- apec
- atable
- bbody
- bbodyrad
- bexrav
- bexriv
- bknpower
- bkn2pow
- bmc
- bremss
- c6mekl
- c6pmekl
- c6pvmkl
- c6vmekl
- cemekl
- cevmkl
- cflow
- compbb
- compLS
- compST
- compTT
- cutoffpl
- disk
- diskbb
- diskline
- diskm
- disko
- diskpn
- equil
- expdec
- gaussian
- gnei
- grad
- grbm
- laor
- lorentz
- meka
- mekal
- mkcflow

apec

An emission spectrum from collisionally-ionized diffuse gas calculated using the APEC code v1.3.1. More information can be found at http://hea-www.harvard.edu/APEC/ which should be consulted by anyone running this model. By default this model reads atomic physics data from the files apec_v1.3.1_coco.fits and apec_v1.3.1_line.fits in the spectral/xspec/manager file. Different files can be specified by using the command xset set APECROOT. There are three options. APECROOT can be set to a version number (eg 1.2.0). In this case the value of APECROOT will be used to replace 1.3.1 in the name of the standard files and the resulting files will be assumed to be in the spectral/xspec/manager directory. Alternatively, a filename root (eg apec_v1.2.0) can be given. This root will be used as a prefix for the _coco.fits and _line.fits in the manager directory. Finally, if neither of these work then the model will assume that the APECROOT value gives the complete directory path e.g. XSPEC> xset APECROOT /foo/bar/apec_v1.2.0 will use /foo/bar/apec_v1.2.0_coco.fits and /foo/bar/apec_v1.2.0_line.fits as input files.

par1 |
= | plasma temperature in keV | |||

par2 |
= | Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Relative abundances are set by the abund command. | |||

par3 |
= | redshift, z | |||

K |
= |
,
where D_{A} is the angular size distance to the
source (cm), n_{e} and n_{H} are the electron and H densities (cm^{-3}) |

atable

XSPEC>model atable{mymod.mod}

uses `mymod.mod` as the input for the model. For specifications of the table
model file, see the OGIP memo 92-009 on the FITS file format for table model
files (available on the WWW or by anonymous ftp from
ftp://legacy.gsfc.nasa.gov/caldb/docs/memos. Example additive table
model files are mekal.mod and raysmith.mod in $XANADU/spectral/xspec/manager
and testpo.mod in $XANADU/src/spectral/session.

bbody

where :

par1 |
= | temperature kT in keV | |||

K |
= | L_{39}/ D_{10}^{2}, where L_{39} is the source luminosity in units
of 10^{39} ergs/sec and D_{10} is the distance to the source in
units of 10 kpc |

bbodyrad

where :

par1 |
= | temperature kT in keV | |||

K |
= | R_{km}^{2}/D_{10}^{2}, where R_{km} is the source radius in km
and D_{10} is the distance to the source in units of 10 kpc |

bexrav

par1 |
= | Gamma1, first power law photon index | |||

par2 |
= | E_{break}, break energy (keV) |
|||

par3 |
= | Gamma2, second power law photon index | |||

par4 |
= | E_{c}, the e-folding energy in keV (if E_{c}=0 there is no cutoff) |
|||

par5 |
= |
rel_{refl}, reflection scaling factor (1 for isotropic source above
disk) |
|||

par6 |
= | redshift, z |
|||

par7 |
= | abundance of elements heavier than He relative to the solar abundances | |||

par8 |
= | iron abundance relative to the above | |||

par9 |
= | cosine of inclination angle | |||

K |
= | photon flux at 1 keV of the cutoff broken power-law only (no reflection) in the observed frame. |

bexriv

Broken power-law spectrum multiplied by exponential high-energy cutoff,
,
and reflected from ionized material. See Magdziarz &
Zdziarski 1995, MNRAS, 273, 837 for details. Ionization and opacities
of the reflecting medium is computed as in the procedure absori. The
output spectrum is the sum of an e-folded broken power law and the
reflection component. The reflection component alone can be obtained
for
*rel*_{refl} < 0. Then the actual reflection normalization is
|*rel*_{refl}|. Note that you need to change then the limits of
*rel*_{refl}excluding zero (as then the direct component appears). If *E*_{c} = 0,there is no cutoff in the power law. The metal and iron abundances are
variable with respect to those set by a command 'abund'. Send questions
or comments to aaz@camk.edu.pl.

