1. Gravitational Redshift in Clusters of Galaxies Marton Trencseni Eotvos University, Budapest

2. Gravitational Redshift Photon escapes from gravitational well Gains potential energy Speed cannot decrease =) The photon redshifts to conserve energy

3. Gravitational redshift in galaxies Possible to measure within galaxies See Coggins’ 2003 PhD thesis (Merrifield): Gravitational Redshifts and the Mass Distribution of Galaxies and Clusters Not what I’m doing…

4. Gravitational redshift in clusters Others have tried before No conclusive results Pre-SDSS datasets were too small

5. Gravitational redshift in clusters With SDSS data, You can’t get a signal from 1 cluster Instead, you re-scale and add several hundred/thousand clusters And measure the average gravitational redshift

6. Dark Matter (DM) If the cluster is sitting in a blob of DM, the gravitational redshift signal might constrain the DM mass Why?

7. Verify cosmology

8. Catalogs NYU catalog: Andreas Berlind (NYU) created an SDSS galaxy cluster catalog based on spectro galaxies in 2006, based on DR3 data

9. Catalogs ELTE catalog: Own based on DR6 spectro galaxies DR6 has roughly twice as many galaxies Smaller errors bars, etc.

10. Clustering Friend-of-Friend (FOF) algorithm 2 parameters: tangential and radial separation If two galaxies’ separation are within the above two limits, they’re friends Make it associative to get the clusters

11. Clustering The trick is to get the two parameters right Too small: only finds cluster cores, clusters break up Too big: field contamination

12. Clustering Berlind (NYU): used cosmological simulations with a-priori cluster membership data and played with the two parameters to get statistics that matched the simulation Careful: predictions that contradict the simulations’ model are meaningless

13. Samples Three volume limited samples Absolute r-magnitude limits: Mr18:M < -18 Mr19:M < -19 Mr20:M < -20 (brightest)

14. Samples brighter

15. Clustering Parameters

16. Clustering results NYU: (DR3) ELTE: (DR6)

17. Cluster richness NYU

18. Cluster richness ELTE

19. Cluster centers We now have clusters Gravitational redshift signal expected at the “center” of the cluster Center = ?

20. cD ellipticals & BCG cD = central diffuse, ellipticals These are usually the brightest galaxies in their cluster, hence they’re also called: BCG = Brightest Cluster Galaxy Usually much (up to 10 times) brighter than the other galaxies in the cluster

21. cD ellipticals Abell S740

22. BCG subsample First cut / selection: Brightest galaxy should be no more than r_max away from the mean ra/dec center of the cluster

23. BCG subsample NYU: (DR3) ELTE: (DR6)

24. Gravitational redshift signal NYU: (DR3) ELTE: (DR6)

25. Bright, stationary BCG subsample Better cut / selection: The BCG should be really bright! R magnitude difference between brightest (cD) and third brightest should be at least 1.0 magnitude The BCG should be stationary! The peculiar velocity of the brightest should be less than 200km/s (small) as compared to the average

26. Bright, stationary BCG subsample NYU (DR3): ELTE (DR6):

27. Gravitational redshift signal NYU (DR3): ELTE (DR6):

28. Supporting evidence? Hypothesis: If there is a gravitational redshift signal, it should depend on various physical parameters like cluster size, brightness, velocity dispersion E.g. bigger, brighter cluster  more massive  stronger signal

29. Supporting evidence? Just showing the NYU (DR3) case: abs.R.magn. velocity disp. radius

30. Dark matter model Blob of DM around cluster Additional blobs of DM around galaxies

31. Dark matter content

32. Assumptions First, naïve model: Flat DM distribution: density is constant w.r.t. radius

33. Cluster DM blob Cluster blob is very large (Mpc), so the potiential well is not very deep For it to result in the measured signal, the DM content of the clusters would have to be huge: ~ 1700kg of DM for 1kg of visible mass Inconsistent with current cosmological models

34. Galaxy DM blob Here the mass is more concentrated ~ 10kg of DM for 1kg of visible mass (Caution: visible mass of BCG galaxy) Consistent with current cosmological models This does not mean that there is no cluster blob, you just can’t measure its gravitational redshift signal…

35. Flat distribution? How naïve is the flat DM assumption? Second, trendy DM model: Navarro-Frenk-White (NFW) density:

36. NFW potential Flat vs. NFW potential: no “big” difference

37. Mass estimated Flat case: Total DM mass ~ 0.65 * z * c^2 * R NFW case: Total DM mass ~ 0.38 * z * c^2 * R

38. ~ 5.5kg of DM for 1kg of visible mass (Caution: visible mass of BCG galaxy) Consistent with current cosmological models Navarro-Frenk-White DM estimate

39. If what we’re measuring is the BCG’s DM blob… Then given that other galaxies are also sitting in DM blobs, and also have some gravitational redshift Then really what we measured is the excess gravitational redshift of the BCG… Self-consistency

40. …Due to the excess DM fluctuation around it

41. Self-consistency … so in reality the gravitational redshift signal may be larger then we measured

42. Self-consistency Handwaving: This fits in nicely with the fact that no signal was measured for Mr18 and Mr19 subsamples, Which are fainter Less cD clusters

43. What have we learned? Gravitational redshift can be measured for clusters with massive galaxy, bright at center Gravitational redshift signal due to blob of DM around cD ~ 6-10kg of DM for 1kg of visible mass Consistent with current cosmological models