4.1.39. 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.

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.
sed: The name of the input SED file, if mode=2. 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). 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}.
fcov: The covering factor of the absorber. Default value: 1 (full covering)
v: Root mean square velocity \sigma_{\mathrm v}
rms: Rms velocity \sigma_{\mathrm b} of line blend components
dv: Velocity distance \Delta v between different blend components
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.

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.