Compute FRED light curves of LMXBs outbursts
Project description
Freddi — compute FRED-like light curves of LMXB
Table of contents
- Overview
- Installation
- Usage
- Physical Background
- Accretion disk wind
- Questions and comments
- License
- BibTex
Overview
The code solves 1-D evolution equation of Shakura-Sunyaev accretion disk. The code is developed to simulate fast-rise exponential-decay (FRED) light curves of low mass X-ray binaries (LMXBs) for the paper “Determination of the turbulent parameter in the accretion disks: effects of self-irradiation in 4U 1543-47 during the 2002 outburst” by Lipunova & Malanchev (2017) 2017MNRAS.468.4735L.
Freddi is written on C++ and available as a couple of binary executables and
Python 3 module.
Installation
Executables
Freddi is represented by two binary executables: the black hole version
freddi and the neutron star version freddi-ns.
Docker
If you are familiar with Docker then you can use pre-compiled binaries inside Docker container:
docker run -v "`pwd`":/data --rm -ti ghcr.io/hombit/freddi freddi -d/data
docker run -v "`pwd`":/data --rm -ti ghcr.io/hombit/freddi freddi-ns --Bx=1e8 -d/data
Build from source
Freddi has following build dependencies:
- Boost 1.57+
- CMake) with any back-end like Make or Ninja
- C++ compiler with C++11 support, e.g.
gccversion 8+ orclang5+
Get requirements on Debian based systems (e.g. Ubuntu):
apt-get install g++ cmake libboost-all-dev
On Red-Hat based systems (e.g. Fedora):
dnf install gcc-c++ cmake boost-devel
Get Freddi source code and compile it:
git clone https://github.com/hombit/freddi
cd freddi
mkdir cmake-build
cd cmake-build
cmake .. # -DSTATIC_LINKING=TRUE
cmake --build .
Uncomment -DSTATIC_LINKING=TRUE to link against static Boost libraries
Now you should have both freddi and freddi-ns executables in the build
directory. You can install these binaries and the default configuration
file freddi.ini by running
cmake --install . --prefix=PREFIX # replace with preferable location
Freddi is known to be built on Linux and macOS.
Python 3
Freddi pre-compiled x86-64 Linux packages for several Python versions
are available on https://pypi.org/project/freddi/ and can be used as is,
while for other systems you should have C++ compiler and Boost
libraries in your system (see executable requirements section
for details) before running this command:
# Please, upgrade your pip
python3 -m pip install -U pip
# Depending on your Python setup, you need or need not --user flag:
python3 -m pip install --user freddi
Usage
Freddi runs from the command line with inline options and/or with a configuration file. Freddi
outputs file freddi.dat with distribution of various physical values over
time. If --fulldata is specified then files freddi_%d.dat for each time step
are created in the same directory with snapshot radial distributions. These
data-files contain whitespace-separated data columns with header lines starting
with # symbol. You can set another prefix instead of freddi with --prefix
option and change the output directory with --dir option. If you choose the
Docker way and would like to specify the directory, then avoid using --dir
option and just replace "`pwd`" with some local path (for more details see
Docker documentation).
Options
The full list of command line options is viewed with --help option. Default
values are given in brackets.
