4.1.11. Dbb: disk blackbody model¶
We take the model for a standard Shakura-Sunyaev accretion disk. The radiative losses from such a disk are given by
where is the loss term in W m
at radius
,
the mass of the central object,
the
accretion rate through the disk and
the inner radius. If
this energy loss is radiated as a black body, we have
with the constant of Stefan-Boltzmann and
the local temperature of the black body. The total spectrum of such a
disk is then obtained by integration over all radii. We do this
integration numerically. Note that for large
,
.
Warning
A popular disk model (diskbb in XSPEC) assumes this
temperature dependence over the full disk. However, we correct it using
the factor in
which corresponds to
the torque-free condition at the inner boundary of the disk.
The photon spectrum of the disk is now given by
where is the inclination of the disk (0 degrees for face-on
disk, 90 degrees for an edge-on disk),
the photon energy,
the outer edge of the disk, and
is defined by
(1)¶
and further the function is defined by
where is defined by
.
In addition to calculating the spectrum, the model also allows to
calculate the average radius of emission at a specified
energy
. This is sometimes useful for time variability
studies (softer photons emerging from the outer parts of the disk).
Given the fit parameters and
, using
(1) it is straightforward to calculate the
product
. Further note that if
, it
is possible to find both
and
, provided the
inclination angle
is known.
The parameters of the model are:
- norm:
Normalisation
(
), in units of
. Default value: 1.
- t:
The nominal temperature
in keV. Default value: 1 keV.
- ro:
The ratio of outer to inner disk radius,
- ener:
Energy
at which the average radius of emission will be calculated
- rav:
Average radius
of all emission at energy
specified by the parameter above. Note that this is not a free parameter, it is calculated each time the model is evaluated.
Recommended citation: Shakura & Sunyaev (1973).