Commit 8fb964bd authored by Michal Dovčiak's avatar Michal Dovčiak
Browse files

Add blackbody reverberation due to partial thermalisation of incident flux.

parent f07f4218
......@@ -34,6 +34,9 @@ _Assumptions of the model:_
* re-processing in the ionised accretion disc is computed for each radius from
REFLIONX tables for constant density slab illuminated by power-law radiation,
* increase in the disc temperature due to partial thermalisation of the
illuminating flux
* the ionisation of the disc is set for each radius according to the amount of
the incident primary flux and the density of the accretion disc,
......@@ -188,30 +191,43 @@ Definition in XSPEC
- radial power-law density profile
* **par15 ... abun**
- Fe abundance (in solar abundance)
* **par16 ... alpha**
* **par16 ... therm**
- fraction of thermalised flux from the overal incident flux illuminating
the disc
- = 0: only the reverberation of reflected radiation is computed
- < 0: only the reverberation of thermal radiation is computed
- > 0: both the thermal and reflection reverberation is included
- abs(par16) > 1: the fraction of thermalisation is computed from
difference between the incident and reflected fluxes
* **par17 ... arate**
- accretion rate in units of L~Edd~ if positive or in Solar mass per
Julian year (365.25 days) if negative
* **par18 ... f_col**
- spectral hardening factor
* **par19 ... alpha**
- position of the cloud centre in GM/c^2 in alpha coordinate (alpha being
the impact parameter in &phi;-direction, positive for approaching side
of the disc)
* **par17 ... beta**
* **par20 ... beta**
- position of the cloud centre in GM/c^2 in beta coordinate (beta being
the impact parameter in &theta;-direction, positive in up direction,
i.e. above the disc)
* **par18 ... rcloud**
* **par21 ... 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**
* **par22 ... zshift**
- overall Doppler shift
* **par20 ... limb**
* **par23 ... limb**
- 0: for isotropic emission (flux ~ 1)
- 1: for Laor's limb darkening (flux ~ 1+2.06&mu;)
- 2: for Haardt's limb brightening (flux ~ ln (1+1/&mu;))
* **par21 ... tab**
* **par24 ... 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**
* **par25 ... sw**
- switch for the way how to compute the refl. spectra
- 1: use the computed ionisation parameter, &xi;, for the interpolation
in reflion, i.e. use proper total incident intensity with the
......@@ -219,30 +235,30 @@ Definition in XSPEC
- 2: use the ionisation parameter, &xi;, 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**
* **par26 ... ntable**
- defines fits file with tables (0 &le; ntable &le; 99), currently the
tables with ntable=80 are correct for this model
* **par24 ... nrad**
* **par27 ... nrad**
- number of grid points in radius
- if negative than the number of radial grid points is dependent on
height as -nrad&nbsp;/&nbsp;height^(&nbsp;0.66)
* **par25 ... division**
* **par28 ... division**
- type of division in radial integration
- 0: equidistant radial grid (constant linear step)
- 1: exponential radial grid (constant logarithmic step)
- >1: mixed radial grid with a constant logarithmic step in the inner
region and with a constant linear step in the outer region; the
total nradius (par24) number of points is divided in the 3:2 ratio
in these regions; the value of par25 gives the transition radius
total nradius (par27) number of points is divided in the 3:2 ratio
in these regions; the value of par28 gives the transition radius
between these regions (in GM/c^(2))
- -1: mixed radial grid with the transition radius at 2&times;height
* **par26 ... nphi**
* **par29 ... nphi**
- number of grid points in azimuth
* **par27 ... deltaT**
* **par30 ... deltaT**
- length of the time bin (GM/c^(3))
* **par28 ... nt**
* **par31 ... nt**
- number of time subbins per one time bin
* **par29 ... t1/f1/E1**
* **par32 ... t1/f1/E1**