./freddi --help
expand
Freddi: numerical calculation of accretion disk evolution:
General options:
-h [ --help ] Produce help message
--config arg Set additional configuration filepath
--prefix arg (=freddi) Set prefix for output filenames. Output
file with distribution of parameters
over time is PREFIX.dat
-d [ --dir ] arg (=.) Choose the directory to write output
files. It should exist
--precision arg (=12) Number of digits to print into output
files
--fulldata Output files PREFIX_%d.dat with radial
structure for every time step. Default
is to output only PREFIX.dat with
global disk parameters for every time
step
Basic binary and disk parameter:
-a [ --alpha ] arg Alpha parameter of Shakura-Sunyaev
model
--alphacold arg Alpha parameter of cold disk, currently
it is used only for Sigma_minus, see
--Qirr2Qvishot. Default is --alpha
values divided by ten
-M [ --Mx ] arg Mass of the central object, in the
units of solar masses
--kerr arg (=0) Dimensionless Kerr parameter of the
black hole
--Mopt arg Mass of the optical star, in units of
solar masses
--rochelobefill arg (=1) Dimensionless factor describing a size
of the optical star. Polar radius of
the star is rochelobefill * (polar
radius of critical Roche lobe)
--Topt arg (=0) Thermal temperature of the optical
star, in units of kelvins
-P [ --period ] arg Orbital period of the binary system, in
units of days
--rin arg Inner radius of the disk, in the units
of the gravitational radius of the
central object GM/c^2. If it isn't set
then the radius of ISCO orbit is used
defined by --Mx and --kerr values
-R [ --rout ] arg Outer radius of the disk, in units of
solar radius. If it isn't set then the
tidal radius is used defined by --Mx,
--Mopt and --period values
--risco arg Innermost stable circular orbit, in
units of gravitational radius of the
central object GM/c^2. If it isn't set
then the radius of ISCO orbit is used
defined by --Mx and --kerr values
Parameters of the disk mode:
-O [ --opacity ] arg (=Kramers) Opacity law: Kramers (varkappa ~ rho /
T^7/2) or OPAL (varkappa ~ rho / T^5/2)
--Mdotout arg (=0) Accretion rate onto the disk through
its outer radius
--boundcond arg (=Teff) Outer boundary movement condition
Values:
Teff: outer radius of the disk moves
inwards to keep photosphere temperature
of the disk larger than some value.
This value is specified by --Thot
option
Tirr: outer radius of the disk moves
inwards to keep irradiation flux of the
disk larger than some value. The value
of this minimal irradiation flux is
[Stefan-Boltzmann constant] * Tirr^4,
where Tirr is specified by --Thot
option
--Thot arg (=0) Minimum photosphere or irradiation
temperature at the outer edge of the
hot disk, Kelvin. For details see
--boundcond description
--Qirr2Qvishot arg (=0) Minimum Qirr / Qvis ratio at the outer
edge of the hot disk to switch
evolution from temperature-based regime
to Sigma_minus-based regime (see Eq.
A.1 in Lasota et al. 2008, --alphacold
value is used as alpha parameter)
--initialcond arg (=powerF) Type of the initial condition for
viscous torque F or surface density
Sigma
Values:
powerF: F ~ xi^powerorder, powerorder
is specified by --powerorder option
linearF: F ~ xi, specific case of
powerF but can be normalised by
--Mdot0, see its description for
details powerSigma: Sigma ~
xi^powerorder, powerorder is specified
by --powerorder option
sineF: F ~ sin( xi * pi/2 )
gaussF: F ~ exp(-(xi-mu)**2 / 2
sigma**2), mu and sigma are specified
by --gaussmu and --gausssigma options
quasistat: F ~ f(h/h_out) * xi *
h_out/h, where f is quasi-stationary
solution found in Lipunova & Shakura
2000. f(xi=0) = 0, df/dxi(xi=1) = 0
Here xi is (h - h_in) / (h_out - h_in)
--F0 arg Initial maximum viscous torque in the
disk, dyn*cm. Can be overwritten via
--Mdisk0 and --Mdot0
--Mdisk0 arg Initial disk mass, g. If both --F0 and
--Mdisk0 are specified then --Mdisk0 is
used. If both --Mdot0 and --Mdisk0 are
specified then --Mdot0 is used
--Mdot0 arg Initial mass accretion rate through the
inner radius, g/s. If --F0, --Mdisk0
and --Mdot0 are specified then --Mdot0
is used. Works only when --initialcond
is set to linearF, sinusF or quasistat
--powerorder arg Parameter for the powerlaw initial
condition distribution. This option
works only with --initialcond=powerF or
powerSigma
--gaussmu arg Position of the maximum for Gauss
distribution, positive number not
greater than unity. This option works
only with --initialcond=gaussF
--gausssigma arg Width of for Gauss distribution. This
option works only with
--initialcond=gaussF
Parameters of self-irradiation.
