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README.md

Table of contents

Description

KYN is a set of the XSPEC models for emission from the black hole accretion disc with the following assumptions and features:

  • space-time around black hole is described by Kerr metric,
  • accretion disc is Keplerian, geometrically thin and optically thick,
  • disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter which is orbiting at the ISCO,
  • disc may be non-axisymmetric - only part of the disc may be emitting (sections in radius and azimuth),
  • obscuration by circular cloud is possible,
  • polarisation properties are computed in some of the models,
  • full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the models,
  • the pre-calculated tables contain impact parameters - α and β coordinates thus in principle non-Keplerian (but still geometrically thin) discs are possible - however, the definitions of the disc velocity would have to be changed inside the code,
  • the computations are parallelized with threads.

Models included:

  • Relativistic fluorescent line models:

    • KYNrline - relativistic line with broken power-law radial emissivity,
    • KYNrlpli - relativistic line in lamp-post geometry.
  • Relativistic convolution models:

    • KYNconv - relativistic convolution model with broken power-law radial emissivity,
    • KYNclp - relativistic convolution model in lamp-post geometry.
  • Relativistic reflection models:

    • KYNlpcr - relativistic reflection model in lamp-post geometry for neutral disc (local emissivity computed by NOAR), polarisation properties are provided
    • KYNrefionx - relativistic reflection model in lamp-post geometry for ionised disc (local emissivity is given by REFLIONX),
    • KYNxillver - relativistic reflection model in lamp-post geometry for ionised disc (local emissivity is given by XILLVER),
    • KYNhrefl - relativistic reflection model with broken power-law emissivity for continuum based on HREFL(POWERLAW).
  • Thermal radiation models:

    • KYNphebb - relativistic thermal radiation with radial power-law temperature profile, polarisation properties are provided
    • KYNbb - relativistic thermal radiation with Novikov-Thorne temperature profile (without self-irradiation and with colour correction factor), polarisation properties are provided.

The KYN package is based upon its first version presented in Dovciak M., Karas V. & Yaqoob T. (2004) ApJS, 153, 205-221.

Installation

Required files

Usage in XSPEC

The code is compiled inside XSPEC with the following command (assuming all the source files and FITS tables are in the directory /path/to/KYN):

  • initpackage kyn lmodel-kyn.dat /path/to/KYN

To use the KYN models inside XSPEC, first the package needs to be loaded and directory with KYN set:

  • lmod kyn /path/to/KYN
  • xset KYDIR /path/to/KYN

Then any model from KYN package may be used, e.g.:

  • mo kynrline

Note: In case of segmentation fault, one may need to increase the stack size, e.g. with the command ulimit -s unlimited or ulimit -s 65532.

Usage outside of XSPEC

  • One also needs the Makefile and libxspec library included in the directory 'other'.

  • The library to work with FITS files (libcfitsio.so) is needed, thus one needs to define the name of the library and path to it in the provided Makefile.

  • The model parameters have to be changed inside the source file:

    • energy in the following lines:

            #define NE     30
            #define E_MIN  0.3
            #define E_MAX  80.
      

      and later choose if linear or exponential energy binning should be used:

            for (ie = 0; ie <= NE; ie++) {
            //  ear[ie] = E_MIN + ie * (E_MAX-E_MIN) / NE;
              ear[ie] = E_MIN * pow(E_MAX/E_MIN, ((double) ie) / NE);
            }
      
    • all basic parameters of the models (physical ones as well as those defining resolution grid for computations) are defined in the following lines:

            param[ 0] = 1.;       // a/M
            param[ 1] = 30.;      // theta_o
            param[ 2] = 1.;       // rin
            param[ 3] = 1.;       // ms
            param[ 4] = 400.;     // rout
            param[ 5] = 0.;       // phi0
            param[ 6] = 360.;     // dphi
            ...
            ...
            ...
      
  • Compile with the make command, e.g.:

    • make kynrline
  • Run the code, e.g.:

    • ./kynrline
  • The model creates the file with the parameters used and the file with the computed spectrum, e.g.:

    • kynrline.txt
    • kynrline_photar.dat

Note:

  • To use KYNLPCR, KYNREFIONX and KYNXILLVER outside of XSPEC one still needs the local installation of XSPEC because its libraries are needed (this might be changed in the future). To compile these models one needs to change definitions of the XSPEC directories inside Makefile.

  • In case of segmentation fault, one may need to increase the stack size, e.g. with the command ulimit -s unlimited or ulimit -s 65532.

