On the use of C-stat in testing models for X-ray spectra

It has been shown that for the analysis of X-ray spectra the C-statistic, contrary to the chi^2-statistic, provides unbiased estimates of the model parameters and their uncertainty ranges. However, it is often stated that the C-statistic cannot be used to carry out statistical tests on the goodness of fit of the model, and therefore several investigations are still based on chi^2-statistics. Here we show that it is straightforward to calculate the expected value and variance of the C-statistic so that it can be used in tests. We provide formulae and simple numerical approximations to evaluate these expected values and variances. We also give examples indicating that tests based on only the expected value and variance of the C-statistic are reliable for spectra even with only ~30 counts. Therefore the C-statistic can be used for statistical tests such as assessing the goodness of fit of a spectral model.Comment: 4 pages, 3 figures, accepted for publication in Astronomy and Astrophysic

Optimal binning of X-ray spectra and response matrix design

A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that by taking into account both the number of photons in a given spectral model bin and their average energy over the bin size, the number of model energy bins and the size of the response matrix can be reduced by a factor of $10-100$. The response matrix should then contain the response at the bin centre as well as its derivative with respect to the incoming photon energy. We provide practical guidelines for how to construct optimal energy grids as well as how to structure the response matrix. A few examples are presented to illustrate the present methods.Comment: 16 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

X-ray emission from thin plasmas. Collisional ionization for atoms and ions of H to Zn

Every observation of astrophysical objects involving a spectrum requires atomic data for the interpretation of line fluxes, line ratios and ionization state of the emitting plasma. One of the processes which determines it is collisional ionization. In this study an update of the direct ionization (DI) and excitation-autoionization (EA) processes is discussed for the H to Zn-like isoelectronic sequences. In the last years new laboratory measurements and theoretical calculations of ionization cross sections have become available. We provide an extension and update of previous published reviews in the literature. We include the most recent experimental measurements and fit the cross sections of all individual shells of all ions from H to Zn. These data are described using an extension of Younger's and Mewe's formula, suitable for integration over a Maxwellian velocity distribution to derive the subshell ionization rate coefficients. These ionization rate coefficients are incorporated in the high-resolution plasma code and spectral fitting tool SPEX V3.0.Comment: Accepted for publication in A&A, 22 pages, 18 figure

Line absorption of He-like triplet lines by Li-like ions. Caveats of using line ratios of triplets for plasma diagnostics

He-like ions produce distinctive series of triplet lines under various astrophysical conditions. However, this emission can be affected by line absorption from Li-like ions in the same medium. We investigate this absorption of He-like triplets and present the implications for diagnostics of plasmas in photoionisation equilibrium using the line ratios of the triplets. Our computations were carried out for the O VI and Fe XXIV absorption of the O VII and Fe XXV triplet emission lines, respectively. The fluorescent emission by the Li-like ions and continuum absorption of the He-like ion triplet lines are also investigated. We determine the absorption of the triplet lines as a function of Li-like ion column density and velocity dispersion of the emitting and absorbing medium. We find O VI line absorption can significantly alter the O VII triplet line ratios in optically-thin plasmas, by primarily absorbing the intercombination lines, and to a lesser extent, the forbidden line. Because of intrinsic line absorption by O VI inside a photoionised plasma, the predicted ratio of forbidden to intercombination line intensity for the O VII triplet increases from 4 up to an upper limit of 16. This process can explain the triplet line ratios that are higher than expected and that are seen in some X-ray observations of photoionised plasmas. For the Fe XXV triplet, line absorption by Fe XXIV becomes less apparent owing to significant fluorescent emission by Fe XXIV. Without taking the associated Li-like ion line absorption into account, the density diagnosis of photoionised plasmas using the observed line ratios of the He-like ion triplet emission lines can be unreliable, especially for low-Z ions.Comment: Accepted for publication in Astronomy & Astrophysics, 6 pages, 4 figure

Results from a Second RXTE Observation of the Coma Cluster

The RXTE satellite observed the Coma cluster for 177 ksec during November and December 2000, a second observation motivated by the intriguing results from the first 87 ksec observation in 1996. Analysis of the new dataset confirms that thermal emission from isothermal gas does not provide a good fit to the spectral distribution of the emission from the inner 1 degree radial region. While the observed spectrum may be fit by emission from gas with a substantial temperature gradient, it is more likely that the emission includes also a secondary non-thermal component. If so, non-thermal emission comprises ~8% of the total 4--20 keV flux. Interpreting this emission as due to Compton scattering of relativistic electrons (which produce the known extended radio emission) by the cosmic microwave background radiation, we determine that the mean, volume-averaged magnetic field in the central region of Coma is B = 0.1-0.3 microgauss.Comment: 10 pages, 1 figure; APJ, in pres

High- and low energy nonthermal X-ray emission from the cluster of galaxies A 2199

We report the detection of both soft and hard excess X-ray emission in the cluster of galaxies A 2199, based upon spatially resolved spectroscopy with data from the BeppoSAX, EUVE and ROSAT missions. The excess emission is visible at radii larger than 300 kpc and increases in strength relative to the isothermal component. The total 0.1-100 keV luminosity of this component is 15 % of the cluster luminosity, but it dominates the cluster luminosity at high and low energies. We argue that the most plausible interpretation of the excess emission is an inverse Compton interaction between the cosmic microwave background and relativistic electrons in the cluster. The observed spatial distribution of the non-thermal component implies that there is a large halo of cosmic ray electrons between 0.5-1.5 Mpc surrounding the cluster core. The prominent existence of this component has cosmological implications, as it is significantly changing our picture of a clusters's particle acceleration history, dynamics between the thermal and relativistic media, and total mass budgets.Comment: Accepted for publication in Astrophysical Journal, Letter

Modeling the interaction of thermonuclear supernova remnants with circumstellar structures: The case of Tycho's supernova remnant

The well-established Type Ia remnant of Tycho's supernova (SN 1572) reveals discrepant ambient medium density estimates based on either the measured dynamics or on the X-ray emission properties. This discrepancy can potentially be solved by assuming that the supernova remnant (SNR) shock initially moved through a stellar wind bubble, but is currently evolving in the uniform interstellar medium with a relatively low density. We investigate this scenario by combining hydrodynamical simulations of the wind-loss phase and the supernova remnant evolution with a coupled X-ray emission model, which includes non-equilibrium ionization. For the explosion models we use the well-known W7 deflagration model and the delayed detonation model that was previously shown to provide good fits to the X-ray emission of Tycho's SNR. Our simulations confirm that a uniform ambient density cannot simultaneously reproduce the dynamical and X-ray emission properties of Tycho. In contrast, models that considered that the remnant was evolving in a dense, but small, wind bubble reproduce reasonably well both the measured X-ray emission spectrum and the expansion parameter of Tycho's SNR. Finally, we discuss possible mass loss scenarios in the context of single- and double-degenerate models which possible could form such a small dense wind bubble.Comment: 12 pages, 7 figures, accepted for publication in MNRA