Qirr = Cirr * (H/r / 0.05)^irrindex * L * psi / (4 pi R^2), where psi is angular distrbution of X-ray radiation:
--Cirr arg (=0) Irradiation factor for the hot disk
--irrindex arg (=0) Irradiation index for the hot disk
--Cirrcold arg (=0) Irradiation factor for the cold disk
--irrindexcold arg (=0) Irradiation index for the cold disk
--h2rcold arg (=0.050000000000000003) Seme-height to radius ratio for the
cold disk
--angulardistdisk arg (=plane) Angular distribution of the disk X-ray
radiation. Values: isotropic, plane
Parameters of flux calculation:
--colourfactor arg (=1.7) Colour factor to calculate X-ray flux
--emin arg (=1) Minimum energy of X-ray band, keV
--emax arg (=12) Maximum energy of X-ray band, keV
--staralbedo arg (=0) Part of X-ray radiation reflected by
optical star, (1 - albedo) heats star's
photosphere. Used only when --starflux
is specified
-i [ --inclination ] arg (=0) Inclination of the system, degrees
--ephemerist0 arg (=0) Ephemeris for the time of the minimum
of the orbital light curve T0, phase
zero corresponds to inferior
conjunction of the optical star, days
--distance arg Distance to the system, kpc
--colddiskflux Add Fnu for cold disk into output file.
Default output is for hot disk only
--starflux Add Fnu for optical star into output
file. Mx, Mopt and period must be
specified, see also Topt and starlod
options. Default output is for hot disk
only
--lambda arg Wavelength to calculate Fnu, Angstrom.
You can use this option multiple times.
For each lambda one additional column
with values of spectral flux density
Fnu [erg/s/cm^2/Hz] is produced
--passband arg Path of a file containing tabulated
passband, the first column for
wavelength in Angstrom, the second
column for transmission factor, columns
should be separated by spaces
Parameters of disk evolution calculation:
--inittime arg (=0) Initial time moment, days
-T [ --time ] arg Time interval to calculate evolution,
days
--tau arg Time step, days
--Nx arg (=1000) Size of calculation grid
--gridscale arg (=log) Type of grid for angular momentum h:
log or linear
--starlod arg (=3) Level of detail of the optical star 3-D
model. The optical star is represented
by a triangular tile, the number of
tiles is 20 * 4^starlod
./freddi-ns --help
expand
Freddi: numerical calculation of accretion disk evolution:
General options:
-h [ --help ] Produce help message
--config arg Set additional configuration filepath
--prefix arg (=freddi) Set prefix for output filenames. Output
file with distribution of parameters
over time is PREFIX.dat
-d [ --dir ] arg (=.) Choose the directory to write output
files. It should exist
--precision arg (=12) Number of digits to print into output
files
--fulldata Output files PREFIX_%d.dat with radial
structure for every time step. Default
is to output only PREFIX.dat with
global disk parameters for every time
step
Basic binary and disk parameter:
-a [ --alpha ] arg Alpha parameter of Shakura-Sunyaev
model
--alphacold arg Alpha parameter of cold disk, currently
it is used only for Sigma_minus, see
--Qirr2Qvishot. Default is --alpha
values divided by ten
-M [ --Mx ] arg Mass of the central object, in the
units of solar masses
--kerr arg (=0) Dimensionless Kerr parameter of the
black hole
--Mopt arg Mass of the optical star, in units of
solar masses
--rochelobefill arg (=1) Dimensionless factor describing a size
of the optical star. Polar radius of
the star is rochelobefill * (polar
radius of critical Roche lobe)
--Topt arg (=0) Thermal temperature of the optical
star, in units of kelvins
-P [ --period ] arg Orbital period of the binary system, in
units of days
--rin arg Inner radius of the disk, in the units
of the gravitational radius of the
central object GM/c^2. If it isn't set
then the radius of ISCO orbit is used
defined by --Mx and --kerr values
-R [ --rout ] arg Outer radius of the disk, in units of
solar radius. If it isn't set then the
tidal radius is used defined by --Mx,
--Mopt and --period values
--risco arg Innermost stable circular orbit, in
units of gravitational radius of the
central object GM/c^2. If it isn't set
then the radius of ISCO orbit is used
defined by --Mx and --kerr values
Parameters of the disk mode:
-O [ --opacity ] arg (=Kramers) Opacity law: Kramers (varkappa ~ rho /
T^7/2) or OPAL (varkappa ~ rho / T^5/2)
--Mdotout arg (=0) Accretion rate onto the disk through
its outer radius
--boundcond arg (=Teff) Outer boundary movement condition
Values:
Teff: outer radius of the disk moves
inwards to keep photosphere temperature
of the disk larger than some value.