KYN models

KYNrline

Relativistically broadened emission line from black hole accretion disc. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. Broken power-law radial emissivity and several limb darkening/brightening laws for emission directionality are implemented. Only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on its first version presented in Dovciak M., Karas V. & Yaqoob T. (2004) ApJS, 153, 205-221.

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... Erest
    • rest energy of the line (keV)
  • par9 ... sigma
    • width of the line - Gaussian sigma (eV)
  • par10 ... q_out
    • power-law index for radial dependence of emissivity for outer region, scales as r-q_out
  • par11 ... q_in
    • power-law index for radial dependence of emissivity for inner region, scales as rbq_in-q_out × r-q_in
  • par12 ... rb
    • boundary between the region with power-law index q_out and q_in
    • if > 0 then the boundary is in units of MSO, i.e. boundary = rb × r~mso~
    • if 2
  • par13 ... jump
    • ratio of local flux in inner region to local flux in outer region at boundary radius defined by rb
  • par14 ... limb
    • limb darkening/brightening law for emission directionality
    • 0: for isotropic emission (flux ~ 1)
    • -1: for Laor's limb darkening (flux ~ 1+2.06μ)
    • -2: for Haardt's limb brightening (flux ~ ln (1+1/μ))
    • if different from 0, -1 and -2 then the local emisivity is ~ mulimb
  • par15 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par16 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par17 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par18 ... zshift
    • overall Doppler shift
  • par19 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par20 ... nrad
    • number of grid points in radius
  • par21 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par22 ... nphi
    • number of grid points in azimuth
  • par23 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par24 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par25 ... nthreads
    • number of threads used for computations
  • par26 ... normtype
    • how to normalize the spectra
    • 0: normalization to the total photon flux
    • > 0: normalization to the photon flux at par26 keV
    • -1: the photon flux is not re-normalized,
    • -2: normalization to the maximum of the photon flux
  • par27 ... norm
    • depending on par26 it sets either the total photon flux, flux at given energy or maximum of the photon flux

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.
  • In this model it is assumed that the local emission is completely linearly polarised in the direction perpendicular to the disc.

KYNrlpli

Relativistically broadened emission line from black hole accretion disc in the lamp-post geometry. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The radial emissivity is given by the disc illumination from a point source located at some height on the system axis. The fluorescent iron line is modelled by Monte Carlo code NOAR (Dumont, A.-M., Abrassart, A., & Collin, S. 2000, A&A, 357, 823) that gives slight limb brightening emission directionality that depends on the primary source power-law photon index. In this model only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is presented in Dovciak, M., Svoboda, J., Goosmann, R. W., et al. (2014) in Proceedings of RAGtime 14-16: Workshops on black holes and neutron stars (Silesian University in Opava), [arXiv:1412.8627].

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... height
    • height on the axis (measured from the center) at which the primary source is located (GM/c2)
  • par9 ... PhoIndex
    • power-law energy index of the primary flux
  • par10 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par11 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par12 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par13 ... zshift
    • overall Doppler shift
  • par14 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par15 ... nrad
    • number of grid points in radius
  • par16 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par17 ... nphi
    • number of grid points in azimuth
  • par18 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par19 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par20 ... nthreads
    • number of threads used for computations
  • par21 ... normtype
    • how to normalize the spectra
    • 0: normalization to the total photon flux
    • > 0: normalization to the photon flux at par21 keV
    • -1: the photon flux is not re-normalized,
    • -2: normalization to the maximum of the photon flux
  • par22 ... norm
    • depending on par21 it sets either the total photon flux, flux at given energy or maximum of the photon flux

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.
  • In this model it is assumed that the local emission is completely linearly polarised in the direction perpendicular to the disc.

KYNconv

Convolution model for relativistic broadening of the emission coming from black hole accretion disc. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. Broken power-law radial emissivity and several limb darkening/brightening laws for emission directionality are implemented. Only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on its first version presented in Dovciak M., Karas V. & Yaqoob T. (2004) ApJS, 153, 205-221.

