1. Masses of Galaxy Groups Brent Tully University of Hawaii

2. Masses of Galaxy Groups Brent Tully University of Hawaii A galaxy group? What’s that?

3. Considerations from theory Spherical infall of cold, collisionless particles: Radius Velocity Radius Time r 2t - object at first turnaround today at t 0 (radius r 1t ) will fully collapse by 2t 0 - object at second turnaround today (radius r 2t ) was at first turnaround at 0.37 t 0

4. Useful observable manifestations of infall and caustics? I. Mass - radius scaling relations t collapse ~  -1/2 ~ (r 3 /M) 1/2

5. Useful observable manifestations of infall and caustics? I. Mass - radius scaling relations t collapse ~  -1/2 ~ (r 3 /M) 1/2 For two structures at the same phase of collapse today: r 1 = r 2 (M 1 /M 2 ) 1/3 r 1 3 /M 1 = r 2 3 /M 2

6. Useful observable manifestations of infall and caustics? I. Mass - radius scaling relations t collapse ~  -1/2 ~ (r 3 /M) 1/2 M ~  rms 2 r 2t So at t collapse = today r 2t 3 /  rms 2 r 2t = constant  rms ~ r 2t

7. Ω m in a flat universe II. Manifestation of Dark Energy: almost no effect on relation between mass and 2nd turnaround radius r 2t but affects the rate of the development of structure so affects the relation between 1st and 2nd turnaround r 1t / r 2t

8. Observations of the caustic of second turnaround (radius r 2t ) NGC 5846 Group Distance = 26 Mpc 3 rd largest knot of E/S0 galaxies within this distance, after Virgo, Fornax  rms = 322 km/s (85 veloc.) r 2t = 840 kpc M = 8 10 13 M  Large dE population (325 candidate members)

9. Caustic of 2 nd turnaround in N5846 group (continued)  rms = 322 km/s r 2t = 840 kpc

10. NGC 5353/4 Group mass = 2.1 10 13 suns  rms = 205 km/s r 2t = 530 kpc

11. NGC 1023 Group mass = 6.4 10 12 suns  rms = 136 km/s r 2t = 350 kpc

12. Virgo region

13. Virgo Cluster V rms = 715 km/s R 2t = 1.96 Mpc M = 9 10 14 M 

14. Virgo region M > 9 10 14 M 

15. Caustic of 2nd turnaround r 2t correlations Red: results from wide field imaging with CFHT MegaCam N5846: Mahdavi et al. 2005, AJ, 130, 1502 N1407: Trentham et al. 2006, MNRAS, 369, 1375 N5353/4: Tully & Trentham 2008, AJ, 135, 1488 N1023: Trentham & Tully 2009, MNRAS, in press M81: Chiboucas et al. 2009, AJ, 137, 3009

16. Caustic of 2nd turnaround r 2t correlations r 2t =  v /390 = 0.193 (M 12 ) 1/3 ==> M 12 = 2.3 10 -6  v 3 virial mass within r 2t (units 10 12 M  ) 1D rms velocity dispersion of galaxies within r 2t

17. Correlation between group mass and dwarf population! No. dwarfs per unit parent halo mass ~ constant Fewer giants per unit parent halo mass in more dynamically evolved halos dwarf: -17 < M R < -11 giant: M R < -17

18. Correlation between group mass and dwarf population! No. dwarfs per unit parent halo mass ~ constant Fewer giants per unit parent halo mass in more dynamically evolved halos evolved groups spiral groups dwarf associations dwarf: -17 < M R < -11 giant: M R < -17

19. Local Group M mw ~ M m31 ~ 1 10 12 M  => r 2t ~ 200 kpc

20. Local Group (continued) r 2t r 1t r 1t = 960 kpc M T (LG) = 1.9 10 12 M 

21. Virgo zero velocity surface ~ 7 Mpc radius

22. The Local Sheet red circles: 2nd turnaround r 2t blue circles: zero velocity r 1t

23. The Local Sheet red circles: 2nd turnaround r 2t blue circles: zero velocity r 1t green circles: zero gravity surface (   =0.7, spherical infall, no angular momentum)

24. Summary Light to mass varies with environment L B = 3.25 10 10 M 12.59 e -(0.6/M 12 ) Observed caustic of 2nd turnaround strongly correlated with virial mass r 2t = 0.193 (M 12 ) 1/3 Mpc and with velocity dispersion interior to 2nd turnaround r 2t =  v / 390 Mpc  mass of parent halo M 12 = 2.3 10 -6  v 3

25. Summary Light to mass varies with environment L B = 3.25 10 10 M 12.59 e -(0.6/M 12 ) Observed caustic of 2nd turnaround strongly correlated with virial mass r 2t = 0.193 (M 12 ) 1/3 Mpc and with velocity dispersion interior to 2nd turnaround r 2t =  v / 390 Mpc  mass of parent halo M 12 = 2.3 10 -6  v 3 No. dwarfs correlated with halo mass N d ~ M.91 dynamically evolved spiral rich

26. Summary Light to mass varies with environment L B = 3.25 10 10 M 12.59 e -(0.6/M 12 ) Observed caustic of 2nd turnaround strongly correlated with virial mass r 2t = 0.193 (M 12 ) 1/3 Mpc and with velocity dispersion interior to 2nd turnaround r 2t =  v / 390 Mpc  mass of parent halo M 12 = 2.3 10 -6  v 3 No. dwarfs correlated with halo mass N d ~ M.91 dynamically evolved spiral rich signatures of dark energy If   = 0.7 r 1t ~ 3.3 r 2t (3.7 r 2t if   = 0) and r ZG ~ 1.4 r 1t