- Overview
- Installation
- Usage
- Physical Background
- Accretion disk wind
- Development guide
- Questions and comments
- License
- BibTex
The code solves 1-D evolution equation of Shakura-Sunyaev accretion alpha-disk around black hole or neutron star. The code is developed to simulate fast-rise exponential-decay (FRED) light curves of low mass X-ray binaries (LMXBs). It has been first presented in 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. Currently, the code can take into account self-irradiation of the disc, winds from the disc surface, disc-magnetosphere interactions. The related papers are Avakyan et al (2021) 2021AstL...47..377A and Lipunova et al (2021) 2021arXiv211008076L.
Freddi is written on C++ and available as a couple of binary executables and
a Python module.
Note that the original Freddi version 1 introduced in Lipunova & Malanchev (2017)
2017MNRAS.468.4735L is still
available in the v1 git branch.
Freddi is represented by two binary executables: the black hole version
freddi and the neutron star version freddi-ns.
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/dataFreddi has following build dependencies:
- Boost 1.57+
- CMake with a back-end build system like Make or Ninja
- C++ compiler with C++17 support, e.g.
gccversion 8+ orclang5+
Get requirements on Debian based systems (e.g. Ubuntu):
apt-get install g++ cmake libboost-all-devOn Red-Hat based systems (e.g. Fedora):
dnf install gcc-c++ cmake boost-develOn macOS via Homebrew:
brew install cmake boostGet 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 locationFreddi is known to be built on Linux and macOS.
Python 2 isn't supported, use Python 3 instead.
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 configurations you should have C++ compiler and Boost
libraries in your system 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 freddiastropy is an optional requirement which must be
installed to use dimensional input via Freddi.from_astropy
Freddi runs from the command line with inline options and/or with configuration
files. 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).
The full list of command line options is viewed with --help option. Default
values are given in brackets.
./freddi --helpexpand
Freddi: numerical calculation of accretion disk evolution:
General options::
-h [ --help ] Produce help message
--config arg Set filepath for additional configuration
file. There is no need to declare a
configuration file with the default name
freddi.ini
--prefix arg (=freddi) Set prefix for output filenames. Output file
with distribution of parameters over time is
PREFIX.dat
--stdout Output temporal distribution to stdout
instead of PREFIX.dat file
-d [ --dir ] arg (=.) Choose the directory to write output files.
It should exist
--precision arg (=12) Number of digits to print into output files
--tempsparsity arg (=1) Output every k-th time moment
--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 parameters
:
-a [ --alpha ] arg Alpha parameter of Shakura-Sunyaev model
--alphacold arg Alpha parameter of cold disk, currently it
is used only for the critical maximum value
of the surface density of the cold disk
Sigma_minus (Lasota et al., 2008, A&A 486,
523) and the cooling front velocity (Ludwig
et al., 1994, A&A 290, 473), see
--Qirr2Qvishot. Default value is --alpha
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) Effective 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. There is no need to set it
for a neutron star. If it isn't set for a
black hole 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 as 90% of the Roche lobe
radius (Papaloizou & Pringle, 1977, MNRAS,
181, 441; see also Artymowicz & Lubow, 1994,
ApJ, 421, 651; http://xray.sai.msu.ru/~galja
/images/tidal_radius.pdf)
--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 model:
-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 the control over
the evolution of the hot disk radius: from
temperature-based regime to Sigma-based
cooling-front regime (see Lipunova et al.
(2021, Section 2.4) and Eq. A.1 in Lasota et
al. 2008; --alpha value is used for
Sigma_plus and --alphacold value is used for
Sigma_minus)
--initialcond arg (=powerF) Type of the initial condition for viscous
torque F or surface density Sigma
Values:
[NB! Here below dimensionless xi = (h -
h_in) / (h_out - h_in)]
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
--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
--windtype arg (=no) Type of the wind
no: no wind
SS73C: super-Eddington spherical wind from
Shakura-Sunyaev 1973
ShieldsOscil1986: toy wind model from
Shields et al. 1986 which was used to obtain
oscillations in the disk luminosity.
Requires --windC_w and --windR_w to be
specified
Janiuk2015: super-Eddington wind from
Janiuk et al 2015. Requires --windA_0 and
--windB_1 to be specified
Shields1986: thermal wind from Begelman et
al. 1983 and Shields et al. 1986. Requires
--windXi_max, --windT_ic and --windPow to be
specified
Woods1996AGN: thermal AGN wind from Woods
et al. 1996. Requires --windC_0 and
--windT_ic to be specified
Woods1996: thermal wind from Woods et al.
1996. Requires --windXi_max, --windT_ic and
--windPow to be specified
toy: a toy wind model used in
arXiv:2105.11974, the mass loss rate is
proportional to the central accretion rate.
Requires --windC_w to be specified
--windC_w arg The ratio of the mass loss rate due to wind
to the central accretion rate, |Mwind|/Macc
--windR_w arg The ratio of the wind launch radius to the
outer disk radius, Rwind/Rout
--windA_0 arg Dimensionless parameter characterizing the
strength of the super-Eddington wind in the
framework of the model Janiuk et al. 2015.
Effective value range from 10 to 25
--windB_1 arg The quantity is of the order of unity.
Characterizes the relationship between the
change in energy per particle and virial
energy.
E = B_1 * k * T
--windXi_max arg Ionization parameter, the ratio of the
radiation and gas pressures
--windT_ic arg Inverse Compton temperature, K.
Characterizes the hardness of the
irradiating spectrum
--windPow arg Multiplicative coefficient to control wind
power
--windC_0 arg Characteristic column density of the wind
mass loss rate from Woods et al. 1996 model,
g/(s*cm^2). For AGN approx value is 3e-13
g/(s*cm^2)
Parameters of self-irradiation:
Qirr = Cirr * (H/r / 0.05)^irrindex * L * psi / (4 pi R^2), where psi is the angular distribution 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) Semi-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 irradiated optical star into
output file. See --Topt, --starlod and
--h2rcold options. Default is output for the
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
for a photon counter detector, 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 --helpexpand
Freddi NS: numerical calculation of accretion disk evolution:
General options::
-h [ --help ] Produce help message
--config arg Set filepath for additional
configuration file. There is no need to
declare a configuration file with the
default name freddi.ini
--prefix arg (=freddi) Set prefix for output filenames. Output
file with distribution of parameters
over time is PREFIX.dat
--stdout Output temporal distribution to stdout
instead of PREFIX.dat file
-d [ --dir ] arg (=.) Choose the directory to write output
files. It should exist
--precision arg (=12) Number of digits to print into output
files
--tempsparsity arg (=1) Output every k-th time moment
--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 parameters
:
-a [ --alpha ] arg Alpha parameter of Shakura-Sunyaev
model
--alphacold arg Alpha parameter of cold disk, currently
it is used only for the critical
maximum value of the surface density of
the cold disk Sigma_minus (Lasota et
al., 2008, A&A 486, 523) and the
cooling front velocity (Ludwig et al.,
1994, A&A 290, 473), see
--Qirr2Qvishot. Default value is
--alpha 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) Effective 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. There is no need
to set it for a neutron star. If it
isn't set for a black hole 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 as 90% of
the Roche lobe radius (Papaloizou &
Pringle, 1977, MNRAS, 181, 441; see
also Artymowicz & Lubow, 1994, ApJ,
421, 651; http://xray.sai.msu.ru/~galja
/images/tidal_radius.pdf)
--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 model:
-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 the
control over the evolution of the hot
disk radius: from temperature-based
regime to Sigma-based cooling-front
regime (see Lipunova et al. (2021,
Section 2.4) and Eq. A.1 in Lasota et
al. 2008; --alpha value is used for
Sigma_plus and --alphacold value is
used for Sigma_minus)
--initialcond arg (=powerF) Type of the initial condition for
viscous torque F or surface density
Sigma
Values:
[NB! Here below dimensionless xi = (h
- h_in) / (h_out - h_in)]
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
quasistat-ns: Distibution of the
initial viscous torque in the disc is
F = F0 * f_F(xi) * (1-h_in/h_out/xi) /
(1-h_in/h_out), where xi=h/h_out and
f_F(xi) is taken from Lipunova &
Shakura (2000)
--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
--windtype arg (=no) Type of the wind
no: no wind
SS73C: super-Eddington spherical wind
from Shakura-Sunyaev 1973
ShieldsOscil1986: toy wind model from
Shields et al. 1986 which was used to
obtain oscillations in the disk
luminosity. Requires --windC_w and
--windR_w to be specified
Janiuk2015: super-Eddington wind from
Janiuk et al 2015. Requires --windA_0
and --windB_1 to be specified
Shields1986: thermal wind from
Begelman et al. 1983 and Shields et al.
1986. Requires --windXi_max, --windT_ic
and --windPow to be specified
Woods1996AGN: thermal AGN wind from
Woods et al. 1996. Requires --windC_0
and --windT_ic to be specified
Woods1996: thermal wind from Woods et
al. 1996. Requires --windXi_max,
--windT_ic and --windPow to be
specified
toy: a toy wind model used in
arXiv:2105.11974, the mass loss rate is
proportional to the central accretion
rate. Requires --windC_w to be
specified
--windC_w arg The ratio of the mass loss rate due to
wind to the central accretion rate,
|Mwind|/Macc
--windR_w arg The ratio of the wind launch radius to
the outer disk radius, Rwind/Rout
--windA_0 arg Dimensionless parameter characterizing
the strength of the super-Eddington
wind in the framework of the model
Janiuk et al. 2015. Effective value
range from 10 to 25
--windB_1 arg The quantity is of the order of unity.
Characterizes the relationship between
the change in energy per particle and
virial energy.
E = B_1 * k * T
--windXi_max arg Ionization parameter, the ratio of the
radiation and gas pressures
--windT_ic arg Inverse Compton temperature, K.
Characterizes the hardness of the
irradiating spectrum
--windPow arg Multiplicative coefficient to control
wind power
--windC_0 arg Characteristic column density of the
wind mass loss rate from Woods et al.
1996 model, g/(s*cm^2). For AGN approx
value is 3e-13 g/(s*cm^2)
Parameters of accreting neutron star:
:
--nsprop arg (=dummy) Neutron star properties name: defines
geometry (default values of --Rx,
--Risco, and --freqx) and
accretion->radiation efficiency of NS
Values:
dummy: NS accretion->radiation
efficiency is R_g * (1 / R_x - 1 /
2R_in), default --freqx is 0, default
Rx is 1e6, default Risco is Kerr value
newt: NS accretion->radiation
efficiency is a function of NS
frequency, calculated in Newtonian
mechanics (see Lipunova+2021), that's
why --freqx must be specified
explicitly
sibgatullin-sunyaev2000: NS
accretion->radiation efficiency and
default values of Rx and Risco are
functions of NS frequency, calculated
for a specific equation of state for a
NS with weak magnetic field
(Sibgatullin & Sunyaev, 2000, Astronomy
Letters, 26, 699), that's why --freqx
must be specified explicitly
--freqx arg Accretor rotation frequency, Hz. This
parameter is not linked to --kerr,
which could be reconciled manually
(currently, --kerr is not needed for
freddi-ns)
--Rx arg Accretor radius, cm
--Bx arg Accretor polar magnetic induction, G
--hotspotarea arg (=1) Total area of the region on the
accretor radiating because of
accretion, normalized by the accretor
surface area
--epsilonAlfven arg (=1) Magnetosphere radius in units of the
Alfven radius, which is defined as
(mu^4/G/M/sqrt(Mdot))^(1/7)
--inversebeta arg (=0) Not currently in use
--Rdead arg (=0) Maximum inner radius of the disk that
can be achieved, cm
--fptype arg (=no-outflow) Scenario to determine the fraction fp
of accreted mass. The rest of the disk
inner accretion rate is propelled away.
Values:
no-outflow: the matter reaching the
inner disk radius always falls onto NS,
fp = 1
propeller: the matter always flows
away, fp = 0
corotation-block: like 'no-outflow'
when the inner disk radius is smaller
than the corotation radius, like
'propeller' otherwise
geometrical: experimental.
Generalization of 'corotation-block'
for the case of misaligned NS magnetic
axis. Requires --fp-geometrical-chi to
be specified
eksi-kutlu2010: Under construction
romanova2018: fp is an analytical
function of the fastness, found from
MHD simulations by Romanova et al.
(2018, NewA, 62, 94): fp = 1 -
par1*fastness^par2. This requires
--romanova2018-par1 and
--romanova2018-par2 to be specified
--fp-geometrical-chi arg angle between the disk rotation axis
and the NS magnetic axis, used for
--fptype=geometrical, degrees
--romanova2018-par1 arg par1 value for --fptype=romanova2018
and --kappattype=romanova2018
--romanova2018-par2 arg par2 value for --fptype=romanova2018
and --kappattype=romanova2018
--kappattype arg (=const) kappa_t describes how strong is the
interaction between the NS
magnetosphere and disk: total
(accelerating) magnetic torque applied
to the disc is kappa_t(R) * mu^2 / R^3.
Values:
const: doesn't depend on radius,
kappa_t = value. Requires
--kappat-const-value to be specified
corstep: kappa_t can be different
inside and outside the corotation
radius. Requires --kappat-corstep-in
and --kappat-corstep-out to be
specified
romanova2018: experimental. Similar
to corstep option, but the outside
value is reduced by the portion taken
away by the outflow (see Table 2 of
Romanova+2018, NewA, 62, 94). Requires
--kappat-romanova2018-in,
--kappat-romanova2018-out
--romanova2018-par1 and --romanova-par2
to be specified
--kappat-const-value arg (=0.33333333333333331)
kappa_t value for --kappattype=const
--kappat-corstep-in arg (=0.33333333333333331)
kappa_t value inside the corotation
radius for --kappattype=corstep
--kappat-corstep-out arg (=0.33333333333333331)
kappa_t value outside the corotation
radius for --kappattype=corstep
--kappat-romanova2018-in arg (=0.33333333333333331)
kappa_t value inside the corotation
radius for --kappattype=romanova2018
--kappat-romanova2018-out arg (=0.33333333333333331)
kappa_t value outside the corotation
radius for --kappattype=romanova2018
--nsgravredshift arg (=off) Neutron star gravitational redshift
flag.
Values:
off: gravitational redshift is not
taken into account
on: redshift is (1 - R_sch / Rx),
where R_sch = 2GM/c^2
Parameters of self-irradiation:
Qirr = Cirr * (H/r / 0.05)^irrindex * L * psi / (4 pi R^2), where psi is the angular distribution 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) Semi-height to radius ratio for the
cold disk
--angulardistdisk arg (=plane) Angular distribution of the disk X-ray
radiation. Values: isotropic, plane
--angulardistns arg (=isotropic) Flag to calculate angular distribution
the NS emission. 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 irradiated optical star
into output file. See --Topt, --starlod
and --h2rcold options. Default is
output for the 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 for a photon counter detector,
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
Write which options are mandatory
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.
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.
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 --period=0.5 --Mopt=0.5 --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 --windtype=Woods1996 --windXi_max=10 --windT_ic=1e8 \
--windPow=1 Here we run a simmulation with for a nine sollar mass blac hole (Kerr parameter is 0.4), surrended by an accretion disc with α=0.5, outer radius equals one sollar radius. Initial torque profile corresponds to one described by Lipunova&Shakura 2000, while outer torque equals 2*10^37 dyn*cm. The irradiation parameter equals 10^-3. We run simmulations for 50 days, with time step of 0.25 days and spatial grid with 1000 nodes. Disk opacity is described by a power-law κ∼ρ/T^5/2. Disk has a thermal wind following Woods et al 1996, with invert compton temperature of hundred million kelvins.
Python bindings can be used as a convenient way to run and analyse Freddi simulations.
You can prepare simulation set-up initializing Freddi
(for black hole accretion disk) or FreddiNeutronStar (for NS) class instance.
These classes accept keyword-only arguments which have the same names and
meanings as command line options, but with three
major exceptions:
- Python package doesn't provide any file output functionality, that's why output arguments like
config,dir,fulldata,starflux,lambdaorpassbandare missed; - all values are assumed to be in CGS units, but you can use
Freddi.from_asrtopyfor dimensional values (see the details bellow); - parameters of wind, NS
fpand NSkappamodels are passed as dictionaries (see the specifications bellow).
The following code snippet would set-up roughly the same simulation as the command-line example
from freddi import Freddi
freddi = Freddi(
alpha=0.5, Mx=9*2e33, rout=1*7e10, period=0.5*86400, Mopt=0.5*2e33,
time=50*86400, tau=0.25*86400, F0=2e+37, colourfactor=1.7, Nx=1000,
distance=5*3e21, gridscale='log', kerr=0.4, Cirr=0.001, opacity='OPAL',
initialcond='quasistat', windtype='Woods1996',
windparams=dict(Xi_max=10, T_ic=1e8, Pow=1),
)Alternatively we can do the same using from_astropy class-method which casts
all astropy.units.Quantity
objects to CGS values. Note that dimensionality isn't checked, and technically
it just does arg.cgs.value for every Quantity argument.
import astropy.units as u
from freddi import Freddi
freddi = Freddi.from_astropy(
alpha=0.5, Mx=9*u.Msun, rout=1*u.Rsun, period=0.5*u.day, Mopt=0.5*u.Msun,
time=50*u.day, tau=0.25*u.day, F0=2e+37, colourfactor=1.7, Nx=1000,
distance=5*u.kpc, gridscale='log', kerr=0.4, Cirr=0.001, opacity='OPAL',
initialcond='quasistat', windtype='Woods1996',
windparams=dict(Xi_max=10, T_ic=1e8, Pow=1),
)Wind model parameters are specified by windparams argument which should be
a dict instance with string keys and numeric values. Command option to
windparams keys relation is: --windC_w -> C_w, --windR_w -> R_w,
--windA_0 -> A_0, --windB_1 -> B_1, --windXi_max -> Xi_max,
windT_ic -> T_ic, --windPow -> Pow, windC_0 -> C_0.
Neutron star f_p model parameters are specified by fpparams mapping with the
same structure as windparams. Command options to fpparams keys relation is:
--fp-geometrical-chi -> chi, romanova2018-par1 -> par1,
romanova2018-par2 -> par2.
Neutron star kappa_t model parameters are specified by kappatparams mapping
with the same structure as windparams. Command options to the mapping keys
relation is: --kappat-const-value -> value, --kappat-corstep-in -> in,
kappat-corstep-out -> out, --kappat-romanova2018-in -> in,
--kappat-romanova2018-out -> out, romanova2018-par1 -> par1,
--romanova2018-par2 -> par2
There are two ways to run a simulation: iterating over time steps, and run the
whole simulation in one shot. Note that in both cases your Freddi object is
mutating and represents the current state of the accretion disk.
Here we use iterator interface which yields another Freddi object for each
time moment.
import astropy.units as u
from freddi import Freddi
freddi = Freddi.from_astropy(
alpha=0.5, Mx=9*u.Msun, rout=1*u.Rsun, period=0.5*u.day, Mopt=0.5*u.Msun,
time=20*u.day, tau=1.0*u.day, Mdot0=5e18, distance=10*u.kpc,
initialcond='quasistat',
)
for state in freddi:
print(f't = {state.t:>7.0f} s, Mdot = {state.Mdot:5.3e} g/s')
assert state.t == freddi.tIn this example we run a simulation via .evolve() method which returns
EvolutionResult object keeping all evolution states internally and providing
temporal distribution of disk's properties.
import astropy.units as u
import matplotlib.pyplot as plt
from freddi import Freddi
freddi = Freddi.from_astropy(
alpha=0.5, Mx=9*u.Msun, rout=1*u.Rsun, period=0.5*u.day, Mopt=0.5*u.Msun,
time=20*u.day, tau=1.0*u.day, Mdot0=5e18, distance=10*u.kpc,
initialcond='quasistat',
)
result = freddi.evolve()
assert result.t[-1] == freddi.t
# Plot Mdot(t)
plt.figure()
plt.title('Freddi disk evolution: accretion rate')
plt.xlabel('t, day')
plt.ylabel(r'$\dot{M}$, g/cm')
plt.plot(result.t / 86400, result.Mdot)
plt.show()
# Plot all F(h) profiles
plt.figure()
plt.title('Freddi disk evolution: viscous torque')
plt.xlabel('r, cm')
plt.ylabel('F, dyn cm')
plt.xscale('log')
plt.yscale('log')
plt.plot(result.R.T, result.F.T)
plt.show()
# Plot evolution of effective temperature of the outer hot disk ring
plt.figure()
plt.title('Freddi disk evolution: outer effective temperature')
plt.xlabel('t, day')
plt.ylabel('T, K')
plt.plot(result.t / 86400, result.last_Tph)
plt.show()Freddi, FreddiNeutronStar and EvolutionResult objects contain dozens of
properties returning various physical values like t for time moment,
Mdot for accretion rate onto central object, R for radius, F for torque,
Tph for effective temperature and so on. first_* and last_* properties
are used to access innermost and outermost hot disk values of radial-distributed
quantities. The complete list of properties can be obtained by dir(Freddi) or
dir(FreddiNeutronStar). Note that the most properties are lazy-evaluated and
require some time to access first time. EvolutionResult provides all the
same properties as underlying Freddi or FreddiNeutronStar objects but with
additional array dimension for temporal distribution, so if Freddi.Lx is a
scalar then EvolutionResult.Lx is an 1-D numpy array of (Nt,) shape,
if Freddi.Sigma is an 1-D array of (Nx,) shape, then
EvolutionResult.Sigma is an 2-D array of (Nt, Nx) shape. Also, note that if
disk shrinks during a simulation, the missing values of EvolutionResult
properties are filled by NaN.
All three classes have flux(lmbd, region='hot', phase=None) method which can
be used to find spectral flux density per unit frequency for optical
emission. lmbd argument can be a scalar or a multidimensional numpy array
of required wavelengths in cm; region could be one of "hot" (hot disk),
"cold" (cold disk), "disk" ("hot" + "cold"), "star" (companion star), and
"all" ("hot" + "cold" + "star"); phase is a binary system orbital phase in
radians, it is required for region="star" and region="all" only, it can be
calculated as 2π t / period + constant.
All properties and methods return values in CGS units.
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 90% of the
Roche lobe size to aproximate the tidal truncation radius obtained by
Papaloizou & Pringle (1977), see --rout help for details.
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).
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
--windtype 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 --windtype=Woods1996.
The option --windtype=Janiuk15 corresponds to the model from work Janiuk et al. (2015)
where the wind is started in the super-Eddington regime.
When choosing option --windtype=Janiuk15, the you must also specify the values of
the super-Eddington wind parameters with --windA0 and --windB1 options.
You can also select the --windtype=toy option, which corresponds to a toy wind model when the user sets
the wind strength relatively to the accretion rate using the option --windPow.
At the moment, Freddi is more focused on simulating outbursts taking into account the thermal wind (--windtype=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 --windtype=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 --windXi_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 --windT_ic.
We use a simple model of irradiated star to simulate periodic variability and
X-ray thermalization by a companion's photosphere. Our model assumes that the
companion star's shape corresponds to equipotential surface which size is set
by --rochelobefill option, unity means that star fills its Roche lobe, any
smaller value decreases star's polar radius correspondingly. Technically,
star's surface is built from 20 * 4^starlod triangles, use --starlod to
set level of detail, --starlod=3 should give few percent precision. Every
triangle has black-body spectrum with bolometric luminosity given by a sum of
star's own luminosity (set by --Topt) and irradiation flux multiplied by
unity minus albedo (set by --staralbedo).
Please note that the model is limited and doesn't implement limb darking or eclipsing.
Freddi uses Cmake as a build system.
The C++ source code is located in cpp folder which has following structure:
main.cppandmain-ns.cppimplementsmain()function forfreddiandfreddi-nscorrespondingly;includefor library header files, it hasnssub-folder for neutron star related stuff;srcfor library C++ files, it also hasnssub-folder;testprovides library unit tests;pywraphas both header and source files forBoost::Python/Boost::NumPybindings.
Note, that we require C++17 standard (while not having idiomatic C++17 code),
and require code to be compiled by modern GCC and CLang on Linux. Please write
unit tests where you can and use ctest to check they pass.
The Python project is specified by pyproject.toml (which lists build
requirements), setup.py and MANIFEST.in files, we use
scikit-build as a build system.
scikit-build uses Python-related section of CMakeLists.txt to build C++
source code into Python extension, and accomplish it with Python files located
in python/freddi directory. Use python setup.py build_ext to build the
extension, optionally with -DSTATIC_LINKING=TRUE to link Boost::Filesystem,
Boost::Python and Boost::NumPy statically. Please, pay attention to two
last libraries, because they should be built against the same Python version as
you use.
python/test contains some tests, you can run them by python3 setup.py test.
test_freddi.pyandtest_ns.pycontain unit tests for Python source;test_analytical.pycontains integration tests to compare analytical solutions of the equation of disk viscous evolution with the numerical solutions ofFreddi;regression.pycontains regression tests to be sure that 1) theFreddioutput is stable vs previous commits, and 2) the Python code gives the same results as binary executables do.
The regression test data are located in python/test/data. Sometimes you need
to update these regression data, for example when you introduce new
command-line option with a default value, add new output column or fix some bug
in physical model. For these purposes you can use generate_test_data.sh
script located in this folder.
Dockerfile is used to build a Docker image with statically-linked binaries,
and Dockerfile.python is used to build a Docker image with
manylinux-compatible Python wheels.
We use Github Actions as a
continuous integration (CI) system. The workflow file is located in
.github/workflows/main.yml and a couple of auxiliary files are located in
.ci folder. CI allows us to test new commits to prevent different bugs:
gccandclangactions test binaries building, execute sampleFreddiprograms, run C++ unit tests, perform C++ regression tests, and check the consistency of theReadme.mdwith programs'--helpoutputcpythonaction builds Python extension module and runs all Python testsdocker-exebuilds a Docker image usingDockerfileand execute sampleFreddiprograms inside a Docker containerdocker-pythonbuilds a Docker image usingDockefile.python, uses wheels it has built to build Python Docker images for several Python versions using.ci/Dockerfile-test-wheels, and runs sample Python scripts withfreddi.Freddiclass
Please keep Readme updated. You can update the help messages in the
Usage section using .ci/update-help-readme.py script.
Check-list:
- Update version in
setup.pyand commit it - Create
gittaggit tag $VERSION - Build new
freddiimage usingDockerfiledocker buildx build --push --platform linux/arm64,linux/amd64 --tag ghcr.io/hombit/freddi:$VERSION . docker pull ghcr.io/hombit/freddi:$VERSION docker tag ghcr.io/hombit/freddi:$VERSION ghcr.io/hombit/freddi:latest docker push ghcr.io/hombit/freddi:latest
- Build new
freddi-pythonimage usingDockerfile.pythondocker buildx build --push --platform linux/arm64,linux/amd64 --tag ghcr.io/hombit/freddi-python:$VERSION -f Dockerfile.python . docker pull ghcr.io/hombit/freddi-python:$VERSION docker tag ghcr.io/hombit/freddi-python:$VERSION ghcr.io/hombit/freddi-python:latest docker push ghcr.io/hombit/freddi-python:latest
- Upload wheels onto PyPi.org
docker run --rm -ti ghcr.io/hombit/freddi-python:$VERSION sh -c "python3.12 -m twine upload /dist/*.tar.gz" # sdist docker run --rm -ti --platform linux/amd64 ghcr.io/hombit/freddi-python:$VERSION sh -c "python3.12 -m twine upload /dist/*.whl" # bdist x86_64 docker run --rm -ti --platform linux/arm64 ghcr.io/hombit/freddi-python:$VERSION sh -c "python3.12 -m twine upload /dist/*.whl" # bdist aarch64
- [Optional] Build executables for GitHub release
- [Optional] Build and upload macOS wheels
- Crate new GitHub release
If you have any problems, questions, or comments, please address them to Issues or to [email protected]
Copyright (c) 2016–2024, 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, for the case of windy calculations please also refer Avakyan et al. (2021) 2021AstL...47..377A, and for the case of magnetised neutron star please also refer Lipunova et al. (2021) 2021arXiv211008076L.
@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}
}
@ARTICLE{2021AstL...47..377A,
author = {{Avakyan}, A.~L. and {Lipunova}, G.~V. and {Malanchev}, K.~L. and {Shakura}, N.~I.},
title = "{Change in the Orbital Period of a Binary System Due to an Outburst in a Windy Accretion Disk}",
journal = {Astronomy Letters},
keywords = {X-ray binaries, wind, transients, period, accretion, Astrophysics - High Energy Astrophysical Phenomena},
year = 2021,
month = jun,
volume = {47},
number = {6},
pages = {377-389},
doi = {10.1134/S1063773721050017},
archivePrefix = {arXiv},
eprint = {2105.11974},
primaryClass = {astro-ph.HE},
adsurl = {https://ui.adsabs.harvard.edu/abs/2021AstL...47..377A},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2021arXiv211008076L,
author = {{Lipunova}, Galina and {Malanchev}, Konstantin and {Tsygankov}, Sergey and {Shakura}, Nikolai and {Tavleev}, Andrei and {Kolesnikov}, Dmitry},
title = "{Physical modeling of viscous disc evolution around magnetized neutron star. Aql X-1 2013 outburst decay}",
journal = {arXiv e-prints},
keywords = {Astrophysics - High Energy Astrophysical Phenomena, Astrophysics - Solar and Stellar Astrophysics},
year = 2021,
month = oct,
eid = {arXiv:2110.08076},
pages = {arXiv:2110.08076},
archivePrefix = {arXiv},
eprint = {2110.08076},
primaryClass = {astro-ph.HE},
adsurl = {https://ui.adsabs.harvard.edu/abs/2021arXiv211008076L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}