Methods and Uncertainties of
Measuring BH masses and
the SMBH in the Quasar at z=6.41
Dan Li
Feb 20, 2008
Reverberation Mapping
  Put
forward by Blandford and McKee, 1982
Reverberation Mapping
  Put
forward by Blandford and McKee, 1982
  Variations in the strength of the central
continuum source  variations in the
strength & profile of the emission-lines
Reverberation Mapping
  Time-lag
between these two variations due
to the light travel time effect 
“phase-space distribution” of the BLR gas
(i.e. its emissivity and moments of its
velocity distribution as functions of position)
Blandford & McKee. 1982
Reverberation Mapping
  Line-width
  FWHM
 Keplerian velocity of the gas
vs. Line Dispersion
(Peterson et al. 2004)
Reverberation Mapping
  Finally,
assume that the motions of the
BLRs are dominated by gravitational field of
the central BH, then
Uncertainties of BH mass estimate
based on RM
  Uncertainties
associated with the RM iteself
 Nature and characteristics (shape, variabiliity
amplitude, etc.) of the continuum variation
 Non-linear response of many emission-lines
 Non-isotropic emissions of BLR
 Contaminations from other lines (Fe II, etc)
  more
uncertainties are introduced by
including the velocity estimates to derive the
mass
Uncertainties of BH mass estimate
based on RM
  Really
gravity-dominated?
  Evidence for Keplerian velocity:
The FWHM of various emission lines
(generate at different distances to the
central continuum source) should follow the
relation
has been tested in the case of NGC5548
Wandel et al. 1999
Reverberation Mapping
Wandel et al. 1999
Uncertainties of BH mass estimate
based on RM
  Really
gravity-dominated?
  Problem: several other models have the same
prediction
 Cloud outflows driven by photoionization when
ionization parameter in the cloud is fixed
 Disk winds driven by line scattering
 Magnetically driven disk winds
 A direct proof of gravity-dominated dynamics is
difficult
Krolik. 2001
Uncertainties of BH mass estimate
based on RM
  How
to derive the velocity from line profiles?
  Depends
on the shape and inclination
distribution of the orbits
  “Virial mass” --- isotropically oriented circular
orbits
Reverberation Mapping
  Shortage
of Reverberation Mapping:
Needs high S/N spectra and an observation
timescale of several years !
Kaspi et al. spent 7.5 years, observed 28
PG quasars, and finally got 17 RM results
Scaling Relations
  Size-Luminosity
Relation
Kaspi et al. 2000
Scaling Relations
Kaspi et al. 2000
Scaling Relations
  Mass-Luminosity
Relation
Kaspi et al. 2000
Scaling Relations
Kaspi et al. 2000
Scaling Relations
  Balmer
lines in Hydrogen spectrum
Scaling Relations
  Substitute
in UV band:
Mg II (2798Å) and C IV (1549Å)
Advantages of Mg II:
i. Similar ionization potentials to the Hβ
ii. Easy to calibrate
McLure & Jarvis. 2002
Scaling Relations
  The
UV size-luminosity relation
  Also
a one-to-one relation between the
Mg II FWHM and Hβ FWHM
McLure & Jarvis. 2002
Scaling Relations
McLure & Jarvis. 2002
Scaling Relations
  UV
mass-luminosity relation
McLure & Jarvis. 2002
Scaling Relations
McLure & Jarvis. 2002
Scaling Relations
  LBQS
& MQS
samples
McLure & Jarvis. 2002
Scaling Relations
  Mg
II vs. C IV ?
  The
mass estimates based on C IV and Hβ
agree with each other very well, while the
estimates based on Mg II are on average 5
times smaller (based on 15 high-redshift
quasars, Dietrich & Hamann, 2004)
The BH in the quasar at z=6.41
(SDSS J1148+5251)
M=3×109 M⊙
H0
Ωm
ΩΛ
z
T(z)
0.3
0.7
8.43×108
70
0.27
0.73
8.89×108
6.41
0.3
0.7
8.20×108
72
0.27
0.73
8.64×108
taccre=8.61×108yrs (initial mass=100M⊙ ,
η=0.1, accreting at Eddington rate)
The BH in the quasar at z=6.41
Willott et al. 2003
The BH in the quasar at z=6.41
Willott et al. 2003
SMBHs in other high-redshift quasars
Dietrich & Hamann. 2003
References
R. D. Blandford, C. F. McKee, 1982
H. Netzer, B. M. Peterson, 1997
A. Wandel et al., 1999
S. Kaspi et al., 2000
J. H. Krolik, 2001
R. J. McLure, M. J. Jarvis, 2002
C. J. Willott et al., 2003
M. Dietrich, F. Hamann, 2004