. 2003) tell us the mass in stars better than luminosities Lensing: relate (on average) to dark matter halo mass Can do as function of environment, age of stellar population


Results
Lensing signal in
stellar mass bins split by morphology Signal on small scales reflects halo mass Signal on large scales reflects fraction in group/cluster
Plot from Mandelbaum et al. 2005, astro-ph/0511164 Early types Late types

100 1000 r [kpc/h]


Results, cont.
(Errors: 95% CL)

Stellar mass traces
halo mass for M <~ 1011 Msun efficiencies peak around 30-40%
stellar

Baryon conversion

Early types Late types


Other g-g lensing measurements
Hoekstra et al. 2005: isolated galaxies in
RCS with photometry only; ~0.3, results for L* galaxies consistent with SDSS Heymans et al. 2006: lensing data from GEMS, stellar masses from COMBO-17, 0.2

Radio-loud AGN
Question: in what small- and large-scale
environments do these galaxies live? Match SDSS Main (spectroscopic) sample against radio surveys: ~5500 with 0.1 **Ongoing work with Cheng Li, Guinevere Kauffmann


Radio-loud AGN
Construct control
M~(2.5±0.6) x 1013 Msun/h

samples (same z, M* properties) Mean halo masses differ by factor of ~2 Consistent with correlations Can be used in modeling their formation/evolution


Optical vs. radio AGN


Galaxy cluster observables
Relate optical observables to cluster mass Understand cluster formation physics,
dynamics, evolution Useful for cluster-count cosmology


Method
R. Reyes, RM, et al. (2008)



~13,000 clusters from the SDSS MaxBCG catalog, photometric z = 0.1 to 0.3 (Koester, et al. 2007) optical tracers: N200, L200, LBCG and combinations N200LBCG, L200LBCG group clusters by tracer measure stacked WL signal determine best-fit M200

R N200 = 10-11, 26-40, 71-190 M200 = 0.65±0.30, 2.48±0.57, 10.96±1.87 в 1014 Mpc/h


Results

Cluster mass



scaling with N200, L200, LBCG residual scaling of cluster mass with LBCG at fixed N200 / L200

N = 0.71±0.14 (~5, 0.10
BCG luminosity


Implications
Evidence for effect from N-body
simulations giving anticorrelation between Lbcg and N200 (formation time effect) constraints on cosmology using optical cluster surveys

Can use combined tracer for more optimal


Lessons:
Galaxy-galaxy lensing measurements
can yield parameters that are directly useful for constraining theories of galaxy formation There is great promise for future advances in our understanding using this method in combination with others