12 things they don't tell you about the dynamics of star clusters - PowerPoint PPT Presentation

12 things they don't tell you about the dynamics of star clusters Douglas Heggie University of Edinburgh, UK With apologies to Ha-Joon Chang 16 September 2015 Lund 1

The things (minus the small print ) 1. Black holes don't escape 2. Low-mass stars don't escape preferentially 3. Primordial binaries don't matter 4. Neutron stars matter 5. There is no equipartition between stellar masses 6. . High-concentration clusters are nowhere near core collapse 7. Star clusters don't fill their tidal radius 8. Escapers don't escape 9. There is no such thing as tidal heating 10. Stars don't escape on the relaxation time scale 11. Lagrange points don't exist 12. . The size of a cluster isn't set at perigalacticon 16 September 2015 Lund 2

Thing 1. Stellar-mass Black holes don't all escape in all clusters What they say 1. Black holes segregate to the centre 2. They then behave like an isolated cluster 3. They have a small relaxation time 4. 2+3 ⇒ the black holes escape very fast 16 September 2015 Lund 3

What they don't say 1. Isolated clusters also expand on the relaxation time scale 2. Expansion counteracts tendency to segregate further 3. Black holes sit inside a much deeper potential well than an isolated cluster. 4. Would-be escapers cannot escape so easily 5. The would-be escapers donate their escape energy to the other stars 6. The black holes drive the expansion of the whole star cluster 7. They escape on the long relaxation time scale of the whole cluster See Breen & H (2013) 16 September 2015 Lund 4

Numerical illustrations Giersz & Mackey, Wilkinson, Davies, Gilmore (2008) H (2014) M4, NGC 6397, 47 Tuc 0 10Gyr Numbers of BH and BH binaries Additional remarks M22 1. Disappearance of BH coincides with “second core collapse” 2. Stellar-mass BH expected in uncollapsed clusters, and not in post-collapse clusters 16 September 2015 Lund 5

Thing 2. Low-mass stars don't always escape preferentially What they say 1. Stars escape in two-body encounters 2. Heavy stars tend to lose energy, low-mass stars tend to gain energy in encounters (tendency to equipartition of energy) 3. It is easier for low-mass stars to gain energy above the escape energy 16 September 2015 Lund 6

What they don't say 1. Heavy stars tend to sink to the centre 2. At high central densities, binary stars form from the heavy stars by three-body encounters 3. One of the stars in a three-body encounter gains high energy 4. Heavy stars escape preferentially in such circumstances See Kruijssen (2009) When the upper stellar mass is large enough, the low-mass stars are least rapidly removed 16 September 2015 Lund 7

Thing 3. Primordial binaries don't matter much, at least for uncollapsed clusters What they say 1. In binaries with P ⪅ 10 year, binary components have more energy than single stars 2. Time scale for changing energy of stars in binary- single interactions ~ relaxation time/binary fraction 3. “Heating” of single stars causes expansion on time scale of a few relaxation times 4. “Heating” by binaries sets the core radius in post- collapse evolution 16 September 2015 Lund 8

What they don't say 1. It's a second-order effect 2. Expansion of the cluster is powered mostly by central stellar-mass black holes 3. Binaries gradually take over as black holes escape, approaching (second) core collapse 4. Questionable if primordial binaries set the post-collapse core radius 47 Tuc ( f b = 0.018) 5. They affect the time to core collapse a lot Evolution of core and half-mass radii Giersz & H (2011) Note: interactions affect the binaries a lot 16 September 2015 Lund 9

Thing 4. Neutron stars matter for some cluster models What they say 1. Neutron stars are about 2% of cluster mass 2. Few-percent effect on relaxation time, escape time scale, etc. 16 September 2015 Lund 10

What they don't tell you Presence or near-absence of NS depends on natal kicks (typically ≫ 1. escape speed from cluster) 2. Presence or absence can change lifetime by factor ~4 (Contenta, Varri, H 2015) 3. Clusters dissolve by two processes a) Two- and three-body encounters (long lifetime) b) Mass-loss of stellar evolution (short lifetime) 4. The models (from Baumgardt & Makino 2003) sit on a separatrix where these processes are finely balanced 16 September 2015 Lund 11

Thing 5. There is no equipartition between stellar masses among visible stars in globular clusters What they say 1. Two-body encounters lead to equipartition in a few relaxation times 16 September 2015 Lund 12

What they don't say 1. I n equipartition low-mass stars would evaporate too quickly 2. Multi-mass King models do not give equipartition (Miocchi 2006) 3. N-body models do not give equipartition (Trenti & van der Marel 2013) 4. Fokker-Planck models do not give equipartition (Inagaki & Saslaw 1985), except at highest masses 16 September 2015 Lund 13

Shogo Inagaki ?1948-2015 16 September 2015 Lund 14 2008

Thing 6. High-concentration clusters are nowhere near core collapse What they say 1. Clusters are evolving from low concentration (large cores) to high concentration (small cores, c ≈ 2.5) 2. 47 Tuc has c = 2.07, a small dense core, and is undergoing rapid evolution towards core collapse 16 September 2015 Lund Harris catalogue 15

What they don't say 1. Models imply that core collapse will take at least another 20 Gyr 16 September 2015 Lund 16

Thing 7. Star clusters don't fill their tidal radius What they say 1. The Galactic tide strips off stars beyond a “tidal radius” 2. King models have a finite “tidal radius” to incorporate this effect 3. Globular clusters fit King models quite well 4. Therefore the radius of globular clusters is determined by the Galactic tide 5. We can use radii of globular clusters to estimate strength of tidal field 16 September 2015 Lund 17

What they don't say 1. Edge radius may be set by initial conditions 2. If a cluster starts smaller than its tidal radius i. It first expands so that its relaxation time is of order its age, until its radius equals the tidal radius ii.After that it contracts, and its relaxation time is of order its remaining lifetime (Henon 1961; Gieles, H & Zhao 2011) 3. GHZ say 2/3 are (i), 1/3 are (ii) 4. Gives a reinterpretation of the “survival triangle” 16 September 2015 Lund 18 Gnedin & Ostriker 1997

Thing 8. Some Escapers don't escape What they say 1. For a cluster on a circular Galactic orbit, switch to rotating frame centred at the cluster 2.Combined potential (cluster, tidal field, centrifugal acceleration) has last closed equipotential V crit 3. Stars with higher energy escape

What they don’t say 1. The condition E > V crit is necessary, not sufficient 2. There’s also a Coriolis acceleration, which can keep high-energy stars inside the cluster 3. There is a population of “potential escapers” 4. Can reach up to 10% of cluster members (Baumgardt 2001) 5. Ignored in all snapshot modelling of globular clusters Henon 1970

Thing 9. There is no such thing as tidal heating on a circular Galactic orbit What they say 1. Clusters exhibit non-Keplerian velocity dispersion profile 2. Tidal field is time-dependent (“bulge shocking”, “disk shocking”) and strongest at large radii Drukier et al 1998 (M15) 3. Velocity dispersion elevated by “tidal heating”, or even something “non-Newtonian”

What they don't say 1. For a cluster on a circular Galactic orbit, in the rotating frame the potential is static. 2. Energy is conserved (Jacobi integral), therefore there is no tidal heating. 3. Velocity dispersion is elevated by potential escapers (see Thing 8) Kuepper et al 2010

Thing 10. Stars don't escape on the relaxation time scale except for very large N What they say 1. Stars escape by two-body encounters, which may elevate the energy of one star above the escape energy. 2. Two-body encounters change stellar energies on the relaxation time scale 3. Stars escape on the relaxation time scale

What they don't say 1. Stars with E > V crit remain as potential escapers for a time 2. During this time E changes on relaxation time scale, and escape becomes easier as E increases 3. The balance of these processes gives an escape time scale (i.e. time scale for loss of mass) ∝ t r /N 1/4 (Baumgardt 2001) 4. Eventually this must turn over to ∝ t r

Thing 11. Lagrange points don't exist for clusters on elliptical orbits What they say 1. There is a point where the attraction of the cluster and Galaxy are in balance. 2. It is an equilibrium point 3. It is a critical point of the “potential” 4. Stars beyond this point are escaping

What they don't say 1. For a cluster on an elliptical Galactic orbit, there is a point where the forces balance, but it's a moving point, not an equilibrium 2. There is no potential, and no critical point 3. The nearest analogue to the Lagrange point of the circular problem is a periodic orbit “Lagrange” periodic orbit for various power-law Galactic potentials

Thing 12. The size of a cluster isn't set at perigalacticon What they say 1. The tidal radius is smallest at perigalacticon 2. Stars beyond the tidal radius escape 3. Cluster members are non-escapers, and must lie inside the tidal radius at perigalacticon