par1 |
= | Gamma1, first power law photon index | |||

par2 |
= | E_{break}, break energy (keV) |
|||

par3 |
= | Gamma2, second power law photon index | |||

par4 |
= | E_{c}, the e-folding energy in keV (if E_{c}=0 there is no cutoff) |
|||

par5 |
= |
rel_{refl}, reflection scaling factor (1 for isotropic source above
disk) |
|||

par6 |
= | redshift, z |
|||

par7 |
= | abundance of elements heavier than He relative to the solar abundances | |||

par8 |
= | iron abundance relative to the above | |||

par9 |
= | cosine of inclination angle | |||

par10 |
= | disk temperature in K | |||

par11 |
= | disk ionization parameter,
where F_{ion} is the
5 eV - 20 keV irradiating flux, n is the density of the reflector;
see Done et al., 1992, ApJ, 395, 275 |
|||

K |
= | photon flux at 1 keV of the cutoff broken power-law only (no reflection) in the observed frame. |

bknpower

where :

par1 |
= | power law photon index for E < break energy | |||

par2 |
= | break point for the energy in keV | |||

par3 |
= | power law photon index for E > break energy | |||

K |
= | photons/keV/cm^{2}/s at 1 keV |

bkn2pow

where :

par1 |
= | power law photon index for E < first break energy | |||

par2 |
= | first break point for the energy in keV | |||

par3 |
= | power law photon index for E between two break energies | |||

par4 |
= | second break point for the energy in keV | |||

par5 |
= | power law photon index for E > second break energy | |||

K |
= | photons/keV/cm^{2}/s at 1 keV |

bmc

par1 |
= | Temperature of thermal photon source in keV. | |||

par2 |
= | Energy spectral index alpha. | |||

par3 |
= | Log of the A parameter. Note that f in Borozdin et al 1999 and
Shrader & Titarchuk 1999 is
10^{par(3)}. |
|||

K |
= | A_{N} defined in in Borozdin et al 1999 and Shrader & Titarchuk (1999) |

bremss

par1 |
= | plasma temperature in keV | |||

K |
= |
,
where D is the distance to the source (cm) and n_{e}, n_{I}
are the electron and ion densities (cm^{-3}) |

c6mekl

A multi-temperature mekal model using sixth-order Chebyshev polynomial for the differential emission measure. The DEM is not constrained to be positive. The abundance is relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6 |
= | Chebyshev polynomial coefficients | |||

par7 |
= | H density (cm^{-3}) |
|||

par8 |
= | abundance wrt to Solar | |||

par9 |
= | Redshift | |||

par10 |
= | 0 calculate, 1 interpolate | |||

K |
= |
,
where D_{A} is the angular size distance to the source (cm),
n_{e} is the electron density (cm^{-3}),
and n_{H} is the hydrogen density (cm^{-3}) |

c6pmekl

A multi-temperature mekal model using the exponential of a sixth-order Chebyshev polynomial for the differential emission measure. (see e.g. Lemen et al. ApJ 341, 474, 1989). The abundance is relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6 |
= | Chebyshev polynomial coefficients | |||

par7 |
= | H density (cm^{-3}) |
|||

par8 |
= | abundance wrt to Solar | |||

par9 |
= | Redshift | |||

par10 |
= | 0 calculate, 1 interpolate | |||

K |
= |
,
where D_{A} is the angular size distance to the source (cm), n_{e} is the electron
density (cm^{-3}), and n_{H} is the hydrogen density (cm^{-3}) |

c6pvmkl

A multi-temperature, variable abundance mekal model using the exponential of a sixth order Chebyshev polynomial for the differential emission measure (eg Lemen etal. ApJ 341, 474, 1989). The abundances are relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6 |
= | Chebyshev polynomial coefficients | |||

par7 |
= | H density (cm^{-3}) |
|||

par8 - par21 |
= | Abundances of He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command) | |||

par22 |
= | Redshift | |||

par23 |
= | 0 calculate, 1 interpolate | |||

K |
= |
,
where D_{A} is the angular size distance to the source (cm), n_{e} is the electron
density (cm^{-3}), and n_{H} is the hydrogen density (cm^{-3}) |

c6vmekl

A multi-temperature, variable-abundance mekal model using the sixth-order Chebyshev polynomial for the differential emission measure. The DEM is not constrained to be positive. The abundances are relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6 |
= | Chebyshev polynomial coefficients | |||

par7 |
= | H density (cm^{-3}) |
|||

par8- par21 |
= | Abundances of He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command) | |||

par22 |
= | Redshift | |||

par23 |
= | 0 calculate, 1 interpolate | |||

K |
= |
,
where D_{A} is the angular size distance to the source (cm), n_{e} is the electron
density (cm^{-3}), and n_{H} is the hydrogen density (cm^{-3}) |

cemekl

A multi-temperature plasma emission model built from the mekal code. Emission measures follow a power-law in temperature (ie emission measure from temperature T is proportional to . The abundance ratios are set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.

