Inverting the dynamical evolution problem of globular clusters: clues to their origin

Transcription

1 Inverting the dynamical evolution problem of globular clusters: clues to their origin Mark Gieles Poul Alexander (Cambridge), Douglas Heggie (Edinburgh) Alice Zocchi, Miklos Peuten, Vincent Hénault-Brunet (Surrey)

2 Young massive clusters? Milky Way GCs McLaughlin 00 µv [mag/arsec 2 ] 25 M? µv [mag/arsec 2 ] 25 NGC log R[arcsec]

3 Galaxy scaling relations Spirals Tully & Fisher 1977 Ellipticals Faber & Jackson 1976 Virial theorem + Mass-to-light ratio + Luminosity-radius relation

4 dsph Ellipticals Faber-Jackson Ultrafaints UCDs Globulars Misgeld & Hilker 11

5 Environment R h / R 1/2 G Roche-filling clusters in Galaxy with flat rotation curve: R h / R 2/3 G R h / R 1/3 G Mackey & Van den Bergh 05

6 Interpretation: survival An often adopted view: 1. Two-body relaxation dominant massloss process; 2. Cluster lifetime proportional to their present day relaxation time; 3. All GCs roughly the same age; 4. Then: rh /Age = constant and so r h / M 1/3 Fall & Rees 1977; Gnedin & Ostriker 1997

7 But Relaxation is diffusion of energy { expansion, and/or escape of stars Hénon 1961, 1965, 1975

8 Simple model for GC evolution M = constant isolated cluster: self-similar expansion Hénon 1965 Radius Mass R / T 2/3 Time

9 Expanding: rh /Age = constant Gieles+ 10 rh ' 3Gyr Faber-Jackson

10 Simple model for GC evolution M = constant isolated cluster: self-similar expansion Hénon 1965 Mass M = M 0 Ṁ t tidally limited cluster: evaporation at constant density Hénon 1961 Radius R / T 2/3 R / M 1/3 Time

11 Expanding: Evaporating: rh /Age = constant h / tidal = constant Gieles+ 10 rh ' 3Gyr Faber-Jackson

12 Simple model for GC evolution Gieles, Heggie & Zhao 11 isolated cluster: self-similar expansion Hénon 1965 tidally limited cluster: evaporation at constant density Hénon 1961

13 The HR diagram of GCs Two-body relaxation dominant mass-loss process Gieles, Heggie & Zhao 11 Milky Way GCs from Harris 1996, 10

14 Are all GCs post-collapse? Most clusters have large cores and some appear not mass segregated Fregeau+ 03, 3007 NGC 6101 Chatterjee+ Dalessandro+

15 Overlooked energy sources before core collapse stellar evolution mass loss stellar-mass black holes Breen & Heggie 13a,b Gieles, Heggie & Church, to be submitted black hole candidates in M22 Strader+ 11

16 Models with a black hole population appear. 1. Pre-collapse (large core), and 2. not segregated stars black holes Peuten+, to be submitted Breen & Heggie 13

17 New models for mass modelling of collisional systems log r [M pc 3 ] Distribution function based models 2. Lowered isothermal : Woolley (1954), King (1966) & Wilson (1975) and models in between 3. Variable amount of radial anisotropy (Michie 1963) 4. Multiple mass components 4 6 All Turn-o stars White dwarfs Neutron stars Black holes (Da Costa & Freeman 1976; Gunn & Griffin 1979) log r [pc] Gieles & Zocchi, ArXiv: See also poster #122 Lowered Isothermal Model Explorer in PYthon: LIMEPY

18 M and NGC2808: twins? MV = -9.2 reff = 3.0 pc RG = 11.1 kpc MV = -9.4 reff = 2.2 pc RG = 10.4 kpc 10 M 10 NGC2808 µv [mag/arsec 2 ] µv [mag/arsec 2 ] log R[arcsec] log R[arcsec] Data: Surface brightness profiles (Trager+ 1995; Noyala & Gebhardt 06) Radial velocities (Lützgendorf+ 12; Lardo+ ; Watkins+ HST Proper motions (Bellini+ 14; Watkins+ )

19 Results 10 M 10 NGC2808 Surface brightness: µv [mag/arsec 2 ] µv [mag/arsec 2 ] log R[arcsec] log R[arcsec] Radial velocities: slos [km/s] 10 5 M slos [km/s] 10 5 NGC2808 Proper motions spm [mas/yr] spm [mas/yr] st/sr 0.6 st/sr log R[arcsec] log R[arcsec]

20 Results 10 M 10 NGC2808 Surface brightness: µv [mag/arsec 2 ] fbh 10-6 µv [mag/arsec 2 ] fbh log R[arcsec] log R[arcsec] Radial velocities: slos [km/s] 10 5 M slos [km/s] 10 5 NGC2808 Proper motions spm [mas/yr] spm [mas/yr] st/sr 0.6 st/sr log R[arcsec] log R[arcsec]

21 Milky Way GCs McLaughlin 00 µv [mag/arsec 2 ] 25 M GC scaling relations follow from simple relaxation argument, insensitive to conditions in the core µv [mag/arsec 2 ] 25 NGC log R[arcsec]

22 Globular cluster population modelling: inverting the evolution mass N-body EMACSS Evolve Me A Cluster of StarS (EMACSS) Alexander & Gieles 12; Gieles+ 14; Alexander+ 14 radius <m> Solve cluster evolution in 10-2 sec. independent of N time Explore initial conditions individual GCs Pijloo+ See also poster #100

23 Hierarchical Bayesian fit to Milky Way GC population Parameterised distributions for initial Mi, RG, ρh log halo with Vc = 2 km/s Isotropic orbit distribution N(M i ) / M i exp ( M i /M ) n(r G ) / R G P ( h ) / exp[ (log( h ) µ) 2 /(2 2 )] pop =(,M,,µ, ) (parameters) X GC =(M,r h,r G ) N (data) 1. Find posterior P(θGC XGC) for individual GCs, priors = P(θpop Ppop) 2. Use Xpop = P(θGC XGC) as observations to find P(θpop Xpop) Hogg et al. 10 Alexander & Gieles to be submitted

24 Hierarchical Bayesian fit to Milky Way GC population Metal poor Metal rich - µ log ' 2.5 log ' 2.5 hlog i surv ' 4.5 ± 0.5 Alexander & Gieles to be submitted Total mass in disrupted clusters ~10 8 M

25 Young massive clusters YMCs power-law mass functions can not be evolved into peaked GCMF! 4.0 Portegies Zwart+ 10 Larsen+ 12/ 14 log dn/d logm Milky Way GCs log M Harris 1996

26 Young massive clusters Young massive clusters different from (metal-poor) globular clusters at birth Milky Way GCs McLaughlin 00 µv [mag/arsec 2 ] 25 M GC scaling relations follow from simple relaxation argument, insensitive to µv [mag/arsec 2 ] 25 NGC2808 conditions in the core log R[arcsec]

27 Ongoing work: following GC evolution in the cosmological contest Renaud, Agertz, Gieles in prep