This value is specified by --Thot
option
Tirr: outer radius of the disk moves
inwards to keep irradiation flux of the
disk larger than some value. The value
of this minimal irradiation flux is
[Stefan-Boltzmann constant] * Tirr^4,
where Tirr is specified by --Thot
option
--Thot arg (=0) Minimum photosphere or irradiation
temperature at the outer edge of the
hot disk, Kelvin. For details see
--boundcond description
--Qirr2Qvishot arg (=0) Minimum Qirr / Qvis ratio at the outer
edge of the hot disk to switch
evolution from temperature-based regime
to Sigma_minus-based regime (see Eq.
A.1 in Lasota et al. 2008, --alphacold
value is used as alpha parameter)
--initialcond arg (=powerF) Type of the initial condition for
viscous torque F or surface density
Sigma
Values:
powerF: F ~ xi^powerorder, powerorder
is specified by --powerorder option
linearF: F ~ xi, specific case of
powerF but can be normalised by
--Mdot0, see its description for
details powerSigma: Sigma ~
xi^powerorder, powerorder is specified
by --powerorder option
sineF: F ~ sin( xi * pi/2 )
gaussF: F ~ exp(-(xi-mu)**2 / 2
sigma**2), mu and sigma are specified
by --gaussmu and --gausssigma options
quasistat: F ~ f(h/h_out) * xi *
h_out/h, where f is quasi-stationary
solution found in Lipunova & Shakura
2000. f(xi=0) = 0, df/dxi(xi=1) = 0
Here xi is (h - h_in) / (h_out - h_in)
--F0 arg Initial maximum viscous torque in the
disk, dyn*cm. Can be overwritten via
--Mdisk0 and --Mdot0
--Mdisk0 arg Initial disk mass, g. If both --F0 and
--Mdisk0 are specified then --Mdisk0 is
used. If both --Mdot0 and --Mdisk0 are
specified then --Mdot0 is used
--Mdot0 arg Initial mass accretion rate through the
inner radius, g/s. If --F0, --Mdisk0
and --Mdot0 are specified then --Mdot0
is used. Works only when --initialcond
is set to linearF, sinusF or quasistat
--powerorder arg Parameter for the powerlaw initial
condition distribution. This option
works only with --initialcond=powerF or
powerSigma
--gaussmu arg Position of the maximum for Gauss
distribution, positive number not
greater than unity. This option works
only with --initialcond=gaussF
--gausssigma arg Width of for Gauss distribution. This
option works only with
--initialcond=gaussF
Parameters of self-irradiation.
Qirr = Cirr * (H/r / 0.05)^irrindex * L * psi / (4 pi R^2), where psi is angular distrbution of X-ray radiation:
--Cirr arg (=0) Irradiation factor for the hot disk
--irrindex arg (=0) Irradiation index for the hot disk
--Cirrcold arg (=0) Irradiation factor for the cold disk
--irrindexcold arg (=0) Irradiation index for the cold disk
--h2rcold arg (=0.050000000000000003) Seme-height to radius ratio for the
cold disk
--angulardistdisk arg (=plane) Angular distribution of the disk X-ray
radiation. Values: isotropic, plane
Parameters of flux calculation:
--colourfactor arg (=1.7) Colour factor to calculate X-ray flux
--emin arg (=1) Minimum energy of X-ray band, keV
--emax arg (=12) Maximum energy of X-ray band, keV
--staralbedo arg (=0) Part of X-ray radiation reflected by
optical star, (1 - albedo) heats star's
photosphere. Used only when --starflux
is specified
-i [ --inclination ] arg (=0) Inclination of the system, degrees
--ephemerist0 arg (=0) Ephemeris for the time of the minimum
of the orbital light curve T0, phase
zero corresponds to inferior
conjunction of the optical star, days
--distance arg Distance to the system, kpc
--colddiskflux Add Fnu for cold disk into output file.
Default output is for hot disk only
--starflux Add Fnu for optical star into output
file. Mx, Mopt and period must be
specified, see also Topt and starlod
options. Default output is for hot disk
only
--lambda arg Wavelength to calculate Fnu, Angstrom.
You can use this option multiple times.
For each lambda one additional column
with values of spectral flux density
Fnu [erg/s/cm^2/Hz] is produced
--passband arg Path of a file containing tabulated
passband, the first column for
wavelength in Angstrom, the second
column for transmission factor, columns
should be separated by spaces
Parameters of disk evolution calculation:
--inittime arg (=0) Initial time moment, days
-T [ --time ] arg Time interval to calculate evolution,
days
--tau arg Time step, days
--Nx arg (=1000) Size of calculation grid
--gridscale arg (=log) Type of grid for angular momentum h:
log or linear
--starlod arg (=3) Level of detail of the optical star 3-D
model. The optical star is represented
by a triangular tile, the number of
tiles is 20 * 4^starlod
Also you can use freddi.ini configuration file to store options. This INI
file contains lines option=value,
option names are the as provided by the help message above. Command line option
overwrites configuration file option. For example, see
default freddi.ini.
Paths where this file is searched are ./freddi.ini (execution path),
$HOME/.config/freddi/freddi.ini, /usr/local/etc/freddi.ini and
/etc/freddi.ini. You can provide configuration file to Docker container as a
volume: -v "`pwd`/freddi.ini":/etc/freddi.ini.
Output values
Freddi outputs time; the accretion rate; the mass of the hot part of the disk;
the outer radius of the hot zone; the irradiation factor; the relative
half-height, effective and irradiation temperature, ratio of the irradiation to
viscous flux at the outer radius of the hot zone; X-ray luminosity (erg/s) in
the band from E_min to E_max (--emin and --emax options); the optical
magnitudes in U, B, V, R, I, and J band (Allen's Astrophysical
Quantities, Cox 2015); the spectral density flux (erg/s/cm^2/Hz) at some wavelengths set by one or more --lambda options.
Snapshot distributions at each time step, if produced, contain the following data: radial coordinate in terms of the specific angular momentum, radius, viscous torque, surface density, effective temperature Teff, viscous temperature Tvis, irradiation temperature Tirr, and the absolute half-height of the disk.
Example
The following arguments instruct Freddi to calculate the decay of the outburst
in the disk with the constant outer radius equal to 1 solar radius. The Kerr
black hole at the distance of 5 kpc has the mass of 9 solar masses, and the
Kerr's parameter is 0.4. The outer disk is irradiated with Cirr=1e-3.
./freddi --alpha=0.5 --Mx=9 --rout=1 --time=50 --tau=0.25 --dir=data/ \
--F0=2e+37 --colourfactor=1.7 --Nx=1000 --distance=5 --gridscale=log \
--kerr=0.4 --Cirr=0.001 --opacity=OPAL --initialcond=quasistat \
--wind=Woods1996 --Xi_max=10 --Tic=1e8 --M_pow=1
Physical Background
Freddi — Fast Rise Exponential Decay: accretion Disk model Implementation — is
designed to solve the differential equation of the viscous evolution of the
Shakura-Sunyaev accretion disk in a stellar binary system. Shakura-Sunyaev disk
is the standard model of accretion of plasma onto the cosmic bodies, like
neutron stars or black holes. Viscous evolution of the accretion disks exibits
itself, for example, in X-ray outbursts of binary stars. Usually, the outbursts
last for several tens of days and many of them are observed by orbital
observatories.
