Dynamical constraints on the Intermediate Mass Black Holes (IMBHs)

Dynamical constraints on the Dynamical constraints on the Intermediate Mass Black Holes (IMBHs)Intermediate Mass Black Holes (IMBHs)

Michela MapelliMichela Mapelli

collaborators: collaborators: Andrea Ferrara, Monica Colpi, Andrea Andrea Ferrara, Monica Colpi, Andrea Possenti,Possenti, Steinn Sigurdsson, Nanda ReaSteinn Sigurdsson, Nanda Rea 11

SISSASISSA

What are the IMBHs?What are the IMBHs?

BHs with mass ~ 20- 5 x 10BHs with mass ~ 20- 5 x 1044 Msun Msun

What is their origin?What is their origin?

- runaway collapse of stars in young - runaway collapse of stars in young clusters clusters (Portegies Zwart & McMillan 2002)(Portegies Zwart & McMillan 2002)

- repeated mergers of a binary BH seed - repeated mergers of a binary BH seed with BHs and stars in globular clusters with BHs and stars in globular clusters (Miller & Hamilton 2002)(Miller & Hamilton 2002)

- remnants of first massive stars - remnants of first massive stars (Heger (Heger et al. 2002)et al. 2002)

22

How can we detect IMBHs?How can we detect IMBHs?

Gebhardt, Rich, Ho Gebhardt, Rich, Ho 20052005

G1: G1: the interpretation of the interpretation of

the surface the surface brightness profilebrightness profileand of the velocity and of the velocity

profile on the basis of profile on the basis of axisymmetric general axisymmetric general models suggests the models suggests the

presence of a presence of a 1.8 (+/- 0.5) x 101.8 (+/- 0.5) x 1044

Msun IMBHMsun IMBH

33


Van den Bosch et al. Van den Bosch et al. 20052005

M15: M15: the interpretation of the interpretation of

the surface the surface brightness profilebrightness profileand of the velocity and of the velocity

profile on the basis of profile on the basis of axisymmetric general axisymmetric general models suggests the models suggests the

presence of apresence of adark central massdark central mass500 (- 500, +2500) 500 (- 500, +2500)

Msun Msun

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Colpi, Mapelli, Possenti 2003Colpi, Mapelli, Possenti 2003

NGC6752: NGC6752: - high concentration of dark - high concentration of dark matter (1000 Msun) from the matter (1000 Msun) from the

acceleration of the 3 acceleration of the 3 innermost millisecond pulsars innermost millisecond pulsars (Ferraro et al. 2003; D'Amico (Ferraro et al. 2003; D'Amico

et al 2002)et al 2002)

- peculiar position (far from - peculiar position (far from the GC center) of the the GC center) of the

millisecond pulsar A and C:millisecond pulsar A and C:

only 4-body interactions with only 4-body interactions with a binary IMBH can explain the a binary IMBH can explain the

position of PSRAposition of PSRA

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ULXs?ULXs?

ULXs:= X-ray sources with LX>1039 erg s-1

SMBHs accreting at sub-Eddington rate

HMXBs with mild beaming

Cons: far-off from the galactic center

Cons: ionized nebulae around ULXs

IMBHs

Cons: too exotic..

How can we detect How can we detect IMBHs?IMBHs?

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PART 1: PART 1:

unvealing binary IMBHs unvealing binary IMBHs in globular clusters in globular clusters

via 3-body encounters via 3-body encounters

PART 2: PART 2:

dynamical constraints on the dynamical constraints on the number of IMBHs in the Milky number of IMBHs in the Milky

WayWay

OUTLINEOUTLINE::

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PART 1: PART 1:

unvealing binary IMBHs unvealing binary IMBHs in globular clusters in globular clusters

via 3-body encounters via 3-body encounters

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BASIC IDEA:BASIC IDEA:

BINARY IMBHs are expected to often (~million years)interact with cluster stars

How can we detect How can we detect IMBHs?IMBHs?

Do cluster stars conserve any memory of this interaction (angular momentum, velocity)?

