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

2. Dark 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.

3. Dark matter around galaxies But what do we know about the mass distribution on scales larger than 100kpc? How can we study this? ? ? ? ?

4. Dark 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.

5. Weak 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…

6. Galaxy-Galaxy Lensing 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.

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

8. Galaxy-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.

9. Results from RCS (Hoekstra et al. 2004) Galaxy-mass correlation function

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

11. 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. larger surveys

12. ~20 years ago… Tyson et al. (1984) Photographic plates ~12000 lenses ~47000 sources Circular velocity <170km/s off to the loonie bin…?

13. ~10 years ago… Brainerd et al. (1996) CCD imaging 439 lenses 511 sources not so crazy after all…?

14. ~10 years ago… Halos are large: s > 100 kpc Brainerd et al. (1996)

15. ~7 years ago… Fischer et al. (2000) 225 sq. deg. SDSS Tens of millions of lens-galaxy pairs Now we’re measuring something!

16. ~3 years ago… Hoekstra et al. (2004) 42 sq. deg. RCS 120,000 lenses 1.5 million sources Now we’re measuring something!

17. Sheldon et al. (2004) Even more SDSS data 120,000 lenses with spectroscopic redshifts! 9 million sources with photometric redshifts! ~3 years ago… Now we’re measuring something!

18.  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? 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:

19. Galaxy 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?

20. Can we use light to infer the distribution of people? NO! Relation between light and people...

21. Where do galaxies form? density galaxy formation threshold galaxies

22. GIF simulations, Colberg et al. Numerical simulations Example of the galaxy distribution based on semi-analytic models.  Star formation  SNe feedback  Chemical enrichment  Gas infall  Merger history

23. Link 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.

24. Relation between light and matter To quantify the relation between galaxies and dark matter we need  galaxy auto-correlation function  galaxy-mass cross-correlation function  mass auto-correlation function RCS VIRMOS b 2 = / r 2 = 2 / ( ) “variance” “correlation”

25. Red: 1.5<B-V<2.0 Blue: 0.75<B-V<1.5 Correlation functions from lensing

26. Red: 1.5<B-V<2.0 Blue: 0.75<B-V<1.5 Bias parameters

27. HOD 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.

28. 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…

29. Results from maximum likelihood analysis: direct comparison with results from numerical simulations. M 200 =(8.8±0.7) x 10 11 h -1 M Good agreement with NFW prediction! Halo mass and extent Hoekstra et al. (2004)

30. Halo mass and extent With photometric redshift information we can learn much more about the lenses! COMBO-17: Kleinheinrich et al. (2006)

31. Mass-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)

32. Mass-luminosity relation M ~ L 1.5

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

34. Stellar mass fractions

35. 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)

36. GEMS: Heymans et al. (2006) Stellar mass fractions HH RM CH

37. Flattening of dark matter halos e halo = f e lens  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 Hoekstra et al. (2004) But see Mandelbaum et al. (2006)!!

38. Conclusions 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!