The basic equation of the viscous evolution relates the surface density and viscous stresses and is of diffusion type. Evolution of the accretion rate can be found on solving the equation. The distribution of viscous stresss defines the emission from the source.
The standard model for the accretion disk is implied, which is developed by Shakura & Sunyaev (1973). The inner boundary of the disk is at the ISCO or can be explicitely set. The boundary conditions in the disk are the zero stress at the inner boundary and the zero accretion rate at the outer boundary. The conditions are suitable during the outbursts in X-ray binary transients with black holes.
In a binary system, the accretion disk is radially confined. In Freddi, the
outer radius of the disk can be set explicitely or calculated as the position of
the tidal truncation radius following Paczynski
(1997) for small mass ratios
of the black using the approximation by Suleimanov et al. (2008).
The parameters at the disk central plane are defined by the analytic approximations (Suleimanov et al. 2007), valid for the effective surface temperatures from 10 000 to 100 000 K, approximately. It is assumed that the gas pressure dominates, the gas is completely ionized, and the photon opacity is defined by the free-free and free-bound transitions. Opacity law is for the solar element abundancies and can be chosen from two types: (1) Kramers' opacity: kappa = 5e24 rho/T^(7/2) cm2/g (2) approximation to OPAL tables: kappa = 1.5e20 rho/T^(5/2) cm2/g (Bell & Lin 1994)
The disk at each radius is in the "hot" state if the gas is completely ionized.
Otherwise, the disk is considered to be "cold" locally. Alpha-parameter in the
cold parts of the disk is appreciably lower than in the hot parts. Thus the
viscous evolution of the disk should proceed more effectively in the hot parts
of the disk. To simulate this, Freddi has an option to control the outer
radius of the hot evolving disk. We assume that the evolution goes through the
quasi-stationary states in the hot zone of variable size. By default, the hot
zone has the constant size, equal to the tidal radius.
The initial distribution of the matter in the disk should be specified with
--initialcond option. Freddi can start from several types of initial
distributions: power-law distribution of the surface density
--initialcond=powerSigma, power-law --initialcond=powerF or sinus-law
--initialcond=sinusF distribution of the viscous torque, quasi-stationary
distribution --initialcond=quasistat. The choice of the initial distribution
defines what type of evolution is to be calculated.
Starting from the quasi-stationary or sinusF distribution, the solution
describes the decaying part of the outburst. Zero-time accretion rate through
the inner edge can be set. In other cases, the rise to the peak is also
computed. Then, initial value of viscous torque at the outer radius (can be set
by --F0) defines uniquely the initial mass of the disk.
Self-irradiation by the central X-rays heats the outer parts of the disk. A
fraction of the bolometric flux is supposed to illuminate the disk surface. This
results in the larger size of the hot disk if such model is assumed. Also, the
optical flux is increased because the flux outgoing from the disk surface is
proportional to Teff^4 = Tvis^4+Tirr^4. Self-irradiation of the disk is
included in the computation if irradiation parameter is not zero. The simplest
way is to set a constant irradiation factor --Cirr (the studies of X-ray novae
suggest the range for Cirr 1e-5—5e-3).
Observed flux depends on the distance to the source and the inclination of the disk plane. The inclination angle is the angle between the line of sight and the normal to the disk. The flux, emitted from the disk surface, is defined by the sum of the visous and irradiating flux, where the viscous flux is calculated taking into account general relativity effects near the black hole, following Page & Thorne (1974) and Riffert & Herold (1995).
Accretion disk wind
Presumably, during an outburst there is an outflow in the form of a wind from the accretion disk around the compact object. The presence of such a wind in the LMXBs is supported by modern observations indicating the expansion of ionized matter. Such an outflow of matter, being an additional source of angular momentum transfer in the disk, can strongly influence its viscous evolution.
However, the nature of such winds and their physical characteristics are an open question. Namely, there are three mechanisms which are considered: heating of matter by central radiation in optically thin regions of the disk (Begelman et al. 1983, Shields et al. 1986, Woods et al. 1996), the pressure of the magnetic field of the disk (Blandford & Payne 1982, Habibi & Abbassi 2019, Nixon & Pringle 2019) and the pressure of local radiation at super-Eddington accretion rates (Shakura & Sunyaev 1973, Proga & Kallman 2002).
Freddi is modernized in such a way that it is able to solve the viscous evolution
equation with an inhomogeneous term that is responsible for the presence of the disk wind.
This term is the dependence of the surface density of the wind mass-loss rate on
the distance along the disk's surface. Different forms of such dependence correspond
to different wind models, and to different classes within Freddi.
One can choose a wind model by setting the
--wind option. The thermal wind model (Woods et al. 1996),
which implies that the outflow of matter occurs due to the heating of the outer parts of the disk
by a central radiation source, can be chosen by setting --wind=Woods1996. The option --wind=Janiuk15
corresponds to the model from work Janiuk et al. (2015)
where the wind is started in the super-Eddington regime. You can also select the --wind=ToyWind option,
which corresponds to a toy wind model when the user sets the wind strength relatively to the accretion rate using the option --windpow.
Compton-heated wind
At the moment, Freddi is more focused on simulating outbursts taking into account the thermal wind (--wind=Woods1996 option).
For a better understanding, let's discuss a little the physics of the process of launching such a wind
and its parameters in the code.
In the standard accretion disk model by Shakura & Sunyaev (1973)
the disk is concave, and, as a result, the disk surface is exposed to the central radiation,
which heats the disk material. As a result, the heated matter, starting from a certain radius,
begins to leave the accretion disk. This process of heating the matter of the accretion disk by means of Compoton
processes was developed in Begelman et al. (1983) and
Shields et al. (1986).
In a later work Woods et al. (1996),
two-dimensional magnetohydrodynamic calculations were performed and the
results of Shields et al. (1986) were generalized.
Woods et al. (1996) give an expression for the surface density of the mass
loss rate as a function of distance along the disk's surface. This function is used in Freddi
to taking thermal wind into account.
Choosing option --wind=Woods1996, it is necessary to set the value of the ionization parameter Xi
(which is proportional to the ratio of the radiation and gas pressures) by the option --Xi_max and the Compoton temperature T_IC
(which determines the hardness of the irradiating spectrum and the size of the region where the wind operates) by the option --Tic.
Questions and comments
If you have any problems, questions, or comments, please address them to Issues or to hombit@gmail.com
License
Copyright (c) 2016–2021, Konstantin L. Malanchev, Galina V. Lipunova & Artur L. Avakyan.
Freddi is distributed under the terms of the
GPLv3.
Please, accompany any results obtained using this code with reference to Lipunova & Malanchev (2017) 2017MNRAS.468.4735L
BibTex
@ARTICLE{2017MNRAS.468.4735L,
author = {{Lipunova}, G.~V. and {Malanchev}, K.~L.},
title = "{Determination of the turbulent parameter in accretion discs: effects of self-irradiation in 4U 1543{\minus}47 during the 2002 outburst}",
journal = {\mnras},
archivePrefix = "arXiv",
eprint = {1610.01399},
primaryClass = "astro-ph.HE",
keywords = {accretion, accretion discs, methods: numerical, binaries: close, stars: black holes, X-rays: individual: 4U 1543-47},
year = 2017,
month = jul,
volume = 468,
pages = {4735-4747},
doi = {10.1093/mnras/stx768},
adsurl = {http://adsabs.harvard.edu/abs/2017MNRAS.468.4735L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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