# 4.1.9. 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).