- the time to be used in XSPEC for the spectrum (0 means average
spectrum, i.e. divided by the flare duration)
- the frequency to be used in XSPEC for the energy dependent Fourier
......@@ -250,21 +266,21 @@ Definition in XSPEC
wrapping frequency)
- positive values are in sec or Hz
- negative values are in GM/c^3 or (GM/c^(3))^(-1)
- if different than par30, the value gives the lower end of the
- if different than par33, the value gives the lower end of the
time/frequency interval of interest
- if same as par30, then the functions are computed for this value of
- if same as par33, then the functions are computed for this value of
the time/frequency of interest
- in case of frequency dependent lags it defines the lower value of the
energy band of interest in keV
* **par30 ... t2/f2/E2**
- used only if different than par29 and if par29 is nonzero
* **par33 ... t2/f2/E2**
- used only if different than par32 and if par32 is nonzero
- its value gives the upper end of the time/frequency interval of
interest
- positive values are in sec or Hz
- negative values are in GM/c^3 or (GM/c^(3))^(-1)
- in case of frequency dependent lags it defines the upper value of the
energy band of interest in keV
* **par31 ... Eref1**
* **par34 ... Eref1**
- it defines the lower value of the reference energy band for lag or
amplitude energy dependence as well as in case of frequency dependent
lags and amplitudes
......@@ -273,107 +289,107 @@ Definition in XSPEC
* for lag-energy spectra, the whole energy band is used as a reference
band, always excluding the current energy bin
* for lag-frequency dependence, the energy reference band is
abs(par31) to abs(par32) excluding overlaping part with energy band
of interest abs(par29) to abs(par30)
* **par32 ... Eref2**
abs(par34) to abs(par35) excluding overlaping part with energy band
of interest abs(par32) to abs(par33)
* **par35 ... Eref2**
- it defines the upper value of the reference energy band for lag-energy
dependence as well as in case of frequency dependent lags
* **par33 ... dt/Af**
- lag shift for lag-energy dependence in case of par35=+6
* **par36 ... dt/Af**
- lag shift for lag-energy dependence in case of par38=+6
- multiplicative factor in case of adding empirical hard lags
Af&times;f^(qf), used for par35=+16;
if par33=-1 then the following hard lags prescription is used (see
Af&times;f^(qf), used for par38=+16 and par38=+18;
if par36=-1 then the following hard lags prescription is used (see
Epitropakis & Papadakis, 2017):
100 * log10(Eref/E) * (f/1e-4)^(-1) s
with Eref being middle of the reference energy band and E middle of
100 * log10(E~ref~/E) * (f/1e-4)^(-1) s
with E~ref~ being middle of the reference energy band and E middle of
the energy band of interest
* **par34 ... Amp/qf**
* **par37 ... Amp/qf**
- multiplicative factor for the amplitude-energy dependence in case of
par35=+5
par38=+5
- powerlaw index in case of adding empirical hard lags Af&times;f^(qf),
used for par35=+16
* **par35 ... xsw**
used for par38=+16 and par38=+18
* **par38 ... xsw**
- defines output in the XSPEC (photar array)
- 0: spectrum for time interval defined by par29 and par30
- 0: spectrum for time interval defined by par32 and par33
- _the following values correspond to energy dependent Fourier transform
at the frequency band defined by par29 and par30:_
at the frequency band defined by par32 and par33:_
- -1: real part of FT of the relative reflection
- -2: imaginary part of FT of the relative reflection
- -3: amplitude of FT of the relative reflection
- -4: phase of FT of the relative reflection
- -5: amplitude for the relative reflection divided by amplitude in the
reference energy band defined by par31 and par32 (integration in
reference energy band defined by par34 and par35 (integration in
frequencies is done in real and imaginary parts first and then
