4.1.41. Tpho: Time-dependent, non-equilibrium, photoionised plasma model

The tpho model computes the state of a photoionised plasma that is out of equilibrium due to changes in the ionising radiation. In the pion model, which corresponds to a photoionisation equilibrium (PIE) plasma, the heating=cooling solution is found for the plasma. However, in the tpho model this is not necessarily the case. Depending on the spectral energy distribution (SED) variation, and the parameters of the plasma (such as its density), heating does not balance cooling in the plasma. The tpho model can be considered to be analogous to the neij model in SPEX, but for a photoionised plasma case.

For the tpho computation the user provides the X-ray lightcurve of the ionising source as an input file. At time=0, the model is calculated at PIE condition like the pion model. Then at time > 0, the heating and cooling processes are calculated as the SED is scaled according to the provided lightcurve. The state of the plasma is evolved and the corresponding non-equilibrium temperature is calculated at each step. At t=final, the evolution and calculations finish, and the final spectrum is displayed in SPEX. The tpho model also has an option to store intermediate results of the computations (from time=0 to time=final) as ASCII outputs for further examination by the user outside of SPEX.

Users also have the option to introduce a time-varying absorber between the light source and the target plasma, with mode = 3. This choice is particularly relevant for scientific cases focused on the evolution of warm absorbers with the presence of an intermittent obscurer at a smaller radius. It is in principle possible to simulate a time-varying SED with changing hardness ratio using the obscuration option.

The parameters of the model are:

nh:

Hydrogen column density in 10^{28} \mathrm{m}^{-2}. Default value: 10^{-4} (corresponding to 10^{24} \mathrm{m}^{-2}).

xi:

the ^{10}\log of the initial (time=0) ionisation parameter \log\xi in units of 10^{-9} W m. Default value: 1.

mode:

This parameter specifies how the ionising SED is taken into account. Mode=1 means use the continuum models that the user has set up in SPEX (e.g. pow). This mode is the same as how the continuum is used in the pion model. Mode=2 means an input SED file in ASCII format is read. Mode=3 means an input SED file in ASCII format is needed, together with a time-varying absorber obscuring the SED.

sed:

The name of the input SED file, if mode=2 or 3. The format of this file is like the file model in SPEX and is as following: the 1st line contains the number of data points, and the next lines provide the energy in keV (1st column) and the flux in 10^{44} photons/s/keV (2nd column). Remember to use ’aval’ instead of ’val’ when setting the name of the parameter in SPEX.

lc:

The name of the file containing the lightcurve. The first column is time in second, and the second column is the X-ray flux (energy per unit area per second). For mode=3, this file should contains two extra columnes. The third column is column density of the absorber in 10^{28} \mathrm{m}^{-2}, and the fourth column is the covering factor of the absorber. Remember to use ’aval’ instead of ’val’ when setting the name of the parameter in SPEX.

hden:

Hydrogen number density in 10^{20} \mathrm{m}^{-3}.

icov:

Type of the covering fraction. Default value: 2 (constant, set by fcov). If icov=1, full covering is applied. If icov=3, covering fraction follows a tangent function that increases with energy. If icov=4, covering fraction follows an inverse tangent function that decreases with energy. See description in pion.

fcov:

The covering factor of the absorber if icov=2. Default value: 1 (full covering). If icov=3 or 4, it sets the covering factor at the high energy end.

lcov:

The covering factor of the absorber at the low energy end. Default value: 1. lcov is applied only when icov=3 or 4. See description in pion.

ecov:

The energy when the covering factor changes from lcov to fcov. Only applied if icov=3 or 4.

acov:

The width of the transit on covering factor. Only applied if icov=3 or 4.

v:

Root mean square velocity \sigma_{\mathrm v}

zv:

Average systematic velocity v of the absorber (using relativistic Doppler shift)

ref:

Reference element for abundances

01..28:

Abundances of H to Ni; only here we take H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni.

info:

Flag for writing out the intermediate calculation results into ASCII files. Info=0 (default) does not write any files, while info=1 writes the intermediate results into a directory called tpho_info. The following ASCII files are produced: plasma.dat (1st column: time (s); 2nd column: ionisation parameter \xi in erg cm /s; 3rd column: T in keV; 4th column: \Xi; 5th column: total heating in \mathrm{W m^{-3}}; 6th column: total cooling in \mathrm{W m^{-3}}; 7th column: electron-ion equilibration time in s). Note: just for info, we adopt for this version electron-ion equilibrium. heatproc.dat with subsequent columns time, \xi, T, \Xi and total heating and cooling in the same units as the file plasma.dat, followed by the contributions to the total heating (Compton scattering, free-free absorption, photo-ionisation, Compton ionisation, Auger electrons, collisional de-excitation, external heating) and to the total cooling (Inverse Compton scattering, collisional ionisation, radiative recombination, bremsstrahlung, collisional excitation and dielectronic recombination); files ion01.dat to ion30.dat, with the ion concentrations of the ions for each element labeled by its atomic number Z (1–30) as a function of time (s); the concentrations are relative to the total hydrogen density; spect.dat (1st column: E in keV, 2nd column: transmission). We note that currently only the final spectrum (at t=final) can be stored; the user however can modify the t=final in the lightcurve file to be able to see the spectrum at the desired time in SPEX.

oxil:

the ^{10}\log ionisation parameter of the obscurer \log\xi in units of 10^{-9} W m. Default value: 1.

ov:

Root mean square velocity of the obscurer \sigma_{\mathrm v}

zv:

Average systematic velocity v of the obscurer (using relativistic Doppler shift)

ofla:

This flag specifies how the ionization parameter is evaluated for the obscurer. ofla=1 means a constant ionization parameter, ofla=2 means that the ionization of the obscurer scales instantaneously with the SED flux.

Warning

Please note the tpho model is currently in the testing phase.

Warning

Please note that if the final time is very large, the computation may take a long time, because time steps are not allowed to be larger than a certain fraction of the thermal time scale; make sure that your parameters are well and reasonable defined.

For questions and issues regarding the model please contact Missagh Mehdipour and Daniele Rogantini.