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Dynamical constraints on the Intermediate Mass Black Holes (IMBHs)

Dynamical constraints on the Intermediate Mass Black Holes (IMBHs). Michela Mapelli collaborators: Andrea Ferrara, Monica Colpi, Andrea Possenti, Steinn Sigurdsson, Nanda Rea. SISSA. 1. What are the IMBHs?.

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Dynamical constraints on the Intermediate Mass Black Holes (IMBHs)

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  1. Dynamical constraints on the Intermediate Mass Black Holes (IMBHs) Michela Mapelli collaborators: Andrea Ferrara, Monica Colpi, Andrea Possenti, Steinn Sigurdsson, Nanda Rea SISSA 1

  2. What are the IMBHs? BHs with mass ~ 20- 5 x 104 Msun What is their origin? - runaway collapse of stars in young clusters (Portegies Zwart & McMillan 2002) - repeated mergers of a binary BH seed with BHs and stars in globular clusters (Miller & Hamilton 2002) - remnants of first massive stars (Heger et al. 2002) 2

  3. How can we detect IMBHs? G1: the interpretation of the surface brightness profile and of the velocity profile on the basis of axisymmetric general models suggests the presence of a 1.8 (+/- 0.5) x 104 Msun IMBH Gebhardt, Rich, Ho 2005 3

  4. How can we detect IMBHs? M15: the interpretation of the surface brightness profile and of the velocity profile on the basis of axisymmetric general models suggests the presence of a dark central mass 500 (- 500, +2500) Msun Van den Bosch et al. 2005 4

  5. How can we detect IMBHs? NGC6752: - high concentration of dark matter (1000 Msun) from the acceleration of the 3 innermost millisecond pulsars (Ferraro et al. 2003; D'Amico et al 2002) - peculiar position (far from the GC center) of the millisecond pulsar A and C: only 4-body interactions with a binary IMBH can explain the position of PSRA 5 Colpi, Mapelli, Possenti 2003

  6. How can we detect IMBHs? ULXs? ULXs:= X-ray sources with LX>1039 erg s-1 SMBHsaccreting at sub-Eddington rate Cons: far-off from the galactic center HMXBswith mild beaming Cons: ionized nebulae around ULXs IMBHs Cons: too exotic.. 6

  7. OUTLINE: PART 1: unvealing binary IMBHs in globular clusters via 3-body encounters PART 2: dynamical constraints on the number of IMBHs in the Milky Way 7

  8. PART 1: unvealing binary IMBHs in globular clusters via 3-body encounters 8

  9. How can we detect IMBHs? BASIC IDEA: BINARY IMBHs are expected to often (~million years)interact with cluster stars Do cluster stars conserve any memory of this interaction (angular momentum, velocity)? We run 3-body simulations (binary IMBH + incoming star) 9

  10. SIMULATIONS: FEBO (FEw BOdy Interactions; Colpi, Mapelli & Possenti 2003) Integrator Runge Kutta 5th order 3- and 4-body interactions What binaries we consider? - M1+M2 = 60-210 Msun - M2/M1 = 1/2 – 1/20 - a = 1, 10, 100, 1000 AU - e =0.7 (thermally averaged value) What incoming stars? - m = 0.5 Msun 10

  11. SIMULATIONS: What the host globular cluster? We consider a DENSE CONCENTRATED cluster (NGC6752) - v1D = 4.9 km/s (Dubath, Meylan & Mayor 1997) - n ~ 105 #/pc3 - DOUBLE King! - indications of a binary IMBH (Colpi, Mapelli, Possenti 2003) 11

  12. 3-body interactions : During a 3-body interaction with a HARD binary, the incoming star acquires kinetic energy from the binary, which hardens 12

  13. 3-body interactions : During a 3-body interaction with a HARD binary, the incoming star acquires kinetic energy from the binary, which hardens 13

  14. RESULTS of SIMULATIONS: - SUPRATHERMAL STARS -ANGULAR MOMENTUM ALIGNMENT 14

  15. SUPRATHERMAL STARs: Stars which after the encounter remain bound to the cluster, but acquire HIGH velocity (from 3 sigma to the escape velocity) 15

  16. ANGULAR MOMENTUM ALIGNMENT: IF THE BINARY TRANSFERS ANGULAR MOMENTUM TO THE INTERACTING STAR 16

  17. ANGULAR MOMENTUM ALIGNMENT: a =10 AU a =100 AU Angular momentum alignment only if the binary is wide! 17

  18. ARE SUPRATHERMAL STARS AND ANGULAR MOMENTUM ALIGNMENT OBSERVABLE EFFECTS? 18

  19. NUMBER OF SUPRATHERMAL STARS: f = fraction of suprathermal (from our simulations) Total number of interacting stars N ~ 130 - 300 19

  20. IMPORTANT TIMESCALES: HARDENING TIMESCALE (Quinlan 1996) HALF MASS RELAXATION TIMESCALE(Binney & Tremaine 1987) GRAVITATIONAL WAVE TIMESCALE(Peters 1964; Quinlan 1996) 20

  21. IMPORTANT TIMESCALES: A binary IMBH can form only in the early stages of the GC life Because of the hardening, current IMBH binaries have a <= 1 AU Because of the gravitational wave emission a >= 0.2 AU Because of the half mass relaxation time, only suprathermal produced in the last 2-3 trh survive No angular momentum alignment N ~ 90-180 21

  22. SELECTION EFFECTS: -PROJECTION EFFECTS: 80 % of suprathermals -only MS, HB and RGB STARS with 0.6< m/msun < 0.9 are observable: 45 % of suprathermals N ~ 30-60 number of observable supra-thermal stars 22

  23. RADIAL DISTRIBUTION of suprathermal stars: How do suprathermal stars evolve in the cluster before thermalization and what is their radial distribution? We integrate the dynamics of suprathermal, accounting for: - cluster potential; - dynamical friction; - kick interactions with other stars; We use an upgraded version of the code by Sigurdsson & Phinney (1995) 23

  24. RADIAL DISTRIBUTION of suprathermal stars: ~ 30 (half of the total) suprathermal stars are within 6 core radii ! No substantial difference with respect to the distribution of RGBs in the cluster 24

  25. Summary The main effects of 3-body interactions between a binary IMBH and cluster stars are: - suprathermal stars; -angular momentum alignment. The angular momentum alignment is significant only if the binary is wide is not observable for current IMBH binaries The observable suprathermal stars are only 30-60 very difficult to observe! 25

  26. Future: Are OBSERVATIONS possible? - HST/STIS had a error of 1-2 km/s - HST/WFPC2 and HST/ACS can achieve a median error ~ 6 km/s in proper motion measurements for NGC6752 the resolution of current telescopes is sufficient. The problem is that suprathermal are few! Van den Bosch et al. (2005) find that M15 has a high concentration of dark mass and rotates. They search for suprathermal stars; but do not find anything. 26

  27. PART 2: dynamical constraints on the number of IMBHs in the Milky Way 27

  28. How many IMBHs are hidden in the Milky Way? •= b- L~ 0.02 R. P. van der Marel (2004) Van der Marel (2004) OUR IDEA: CONSTRAIN THE DENSITY OF IMBHs using the LINK between ULXs and IMBHs 28

  29. ULXs can be IMBHs accreting: In binary systems PROBLEMs: 1. LX>1040 erg s-1 only for ~ 1 Myr Only 1 galaxy in 103-104 may harbor 1 ULX with LX>1040 erg s-1 (Madhusudhan et al. 2005) 2. Simulations of accreting IMBHs show too many high luminosity (LX>1040 erg s-1 ) ULXs(Madhusudhan et al. 2005) 3. Few ULXs have certain optical identification with companion stars (Liu et al. 2005) GAS in MOLECULAR CLOUDs (Mii & Totani 2005) 29

  30. BASIC IDEA: No ULXs are detected in the Milky Way. What is the maximum density of IMBHs for which no ULX is expected to form in the Galaxy due to IMBHs accreting molecular gas? 30

  31. SIMULATIONS: Public code GADGET 2 (Springel 2005) Milky Way model with embedded IMBHs Milky Way: - 1.3 x1012 Msun NFW rigid halo - 4 x 1010 Msun disk - 1 010 Msun bulge 31

  32. SIMULATIONS: Free code GADGET 2 (Springel 2005) Milky Way model with embedded IMBHs IMBHs: - HALO population: NFWorDiemand, Madau & Moore(2005;DMM) for IMBHs born in a n-s fluctuation - 1 04 Msun each one - different densities: 0.1-10-5b (106 - 500 IMBHs) 32

  33. Deriving the NUMBER of ULXs: Our simulation with the IMBHs: • = 10-3 b DMM 33

  34. Deriving the NUMBER of ULXs: We define a molecular disk: z=75 pc; R~20 kpc And we select the IMBHs which are passing through this disk 34

  35. Deriving the NUMBER of ULXs: We define a molecular disk: z=75 pc; R~20 kpc Volume fraction of molecular disk occupied by clouds:f~0.017 (Agol & Kamionkowski 2002) We extract from our simulations a fraction f of the IMBHs passing through the molecular disk and derive for them theBondi-Hoyle luminosity: If Lx > 1039 erg s-1 we consider them ULXs 35

  36. What is the expected efficiency of the accretion? IMBHs are able to transfer angular momentum to the gas if their velocity is <~100 km/s (Agol & Kamionkowski) They are expected to form an ACCRETION DISK What kind of accretion disk? ADAF accretion disk (Quataert & Narayan): efficiency h = 0.001 THIN accretion disk (Shakura-Sunyaev): efficiency h = 0.1 36

