Galaxy-Galaxy Lensing What did we learn? What can we learn? Henk Hoekstra.

Galaxy-Galaxy LensingGalaxy-Galaxy Lensing

What did we learn?What can we learn?

Henk Hoekstra

Dark matter in galaxiesDark matter in galaxies

Rotation curves and strong lensing studies have provided strong constraints on the mass distribution on scales of a few tens of kpc.

Dark matter around galaxiesDark matter around galaxies

But what do we know about the mass distribution on scales larger than 100kpc? How can we study this?

??

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Dark matter around galaxiesDark matter around galaxies

With suitable tracers we can try to probe the gravitational field on such large scales:

• Globular clusters• Planetary nebulae

Or on even larger scales:

• Satellite galaxies

However, interlopers and (unknown) velocity anisotropies may complicate the interpretation of these results.

Weak gravitational lensingWeak gravitational lensing

The (surface) density of galaxies is typically too low to produce significant lensing effects. Only in the case of massive ellipticals one has some chance of observing this effect.

Any mass distribution contributes to the weak lensing signal:

• even low mass galaxies!• even at large radii!

However, the signals are extremely small…


How small?

The differential deflection of the distant galaxy by the lens will change the shape by a percent at most…

We don’t see multiple images/large distortions

The signal is only detectable by taking the ensemble averaged measurements for a large sample of lenses.


We measure the combined signal of many lenses…and have worry about clustering and contamination by satellite galaxies.

Galaxy-mass correlation functionGalaxy-mass correlation function

The amount of dark matter The extent of halos (truncation) The shapes of halos (flattening) Law of gravity in theories without dark matter Galaxy biasing (galaxy formation)

We measure the tangential alignment of background galaxies around an ensemble of lenses. The signal as a function of radius yields the galaxy-mass cross-correlation function.

Results from RCS (Hoekstra et al. 2004)

Galaxy-mass correlation functionGalaxy-mass correlation function

Contamination…Contamination…

Agustsson & Brainerd (2006): on scales <250kpc satellite galaxies are aligned radially toward their host…

A brief history of …A brief history of …

… galaxy-galaxy lensing is a new area of research, although the oldest application of weak lensing.

1984: first attempt to measure the signal (Tyson et al.) 1996: first detection (Brainerd et al.) 2000: first accurate measurement from SDSS (Fischer et al.)

Since then several results, mainly from SDSS (e.g., McKay et al.; Guzik & Seljak) and RCS have been published.

larg

er

surv

eys

~20 years ago…~20 years ago…

Tyson et al. (1984)

Photographic plates~12000 lenses~47000 sources

Circular velocity <170km/s

off to the loonie bin…?


Brainerd et al. (1996)

CCD imaging

439 lenses511 sources

not so crazy after all…?


Halos are large: s > 100 kpc

Brainerd et al. (1996)


Fischer et al. (2000)

225 sq. deg. SDSS

Tens of millions of lens-galaxy pairs

Now we’re measuring something!


Hoekstra et al. (2004)

42 sq. deg. RCS

120,000 lenses1.5 million sources


Sheldon et al. (2004)

Even more SDSS data

120,000 lenses with spectroscopic redshifts!

9 million sources with photometric redshifts!



We can interpret in terms of a theoretical model (e.g., simulations or analytic models) Deconvolve the correlation function (use of the observed positions of galaxies) Look at isolated halos

How to interpret this?How to interpret this?

The cross-correlation function is the convolution of the dark matter distribution around galaxies and the clustering properties of the lenses.

We have some options to infer information about the properties of the dark matter halos around galaxies:

Galaxy biasingGalaxy biasing

The observed light of galaxies can tell us much about their formation, but we know little about the underlying dark matter distribution which also must be of relevance in the process of galaxy formation.

Do galaxies trace the dark matter distribution? What can we learn about galaxy dark matter halos?

galaxy formation cosmology?

Can we use light to infer the distribution of people?

NO!

Relation between light and people...Relation between light and people...

Where do galaxies form?Where do galaxies form?d

en

sity

galaxy formation threshold

galaxies

GIF simulations, Colberg et al.

Numerical simulationsNumerical simulations

Example of the galaxy distribution based on semi-analytic models.

Star formation SNe feedback Chemical enrichment Gas infall Merger history

Link with studies of galaxy formationLink with studies of galaxy formation

The relation between the galaxies and the underlying mass distribution can provide important information about the way galaxies form.

Weak lensing provides a unique way

to study the biasing relations as a function of scale, far into the non-linear regime, with higher precision than conventional methods.

The measurements by themselves do not tell us how galaxies form. But their value is in the comparison with models of galaxy formation.

Relation between light and matterRelation between light and matter

To quantify the relation between galaxies and dark matterwe need

galaxy auto-correlation function <N2> galaxy-mass cross-correlation function <NM>

mass auto-correlation function <M2>

RCS

VIRMOS

b2 = <N2> / <M2>

r2 = <NM>2 / (<N2> <M2>)

“variance”

“correlation”

Red: 1.5<B-V<2.0 Blue: 0.75<B-V<1.5

Correlation functionsCorrelation functions

from lensing

Red: 1.5<B-V<2.0 Blue: 0.75<B-V<1.5

Bias parametersBias parameters

HOD modelsHOD models

The bias parameters are a simple but rather blunt way to look at the correlation functions. An alternative approach is to study the signal(s) in terms of a halo model.

The second and higher order correlation functions (see Patrick Simon on Friday) can provide unique and powerful constraints on such models.

We can deconvolve the correlation function using a parameterized mass model for the galaxies (maximum likelihood analysis). Here we consider an NFW profile.

Drawbacks:

We have to assume that all matter is associated with galaxy halos. Result depends on the adopted mass model. Maximum likelihood always gives an answer…

Deconvolving…Deconvolving…

Results from maximum likelihood analysis: direct comparison with results from numerical simulations.

M200=(8.8±0.7) x 1011 h-1 M

Good agreement withNFW prediction!

Halo mass and extentHalo mass and extent


Halo mass and extentHalo mass and extent

With photometric redshift information we can learn much more about the lenses!

COMBO-17: Kleinheinrich et al. (2006)

Mass-luminosity relationMass-luminosity relation

The photometric redshifts enable the study of the lensing signal as a function of luminosity for galaxies with 0.2<z<0.4

“isolated” lenses and small scale signal:Hoekstra et al. (2005)

Mass-luminosity relationMass-luminosity relation

M ~ L1.5

M/L vs. colour (=galaxy type)M/L vs. colour (=galaxy type)

Stellar mass fractionsStellar mass fractions


The fraction of baryons that is converted into stars is low:

Early type galaxies: ~12%Late type galaxies: ~37%

Progenitors of early type galaxies must have had low fractions of their mass in stars!

This suggests a high formation redshift (at least for the stars)

GEMS: Heymans et al. (2006)


HHRMCH

Flattening of dark matter halosFlattening of dark matter halos

ehalo= f elens

Halos are aligned with the light Spherical halos excluded with 99.5% confidence Good agreement with CDM predictions

We use a simple model:

and determine f


But see Mandelbaum et al. (2006)!!

ConclusionsConclusions

Galaxy-galaxy lensing (and higher order!) results are improving rapidly and can provide unique constraints on the properties of dark matter halos around galaxies.

Photometric redshift information adds an important dimension: now we can study the signal as a function of galaxy properties.

Lots of new data coming!

Galaxy-Galaxy Lensing What did we learn? What can we learn? Henk Hoekstra.

Documents

galaxygalaxy lensing

small slide

distant galaxy

dark matter halos

low mass galaxies

satellite galaxies

henk hoekstra slide

mass distribution