Lecture 16 Measurement of masses of SMBHs: Sphere of influence of a SMBH Gas and stellar dynamics, maser disks Stellar proper motions Mass vs velocity dispersion relation Reverberation mapping

GRS NS star mass limit Chandrasekhar mass J J , M = M O (Demorest et al. 2010) Casares 2006

Greiner et al. 2001, Nature, 414, 522

(erroneously thought to be at 15 Mpc, but actually at 30 Mpc!)

How can we be sure that a SMBH resides at the center of A galaxy (and not, for instance, a compact star cluster) ? For example, if we notice that the mass-to-light ratio increases Toward 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 high Inferred 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 larger Than the Schwarzschild radius.

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 (ATHENA)

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 km/s ! Very precise determination of SMBH mass: ( ) e6 M  Schoedel et al. 2002, Nature, 419, 694 Ghez et al. 2005, ApJ, 620, 744 Ghez et al. 2008, ApJ, 689, 1044

1”1”

Stellar orbits in the proximity of the Galactic Center

SMBH mass determination thru stellar dynamics Stellar dynamics is more precise than gas dynamics because Gas motion may be not Keplerian, while star orbits are always Keplerian Continuity equation (Collisionless Boltzmann Equation) And Poisson equation Many assumptions are necessary

Stellar kinematic is derived from the absorption lines Velocity profiles arcsec

Dynamical Study of M31 (770 kpc) Surface brightness Radial profile Velocity dispersion radial profile: it rises toward the nucleus The rotation curve is Keplerian And matches perfectly the Expectation of an exponential Disk M BH = (3.0 ± 1.5)×10 7 M ☉

The SMBH in M87 M BH = (3.2 ± 0.9)×10 9 M ☉ Macchetto et al. 1997

Microwave Amplification thru Stimulated Emission of Radiation (MASER)

NGC4258 (a.k.a. M106, 7 Mpc), Hα images Ford et al. 1986; Cecil et al. 2000; Ferrarese & Ford 2005 Kitt Peak 0.9m telescope HST WFPC

NGC4258: VLA map at 22 GHz Cecil et al. 2000

Water maser at 22 GHz observed with VLBI in NGC4258 Cecil et al. 2000

Water maser at 22 GHz observed with VLBI in NGC4258

Miyoshi et al. 1995

mas NGC4258 (7 Mpc) Water megamasers observed at 22 GHz with the VLBA: 1 mas = pc H 2 O is in Keplerian motion M BH ~ 4×10 7 M ☉

M BH - σ relationship Beyond cz ~ km/s (i.e. ~150 Mpc), it becomes very difficult or impossible to measure SMBH masses of inactive Galaxies. One can rely upon the M BH -  relationship Milky Way !

It is possible to measure SMBH masses in active Galaxies 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

Reverberation mapping Right: Light curves of Continuum and Emission lines Of Seyfert Galaxy NGC5548 Left: Correlation function of each Curve with the Optical 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: (2005) [arXiv:astro-ph/ ] See also: John Kormendy & Douglas Richstone Inward Bound: the search for Supermassive Black Holes in Galactic Nuclei ARA&A, 33, 581 (2005)