the amplitudes are computed)
- -6: lag for the relative reflection with respect to reference energy
band defined by par31 and par32 (integration in frequencies is
band defined by par34 and par35 (integration in frequencies is
done in real and imaginary parts first and then the lags are
computed with frequency at half of the wrapping frequency or
middle of the frequency band)
- -7: amplitude for the relative reflection divided by amplitude in
the reference energy band defined by par31 and par32 (integration
the reference energy band defined by par34 and par35 (integration
in frequencies here is done in amplitudes directly)
- -8: lag for the relative reflection with respect to reference energy
band defined by par31 and par32 (integration in frequencies here
band defined by par34 and par35 (integration in frequencies here
is done in lags directly)
- 1: real part of FT including primary radiation
- 2: imaginary part of FT including primary radiation
- 3: amplitude of FT including primary radiation
- 4: phase of FT including primary radiation
- 5: amplitude including the primary radiation divided by amplitude in
the reference energy band defined by par31 and par32 (integration
the reference energy band defined by par34 and par35 (integration
in frequencies is done in real and imaginary parts first and then
the amplitudes are computed)
- 6: lag diluted by primary radiation with respect to reference energy
band defined by par31 and par32 (integration in frequencies is
band defined by par34 and par35 (integration in frequencies is
done in real and imaginary parts first and then the lags are
computed with frequency at half of the wrapping frequency or
middle of the frequency band)
- 7: amplitude including the primary radiation divided by amplitude in
the reference energy band defined by par31 and par32 (integration
the reference energy band defined by par34 and par35 (integration
in frequencies here is done in amplitudes directly)
- 8: lag diluted by primary radiation with respect to reference energy
band defined by par31 and par32 (integration in frequencies here
band defined by par34 and par35 (integration in frequencies here
is done in lags directly)
- _the following values correspond to frequency dependent Fourier
transform for the energy band of interest defined by par29 and par30:_
transform for the energy band of interest defined by par32 and par33:_
- -11: real part of FT of the relative reflection
- -12: imaginary part of FT of the relative reflection
- -13: amplitude of FT of the relative reflection
- -14: phase of FT of the relative reflection
- -15: amplitude for the relative reflection divided by amplitude in
the reference energy band defined by par31 and par32 (rebinning
the reference energy band defined by par34 and par35 (rebinning
here is done in real and imaginary parts first and then the
amplitudes are computed)
- -16: lag for the relative reflection with respect to reference energy
band defined by par31 and par32 (rebinning here is done in real
band defined by par34 and par35 (rebinning here is done in real
and imaginary parts first and then the lags are computed)
- -17: amplitude for the relative reflection divided by amplitude in
the reference energy band defined by par31 and par32 (rebinning
the reference energy band defined by par34 and par35 (rebinning
here is done in amplitudes directly)
- -18: lag for the relative reflection with respect to reference energy
band defined by par31 and par32 (rebinning here is done in lags
band defined by par34 and par35 (rebinning here is done in lags
directly)
- 11: real part of FT including primary radiation
- 12: imaginary part of FT including primary radiation
- 13: amplitude of FT including primary radiation
- 14: phase of FT including primary radiation
- 15: amplitude including the primary radiation divided by amplitude in
