arXiv subjects

Johannes Buchner

Publications and source records attributed to Johannes Buchner.

At least 127 records · Page 7Linked to original sources

arXiv2019

X-ray spectral and eclipsing model of the clumpy obscurer in active galactic nuclei

We present a unification model for a clumpy obscurer in active galactic nuclei (AGN) and investigate the properties of the resulting X-ray spectrum. Our model is constructed to reproduce the column density distribution of the AGN population and cloud eclipse events in terms of their angular sizes and frequency. We developed and release a generalised Monte Carlo X-ray radiative transfer code, XARS, to compute X-ray spectra of obscurer models. The geometry results in strong Compton scattering, causing soft photons to escape also along Compton-thick sight lines. This makes our model spectra very similar to the Brightman & Nandra TORUS model. However, only if we introduce an additional Compton-thick reflector near the corona, we achieve good fits to NuSTAR spectra. This additional component in our model can be interpreted as part of the dust-free broad-line region, an inner wall or rim, or a warped disk. It cannot be attributed to a simple disk because the reflector must simultaneously block the line of sight to the corona and reflect its radiation. We release our model as an Xspec table model and present corresponding CLUMPY infrared spectra, paving the way for self-consistent multi-wavelength analyses.

astro-ph.HE↗

arXiv2019

On the Prevalence of Super-Massive Black Holes over Cosmic Time

We investigate the abundance of Super-Massive Black Hole (SMBH) seeds in primordial galaxy halos. We explore the assumption that dark matter halos outgrowing a critical halo mass M_c have some probability p of having spawned a SMBH seed. Current observations of local, intermediate-mass galaxies constrain these parameters: For $M_c=10^{11}M_\odot$, all halos must be seeded, but when adopting smaller M_c masses the seeding can be much less efficient. The constraints also put lower limits on the number density of black holes in the local and high-redshift Universe. Reproducing z~6 quasar space densities depends on their typical halo mass, which can be constrained by counting nearby Lyman Break Galaxies and Lyman Alpha Emitters. For both observables, our simulations demonstrate that single-field predictions are too diverse to make definitive statements, in agreement with mixed claims in the literature. If quasars are not limited to the most massive host halos, they may represent a tiny fraction (~10^-5) of the SMBH population. Finally, we produce a wide range of predictions for gravitational events from SMBH mergers. We define a new diagnostic diagram for LISA to measure both SMBH space density and the typical delay between halo merger and black hole merger. While previous works have explored specific scenarios, our results hold independent of the seed mechanism, seed mass, obscuration, fueling methods and duty cycle.

astro-ph.GA↗

arXiv2018

The Accretion History of AGN I: Supermassive Black Hole Population Synthesis Model

As matter accretes onto the central supermassive black holes in active galactic nuclei (AGN), X-rays are emitted. We present a population synthesis model that accounts for the summed X-ray emission from growing black holes; modulo the efficiency of converting mass to X-rays, this is effectively a record of the accreted mass. We need this population synthesis model to reproduce observed constraints from X-ray surveys: the X-ray number counts, the observed fraction of Compton-thick AGN [$\log$ (N$_{\rm H}$/cm$^{\rm -2}$) $>$ 24] and the spectrum of the cosmic X-ray background (CXB), after accounting for selection biases. Over the past decade, X-ray surveys by {\it XMM-Newton}, {\it Chandra}, \textit{NuSTAR} and \textit{Swift}-BAT have provided greatly improved observational constraints. We find that no existing X-ray luminosity function (XLF) consistently reproduces all these observations. We take the uncertainty in AGN spectra into account, and use a neural network to compute an XLF that fits all observed constraints, including observed Compton-thick number counts and fractions. This new population synthesis model suggests that, intrinsically, 50$\pm$9\% (56$\pm$7\%) of all AGN within z $\simeq$ 0.1 (1.0) are Compton-thick.