par1 |
= | index for power-law emissivity function | |||

par2 |
= | maximum temperature | |||

par3 |
= | nH (cm^{-3}) |
|||

par4 |
= | Abundance relative Solar | |||

par5 |
= | Redshift | |||

par6 |
= | 0 calculate, 1 interpolate | |||

K |
= | Normalization |

cevmkl

A multi-temperature plasma emission model built from the mekal code. Emission measures follow a power-law in temperature (ie emission measure from temperature T is proportional to . The abundances are relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.

par1 |
= | index for power-law emissivity function | |||

par2 |
= | maximum temperature | |||

par3 |
= | nH (cm^{-3}) |
|||

par4- par17 |
= | Abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command) | |||

par18 |
= | Redshift | |||

par19 |
= | 0 calculate, 1 interpolate | |||

K |
= | Normalization |

cflow

par1 |
= | index for power-law emissivity function | |||

par2 |
= | low temperature (keV) | |||

par3 |
= | high temperature (keV) | |||

par4 |
= | abundance relative Solar | |||

par5 |
= | redshift | |||

K |
= | Mass accretion rate (solar mass/yr) |

compbb

par1 |
= | blackbody temperature (keV) | |||

par2 |
= | electron temperature of the hot plasma (keV) | |||

par3 |
= | optical depth of the plasma | |||

K |
= | L_{39}^{2}/D_{10}^{2}, where L_{39} is the source
luminosity in units of 10^{3}9 ergs/sec and D_{10} is the distance to the source in
units of 10 kpc (the same definition as for the bbodyrad model) |

compLS

par1 |
= | temperature in keV | |||

par2 |
= | optical depth | |||

K |
= | Normalization |

compST

par1 |
= | temperature in keV | |||

par2 |
= | optical depth | |||

K |
= | , where N is the total number of photons from the source, d is the distance to the source, and f is the factor , where z is the spectral index, y is the injected photon energy in units of the temperature, and is the incomplete gamma function. | |||

= |

compTT

This is an analytic model describing Comptonization of soft photons in a
hot plasma, developed by L. Titarchuk (see ApJ, 434, 313). This replaces
the Sunyaev-Titarchuk Comptonization model in the sense that the theory
is extended to include relativistic effects. Also, the approximations used
in the model work well for both the optically thin and thick regimes. The
Comptonized spectrum is determined completely by the plasma temperature and
the so-called
parameter which is independent of geometry. The
optical depth is then determined as a function of
for a given
geometry. Thus `par5` switches between spherical and disk geometries so
that
is not a direct input here. This parameter MUST be frozen.
If
,
is obtained from the optical depth using analytic
approximation (e.g. Titarchuk 1994). If
and
,
is
obtained by interpolation from a set of accurately calculated pairs of
and
from Sunyaev & Titarchuk 1985 (A&A 143, 374).

In this incarnation of the model, the soft photon input spectrum is a Wien law [ photons] because this lends itself to a particularly simple analytical form of the model. For present X-ray detectors this should be adequate. Note that in energy flux space the peak of the Wien law occurs at 3kT as opposed to 2.8kT for a blackbody.

The plasma temperature may range from 2-500 keV, but the model is not valid for simultaneously low temperatures and low optical depth, or for high temperatures and high optical depth. The user is strongly urged to read the following references (esp. HT95 Fig 7) before and after using this model in order to fully understand and appreciate the physical assumptions made: Titarchuk, L., 1994, ApJ, 434, 313; Hua, X-M., Titarchuk, L., 1995, ApJ, 449, 188; Titarchuk, L., Lyubarskij, Y., 1995, ApJ, 450, 876.

par1 |
= | Redshift. | |||

par2 |
= | Input soft photon (Wien) temperature (keV). | |||

par3 |
= | Plasma temperature (keV). | |||

par4 |
= | Plasma optical depth. | |||

par5 |
= | Geometry switch. ABS( par5) <=1 : disk, >1: sphere.
: use analytic approx for
vs. .
: Get beta vs. tau from interpolation. |
|||

