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Artistic concept of a HMXB: a collapsed star (NS or BH) Accretes mass from a massive O or B star

Binary mass function

Radial velocity curve of HD 226868, the O9.7Iab companion star in the HMBX Cyg X-1, folded on the 5.6-day orbital period

Phase (1 = 5.6 days)

km/s

Binary mass function of Cyg X-1: F(Mx) = 0.25 M

Mass of companion ~ 33 M

For i = 90 deg --> Mx = 7 M

It cannot be a neutron star!!

NS

sta

r m

ass

limit

Ch

and

rase

khar

mas

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(erroneously thought to beat 15 Mpc, butactually at 30 Mpc!)

How can we be sure that a SMBH resides at the center ofA galaxy (and not, for instance, a compact star cluster) ?For example, if we notice that the mass-to-light ratio increasesToward the center of the galaxy, is that a proof of SMBH?

No, it is not. It is difficult to get incontrovertible proof.

Hints are fast variability, superluminal motion, very highInferred mass densities, high luminosities….

Most importantly, we must resolve the sphere of influence of the putative central SMBH

Sphere of influence of BH

In the case of SMBHs inhabiting galactic nuclei, the “sphere of influence” is defined as the region of space within which the gravitational potential of the SMBH dominates over that of the surrounding stars.

The radius of the sphere of influence is about e6 times largerThan the Schwarzschild radius of a SMBH.

Beyond a few thousand Schwarzschild radii from the central SMBH, but within the sphere of influence, the motion of stars and gas is predominantly Keplerian (relativistic effects are minimal), with a component due to the combined gravitational potential of stars, dust, gas, dark matter, and anything else contributing mass to within that region. Beyond the sphere of influence, the gravitational dominance of the SMBH quickly vanishes.

For AGNs one can also use accretion disk theory

8600

The SMBH at the centre of our Galaxy

Sgr A* is a compact radio source: VLBI observations at 86 GHz set a limit of 1 AU on its size.

Proper motion studies with adaptive optics in K band (angular resolution of 50 mas ~ 40 AU) for ~40 stars within 1.2 arcsec of Sgr A*. Stellar orbits followed up for years, maximum approach is 45 AU, period of 15.2 yrs, velocity of 12000 km/s !

Very precise determination of SMBH mass:

(4.5+-0.4) e6 M

Ghez et al. 2005, ApJ, 620, 744Ghez et al. 2008, ApJ, 689, 1044 Schoedel et al. 2002, Nature, 419, 694

1”

Stellar orbits in the proximity of the Galactic Center

SMBH mass determination thru stellar dynamics

Stellar dynamics is more precise than gas dynamics becauseGas motion may be not Keplerian, while star orbits are alwaysKeplerian

Continuity equation (Collisionless Boltzmann Equation)And Poisson equation

Many assumptions are necessary

Stellar kinematic is derived from theabsorption lines

Velocity

profiles

arcsec

Dynamical Study of M31 (770 kpc)

Surface brightnessRadial profile

Velocity dispersion radialprofile: it rises toward thenucleus

The rotation curve is Keplerian And matches perfectly the Expectation of an exponential Disk

MBH =  (3.0 ± 1.5)×107 M☉

M87 (= Virgo A, 20 Mpc)

The SMBH in M87

MBH =  (3.2 ± 0.9)×109 M☉

Microwave Amplification thru Stimulated Emission of Radiation (MASER)

Water maser at 22 GHz observed with VLBI in NGC4258

mas

NGC4258 (7 Mpc)

Water megamasersobserved at 22 GHz with the VLBA:

1 mas = 0.035 pc

H2O is in Keplerian motion

MBH ~  4×107 M☉

MBH - σ relationship

Beyond cz ~ 10000 km/s (i.e. ~150 Mpc),it becomes very difficult or impossible to measure SMBH masses of inactiveGalaxies. One can rely upon the MBH - relationship

Milky Way !

However, it is possible to measure SMBH masses in activeGalaxies at large distances with various methods

Schematic view of an AGN

AGN have broad (FWHM of several thousands of km/s) and luminous emission lines

Reverberationmapping

Right:Light curves ofContinuum andEmission linesOf Seyfert Galaxy NGC5548

Left:Correlation function of eachCurve with theOptical continuum

Excellent review on Supermassive Black Holes:

Laura Ferrarese and Holland Ford

Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research

Space Science Reviews 116: 523-624 (2005)[arXiv:astro-ph/0411247]