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... q_out
    • power-law index for radial dependence of emissivity for outer region, scales as r-q_out
  • par9 ... q_in
    • power-law index for radial dependence of emissivity for inner region, scales as rbq_in-q_out × r-q_in
  • par10 ... rb
    • boundary between the region with power-law index q_out and q_in
    • if > 0 then the boundary is in units of MSO, i.e. boundary = rb × r~mso~
    • if 2
  • par11 ... jump
    • ratio of local flux in inner region to local flux in outer region at boundary radius defined by rb
  • par12 ... limb
    • limb darkening/brightening law for emission directionality
    • 0: for isotropic emission (flux ~ 1)
    • -1: for Laor's limb darkening (flux ~ 1+2.06μ)
    • -2: for Haardt's limb brightening (flux ~ ln (1+1/μ))
    • if different from 0, -1 and -2 then the local emisivity is ~ mulimb
  • par13 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par14 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par15 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par16 ... zshift
    • overall Doppler shift
  • par17 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par18 ... nrad
    • number of grid points in radius
  • par19 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par20 ... nphi
    • number of grid points in azimuth
  • par21 ... ne_loc
    • number of grid points in local energy (energy resolution of local flux), the grid is equidistant in logarithmic scale
  • par22 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par23 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par24 ... nthreads
    • number of threads used for computations
  • par25 ... normtype
    • how to normalize the spectra
    • 0: normalization to the total photon flux
    • > 0: normalization to the photon flux at par25 keV
    • -1: the photon flux is not re-normalized,
    • -2: normalization to the maximum of the photon flux

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • There are several restrictions that arise from the fact that we use existing XSPEC models for definition of the local flux:
    • only the energy dependence of the photon flux can be defined by local XSPEC models,
    • only a certain type of radial dependence of the local photon flux can be imposed; here we have chosen to use a broken power-law radial dependence,
    • there is no intrinsic azimuthal dependence of the local photon flux, the only azimuthal dependence comes through limb darkening/brightening law (emission angle depends on azimuth)
    • local flux can highly depend on the energy resolution, i.e. on the energy binning used, if the energy resolution is not high enough. This is because the flux is defined in the centre of each bin. A large number of bins is needed for highly varying local flux with energy.
  • Accuracy vs. speed trade off depends mainly on nrad, nphi and ne_loc.
  • In this model it is assumed that the local emission is completely linearly polarised in the direction perpendicular to the disc.

KYNclp

Convolution model for relativistic broadening of the emission from black hole accretion disc in the lamp-post geometry. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The radial emissivity is given by the disc illumination from a point source located at some height on the system axis. The emission directionality is modelled by Monte Carlo code NOAR (Dumont, A.-M., Abrassart, A., & Collin, S. 2000, A&A, 357, 823) that gives slight limb brightening emission law. In this model only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is presented in Dovciak, M., Svoboda, J., Goosmann, R. W., et al. (2014) in Proceedings of RAGtime 14-16: Workshops on black holes and neutron stars (Silesian University in Opava), [arXiv:1412.8627].

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... height
    • height on the axis (measured from the center) at which the primary source is located (GM/c2)
  • par9 ... PhoIndex
    • power-law energy index of the primary flux
  • par10 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par11 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par12 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par13 ... zshift
    • overall Doppler shift
  • par14 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par15 ... nrad
    • number of grid points in radius
  • par16 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par17 ... nphi
    • number of grid points in azimuth
  • par18 ... ne_loc
    • number of grid points in local energy (energy resolution of local flux), the grid is equidistant in logarithmic scale
  • par19 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par20 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par21 ... nthreads
    • number of threads used for computations
  • par22 ... normtype
    • how to normalize the spectra
    • 0: normalization to the total photon flux
    • > 0: normalization to the photon flux at par22 keV
    • -1: the photon flux is not re-normalized,
    • -2: normalization to the maximum of the photon flux

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • There are several restrictions that arise from the fact that we use existing XSPEC models for definition of the local flux:
    • only the energy dependence of the photon flux can be defined by local XSPEC models,
    • only a certain type of radial dependence of the local photon flux can be imposed; here we have chosen to use radial emissivity profile given by an illumination by a point source on the system axis,
    • there is no intrinsic azimuthal dependence of the local photon flux, the only azimuthal dependence comes through limb darkening/brightening law (emission angle depends on azimuth)
    • local flux can highly depend on the energy resolution, i.e. on the energy binning used, if the energy resolution is not high enough. This is because the flux is defined in the centre of each bin. A large number of bins is needed for highly varying local flux with energy.
  • Accuracy vs. speed trade off depends mainly on nrad, nphi and ne_loc.
  • In this model it is assumed that the local emission is completely linearly polarised in the direction perpendicular to the disc.

KYNlpcr

Neutral reflection spectrum from black hole accretion disc in the lamp-post geometry. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The radial emissivity is determined by the disc illumination from a point source located at some height on the system axis. The primary source is isotropic and emits power-law radiation. Re-processing in the neutral disc is modelled by Monte Carlo code NOAR (Dumont, A.-M., Abrassart, A., & Collin, S. 2000, A&A, 357, 823) that gives slight limb brightening emission directionality. In this model only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on KY package of models first presented in Dovciak M., Karas V. & Yaqoob T. 2004, ApJS, 153, 205-221 and later in Dovciak, M., Svoboda, J., Goosmann, R. W., et al. (2014) in Proceedings of RAGtime 14-16: Workshops on black holes and neutron stars (Silesian University in Opava), [arXiv:1412.8627].

This model includes a physical model of polarisation of continuum radiation by reflection from the accretion disc based on Rayleigh scattering in single scattering approximation for both unpolarised and linearly polarised primary radiation, see Chandrasekhar (1960) "Radiative Transfer". The fluorescent lines in this model are intrinsically unpolarised. The relativistic change of polarisation angle for all photon paths from the lamp to the disc, the lamp to the observer as well as the disc to the observer were taken into account.

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... M/M8
    • black hole mass in units of 108 solar masses
  • par9 ... height
    • height on the axis (measured from the center) at which the primary source is located (GM/c2)
  • par10 ... PhoIndex
    • power-law energy index of the primary flux
  • par11 ... L/L~Edd~
    • dE/dt, the observed (if positive) or the intrinsic local (if negative) primary isotropic flux in the X-ray energy range 2-10keV in units of L~Edd~
  • par12 ... Np:Nr
    • ratio of the primary to the reflected normalization
    • 1: self-consistent model for isotropic primary source
    • 0: only reflection, primary source is hidden
    • if positive then L/L~Edd~ (par11) means the luminosity towards the observer
    • if negative then L/L~Edd~ (par11) means the luminosity towards the disc
  • par13 ... line
    • whether to include lines and/or reflection continuum in the spectra
    • 0: only continuum
    • 1: Kα Fe line with continuum
    • 2: Kα and Kβ lines with continuum
    • 3: all lines computed by NOAR for neutral disc
    • -1: only Kα Fe line without the reflection continuum
    • -2: Kα and Kβ lines without the reflection continuum
    • -3: all lines computed by NOAR for neutral disc without the reflection continuum
  • par14 ... E_cut
    • cut-off energy
  • par15 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par16 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par17 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par18 ... zshift
    • > 0: the overall Doppler shift z; the distance of the source is computed from the Hubble law, D = zc/H, with the Hubble constant H = 70 km/s/Mpc; this distance is used to compute the correct normalisation of the spectrum, thus norm parameter (the normalisation of the model) should be frozen to unity
    • = 0: the overall Doppler shift is set to z = 0; the distance to the source and thus the correct normalisation is defined by the normalisation parameter
  • par19 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par20 ... nrad
    • number of grid points in radius
  • par21 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par22 ... nphi
    • number of grid points in azimuth
  • par23 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par24 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par25 ... poldeg
    • intrinsic polarisation degree of primary radiation, used only if par24 > 0
  • par26 ... polangle
    • intrinsic polarisation angle of primary radiation measured counter-clockwise from the axis in degrees when looking towards the incoming photon, zero for polarisation parallel with the axis, used only if par24 > 0
  • par27 ... nthreads
    • number of threads used for computations
  • par28 ... norm
    • if the overall Doppler shift zshift = 0, then norm = 1/D2 where D is the distance to the source in Mpc; in all other cases this parameter should be frozen to 1!

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge), KYRMS (the marginally stable orbit), KYLXLAMP (intrinsic luminosity of the primary source in 2-10keV) and KYREFL (ratio of the reflection photon flux to the primary flux at the observer) are added to the XSPEC internal switches. XSPEC xset command shows their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.

KYNrefionx

Ionised reflection spectrum from black hole accretion disc in the lamp-post geometry. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The radial emissivity is given by the disc illumination from a point source located at some height on the system axis. The primary source is isotropic and emits power-law radiation. The disc ionisation state changes with radius and depends on the illumination patern as well as the radial density profile of the disc. Re-processing in the ionised disc is taken from REFLION(X) tables, see Ross & Fabian (2005) MNRAS, 358, 211. Several limb darkening/brightening laws for emission directionality are implemented. In this model only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on KY package of models first presented in Dovciak M., Karas V. & Yaqoob T. 2004, ApJS, 153, 205-221 and later in Dovciak, M., Svoboda, J., Goosmann, R. W., et al. (2014) in Proceedings of RAGtime 14-16: Workshops on black holes and neutron stars (Silesian University in Opava), [arXiv:1412.8627].

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... M/M8
    • black hole mass in units of 108 solar masses
  • par9 ... height
    • height on the axis (measured from the center) at which the primary source is located (GM/c2)
  • par10 ... PhoIndex
    • power-law energy index of the primary flux
  • par11 ... L/L~Edd~
    • dE/dt, the observed (if positive) or the intrinsic local (if negative) primary isotropic flux in the X-ray energy range 2-10keV in units of L~Edd~
  • par12 ... Np:Nr
    • ratio of the primary to the reflected normalization
    • 1: self-consistent model for isotropic primary source
    • 0: only reflection, primary source is hidden
    • if positive then L/L~Edd~ (par11) means the luminosity towards the observer
    • if negative then L/L~Edd~ (par11) means the luminosity towards the disc
  • par13 ... density/ionisation
    • density profile normalization in 1015 cm-3 if positive
    • ionisation profile normalisation if it is negative
    • this parameter cannot be zero
  • par14 ... den_prof/ion_prof
    • radial power-law density profile if par13 is positive
    • radial ionisation profile if par13 is negative
    • the radial profiles in both cases are given by abs(par13) × rpar14
  • par15 ... abun
    • Fe abundance (in solar abundance)
  • par16 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par17 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par18 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par19 ... zshift
    • > 0: the overall Doppler shift z; the distance of the source is computed from the Hubble law, D = zc/H, with the Hubble constant H = 70 km/s/Mpc; this distance is used to compute the correct normalisation of the spectrum, thus norm parameter (the normalisation of the model) should be frozen to unity
    • = 0: the overall Doppler shift is set to z = 0; the distance to the source and thus the correct normalisation is defined by the normalisation parameter
  • par20 ... limb
    • 0: for isotropic emission (flux ~ 1)
    • 1: for Laor's limb darkening (flux ~ 1+2.06μ)
    • 2: for Haardt's limb brightening (flux ~ ln (1+1/μ))
  • par21 ... tab
    • which REFLION table to use
    • 1: REFLION (the old one, lower cut-off energy at 1eV, not good for PhoIndex > 2)
    • 2: REFLIONX (the newer one, lower cut-off energy at 100eV)
  • par22 ... sw
    • switch for the way how to compute the refl. spectra
    • 1: use the computed ionisation parameter, ξ, for the interpolation in REFLION, i.e. use proper total incident intensity with the shifted cut-offs
    • 2: use the ionisation parameter, ξ, correspondent to the computed normalization of the incident flux, i.e. do not shift the cut-offs when computing the total incident intensity
  • par23 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par24 ... nrad
    • number of grid points in radius
  • par25 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par26 ... nphi
    • number of grid points in azimuth
  • par27 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par28 ... nthreads
    • number of threads used for computations
  • par29 ... norm
    • if the overall Doppler shift zshift = 0, then norm = 1/D2 where D is the distance to the source in Mpc; in all other cases this parameter should be frozen to 1!

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge), KYRMS (the marginally stable orbit), KYLXLAMP (intrinsic luminosity of the primary source in 2-10keV) and KYREFL (ratio of the reflection photon flux to the primary flux at the observer) are added to the XSPEC internal switches. XSPEC xset command shows their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.

KYNxillver

Ionised reflection spectrum from black hole accretion disc in the lamp-post geometry. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The radial emissivity is given by the disc illumination from a point source located at some height on the system axis. The primary source is isotropic and emits power-law radiation. The disc ionisation state changes with radius and depends on the illumination patern as well as the radial density profile of the disc. Re-processing in the ionised disc is taken from XILLVER tables, see Garcia & Kallman (2010), ApJ, 718, 695, Garcia et al. (2013), ApJ, 768, 2 and Garcia et al. (2016), MNRAS, 462, 751. In this model only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on KY package of models first presented in Dovciak M., Karas V. & Yaqoob T. (2004), ApJS, 153, 205-221 and later in Dovciak, M., Svoboda, J., Goosmann, R. W., et al.: (2014), in Proceedings of RAGtime 14-16: Workshops on black holes and neutron stars (Silesian University in Opava), [arXiv:1412.8627].