K |
= | Normalization |

cutoffpl

where :

par1 |
= | power law photon index | |||

par2 |
= | e-folding energy of exponential rolloff (in keV) | |||

K |
= | photons/keV/cm^{2}/s at 1 keV |

disk

par1 |
= | accretion rate in Eddington Luminosities | |||

par2 |
= | central mass in solar mass units | |||

par3 |
= | inner disk radius in gravitational (= 3 Schwarzschild) radii | |||

par4 |
= | distance in kpc | |||

K |
= |
,
where i is the inclination of the disk and d is
the distance in units of 10 kpc |

diskbb

par1 |
= | temperature at inner disk radius (keV) | |||

K |
= | ((Rin/km)/(D/10kpc))^{2}
,
where Rin is the inner
disk radius, D the distance to the source, and
the angle of the disk |

diskline

par1 |
= | line energy | |||

par2 |
= | power law depend. of emissivity. If this parameter is 10 or greater then the accretion disk emissivity law is used. Otherwise the emissivity scales as . | |||

par3 |
= | inner radius (units of GM/c^{2}) |
|||

par4 |
= | outer radius (units of GM/c^{2}) |
|||

par5 |
= | inclination (degrees) | |||

K |
= | photons/cm^{2}/s in the spectrum |

diskm

par1 |
= | accretion rate in Eddington luminosities | |||

par2 |
= | central mass in units of solar mass | |||

par3 |
= | inner disk radius in gravitational ( = 3 Schwarzschild) radii | |||

par4 |
= | viscosity | |||

K |
= | cos(i)/d^{2}, where i is the inclination of the disk
and d is the distance in units of 10 kpc |

disko

par1 |
= | accretion rate in Eddington luminosities | |||

par2 |
= | central mass in units of solar mass | |||

par3 |
= | inner disk radius in gravitational ( = 3 Schwarzschild) radii | |||

par4 |
= | viscosity | |||

K |
= | cos(i)/d^{2}, where i is the inclination of the disk and d is the distance in units of 10 kpc |

diskpn

Blackbody spectrum of an accretion disk. This is an extention of diskbb
model, including corrections for temperature distribution near the
black hole. The temperature distribution was calculated in
Paczynski-Wiita pseudo-Newtonian potential. An accretion rate can be
computed from the maximum temperature found. For details see
Gierlinski et al., 1999, MNRAS, 309, 496. Please note that the inner
disk radius (`par2`) can be a free parameter only close to
otherwise par2 is strongly correlated with K.

par1 |
= | maximum temperature in the disk (keV) | |||

par2 |
= | inner disk radius in
R_{g} = GM / c^{2} units,
6 <= par2 <= 1000 |
|||

K |
= |
- normalization, where M - central
mass in solar masses, D - distance to the source (kpc), i -
inclination of the disk,
- color/effective temperature ratio. |

equil

par1 |
= | plasma temperature (keV) | |||

par2 |
= | Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Abundances are given by the Anders & Grevesse mixture. | |||

par3 |
= | redshift z |
|||

K |
= |
,
where D_{A} is the angular size distance to the
source (cm), n_{e} and n_{H} are the electron and H densities (cm^{-3}) |

The references for this model are as follows :

- Borkowski, Lyerly & Reynolds, 2001, ApJ, 548, 820
- Hamilton, A.J.S., Sarazin, C. L. & Chevalier, R. A. , 1983,
ApJS, 51,115
- Borkowski, K.J., Sarazin, C.L. & Blondin, J.M. 1994, ApJ,
429, 710
- Liedahl, D.A., Osterheld, A.L. & Goldstein, W.H. 1995, ApJ, 438, L115

expdec

An exponential decay.

where:

par1 |
= | exponential factor |

gaussian

where :

par1 |
= | line energy in keV | |||

par2 |
= | line width () in keV | |||

K |
= | total photons/cm^{2}/s in the line |

gnei

par1 |
= | plasma temperature (keV) | |||

par2 |
= | Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Abundances are given by the Anders & Grevesse mixture. | |||

par3 |
= | Ionization timescale in units of s/cm^{3}. |
|||

par4 |
= | Ionization timescale averaged plasma temperature (keV). | |||

par5 |
= | redshift z |
|||

K |
= |
,
where D_{A} is the angular size distance to the
source (cm), n_{e} and n_{H} are the electron and H densities (cm^{-3}) |

grad

General Relativistic Accretion Disk model around a Schwarzschild black hole. Inner radius is fixed to be 3 Schwarzschild radii, thus the energy conversion efficiency is 0.057. See Hanawa, T., 1989, ApJ, 341, 948 and Ebisawa, K. Mitsuda, K. and Hanawa, T. 1991, ApJ, 367, 213. Several bugs were found in the old GRAD model which was included in xspec 11.0.1ae and before. Due to these bugs, it turned out that the mass obtained by fitting the old GRAD model to the observation was 1.4 times over-estimated. These bugs were fixed, and a new parameter (par6) was added to make the distinction between the old and new codes clear.

