Chandra observations of large samples of galaxy clusters detected in X-rays by ROSAT provide a new, robust determination of the cluster mass functions at low and high redshifts. Statistical and systematic errors are now sufficiently small, and the redshift leverage sufficiently large for the mass function evolution to be used as a useful growth of a structure-based dark energy probe. In this paper, we present cosmological parameter constraints obtained from Chandra observations of 37 clusters withz �= 0.55 derived from 400 deg 2 ROSAT serendipitous survey and 49 brightest z ≈ 0.05 clusters detected in the All-Sky Survey. Evolution of the mass function between these redshifts requires ΩΛ > 0 with a ∼ 5σ significance, and constrains the dark energy equation- of-state parameter to w0 =− 1.14 ± 0.21, assuming a constant w and a flat universe. Cluster information also significantly improves constraints when combined with other methods. Fitting our cluster data jointly with the latest supernovae, Wilkinson Microwave Anisotropy Probe, and baryonic acoustic oscillation measurements, we obtain w0 =− 0.991 ± 0.045 (stat) ±0.039 (sys), a factor of 1.5 reduction in statistical uncertainties, and nearly a factor of 2 improvement in systematics compared with constraints that can be obtained without clusters. The joint analysis of these four data sets puts a conservative upper limit on the masses of light neutrinos mν < 0.33 eV at 95% CL. We also present updated measurements of ΩMh and σ8 from the low-redshift cluster mass function.

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Chandra Cluster Cosmology Project III: Cosmological Parameter Constraints

Context. Aims. Active galactic nuclei are known to have complex X-ray spectra that depend on both the properties of the accreting super-massive black hole (e.g. mass, accretion rate) and the distribution of obscuring material in its vicinity (i.e. the “torus”). Often however, simple and even unphysical models are adopted to represent the X-ray spectra of AGN, which do not capture the complexity and diversity of the observations. In the case of blank field surveys in particular, this should have an impact on e.g. the determination of the AGN luminosity function, the inferred accretion history of the Universe and also on our understanding of the relation between AGN and their host galaxies. Methods. We develop a Bayesian framework for model comparison and parameter estimation of X-ray spectra. We take into account uncertainties associated with both the Poisson nature of X-ray data and the determination of source redshift using photometric methods. We also demonstrate how Bayesian model comparison can be used to select among ten different physically motivated X-ray spectral models the one that provides a better representation of the observations. This methodology is applied to X-ray AGN in the 4 Ms Chandra Deep Field South.Results. For the ~350 AGN in that field, our analysis identifies four components needed to represent the diversity of the observed X-ray spectra: (1) an intrinsic power law; (2) a cold obscurer which reprocesses the radiation due to photo-electric absorption, Compton scattering and Fe-K fluorescence; (3) an unabsorbed power law associated with Thomson scattering off ionised clouds; and (4) Compton reflection, most noticeable from a stronger-than-expected Fe-K line. Simpler models, such as a photo-electrically absorbed power law with a Thomson scattering component, are ruled out with decisive evidence (B > 100). We also find that ignoring the Thomson scattering component results in underestimation of the inferred column density, N H , of the obscurer. Regarding the geometry of the obscurer, there is strong evidence against both a completely closed (e.g. sphere), or entirely open (e.g. blob of material along the line of sight), toroidal geometry in favour of an intermediate case. Conclusions. Despite the use of low-count spectra, our methodology is able to draw strong inferences on the geometry of the torus. Simpler models are ruled out in favour of a geometrically extended structure with significant Compton scattering. We confirm the presence of a soft component, possibly associated with Thomson scattering off ionised clouds in the opening angle of the torus. The additional Compton reflection required by data over that predicted by toroidal geometry models, may be a sign of a density gradient in the torus or reflection off the accretion disk. Finally, we release a catalogue of AGN in the CDFS with estimated parameters such as the accretion luminosity in the 2−10 keV band and the column density, N H , of the obscurer.