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... M/M8
    • black hole mass in units of 108 solar masses
  • par9 ... height
    • height on the axis (measured from the center) at which the primary source is located (GM/c2)
  • par10 ... PhoIndex
    • power-law energy index of the primary flux
  • par11 ... L/L~Edd~
    • dE/dt, the observed (if positive) or the intrinsic local (if negative) primary isotropic flux in the X-ray energy range 2-10keV in units of L~Edd~
  • par12 ... Np:Nr
    • ratio of the primary to the reflected normalization
    • 1: self-consistent model for isotropic primary source
    • 0: only reflection, primary source is hidden
    • if positive then L/L~Edd~ (par11) means the luminosity towards the observer
    • if negative then L/L~Edd~ (par11) means the luminosity towards the disc
  • par13 ... density/ionisation
    • density profile normalization in 1015 cm-3 if positive, i.e. n = par13 × rpar14
    • ionisation profile normalisation if it is negative and constant density xillver tables are used, i.e. ξ = -par13 × rpar14
    • ionisation parameter if it is negative and xillver tables dependent on density are used, i.e. ξ = -par13
    • this parameter cannot be zero
  • par14 ... den_prof/ion_prof/density
    • radial power-law density profile if par13 is positive
    • radial ionisation profile if par13 is negative and constant density xillver tables are used
    • density in 1015 cm-3 if par13 is negative and xillver tables dependent on density are used
  • par15 ... abun
    • Fe abundance (in solar abundance)
  • par16 ... E_cut
    • the observed (if positive) or intrinsic local at the source (if negative) cut-off energy of the primary X-ray radiation
  • par17 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par18 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par19 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par20 ... zshift
    • > 0: the overall Doppler shift z; the distance of the source is computed from the Hubble law, D = zc/H, with the Hubble constant H = 70 km/s/Mpc; this distance is used to compute the correct normalisation of the spectrum, thus norm parameter (the normalisation of the model) should be frozen to unity
    • = 0: the overall Doppler shift is set to z = 0; the distance to the source and thus the correct normalisation is defined by the normalisation parameter
  • par21 ... limb
    • only used for angle averaged XILLVER tables
    • 0: for isotropic emission (flux ~ 1)
    • 1: for Laor's limb darkening (flux ~ 1+2.06μ)
    • 2: for Haardt's limb brightening (flux ~ ln (1+1/μ))
  • par22 ... tab
    • which XILLVER table to use
    • 1: xillver.fits, angle averaged with cut-off energy at 300 keV
    • 2: xillver-a.fits, angle dependent with cut-off energy at 300 keV
    • 3: xillver-Ec.fits, angle averaged with free cut-off energy
    • 4: xillver-a-Ec.fits, angle dependent with free cut-off energy
    • 5: xillver-a-Ec2.fits, angle dependent with free cut-off energy
    • 6: xillver-a-Ec3.fits, angle dependent with free cut-off energy
    • 7: xillver-a-Ec4.fits, angle dependent with free cut-off energy
    • 8: xillver-a-Ec5.fits, angle dependent with free cut-off energy
    • 11: xillverD-4.fits, angle dependent with cut-off energy at 300 keV for disc density 1015-1019 cm-3
  • par23 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par24 ... nrad
    • number of grid points in radius
  • par25 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par26 ... nphi
    • number of grid points in azimuth
  • par27 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par28 ... nthreads
    • number of threads used for computations
  • par29 ... norm
    • if the overall Doppler shift zshift = 0, then norm = 1/D2 where D is the distance to the source in Mpc; in all other cases this parameter should be frozen to 1!

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge), KYRMS (the marginally stable orbit), KYLXLAMP (intrinsic luminosity of the primary source in 2-10keV), KYREFL (ratio of the reflection photon flux to the primary flux at the observer), KYXIIN (ionisation parameter at the inner disc edge) and KYXIOUT (ionisation parameter at the outer disc edge) are added to the XSPEC internal switches. XSPEC xset command shows their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.

KYNhrefl

Compton reflection model for a black hole accretion disc. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. This model is based on an existing multiplicative HREFL model in combination with the POWERLAW model. Local emission is the same as in HREFL*POWERLAW with the parameters thetamin = 0 and thetamax = 90 (i.e. it is assumed that the disc is illuminated from all directions isotropically) and with a broken power-law radial dependence added. This model can be interpreted as a Compton-reflection model for which the source of primary irradiation is near above the disc, in contrast to the lamp-post scheme with the source on the axis. The approximations for Compton reflection used in HREFL (and therefore also in this model) are valid below ~15keV (in the disc rest frame). Only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on its first version presented in Dovciak M., Karas V. & Yaqoob T. (2004) ApJS, 153, 205-221.

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... PhoIndex
    • power-law energy index of the primary flux
  • par9 ... q_out
    • power-law index for radial dependence of emissivity for outer region, scales as r-q_out
  • par10 ... q_in
    • power-law index for radial dependence of emissivity for inner region, scales as rbq_in-q_out × r-q_in
  • par11 ... rb
    • boundary between the region with power-law index q_out and q_in
    • if > 0 then the boundary is in units of MSO, i.e. boundary = rb × r~mso~
    • if 2
  • par12 ... jump
    • ratio of local flux in inner region to local flux in outer region at boundary radius defined by rb
  • par13 ... Feabun
    • iron abundance relative to Solar
  • par14 ... FeKedge
    • iron K-edge energy
  • par15 ... Escfrac
    • normalization of the original powerlaw emission
  • par16 ... covfac
    • normalization of the reflected emission
  • par17 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par18 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par19 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par20 ... zshift
    • overall Doppler shift
  • par21 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par22 ... nrad
    • number of grid points in radius
  • par23 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par24 ... nphi
    • number of grid points in azimuth
  • par25 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par26 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par27 ... nthreads
    • number of threads used for computations
  • par28 ... norm

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.
  • In this model it is assumed that the local emission is completely linearly polarised in the direction perpendicular to the disc.

KYNphebb

Phenomenological thermal emission from a black hole accretion disc. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The radial dependence of the disc black-body temperature is a simple powerlaw. The local flux is defined as flux ~ E2/(exp(E/kT)-1), where T=Tin*(r/rin)-BBindex. Only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on KY package of models first presented in Dovciak M., Karas V. & Yaqoob T. (2004) ApJS, 153, 205-221.

The polarisation in this model is computed from Chandrasekhar's formular for infinite optical depth (parameter tau=11) or by the STOKES Monte Carlo code for optical depths tau = 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0. stored in the tables 'goosmann.fits' (computed by the author of the STOKES code Rene Goosmann, see Goosmann & Gaskell 2007, A&A, 465, 129, http://www.stokes-program.info). The tau=10 results are the same as tau=infinity. The tables correspond to a model setup as follows: a plane-parallel electron scattering disc is irradiated from its midplane and evaluated for the Stokes parameters I and Q at 40 different viewing angles, which are given by their cosine values. The values of I and Q are normalized by the total number of photons sampled. A positive value of Q denotes a polarization vector that is parallel with the disk's symmetry axis, a negative value stands for a vector being perpendicular to this axis. The U values are basically zero in all cases. The intrinsic irradiation at the midplane is assumed to be isotropic at every point. The electron scattering is realized by Thomson scattering and therefore wavelength-independent.

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
    • if outer edge is equal or larger than 1000 GM/c2 then the emission from above this radius is added
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... Tin
    • temperature in keV at the inner edge of the disc
  • par9 ... BBindex
    • radial power-law index for radial dependence of the black-body temperature
  • par10 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par11 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par12 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par13 ... zshift
    • overall Doppler shift
  • par14 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par15 ... nrad
    • number of grid points in radius
  • par16 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par17 ... nphi
    • number of grid points in azimuth
  • par18 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par19 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on, different approximation for computed flux is used with non-isotropic emission directionality
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par20 ... tau
    • tau of the disc atmosphere,
    • tables created by Monte Carlo code Stokes for tau = 0.2, 0.5, 1, 2, 5, 10 are used for tau ≤ 10
    • Chandrasekhar's relations for infinite optical depth are used for tau > 10 (I in tables is actually the same already for tau=5 and Q for tau=10)
  • par21 ... nthreads
    • number of threads used for computations
  • par22 ... norm
    • equals to 1/D2 where D is a source distance in 10kpc

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.

KYNbb

Thermal emission from a black hole accretion disc. Black hole may be rotating (Kerr black hole), accretion disc is assumed to be Keplerian, geometrically thin and optically thick. The local flux is a black body radiation with the Novikov-Thorne radial temperature profile. Only part of the disc may be set to be emitting radiation (sections defined in radius and azimuth). Obscuration by circular cloud is possible. Full relativistic ray-tracing code in vacuum was used for photon paths to compute the tables of transfer functions used in the model. Disc area below ISCO may be chosen to emit radiation, in which case material there is assumed to be freely falling and has the same energy and angular momentum as the matter orbiting at the ISCO. The model is based on KY package of models first presented in Dovciak M., Karas V. & Yaqoob T. (2004) ApJS, 153, 205-221.

