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تسجيل مستخدم جديدAccurate determination of the free-free Gaunt factor. II - relativistic Gaunt factors
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When modelling an ionised plasma, all spectral synthesis codes need the thermally averaged free-free Gaunt factor defined over a very wide range of parameter space in order to produce an accurate prediction for the spectrum. Until now no data set exists that would meet these needs completely. We have therefore produced a table of relativistic Gaunt factors over a much wider range of parameter space than has ever been produced before. We present tables of the thermally averaged Gaunt factor covering the range log10(gamma^2) = -6 to 10 and log10(u) = -16 to 13 for all atomic numbers Z = 1 through 36. The data were calculated using the relativistic Bethe-Heitler-Elwert (BHE) approximation and were subsequently merged with accurate non-relativistic results in those parts of the parameter space where the BHE approximation is not valid. These data will be incorporated in the next major release of the spectral synthesis code Cloudy. We also produced tables of the frequency integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to 10 for all values of Z between 1 and 36. All the data presented in this paper are available online.
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Modern spectral synthesis codes need the thermally averaged free-free Gaunt factor defined over a very wide range of parameter space in order to produce an accurate prediction for the spectrum emitted by an ionized plasma. Until now no set of data ex
ists that would meet this need in a fully satisfactory way. We have therefore undertaken to produce a table of very accurate non-relativistic Gaunt factors over a much wider range of parameters than has ever been produced before. We first produced a table of non-averaged Gaunt factors, covering the parameter space log10(epsilon_i) = -20 to +10 and log10(w) = -30 to +25. We then continued to produce a table of thermally averaged Gaunt factors covering the parameter space log10(gamma^2) = -6 to +10 and log10(u) = -16 to +13. Finally we produced a table of the frequency integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to +10. All the data presented in this paper are available online.
Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by $kappa$-distributions. The free-free spectrum and radiative loss
es depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than $10^{-10}$ in units of $z^2Ry$. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the $kappa$ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing $kappa$. Tables of these Gaunt factors are provided.
Tracking the thermal evolution of plasmas, characterized by an n-distribution, using numerical simulations, requires the determination of the emission spectra and of the radiative losses due to free-free emission from the correspond- ing temperature
averaged and total Gaunt factors. Detailed calculations of the latter are presented, associated to n-distributed electrons with the parameter n ranging from 1 (corresponding to the Maxwell-Boltzmann distribu- tion) to 100. The temperature averaged and total Gaunt factors, with decreasing n tend to those obtained with the Maxwell-Boltzmann distribution. Radiative losses due to free-free emission in a plasma evolving under collisional ionization equilibrium conditions and composed by H, He, C, N, O, Ne, Mg, Si, S, and Fe ions, are presented. These losses decrease with the decrease in the parameter n reaching a minimum when n = 1, and, thus converging to the losses of a thermal plasma. Tables of the thermal averaged and total Gaunt factors calculated for n distributions and a wide range electron and photon energies are presented.
Electron-ion Bremsstrahlung (free-free) emission and absorption occur in many astrophysical plasmas for a wide range of physical conditions. This classical problem has been studied multiple times, and many analytical and numerical approximations exis
t. However, accurate calculations of the transition from the non-relativistic to the relativistic regime remain sparse. Here we provide a comprehensive study of the free-free Gaunt factors for ions with low charge (Z<=10). We compute the Gaunt factor using the expressions for the differential cross section given by Elwert & Haug (EH) and compare to various limiting cases. We develop a new software package, BRpack, for direct numerical applications. This package uses a combination of pre-computed tables and analytical approximations to efficiently cover a wide range of electron and photon energies, providing a representation of the EH Gaunt factor to better than 0.03% precision for Z<=2. Our results are compared to those of previous studies highlighting the improvements achieved here. BRpack should be useful in computations of spectral distortions of the cosmic microwave background, radiative transfer problems during reionization or inside galaxy clusters, and the modeling of galactic free-free foregrounds. The developed computational methods can furthermore be extended to higher energies and ion charge.
We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylind
rical radius R_j. We find that equilibria in which the Lorentz factor gamma(R) increases monotonically with increasing radius R are stable. On the other hand, equilibria in which gamma(R) reaches a maximum value at an intermediate radius and then declines to a smaller value gamma_j at R_j are unstable. The most rapidly growing mode is an m=1 kink instability which has a growth rate ~ (0.4 / gamma_j) (c/R_j). The e-folding length of the equivalent convected instability is ~2.5 gamma_j R_j. For a typical jet with an opening angle theta_j ~ few / gamma_j, the mode amplitude grows weakly with increasing distance from the base of the jet, much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion.
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