kerrbb, zkerrbb: multi-temperature blackbody model for thin accretion disk around a Kerr black hole

A multi-temperature blackbody model for a thin, steady state, general relativistic accretion disk around a Kerr black hole. The effect of self-irradiation of the disk is considered, and the torque at the inner boundary of the disk is allowed to be non-zero. This model is intended as an extension to grad, which assumes that the black hole is non-rotating. For details see Li et al. (2005).

The redshift version zkerrbb has the mass accretion rate parameter in units of Solar masses per year and the distance parameter replaced by redshift.

Parameters for kerrbb:

par1 eta, ratio of the disk power produced by a torque at the disk inner boundary to the disk power arising from accretion. It must be $\geq 0$ and $\leq 1$ . When eta = 0, the solution corresponds to that of a standard Keplerian disk with zero torque at the inner boundary.

par2 specific angular momentum of the black hole in units of the black hole mass M (geometrized units G=c=1). Should be $\geq -1$ and <1.

par3 disk's inclination angle (the angle between the axis of the disk and the line of sight). It is expressed in degrees. i=0 is for a "face-on" accretion disk. i should be $\leq 85$ degree.

par4 the mass of the black hole in units of the solar mass.

par5 the “effective” mass accretion rate of the disk in units of $10^{18}$ g/s. When eta = 0 (zero torque at the inner boundary), this is just the mass accretion rate of the disk. When eta is nonzero, the effective mass accretion rate = (1+eta) times the true mass accretion rate of the disk. The total disk luminosity is then “epsilon” times “the effective mass accretion rate” times c, where epsilon is the radiation efficiency of a standard accretion disk around the Kerr black hole

par6 the distance from the observer to the black hole in units of kpc.

par7 spectral hardening factor, T $_{col}$ /T $_{eff}$ . It should be greater than 1.0, and considered to be 1.5-1.9 for accretion disks around a stellar-mass black hole. See, e.g., Shimura & Takahara (1995)

par8 a flag to switch on/off the effect of self-irradiation (never allowed to be free). Self-irradiation is included when > 0. Self-irradiation is not included when $\leq 0$ .

par9 a flag to switch on/off the effect of limb-darkening (never allowed to be free). The disk emission is assumed to be limb-darkened when >0. The disk emission is assumed to be isotropic when lflag is $\leq 0$ .

K normalization. Should be set to 1 if the inclination, mass and distance are frozen.

Parameters for zkerrbb:

par1 eta, ratio of the disk power produced by a torque at the disk inner boundary to the disk power arising from accretion. It must be $\geq 0$ and $\leq 1$ . When eta = 0, the solution corresponds to that of a standard Keplerian disk with zero torque at the inner boundary.

par2 specific angular momentum of the black hole in units of the black hole mass M (geometrized units G=c=1). Should be $\geq -1$ and <1.

par3 disk's inclination angle (the angle between the axis of the disk and the line of sight). It is expressed in degrees. i=0 is for a "face-on" accretion disk. i should be $\leq 85$ degree.

par4 the mass of the black hole in units of the solar mass.

par5 the “effective” mass accretion rate of the disk in units of $M_{\odot}$ /yr. When eta = 0 (zero torque at the inner boundary), this is just the mass accretion rate of the disk. When eta is nonzero, the effective mass accretion rate = (1+eta) times the true mass accretion rate of the disk. The total disk luminosity is then “epsilon” times “the effective mass accretion rate” times c, where epsilon is the radiation efficiency of a standard accretion disk around the Kerr black hole

par6 the redshift of the black hole.

par7 spectral hardening factor, T $_{col}$ /T $_{eff}$ . It should be greater than 1.0, and considered to be 1.5-1.9 for accretion disks around a stellar-mass black hole. See, e.g., Shimura & Takahara (1995)

par8 a flag to switch on/off the effect of self-irradiation (never allowed to be free). Self-irradiation is included when > 0. Self-irradiation is not included when $\leq 0$ .

par9 a flag to switch on/off the effect of limb-darkening (never allowed to be free). The disk emission is assumed to be limb-darkened when >0. The disk emission is assumed to be isotropic when lflag is $\leq 0$ .

K normalization. Should be set to 1 if the inclination, mass and distance are frozen.

par1	eta, ratio of the disk power produced by a torque at the disk inner boundary to the disk power arising from accretion. It must be $\geq 0$ and $\leq 1$ . When eta = 0, the solution corresponds to that of a standard Keplerian disk with zero torque at the inner boundary.
par2	specific angular momentum of the black hole in units of the black hole mass M (geometrized units G=c=1). Should be $\geq -1$ and <1.
par3	disk's inclination angle (the angle between the axis of the disk and the line of sight). It is expressed in degrees. i=0 is for a "face-on" accretion disk. i should be $\leq 85$ degree.
par4	the mass of the black hole in units of the solar mass.
par5	the “effective” mass accretion rate of the disk in units of $10^{18}$ g/s. When eta = 0 (zero torque at the inner boundary), this is just the mass accretion rate of the disk. When eta is nonzero, the effective mass accretion rate = (1+eta) times the true mass accretion rate of the disk. The total disk luminosity is then “epsilon” times “the effective mass accretion rate” times c, where epsilon is the radiation efficiency of a standard accretion disk around the Kerr black hole
par6	the distance from the observer to the black hole in units of kpc.
par7	spectral hardening factor, T $_{col}$ /T $_{eff}$ . It should be greater than 1.0, and considered to be 1.5-1.9 for accretion disks around a stellar-mass black hole. See, e.g., Shimura & Takahara (1995)
par8	a flag to switch on/off the effect of self-irradiation (never allowed to be free). Self-irradiation is included when > 0. Self-irradiation is not included when $\leq 0$ .
par9	a flag to switch on/off the effect of limb-darkening (never allowed to be free). The disk emission is assumed to be limb-darkened when >0. The disk emission is assumed to be isotropic when lflag is $\leq 0$ .
K	normalization. Should be set to 1 if the inclination, mass and distance are frozen.