astro-ph.GA↗

arXiv2018

Investigating ULX accretion flows and cyclotron resonance in NGC 300 ULX1

Methods. We analyzed broadband XMM-Newton and NuSTAR observations of NGC 300 ULX1, performing phase-averaged and phase-resolved spectroscopy. We compared two physically motivated models for the source spectrum: Non-thermal accretion column emission modeled by a power law with high-energy exponential roll-off (AC model) vs multicolor thermal emission from an optically thick accretion envelope plus a hard power-law tail (MCAE model). We combine the findings of our Bayesian analysis with qualitative physical considerations to evaluate the suitability of each model. Results. The low-energy part (<2 keV) of the source spectrum is dominated by non-pulsating, multicolor thermal emission. The (pulsating) high energy continuum is more ambiguous. If modelled with the AC model a residual structure is detected, that can be modeled using a broad Gaussian absorption line centered at ~12 keV. However, the same residuals can be successfully modeled using the MCAE model, without the need for the absorption-like feature. Model comparison, using the Bayesian approach strongly indicates that the MCAE model -- without the absorption line -- is the preferred model. Conclusions. All models considered strongly indicate the presence of an accretion disk truncated at a large distance from the central object, as has been recently suggested for a large fraction of both pulsating and non-pulsating ULXs. The hard, pulsed emission is not described by a smooth spectral continuum. If modelled by a broad Gaussian absorption line, the fit residuals can be interpreted as a cyclotron scattering feature (CRSF) compatible with a ~10^12 G magnetic field. However, the MCAE model describes the spectral and temporal characteristics of the source emission, without the need for an absorption feature and yields physically meaningful parameter values. Therefore strong doubts are cast on the presence of a CRSF in NGC 300 ULX1.

astro-ph.HE↗

arXiv2018

Collaborative Nested Sampling: Big Data vs. complex physical models

The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing with variable errors, and deriving parameter uncertainties is often an after-thought. Classic forward-folding analyses with Markov Chain Monte Carlo or Nested Sampling enable parameter estimation and model comparison, even for complex and slow-to-evaluate physical models. However, these approaches require independent runs for each data set, implying an unfeasible number of model evaluations in the Big Data regime. Here I present a new algorithm, collaborative nested sampling, for deriving parameter probability distributions for each observation. Importantly, the number of physical model evaluations scales sub-linearly with the number of data sets, and no assumptions about homogeneous errors, Gaussianity, the form of the model or heterogeneity/completeness of the observations need to be made. Collaborative nested sampling has immediate application in speeding up analyses of large surveys, integral-field-unit observations, and Monte Carlo simulations.

stat.CO↗

arXiv2018

X-UDS: The Chandra Legacy Survey of the UKIDSS Ultra Deep Survey Field

We present the X-UDS survey, a set of wide and deep Chandra observations of the Subaru-XMM Deep/UKIDSS Ultra Deep Survey (SXDS/UDS) field. The survey consists of 25 observations that cover a total area of 0.33 deg$^{2}$. The observations are combined to provide a nominal depth of ~600 ksec in the central 100 arcmin$^{2}$ region of the field that has been imaged with Hubble/WFC3 by the CANDELS survey and $\sim$200 ksec in the remainder of the field. In this paper, we outline the survey's scientific goals, describe our observing strategy, and detail our data reduction and point source detection algorithms. Our analysis has resulted in a total of 868 band-merged point sources detected with a false-positive Poisson probability of $<1\times10^{-4}$. In addition, we present the results of an X-ray spectral analysis and provide best-fitting neutral hydrogen column densities, $N_{\rm H}$, as well as a sample of 51 Compton-thick active galactic nucleus candidates. Using this sample, we find the intrinsic Compton-thick fraction to be 30-35% over a wide range in redshift ($z=0.1-3$), suggesting the obscured fraction does not evolve very strongly with epoch. However, if we assume that the Compton-thick fraction is dependent on luminosity, as is seen for Compton-thin sources, then our results are consistent with a rise in the obscured fraction out to $z\sim3$. Finally, an examination of the host morphologies of our Compton-thick candidates shows a high fraction of morphological disturbances, in agreement with our previous results. All data products described in this paper are made available via a public website.

astro-ph.GA↗

arXiv2018

Dramatic X-ray spectral variability of a Compton-thick type-1 QSO at $z\sim 1$

We report on the discovery of a dramatic X-ray spectral variability event observed in a $z\sim 1$ broad line type-1 QSO. The XMM-Newton spectrum from the year 2000 is characterized by an unobscured power-law spectrum with photon index of $Γ\sim 2$, a column density of $N_{\mathrm{H}}\sim 5\times 10^{20}\,\mathrm{cm^{-2}}$, and no prominent reflection component. Five years later, Chandra captured the source in a heavily-obscured, reflection-dominated state. The observed X-ray spectral variability could be caused by a Compton-thick cloud with $N_{\mathrm{H}}\sim 2\times 10^{24}\,\mathrm{cm^{-2}}$ eclipsing the direct emission of the hot corona, implying an extreme $N_{\mathrm{H}}$ variation never before observed in a type-1 QSO. An alternative scenario is a corona that switched off in between the observations. In addition, both explanations require a significant change of the X-ray luminosity prior to the obscuration or fading of the corona and/or a change of the relative geometry of the source/reflector system. Dramatic X-ray spectral variability of this kind could be quite common in type-1 QSOs, considering the relatively few datasets in which such an event could have been identified. Our analysis implies that there may be a population of type-1 QSOs which are Compton-thick in the X-rays when observed at any given time.