We run 3-body simulations (binary IMBH + incoming star)

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SIMULATIONS:SIMULATIONS:

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

FEBO (FEw BOdy Interactions; Colpi, Mapelli &

Possenti 2003)Integrator Runge Kutta 5th order

3- and 4-body interactions

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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 binaryIMBH (Colpi, Mapelli, Possenti 2003)

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3-body interactions :3-body interactions :

During a 3-During a 3-body body

interaction interaction with a HARD with a HARD

binary, binary, the incoming the incoming star acquires star acquires kinetic energy kinetic energy

from the from the binary, which binary, which

hardenshardens1122

3-body interactions :3-body interactions :

During a 3-During a 3-body body

interaction interaction with a HARD with a HARD

binary, binary, the incoming the incoming star acquires star acquires kinetic energy kinetic energy

from the from the binary, which binary, which

hardenshardens1313

RESULTS of SIMULATIONS:RESULTS of SIMULATIONS:

- SUPRATHERMAL STARS

-ANGULAR MOMENTUM ALIGNMENT

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SUPRATHERMAL STARs:SUPRATHERMAL STARs:

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

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ANGULAR MOMENTUM ANGULAR MOMENTUM ALIGNMENT:ALIGNMENT:

IF

THE BINARY TRANSFERS ANGULAR MOMENTUM TO THE INTERACTING STAR

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ANGULAR MOMENTUM ANGULAR MOMENTUM ALIGNMENT:ALIGNMENT:

Angular momentum alignment only if Angular momentum alignment only if the binary is wide!the binary is wide!

a =10 AUa =10 AU a =100 AUa =100 AU

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ARE ARE SUPRATHERMAL STARS SUPRATHERMAL STARS

AND AND ANGULAR MOMENTUM ANGULAR MOMENTUM

ALIGNMENT ALIGNMENT OBSERVABLE EFFECTS?OBSERVABLE EFFECTS?

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NUMBER OF SUPRATHERMAL NUMBER OF SUPRATHERMAL STARS:STARS:

f = fraction of suprathermal (from our simulations)

Total number of interacting stars

N ~ 130 - 300

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IMPORTANT TIMESCALES:IMPORTANT TIMESCALES:

HARDENING TIMESCALE (Quinlan 1996)

HALF MASS RELAXATION TIMESCALE (Binney & Tremaine 1987)

GRAVITATIONAL WAVE TIMESCALE (Peters 1964; Quinlan 1996)

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IMPORTANT TIMESCALES: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 No angular momentum alignmentalignment

N ~ 90-180N ~ 90-1802211

SELECTION EFFECTS: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 ~ 30-60number of observable supra-thermal stars

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RADIAL DISTRIBUTION of suprathermal RADIAL DISTRIBUTION of suprathermal stars:stars:

How do suprathermal stars evolve in the cluster How do suprathermal stars evolve in the cluster beforebeforethermalization and what is their radial thermalization and what is their radial distribution?distribution?We integrate the dynamics of suprathermal, We integrate the dynamics of suprathermal, accounting for:accounting for:

- cluster potential;- cluster potential;- dynamical friction;- dynamical friction;- kick interactions with other stars;- kick interactions with other stars;

We use an upgraded version of the code by We use an upgraded version of the code by Sigurdsson & Phinney (1995)Sigurdsson & Phinney (1995)

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RADIAL DISTRIBUTION of suprathermal RADIAL DISTRIBUTION of suprathermal stars:stars:

~ 30 (half of the ~ 30 (half of the total) suprathermal total) suprathermal stars are within 6 stars are within 6 core radii !core radii !

No substantial No substantial difference with difference with respect to the respect to the distribution of RGBs distribution of RGBs in the clusterin the cluster

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SummarySummary The main effects of 3-body interactions The main effects of 3-body interactions between a binary IMBH and cluster stars between a binary IMBH and cluster stars are:are: - suprathermal stars;- suprathermal stars; -angular momentum -angular momentum alignment.alignment. The angular momentum alignment is The angular momentum alignment is significant only if the binary is wide significant only if the binary is wide is not observable for current IMBH is not observable for current IMBH binariesbinaries

The observable suprathermal stars are The observable suprathermal stars are only 30-60only 30-60 very difficult to observe!very difficult to observe!

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FuturFuture:e: Are OBSERVATIONS possible?Are OBSERVATIONS possible?

