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

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

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

Simultaneous X-ray and Ultraviolet spectroscopy of the Seyfert galaxy NGC 5548. III. X-ray time variability

The Seyfert 1 galaxy NGC 5548 was observed for a week by Chandra using both the HETGS and LETGS spectrometers. In this paper we study the time variability of the continuum radiation. During our observation, the source showed a gradual increase in flux over four days, followed by a rapid decrease and flattening of the light curve afterwards. Superimposed upon these relatively slow variations several short duration bursts or quasi-periodic oscillations occured with a typical duration of several hours and separation between 0.6-0.9 days. The bursts show a delay of the hard X-rays with respect to the soft X-rays of a few hours. We interprete these bursts as due to a rotating, fluctuating hot spot at approximately 10 gravitational radii; the time delay of the hard X-rays from the bursts agree with the canonical picture of Inverse Compton scattering of the soft accretion disk photons on a hot medium that is relatively close to the central black hole.Comment: 6 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Suzaku observations of X-ray excess emission in the cluster of galaxies A3112

We analysed the Suzaku XIS1 data of the A3112 cluster of galaxies in order to examine the X-ray excess emission in this cluster reported earlier with the XMM-Newton and Chandra satellites. The best-fit temperature of the intracluster gas depends strongly on the choice of the energy band used for the spectral analysis. This proves the existence of excess emission component in addition to the single-temperature MEKAL in A3112. We showed that this effect is not an artifact due to uncertainties of the background modeling, instrument calibration or the amount of Galactic absorption. Neither does the PSF scatter of the emission from the cool core nor the projection of the cool gas in the cluster outskirts produce the effect. Finally we modeled the excess emission either by using an additional MEKAL or powerlaw component. Due to the small differencies between thermal and non-thermal model we can not rule out the non-thermal origin of the excess emission based on the goodness of the fit. Assuming that it has a thermal origin, we further examined the Differential Emission Measure (DEM) models. We utilised two different DEM models, a Gaussian differential emission measure distribution (GDEM) and WDEM model, where the emission measure of a number of thermal components is distributed as a truncated power law. The best-fit XIS1 MEKAL temperature for the 0.4-7.0 keV band is 4.7+-0.1 keV, consistent with that obtained using GDEM and WDEM models.Comment: 8 pages, 10 figures, accepted to A&

The temperature structure in the core of Sersic 159-03

We present results from a new 120 ks XMM-Newton observation of the cluster of galaxies Sersic 159-03. In this paper we focus on the high-resolution X-ray spectra obtained with the Reflection Grating Spectrometer (RGS). The spectra allow us to constrain the temperature structure in the core of the cluster and determine the emission measure distribution as a function of temperature. We also fit the line widths of mainly oxygen and iron lines.Comment: 7 pages and 4 figures. Contribution to the proceedings of the COSPAR Scientific Assembly, session E1.2 "Clusters of Galaxies: New Insights from XMM-Newton, Chandra and INTEGRAL", july 2004, Paris (France). Accepted for publication in Advances in Space Researc

Contrasting the UV and X-ray O VI Column Density Inferred for the Outflow in NGC 5548

We compare X-ray and UV spectroscopic observations of NGC 5548. Both data sets show O VI absorption troughs associated with the AGN outflow from this galaxy. We find that the robust lower limit on the column density of the O VI X-ray trough is seven times larger than the column density found in a study of the O VI UV troughs. This discrepancy suggests that column densities inferred for UV troughs of Seyfert outflows are often severely underestimated. We identify the physical limitations of the UV Gaussian modeling as the probable explanation of the O VI column density discrepancy. Specifically, Gaussian modeling cannot account for a velocity dependent covering fraction, and it is a poor representation for absorption associated with a dynamical outflow. Analysis techniques that use a single covering fraction value for each absorption component suffer from similar limitations. We conclude by suggesting ways to improve the UV analysis.Comment: 16 pages, 1 figure, accepted for publication in Ap

The interstellar oxygen-K absorption edge as observed by XMM-Newton

High resolution X-ray spectra of the Reflection Grating Spectrometer (RGS) on board the XMM satellite are used to resolve the oxygen K absorption edge. By combining spectra of low and high extinction sources, the observed absorption edge can be split in the true interstellar (ISM) extinction and the instrumental absorption. The detailed ISM edge structure closely follows the edge structure of neutral oxygen as derived by theoretical R-matrix calculations. However, the position of the theoretical edge requires a wavelength shift. In addition the detailed instrumental RGS absorption edge structure is presented. All results are verified by comparing to a subset of Chandra LETG-HRC observations.Comment: LaTeX2e A&A style, 10 pages, 12 postscript figures, accepted for publication in Astronomy and Astrophysic