The polarisation in this model is computed from Chandrasekhar's formular for infinite optical depth (parameter tau=11) or by the STOKES Monte Carlo code for optical depths tau = 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0. stored in the tables 'goosmann.fits' (computed by the author of the STOKES code Rene Goosmann, see Goosmann & Gaskell 2007, A&A, 465, 129, http://www.stokes-program.info). The tau=10 results are the same as tau=infinity. The tables correspond to a model setup as follows: a plane-parallel electron scattering disc is irradiated from its midplane and evaluated for the Stokes parameters I and Q at 40 different viewing angles, which are given by their cosine values. The values of I and Q are normalized by the total number of photons sampled. A positive value of Q denotes a polarization vector that is parallel with the disk's symmetry axis, a negative value stands for a vector being perpendicular to this axis. The U values are basically zero in all cases. The intrinsic irradiation at the midplane is assumed to be isotropic at every point. The electron scattering is realized by Thomson scattering and therefore wavelength-independent.

Definition of the parameters:

  • par1 ... a/M
    • black hole angular momentum (-1 ≤ a/M ≤ 1)
  • par2 ... theta_o
    • observer inclination in degrees (0°-pole, 90°-disc)
  • par3 ... rin
    • inner edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
  • par4 ... ms
    • switch for inner edge
    • 0: we integrate from inner edge = par3
    • 1: if the inner edge of the disc is below marginally stable orbit (MSO) then we integrate emission above MSO only
    • 2: we integrate from inner edge given in units of MSO, i.e. inner edge = par3 × r~mso~ (the same applies for outer edge)
  • par5 ... rout
    • outer edge of non-zero disc emissivity (in GM/c2 or in r~mso~)
    • if outer edge is equal or larger than 1000 GM/c2 then the emission from above this radius is added
  • par6 ... phi
    • lower azimuth of non-zero disc emissivity (degrees)
  • par7 ... dphi
    • (phi + dphi) is upper azimuth of non-zero disc emissivity 0° ≤ dphi ≤ 360°
  • par8 ... BHmass
    • the black hole mass in units of Solar mass
  • par9 ... arate
    • accretion rate in units of Solar mass per Julian year (365.25days)
  • par10 ... f_col
    • spectral hardening factor
  • par11 ... alpha
    • position of the cloud centre in GM/c2 in alpha coordinate (alpha being the impact parameter in φ-direction, positive for approaching side of the disc)
  • par12 ... beta
    • position of the cloud centre in GM/c2 in beta coordinate (beta being the impact parameter in θ-direction, positive in up direction, i.e. above the disc)
  • par13 ... rcloud
    • radius of the obscuring cloud
    • the meaning of cloud is inverted for negative values of rcloud, i.e. only the radiation transmitted through the cloud is computed
  • par14 ... zshift
    • overall Doppler shift
  • par15 ... ntable
    • table of relativistic transfer functions used in the model (defines FITS file with tables), 0 ≤ ntable ≤ 99, currently the tables with ntable=80 are correct for this model
  • par16 ... nrad
    • number of grid points in radius
  • par17 ... division
    • type of division in radial integration
    • 0: equidistant radial grid (constant linear step)
    • 1: exponential radial grid (constant logarithmic step)
  • par18 ... nphi
    • number of grid points in azimuth
  • par19 ... smooth
    • whether to smooth the resulting spectrum
    • 0: no smoothing
    • 1: simple smoothing
  • par20 ... Stokes
    • definition of output
    • 0: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched off
    • 1: photon number density flux per bin (Stokes parameter I devided by energy) with the polarisation computations switched on, different approximation for computed flux is used with non-isotropic emission directionality
    • 2: Stokes parameter Q devided by energy
    • 3: Stokes parameter U devided by energy
    • 4: Stokes parameter V devided by energy
    • 5: degree of polarisation
    • 6: linear polarisation angle ψ = 0.5 atan(U/Q)
    • 7: circular polarisation angle β = 0.5 asin(V/sqrt(Q2+U2+V2))
  • par21 ... tau
    • tau of the disc atmosphere,
    • tables created by Monte Carlo code Stokes for tau = 0.2, 0.5, 1, 2, 5, 10 are used for tau ≤ 10
    • Chandrasekhar's relations for infinite optical depth are used for tau > 10 (I in tables is actually the same already for tau=5 and Q for tau=10)
  • par22 ... nthreads
    • number of threads used for computations
  • par23 ... norm
    • equals to 1/D2 where D is a source distance in 10kpc

Note:

  • KYRH (the black hole horizon), KYRIN (the disc inner edge) and KYRMS (the marginally stable orbit) are added to the XSPEC internal switches. Use xset command to show their current values.
  • Accuracy vs. speed trade off depends mainly on nrad and nphi.