par1 |
= | distance (kpc) | |||

par2 |
= | disk inclination angle (deg; 0 for face-on) | |||

par3 |
= | mass of the central object (solar units) | |||

par4 |
= | mass accretion rate (10^{18} g/s) |
|||

par5 |
= | spectral hardening factor, T_{col}/T_{eff}. 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 and Takahara, 1995, ApJ, 445,
780 |
|||

par6 |
= | A flag to switch on/off the relativistic effects (never allowed to be free). If positive, relativistic calculation; if negative or zero, Newtonian calculation (inner radius is still fixed at 3 Schwarzschild radii, and the efficiency is 1/12). | |||

K |
= | Should be fixed to 1. |

grbm

A model for gamma-ray burst continuum spectra developed by D. Band, et. al., 1993 (ApJ 413, 281).

where:

par1 |
= | first power law index | |||

par2 |
= | second power law index | |||

par3 |
= | characteristic energy in keV | |||

K |
= | normalization constant |

laor

An emission line from an accretion disk around a black hole. Ari Laor's calculation including GR effects (ApJ 376, 90).

par1 |
= | Line energy in keV | |||

par2 |
= | power law depend. of emissivity (scales as ) | |||

par3 |
= | inner radius (units of GM/c^{2}) |
|||

par4 |
= | outer radius (units of GM/c^{2}) |
|||

par5 |
= | inclination (degrees) | |||

K |
= | photons/cm^{2}/s in the line |

lorentz

A Lorentzian line profile.

where :

par1 |
= | line energy in keV | |||

par2 |
= | line width () in keV | |||

K |
= | total photons/cm^{2}/s in the line |

meka

par1 |
= | plasma temperature in keV | |||

par2 |
= | hydrogen density in cm^{-3} |
|||

par3 |
= | Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Abundances are set by the abund command. | |||

par4 |
= | redshift, z | |||

K |
= |
,
where D_{A} is the angular size distance to the source (cm), n_{e} and n_{H} are
the electron and H densities (cm^{-3}) |

The references for the MEKA model are as follows :

- Mewe, R., Gronenschild, E.H.B.M., and van den Oord, G.H.J. 1985,
*A&AS*, 62, 197 - Mewe, R., Lemen, J.R., and van den Oord, G.H.J. 1986,
*A&AS*, 65, 511 - Kaastra, J.S. 1992, An X-Ray Spectral Code for Optically Thin Plasmas (Internal SRON-Leiden Report, updated version 2.0)

Similar credit may also be given for the adopted ionization balance

- Arnaud, M., and Rothenflug, M. 1985,
*A&AS*, 60, 425 - Arnaud, M., and Raymond, J. 1992,
*ApJ*, 398, 394

mekal

An emission spectrum from hot diffuse gas based on the model calculations of Mewe and Kaastra with Fe L calculations by Liedahl. The model includes line emissions from several elements. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.

par1 |
= | plasma temperature in keV | |||

par2 |
= | hydrogen density in cm^{-3} |
|||

par3 |
= | Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Abundances are set by the abund command. | |||

par4 |
= | redshift, z | |||

par5 |
= | 0 calculate, 1 interpolate | |||

K |
= |
,
where D_{A} is the angular size distance to the
source (cm), n_{e} and n_{H} are the electron and H densities (cm^{-3}) |

The references for the MEKAL model are as follows :

- Mewe, R., Gronenschild, E.H.B.M., and van den Oord, G.H.J. 1985,
*A&AS*, 62, 197 - Mewe, R., Lemen, J.R., and van den Oord, G.H.J. 1986,
*A&AS*, 65, 511 - Kaastra, J.S. 1992, An X-Ray Spectral Code for Optically Thin Plasmas
(Internal SRON-Leiden Report, updated version 2.0)
- Liedahl, D.A., Osterheld, A.L., and Goldstein, W.H. 1995, ApJL, 438, 115

Similar credit may also be given for the adopted ionization balance

- Arnaud, M., and Rothenflug, M. 1985,
*A&AS*, 60, 425 - Arnaud, M., and Raymond, J. 1992,
*ApJ*, 398, 394

mkcflow

par1 |
= | low temperature (keV) | |||

par2 |
= | high temperature (keV) | |||

par3 |
= | abundance relative to Solar | |||

par4 |
= | redshift | |||

par5 |
= | 0 calculate, 1 interpolate | |||

K |
= | Mass accretion rate (solar mass/yr) |