- HST/STIS had a error of 1-2 km/s- HST/STIS had a error of 1-2 km/s

- HST/WFPC2 and HST/ACS can achieve a - HST/WFPC2 and HST/ACS can achieve a median error ~ 6 km/s in proper motion median error ~ 6 km/s in proper motion measurements for NGC6752measurements for NGC6752

the resolution of current telescopes is the resolution of current telescopes is sufficient.sufficient. The problem is that suprathermal are The problem is that suprathermal are few!few! Van den Bosch et al. (2005)Van den Bosch et al. (2005) find that M15 find that M15 has a high concentration of dark mass and has a high concentration of dark mass and rotates.rotates. They search for suprathermal stars; but do They search for suprathermal stars; but do not find anything.not find anything.

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PART 2: PART 2:

dynamical constraints dynamical constraints on the number of IMBHson the number of IMBHs

in the Milky Wayin the Milky Way

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How many IMBHs are hidden in the Milky How many IMBHs are hidden in the Milky Way?Way?

••= = bb- -

LL~ 0.02~ 0.02

R. P. van der Marel (2004)

OUR IDEA:OUR IDEA:

CONSTRAIN THE DENSITY OF IMBHs CONSTRAIN THE DENSITY OF IMBHs using the using the

LINK between ULXs and IMBHsLINK between ULXs and IMBHs

Van der Marel (2004)Van der Marel (2004)

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ULXs can be IMBHs accreting:

In binary systems

GAS in MOLECULAR CLOUDs (Mii & Totani GAS in MOLECULAR CLOUDs (Mii & Totani 2005)2005)

PROBLEMs:1. LX>1040 erg s-1 only for ~ 1 Myr

3. Few ULXs have certain optical identification with companion stars (Liu et al. 2005)

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)

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No ULXs are detected in the Milky Way.No ULXs are detected in the Milky Way.

What is the maximum density of IMBHs for which no ULX is What is the maximum density of IMBHs for which no ULX is expected to form in the Galaxy due to IMBHs accreting expected to form in the Galaxy due to IMBHs accreting

molecular gas?molecular gas?

BASIC IDEA:BASIC IDEA:

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Milky Way model with embedded IMBHs Milky Way:- 1.3 x1012 Msun NFW rigid halo

- 4 x 1010 Msun disk

- 1 010 Msun bulge

Public code GADGET 2 (Springel 2005)

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Milky Way model with embedded IMBHs

Free code GADGET 2 (Springel 2005)

IMBHs:

- HALO population: NFW or Diemand, Madau & Moore (2005; DMM) for IMBHs born in a fluctuation

- 1 04 Msun each one

- different densities: 0.1-10-5 b

(106 - 500 IMBHs)

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Deriving the NUMBER of ULXs:Deriving the NUMBER of ULXs:

Our simulation with the IMBHs: • = 10-3 b DMM

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We define a molecular disk: z=75 pc; R~20 kpc

And we select the IMBHs which are passing through this disk

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We define a molecular disk: z=75 pc; R~20 kpcVolume 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 diskand derive for them the Bondi-Hoyle luminosity:

If Lx > 1039 erg s-1 we consider them

ULXs3355

What is the expected What is the expected efficiency of the efficiency of the

accretion?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?

THIN accretion disk (Shakura-Sunyaev):efficiency = 0.1

ADAF accretion disk (Quataert & Narayan):efficiency = 0.001

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• = 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 The upper limit is • • = 10= 10-3-3 bb for a DMM profile for a DMM profile

or or • • = 10= 10-1-1 bb for a NFW profile for a NFW profile

Results for the THIN accretion Results for the THIN accretion disk:disk:

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ULX radial and luminosity distribution:

Disagreement with Liu & Bregman 2005

agreement with observations (Brassington 2005)

Results for the THIN accretion Results for the THIN accretion disk:disk:

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• = 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 The upper limit is • • = 10= 10-1-1 bb for a DMM profile for a DMM profile

or or • • >> 10 10-1-1 bb for a NFW profile for a NFW profile

Results for the ADAF accretion Results for the ADAF accretion disk:disk:

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Can we derive stronger Can we derive stronger constrains, if we constrains, if we

consider the other X-ray consider the other X-ray sources (not only ULXs)?sources (not only ULXs)?

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NON-ULX sources due to IMBH NON-ULX sources due to IMBH accreting MOLECULAR or ATOMIC accreting MOLECULAR or ATOMIC

GAS: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

Non ULX sources can be due to the accretion of not only molecular, but also atomic, less dense gas

How to model the atomic How to model the atomic gas?gas?

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GAS: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 fraction fCH + fWH of

the IMBHs passing through the atomic H diskand derive their Bondi-Hoyle luminosity

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GAS:GAS:Results for the THIN accretion Results for the THIN accretion

disk:disk:

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GAS:GAS:Results for the ADAF accretion Results for the ADAF accretion

disk:disk:

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Comparison with observations: 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 What kind of observed Galactic sources could correspond to them?could correspond to them?

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We cannot consider all the sources with 1031<Lx<1039 erg s-1 , because we require completeness.

We consider the 2nd IBIS/ISGRI CATALOGUE (Bird We consider the 2nd IBIS/ISGRI CATALOGUE (Bird et al. 2005): survey of the 50% of the Galaxy, from et al. 2005): survey of the 50% of the Galaxy, from

20 to 40 KeV20 to 40 KeV

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 andall the sources whose spectrum is typical of a NS

ONLY 3 SOURCES in the IBIS/ISGRI ONLY 3 SOURCES in the IBIS/ISGRI catalogue catalogue

(6 expected in the Galaxy)(6 expected in the Galaxy)have 10have 103636<Lx<10<Lx<103939 erg s erg s-1-1 , and are no , and are no

HMXBs/LMXBsHMXBs/LMXBs4466

Comparison with observations: Comparison with observations: THIN DISK THIN DISK ONLY 3 SOURCES in the IBIS/ISGRI catalogue ONLY 3 SOURCES in the IBIS/ISGRI catalogue

(6 expected in the Galaxy)(6 expected in the Galaxy)have 10have 103636<Lx<10<Lx<103939 erg s erg s-1-1 , and are no HMXBs/LMXBs , and are no HMXBs/LMXBs

Sources with 10Sources with 103636<Lx<10<Lx<103939 erg s erg s-1-1 , in our , in our simulations: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 The upper limit is • • = 10= 10-4-4-10-10-3-3 bb for a DMM profile for a DMM profile

or or • • = 10= 10-3-3-10-10-2-2 bb for a NFW profile for a NFW profile

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Comparison with observations: ADAF Comparison with observations: ADAF disk disk ONLY 3 SOURCES in the IBIS/ISGRI catalogue ONLY 3 SOURCES in the IBIS/ISGRI catalogue

(6 expected in the Galaxy)(6 expected in the Galaxy)have 10have 103636<Lx<10<Lx<103939 erg s erg s-1-1 , and are no HMXBs/LMXBs , and are no HMXBs/LMXBs

Sources with 10Sources with 103636<Lx<10<Lx<103939 erg s erg s-1-1 , in our , in our simulations: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 The upper limit is • • = 10= 10-3-3-10-10-2-2 bb for a DMM profile for a DMM profile

or or • • = 10= 10-1-1 bb for a NFW profile for a NFW profile

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Conclusions: Conclusions: We studied IMBHs accreting molecular/atomic gas through N-body simulations of the Milky Way.

The upper limit of the IMBH density obtained by requiring that no ULX is present in our simulation is 1010-3-3 bb (DMM profile;104 IMBHs in the Milky Way)

for the THIN DISK model and 1010-1-1 bb (DMM profile;

106 IMBHs in the Milky Way) for the ADAF model

If we also consider NON-ULTRA-LUMINOUS X-ray sources, the upper limit is ~1010-3-3 bb (DMM) for the

THIN DISK model and 1010-3-3 -10 -10-2-2 bb (DMM) for the

ADAF

The main uncertainty is the radiative efficiency: do the IMBHs accrete via THIN or ADAF disk (if any) ?

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Future: Future:

Our limit is the mass of IMBHS (104 Msun) in our simulations.

Approximatively, we can extend our results (for the ULXs) to lower BH masses using an equation by Mii & Totani (2005)

However, we need higher resolution, in our simulations, to consider lower IMBH masses and to study the effects of DYNAMICAL FRICTION

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Thank youThank you

What are the IMBHs?What are the IMBHs?

