Gravitational Redshift in Clusters of Galaxies

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

2. Gravitational Redshift • Photon escapes from gravitational well • Gains potential energy • Speed cannot decrease =) • The photon redshiftsto 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. Why? • Dark Matter (DM) • If the cluster is sittingin a blob of DM, thegravitational redshiftsignal might constrainthe DM mass

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. cDellipticals & 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. cDellipticals • Abell S740

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

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

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

25. Bright, stationary BCG subsample • Bettercut / selection: • TheBCGshould be really bright! • R magnitude difference between brightest (cD) and third brightest should be at least 1.0 magnitude • TheBCGshould 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 redshiftsignal, 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 ofDM 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. Navarro-Frenk-White DM estimate • ~ 5.5kg of DM for 1kg of visible mass • (Caution: visible mass of BCG galaxy) • Consistent with current cosmological models

39. Self-consistency • If what we’re measuring is theBCG’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…

40. Self-consistency • …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