the reference energy band defined by par31 and par32 (rebinning
the reference energy band defined by par34 and par35 (rebinning
here is done in real and imaginary parts first and then the
amplitudes are computed)
- 16: lag diluted by primary radiation with respect to reference energy
band defined by par31 and par32 (rebinning here is done in real
band defined by par34 and par35 (rebinning here is done in real
and imaginary parts first and then the lags are computed)
- 17: amplitude including the primary radiation divided by amplitude in
the reference energy band defined by par31 and par32 (rebinning
the reference energy band defined by par34 and par35 (rebinning
here is done in amplitudes directly)
- 18: lag diluted by primary radiation with respect to reference energy
band defined by par31 and par32 (rebinning here is done in lags
band defined by par34 and par35 (rebinning here is done in lags
directly)
* **par36 ... nthreads**
* **par39 ... nthreads**
- how many threads should be used for computations
* **par37 ... norm**
* **par40 ... norm**
- **has to be set to unity!**
Definition outside XSPEC
......@@ -427,28 +443,31 @@ Definition outside XSPEC
param[12] = 1.; // density
param[13] = 0.; // den_prof
param[14] = 1.; // abun
param[15] = -6.; // alpha
param[16] = 0.; // beta
param[17] = 0.; // rcloud
param[18] = 0.; // zshift
param[19] = 0.; // limb
param[20] = 2.; // tab
param[21] = 2.; // sw
param[22] = 80.; // ntable
param[23] = -4488.; // nrad
param[24] = -1.; // division
param[25] = 180.; // nphi
param[26] = 1.; // deltaT
param[27] = 1.; // nt
param[28] = 2.e-4; // t1/f1/E1
param[29] = 8.e-4; // t2/f2/E2
param[30] = -1.; // Eref1
param[31] = 3.; // Eref2
param[32] = 0.; // dt/Af
param[33] = 1.; // Amp/qf
param[34] = 6.; // xsw
param[35] = 4.; // nthreads
param[36] = 1.; // norm
param[15] = 0.; // thermalisation
param[16] = 0.1; // arate
param[17] = 2.4; // f_col
param[18] = -6.; // alpha
param[19] = 0.; // beta
param[20] = 0.; // rcloud
param[21] = 0.; // zshift
param[22] = 0.; // limb
param[23] = 2.; // tab
param[24] = 2.; // sw
param[25] = 80.; // ntable
param[26] = -4488.; // nrad
param[27] = -1.; // division
param[28] = 180.; // nphi
param[29] = 1.; // deltaT
param[30] = 1.; // nt
param[31] = 2.e-4; // t1/f1/E1
param[32] = 8.e-4; // t2/f2/E2
param[33] = -1.; // Eref1
param[34] = 3.; // Eref2
param[35] = 0.; // dt/Af
param[36] = 1.; // Amp/qf
param[37] = 6.; // xsw
param[38] = 4.; // nthreads
param[39] = 1.; // norm
- some parameters are later changed in the loops for convenience (to
create files for grid of parameters), see lines as:
......
kynrefrev 36 0. 1.0e20 c_KYNrefrev add 0
kynrefrev 39 0. 1.0e20 c_KYNrefrev add 0
a/M GM/c 1. 0. 0. 1. 1. 0.2
theta_o deg 30. 0. 0. 89. 89. 5.
rin GM/c^2 1. 1. 1. 1000. 1000. -0.5
......@@ -14,6 +14,9 @@ Np:Nr " " 1.0 0. 0. 10. 10. -0.1
density " " 1. 1e-8 1e-8 1e+8 1e+8 5.
den_prof " " 0. -5. -5. 0. 0. 0.1
abun " " 1. 0.1 0.1 20. 20. 0.01
therm " " 0. -2. -2. 2. 2. -0.1
arate Ledd 0.1 1.e-5 1.e-5 100. 100. -0.1
f_col " " 2.4 1. 1. 3. 3. -0.1
alpha GM/c^2 -6. -100. -100. 100. 100. 1.
beta GM/c^2 0. -100. -100. 100. 100. 1.
rcloud GM/c^2 0. 0. 0. 100. 100. 1.
......@@ -23,15 +26,15 @@ $tab 2.
$sw 2.
ntable " " 80. 0. 0. 99. 99. -1.
nrad " " -4488. -10000. -10000. 10000. 10000. -100.
division " " -1. -1. -1. 1. 1. -1.
division " " -1. -1. -1. 1. 1. -1.
nphi " " 180. 1. 1. 20000. 20000. -100.
deltaT GM/c^3 1. 1e-3 1e-3 10. 10. -0.05
nt " " 1. 1. 1. 10. 10. -1.
nt_ratio " " 1. 1. 1. 10. 10. -1.
t1/f1/E1 s/Hz/keV 0.3 -1e8 -1e8 1e16 1e16 -1.
t2/f2/E2 s/Hz/keV 0.8 -1e8 -1e8 1e16 1e16 -1.
Eref1 keV 1. -1. -1. 100. 100. -1.
Eref2 keV 3. 0. 0. 100. 100. -1.
dt/Af s/- 0. -1e8 -1e8 1e8 1e8 -1.
Amp/qf " " 1. -1e8 -1e8 1e8 1e8 -1.
Amp/qf " " 1. -1e8 -1e8 1e8 1e8 -1.
$xsw 16.
nthreads " " 4. 1. 1. 100. 100. -1.
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