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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
Chandrasekhar mass
NS star mass limit
J1614-2230, M = 1.97 +-0.04 MO (Demorest et al. 2010)
Casares 2006
GRS1915+105
J1614-2230
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.
(ATHENA)
600
8
For AGNs one can also use accretion disk theory
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
Schoedel et al. 2002, Nature, 419, 694
Ghez et al. 2005, ApJ, 620, 744
Ghez et al. 2008, ApJ, 689, 1044
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
MBH = (3.0 ± 1.5)×107
M☉
The SMBH in M87
MBH = (3.2 ± 0.9)×109 M☉
Macchetto et al. 1997
Microwave Amplification thru Stimulated Emission
of Radiation (MASER)
NGC4258 (a.k.a. M106, 7 Mpc), Hα images
Kitt Peak 0.9m telescope
HST WFPC
Ford et al. 1986; Cecil et al. 2000; Ferrarese & Ford 2005
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
Water maser at 22 GHz observed with VLBI in NGC4258
Miyoshi et al. 1995
NGC4258 (7 Mpc)
Water megamasers
observed at 22 GHz
with the VLBA:
mas
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 inactive
Galaxies. One can
rely upon the MBH - 
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: 523-624 (2005)
[arXiv:astro-ph/0411247]
See also:
John Kormendy & Douglas Richstone
Inward Bound: the search for Supermassive Black
Holes in Galactic Nuclei
ARA&A, 33, 581 (2005)