Using Broad Disk Emission Lines as
Diagnostics to Fit for the
Spin of a Black Hole with the New Models kerrdisk and kerrconv
Laura W. Brenneman and Christopher S. Reynolds
(University of Maryland,
College Park)
Abstract
We present an analysis of the observed broad iron line feature and
putative warm absorber in the long 2001 XMM-Newton observation
of the Seyfert-1.2 galaxy MCG-6-30-15. The new kerrdisk model
we have designed for simulating line emission from accretion disk
systems allows black hole spin to be a free parameter in the fit,
enabling the user to formally constrain the angular momentum of a
black hole, among other physical parameters of the system. In an
important extension of previous work, we derive constraints on the
black hole spin in MCG-6-30-15 using a self-consistent model for
X-ray reflection from the surface of the accretion disk while
simultaneously accounting for absorption by dusty photoionized
material along the line of sight (the warm absorber). Even including
these complications, the XMM-Newton/EPIC-pn data require extreme
relativistic broadening of the X-ray reflection spectrum; assuming no
emission from within the radius of marginal stability, we derive a
formal constraint on the dimensionless black hole spin parameter of
a > 0.987 at 90% confidence. The principal
unmodeled effect that can significantly reduce the inferred black hole
spin is powerful emission from within the radius of marginal
stability. Although significant theoretical developments are required
to fully understand this region, we argue that the need for a rapidly
spinning black hole is robust to physically plausible levels of
emission from within the radius of marginal stability. In particular,
we show that a non-rotating black hole is strongly ruled out.
Postscript file
of journal paper (1.3 Mb)
PDF file of
journal paper (802 kb)
Downloadable Files
In order to run the kerrdisk or kerrconv models, the user must
download the model codes spin.f and spinconv.f, as well as
their lmodel.dat entries (lmodel_chunk.dat) for use
in XSPEC. Additionally, since kerrdisk refers to a table of
calculated photon transfer funtions (kerrtable.dat), this table must
also be downloaded. All files should be placed in the user's local
models directory ($LMODDIR), and will become active when XSPEC is
recompiled. The user must also edit the spin.f file to specify the
full path to kerrtable.dat in the local models directory where indicated.
The lmodel.dat entries should be placed in the user's
lmodel.dat file, already in this directory. For documentation on
downloading, installing and compiling XSPEC software, click here .
Whenever using these models or
presenting results obtained through use of these models, please
reference the journal paper (Brenneman & Reynolds, 2006, ApJ, in
press).
kerrdisk (spin.f, 12 kb)
kerrconv (spinconv.f, 3 kb)
lmodel.dat entries for
each (lmodel_chunk.dat, 1 kb)
Reference table
(kerrtable.dat, 40 Mb)
Model Use and Syntax
The additive model kerrdisk has ten input parameters to be
specified by the user: (1) rest frame line energy in keV, (2)
emissivity index for the inner disk, (3) emissivity index for the
outer disk, (4) break radius separating the inner and outer portions
of the disk in units of gravitational radii, (5) dimensionless black
hole spin, (6) disk inclination angle to the line of sight in degrees,
(7) inner radius of the disk in units of the radius of marginal
stability (r_ms), (8) outer radius of the disk in units of r_ms,
(9) cosmological redshift of the source, and (10) normalization (flux)
of the line in photons per square centimeter per second. The
convolution model kerrconv has the same basic set of
parameters, but because it uses a kerrdisk kernel to smear
the entire spectrum with relativistic effects, it does not require an
input line energy or a normalization (flux) parameter. When called,
the model takes several seconds to return a line profile for a given
set of input parameters as it refers to the table of photon transfer
functions and linearly interpolates between TF values along the line.
As a result, when fitting, both kerrdisk and
kerrconv can take several hours to run, depending on the
number of iterations required by the fit. The models are therefore
best used when one already has an idea of the parameter space involved
in the data being used, i.e. as a more precise follow-up fit after
models such as laor and diskline have already been
employed for a first look.
Revisions
18th January 2008 : Modified to improve portability to MAC Intel
For further details and discussion, please refer to the journal
paper, linked above.