BHs with mass ~ 20- 5 x 10BHs with mass ~ 20- 5 x 1044 Msun Msun

What is their origin?What is their origin?

- runaway collapse of stars in young - runaway collapse of stars in young clusters clusters (Portegies Zwart & McMillan 2002)(Portegies Zwart & McMillan 2002)

- repeated mergers of a binary BH seed - repeated mergers of a binary BH seed with BHs and stars in globular clusters with BHs and stars in globular clusters (Miller & Hamilton 2002)(Miller & Hamilton 2002)

- remnants of first massive stars - remnants of first massive stars (Heger (Heger et al. 2002)et al. 2002)

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IMBHs: - HALO population: NFW or Diemand, Madau & Moore (2005; DMM)

for IMBHs born in a fluctuation

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IMBHs: - DENSITY of IMBHs (Volonteri et al. 2003):

- NUMBER of IMBHs in the Milky Way

- 1 04 Msun each one:

- different densities: 0.1-10-5 b (106 - 500 IMBHs)

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Mii & Totani (2005)Mii & Totani (2005)

The constraint (THIN DISK)•• =10=10-3-3 bb

corresponding to 104Msun IMBHs

becomes•• =10=10-2-2 bb if we consider 103Msun IMBHs

Can we extend to lower IMBH Can we extend to lower IMBH masses?masses?

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Agol & Kamionkowski Agol & Kamionkowski (2002)(2002)Formation of an accretion disK:

Accreted angular momentum

Accretion radius

Density fluctuations of the gas

Keplerian angular momentum due to the BH

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• = 10-3 b DMM NX = 45 +/-

12• = 10-1 b DMM NX = 4056

+/- 125

• = 10-3 b NFW NX = 5 +/- 4

• = 10-1 b NFW NX = 495 +/-

39These are non-pulsated, variable sources, maybe transient, with 1031<Lx<1039 erg s-1 and faint optical counterpart (absorption)

What kind of observed Galactic sources What kind of observed Galactic sources could correspond to them?could correspond to them?

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LUMINOSITY FUNCTIONS:

Mii & Totani (2005) 5757

BH SPECTRUM (no accretion disc):

Beskin & Karpov 2005

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DMM profile :

Diemand, Madau, Moore 20055959

DMM profile :

NFW:

DMM:

Diemand, Madau, Moore 2005

Navarro, Frenk, White 1996

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Luminosity distributionLuminosity distributionComparison with Comparison with

observations:observations:

+= Antennae (Brassington et al. 2005)

•• = simulations 6161

IMBH density:IMBH density:

Volonteri et al. (2003)

Shapiro (2005); Volonteri & Rees (2005) 6262



Milky Way:- 1.3 x1012 Msun NFW rigid halo- 4 x 1010 Msun disk- 1 010 Msun bulge


IMBHs: - HALO population: NFW or Diemand, Madau & Moore (2005; DMM)

- 1 04 Msun each one

- different densities: 0.1-10-5 b

(106 - 500 IMBHs)6363

Van den Bosch et al. Van den Bosch et al. 20052005

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What the host globular cluster?

We consider a LOOSE cluster (M4)

- v1D = 3.5 km/s (Peterson, Rees & Cudworth1995)

- n ~ 2 x 10^4 #/pc^3

- nearest GC!

- data from Richer et al. 2004

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Energetic exchanges:

M1=100 Msun; M2=50 Msun

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Energetic exchanges:

M1=50-100 Msun; M2=10-50 Msun 6767


The choice of the maximum impact parameter (bmax)

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HARD HARD BINARIES :=BINARIES :=

FINAL FINAL VELOCITIES:VELOCITIES:

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FEBO (FEw BOdy Interactions; Colpi, Mapelli &

Possenti 2003)Integrator Runge Kutta 5th order

INITIAL PARAMETERs:

- imperturbed relative velocity u between binary CM and star homogeneous in u

- impact parameter homogeneous in b2

- 3 orientation angles

- phasis of the binary (Hut & Bahcall 1983)

3- and 4-body interactions

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The choice of the maximum impact parameter (bmax)All the events with non-negligible energetic exchange must be considered

We find bmax from the cross-sections by imposing thatall the encounterswith E/E >10-3

are simulated

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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

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Dynamical constraints on the Intermediate Mass Black Holes (IMBHs)

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