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X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue

The second catalog of active galactic nuclei (AGNs) detected by the Fermi Large Area Telescope (LAT) in two years of scientific operation is presented. The second LAT AGN catalog (2LAC) includes 1017 γ-ray sources located at high Galactic latitudes (|b| > 10°) that are detected with a test statistic (TS) greater than 25 and associated statistically with AGNs. However, some of these are affected by analysis issues and some are associated with multiple AGNs. Consequently, we define a Clean Sample which includes 886 AGNs, comprising 395 BL Lacertae objects (BL Lac objects), 310 flat-spectrum radio quasars (FSRQs), 157 candidate blazars of unknown type (i.e., with broadband blazar characteristics but with no optical spectral measurement yet), 8 misaligned AGNs, 4 narrow-line Seyfert 1 (NLS1s), 10 AGNs of other types, and 2 starburst galaxies. Where possible, the blazars have been further classified based on their spectral energy distributions (SEDs) as archival radio, optical, and X-ray data permit. While almost all FSRQs have a synchrotron-peak frequency 1015 Hz. The 2LAC represents a significant improvement relative to the first LAT AGN catalog (1LAC), with 52% more associated sources. The full characterization of the newly detected sources will require more broadband data. Various properties, such as γ-ray fluxes and photon power-law spectral indices, redshifts, γ-ray luminosities, variability, and archival radio luminosities and their correlations are presented and discussed for the different blazar classes. The general trends observed in 1LAC are confirmed.

https://iopscience.iop.org/article/10.1088/0004-637X/743/2/171/pdf

The second catalog of active galactic nuclei detected by the Fermi Large Area Telescope

We discuss the measurements of the galaxy cluster mass functions at z 0.05 and z 0.5 using high-quality Chandra observations of samples derived from the ROSAT PSPC All-Sky and 400 deg2 surveys. We provide a full reference for the data analysis procedures, present updated calibration of relations between the total cluster mass and its X-ray indicators (TX , M gas, and YX ) based on a subsample of low-z relaxed clusters, and present a first measurement of the evolving LX -M tot relation (with M tot estimated from YX ) obtained from a well defined statistically complete cluster sample and with appropriate corrections for the Malmquist bias applied. Finally, we present the derived cluster mass functions, estimate the systematic uncertainties in this measurement, and discuss the calculation of the likelihood function. We confidently measure the evolution in the cluster comoving number density at a fixed mass threshold, e.g., by a factor of 5.0 ? 1.2 at M 500 = 2.5 ? 1014 h ?1 M ? between z = 0 and 0.5. This evolution reflects the growth of density perturbations, and can be used for the cosmological constraints complementing those from the distance-redshift relation.

https://iopscience.iop.org/article/10.1088/0004-637X/692/2/1033/pdf

Chandra Cluster Cosmology Project. II. Samples and X-Ray Data Reduction

The likelihood ratio test (LRT) and the related F-test, popularized in astrophysics by Eadie and coworkers in 1971, Bevington in 1969, Lampton, Margon, & Bowyer, in 1976, Cash in 1979, and Avni in 1978, do not (even asymptotically) adhere to their nominal χ2 and F-distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source detections and nondetections into doubt. Although the above authors illustrate the many legitimate uses of these statistics, in some important cases it can be impossible to compute the correct false positive rate. For example, it has become common practice to use the LRT or the F-test to detect a line in a spectral model or a source above background despite the lack of certain required regularity conditions. (These applications were not originally suggested by Cash or by Bevington.) In these and other settings that involve testing a hypothesis that is on the boundary of the parameter space, contrary to common practice, the nominal χ2 distribution for the LRT or the F-distribution for the F-test should not be used. In this paper, we characterize an important class of problems in which the LRT and the F-test fail and illustrate this nonstandard behavior. We briefly sketch several possible acceptable alternatives, focusing on Bayesian posterior predictive probability values. We present this method in some detail since it is a simple, robust, and intuitive approach. This alternative method is illustrated using the gamma-ray burst of 1997 May 8 (GRB 970508) to investigate the presence of an Fe K emission line during the initial phase of the observation. There are many legitimate uses of the LRT and the F-test in astrophysics, and even when these tests are inappropriate, there remain several statistical alternatives (e.g., judicious use of error bars and Bayes factors). Nevertheless, there are numerous cases of the inappropriate use of the LRT and similar tests in the literature, bringing substantive scientific results into question.

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Statistics, Handle with Care: Detecting Multiple Model Components with the Likelihood Ratio Test

Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

W. Cash

Papers

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques