Systematic errors in the maximum likelihood regression of Poisson count data: introducing the overdispersed chi-square distribution

This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash goodness-of-fit statistic, indicate a poor fit that is attributable to overdispersion of the data. Overdispersion in Poisson data is treated as an intrinsic model variance that can be estimated from the best-fit model, using the maximum-likelihood Cmin statistic. The paper also studies the effects of such systematic errors on the Delta C likelihood-ratio statistic, which can be used to test for the presence of a nested model component in the regression of Poisson count data. The paper introduces an overdispersed chi-square distribution that results from the convolution of a chi-square distribution that models the usual Delta C statistic, and a zero-mean Gaussian that models the overdispersion in the data. This is proposed as the distribution of choice for the Delta C statistic in the presence of systematic errors. The methods presented in this paper are applied to XMM-Newton data of the quasar 1ES 1553+113 that were used to detect absorption lines from an intervening warm-hot intergalactic medium (WHIM). This case study illustrates how systematic errors can be estimated from the data, and their effect on the detection of a nested component, such as an absorption line, with the Delta C statistic.Comment: MNRAS accepted, MN-22-4879-MJ.R

Linear regression for Poisson count data: A new semi-analytical method with applications to COVID-19 events

This paper presents the application of a new semi-analytical method of linear regression for Poisson count data to COVID-19 events. The regression is based on the Bonamente and Spence (2022) maximum-likelihood solution for the best-fit parameters, and this paper introduces a simple analytical solution for the covariance matrix that completes the problem of linear regression with Poisson data. The analytical nature for both parameter estimates and their covariance matrix is made possible by a convenient factorization of the linear model proposed by J. Scargle (2013). The method makes use of the asymptotic properties of the Fisher information matrix, whose inverse provides the covariance matrix. The combination of simple analytical methods to obtain both the maximum-likelihood estimates of the parameters, and their covariance matrix, constitute a new and convenient method for the linear regression of Poisson-distributed count data, which are of common occurrence across a variety of fields. A comparison between this new linear regression method and two alternative methods often used for the regression of count data -- the ordinary least-square regression and the $\chi^2$ regression -- is provided with the application of these methods to the analysis of recent COVID-19 count data. The paper also discusses the relative advantages and disadvantages among these methods for the linear regression of Poisson count data.Comment: Accepted in Frontiers in Applied Mathematics and Statistic

The Effect of Helium Sedimentation on Galaxy Cluster Masses and Scaling Relations

Recent theoretical studies predict that the inner regions of galaxy clusters may have an enhanced helium abundance due to sedimentation over the cluster lifetime. If sedimentation is not suppressed (e.g., by tangled magnetic fields), this may significantly affect the cluster mass estimates. We use Chandra X-ray observations of eight relaxed galaxy clusters to investigate the upper limits to the effect of helium sedimentation on the measurement of cluster masses and the best-fit slopes of the Y_X - M_500 and Y_X - M_2500 scaling relations. We calculated gas mass and total mass in two limiting cases: a uniform, un-enhanced abundance distribution and a radial distribution from numerical simulations of helium sedimentation on a timescale of 11 Gyrs. The assumed helium sedimentation model, on average, produces a negligible increase in the gas mass inferred within large radii (r < r500) (1.3 +/- 1.2 per cent) and a (10.2 +/- 5.5) per cent mean decrease in the total mass inferred within r < r500. Significantly stronger effects in the gas mass (10.5 +/- 0.8 per cent) and total mass (25.1 +/- 1.1 per cent) are seen at small radii owing to a larger variance in helium abundance in the inner region, r < 0.1 r500. We find that the slope of the Y_X -M_500 scaling relation is not significantly affected by helium sedimentation.Comment: 11 pages, 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&

Revisiting the soft X-ray excess emission in clusters of galaxies observed with XMM-Newton

We analyze four XMM-Newton galaxy clusters in order to test whether their soft X-ray excess emission in the 0.2-0.5 keV band as reported by Kaastra et al. (2003) maintains after the application of the current knowledge of the XMM-Newton background and calibration. We show that in the bright central 500 kpc regions the details of the background modeling are insignificant. Thus, the cluster soft excess is not a background artifact, contrary to recent claims by Bregman et al. (2006). We find evidence that the change in PN calibration between years 2002 and 2005 results in significant decrease of the soft excess signal. However, the MOS instruments measure significant amounts of soft excess, or sub-Galactic NH. These differences are compatible with the current level of uncertainty in the calibration of both instruments.Comment: ApJ in press, minor stylistic change

The extreme ultraviolet excess emission in five clusters of galaxies revisited

Evidence for excess extreme ultraviolet (EUV) emission over a tail of X-ray gas bremsstrahlung emission has been building up recently, but in some cases remains controversial, mostly due to the moderate quality of the EUV data. In order to improve the signal to noise ratio in the EUV, we have performed the wavelet analysis and image reconstructions for five clusters of galaxies observed both at EUV and X-ray energies with the EUVE and ROSAT satellites respectively. The profiles of the EUV and X-ray reconstructed images all differ at a very large confidence level and an EUV excess over a thermal bremsstrahlung tail is detected in all five clusters (Abell 1795, Abell 2199, Abell 4059, Coma and Virgo) up to large radii. These results, coupled with recent XMM-Newton observations, suggest that the EUV excess is probably non thermal in origin.Comment: accepted for publication in Astronomy & Astrophysics, final versio

Extreme ultra-violet and soft X-ray extinction by dust in clusters of galaxies

Abstract. Intergalactig dust in galaxy clusters, recently detected in the central Coma cluster by ISO far infra-red observations, may present substantial opacity to extreme ultraviolet (EUV) and soft X-ray photons. Low-energy X-ray photons in clusters of galaxies are produced by a hot intra-cluster medium (ICM) and oftentimes, in addition, by a yet unidentified soft excess source. EUV and soft X-ray radiation from the central regions of many galaxy clusters is often depleted with respect to the predictions from the hot ICM alone, while at large radii soft excess emission is detected above the hot ICM radiation. A scenario is here proposed whereby in the centers of some galaxy clusters intergalactic dust is responsible for intrinsic EUV and soft X-ray extinction, or for the lack or lesser soft excess emission with respect to outer cluster regions