  37. Results for the THIN accretion disk: • = 10-3 b DMM NULX = 0.2 +/- 0.2 • = 10-1b DMM NULX = 40 +/- 6 • = 10-3b NFW NULX ~ 0 • = 10-1b NFW NULX = 0.5 +/- 0.5 The upper limit is • = 10-3b for a DMM profile or • = 10-1b for a NFW profile 37

  38. Results for the THIN accretion disk: ULX radial and luminosity distribution: agreement with observations (Brassington 2005) Disagreement with Liu & Bregman 2005 38

  39. Results for the ADAF accretion disk: • = 10-3 b DMM NULX = 0.002 +/- 0.002 • = 10-1b DMM NULX = 0.5 +/- 0.5 • = 10-3b NFW NULX ~ 0 • = 10-1b NFW NULX = 0.007 +/- 0.007 The upper limit is • = 10-1b for a DMM profile or • > 10-1b for a NFW profile 39

  40. Can we derive stronger constrains, if we consider the other X-ray sources (not only ULXs)? 40

  41. NON-ULX sources due to IMBH accreting MOLECULAR or ATOMIC GAS: Non ULX sources can be due to the accretion of not only molecular, but also atomic, less dense gas How to model the atomic gas? 3-phases of atomic gas: COLD and neutral: T~102 K, n ~ 1 cm-3 WARM: T~104 K, n ~ 0.03cm-3 HOT: T~106 K, n ~10-3 cm-3 41

  42. NON-ULX sources due to IMBH accreting MOLECULAR or ATOMIC GAS: We define an atomic hydrogen disk: z=100pc, R~20kpc Volume fraction of atomic H disk occupied by COLD H : fCH~0.48 (Agol & Kamionkowski 2002) Volume fraction of atomic H disk occupied by WARM H : fWH~0.2 (Rosen & Bregman 1995) We extract from our simulations a fractionfCH+ fWH of the IMBHs passing through the atomic H disk and derive their Bondi-Hoyle luminosity 42

  43. NON-ULX sources due to IMBH accreting MOLECULAR or ATOMIC GAS: Results for the THIN accretion disk: 43

  44. NON-ULX sources due to IMBH accreting MOLECULAR or ATOMIC GAS: Results for the ADAF accretion disk: 44

  45. Comparison with observations: These are non-pulsated, variable, maybe transient sources, with 1031<Lx<1039 erg s-1 and faint optical counterpart (absorption) What kind of observed Galactic sources could correspond to them? 45

  46. Comparison with observations: We consider the 2nd IBIS/ISGRI CATALOGUE (Bird et al. 2005): survey of the 50% of the Galaxy, from 20 to 40 KeV We cannot consider all the sources with 1031<Lx<1039 erg s-1 , because we require completeness. We consider sources with 1036<Lx<1039 erg s-1 , where the IBIS/ISGRI catalogue is complete We exclude all the sources identified as HMXBs or LMXBs and all the sources whose spectrum is typical of a NS ONLY 3 SOURCES in the IBIS/ISGRI catalogue (6 expected in the Galaxy) have 1036<Lx<1039 erg s-1 , and are no HMXBs/LMXBs 46

  47. Comparison with observations: THIN DISK ONLY 3 SOURCES in the IBIS/ISGRI catalogue (6 expected in the Galaxy) have 1036<Lx<1039 erg s-1 , and are no HMXBs/LMXBs Sources with 1036<Lx<1039 erg s-1 , in our simulations: • = 10-3 b DMM NX = 18 +/- 7 • = 10-1b DMM NX = 1650 +/- 70 • = 10-3b NFW NX = 0.4 +/- 0.4 • = 10-1b NFW NX = 148 +/- 21 The upper limit is • = 10-4-10-3b for a DMM profile or • = 10-3-10-2b for a NFW profile 47

  48. Comparison with observations: ADAF disk ONLY 3 SOURCES in the IBIS/ISGRI catalogue (6 expected in the Galaxy) have 1036<Lx<1039 erg s-1 , and are no HMXBs/LMXBs Sources with 1036<Lx<1039 erg s-1 , in our simulations: • = 10-3 b DMM NX = 1.2 +/- 1.0 • = 10-1b DMM NX = 236 +/- 15 • = 10-3b NFW NX ~ 0 • = 10-1b NFW NX = 5 +/- 3 The upper limit is • = 10-3-10-2b for a DMM profile or • = 10-1b for a NFW profile 48

  49. Conclusions: We studied IMBHs accreting molecular/atomicgas through N-body simulations of the Milky Way. The main uncertainty is the radiative efficiency: do theIMBHs accrete via THIN or ADAF disk (if any) ? The upper limit of the IMBH density obtained by requiring that noULXis present in our simulation is 10-3b(DMM profile;104IMBHs in the Milky Way) for the THIN DISK model and 10-1b(DMM profile; 106 IMBHs in the Milky Way) for the ADAF model If we also considerNON-ULTRA-LUMINOUS X-ray sources, the upper limit is~10-3b(DMM) for the THIN DISK model and10-3 -10-2b(DMM) for the ADAF 49

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