astro-ph.GA↗

arXiv2018

Relativistic reflection from accretion disks in the population of Active Galactic Nuclei at z=0.5-4

We report the detection of relativistically broadened iron K alpha emission in the X-ray spectra of AGN detected in the 4Ms CDF-S. Using the Bayesian X-ray analysis (BXA) package, we fit 199 hard band (2-7 keV) selected sources in the redshift range z=0.5--4 with three models: (i) an absorbed power-law, (ii) the first model plus a narrow reflection component, and (iii) the second model with an additional relativistic broadened reflection. The Bayesian evidence for the full sample of sources selects the model with the additional broad component as being 10^5 times more probable to describe the data better than the second model. For the two brightest sources in our sample, CID 190 (z=0.734) and CID 104 (z=0.543), BXA reveals the relativistic signatures in the individual spectra. We estimate the fraction of sources containing a broad component to be 54^{+35}_{-37}% (107/199 sources). Considering that the low signal-to-noise ratio of some spectra prevents the detection of the broad iron K alpha line, we infer an intrinsic fraction with broad emission of around two thirds. The detection of relativistic signatures in the X-ray spectra of these sources suggests that they are powered by a radiatively efficient accretion disk. Preliminary evidence is found that the spin of the black hole is high, with a maximally spinning Kerr BH model (a=1) providing a significantly better fit than a Schwarzschild model (a=0). Our analysis demonstrate the potential of X-ray spectroscopy to measure this key parameter in typical SMBH systems at the peak of BH growth.

astro-ph.HE↗

arXiv2018

XZ: Deriving redshifts from X-ray spectra of obscured AGN

Context: Redshifts are fundamental for our understanding of extragalactic X-ray sources. Ambiguous counterpart associations, expensive optical spectroscopy and/or multimission multiwavelength coverage to resolve degeneracies make estimation often difficult in practice. Aims: We attempt to constrain redshifts of obscured Active Galactic Nuclei (AGN) using only low-resolution X-ray spectra. Methods: Our XZ method fits AGN X-ray spectra with a moderately complex spectral model incorporating a corona, torus obscurer and warm mirror. Using the Bayesian X-ray Astronomy (BXA) package, we constrain redshift, column density, photon index and luminosity simultaneously. The redshift information primarily comes from absorption edges in Compton-thin AGN, and from the Fe K$α$ fluorescent line in heavily obscured AGN. A new generic background fitting method allows us to extract more information from limited numbers of source counts. Results: We derive redshift constraints for 74/321 hard-band detected sources in the Chandra deep field South. Comparing with spectroscopic redshifts, we find an outlier fraction of 8%, indicating that our model assumptions are valid. For three Chandra deep fields, we release our XZ redshift estimates. Conclusions: The independent XZ estimate is easy to apply and effective for a large fraction of obscured AGN in todays deep surveys without the need for any additional data. Comparing to different redshift estimation methods, XZ can resolve degeneracies in photometric redshifts, help to detect potential association problems and confirm uncertain single-line spectroscopic redshifts. With high spectral resolution and large collecting area, this technique will be highly effective for Athena/WFI observations.

astro-ph.IM↗

arXiv2017

ALMA and GMRT constraints on the off-axis gamma-ray burst 170817A from the binary neutron star merger GW170817

Binary neutron-star mergers (BNSMs) are among the most readily detectable gravitational-wave (GW) sources with LIGO. They are also thought to produce short $γ$-ray bursts (SGRBs), and kilonovae that are powered by r-process nuclei. Detecting these phenomena simultaneously would provide an unprecedented view of the physics during and after the merger of two compact objects. Such a Rosetta Stone event was detected by LIGO/Virgo on 17 August 2017 at a distance of $\sim 44$ Mpc. We monitored the position of the BNSM with ALMA at 338.5 GHz and GMRT at 1.4 GHz, from 1.4 to 44 days after the merger. Our observations rule out any afterglow more luminous than $3\times 10^{26}~{\rm erg\,s}^{-1}\,{\rm Hz}^{-1}$ in these bands, probing $>$2--4 dex fainter than previous SGRB limits. We match these limits, in conjunction with public data announcing the appearance of X-ray and radio emission in the weeks after the GW event, to templates of off-axis afterglows. Our broadband modeling suggests that GW170817 was accompanied by a SGRB and that the GRB jet, powered by $E_{\rm AG,\,iso}\sim10^{50}$~erg, had a half-opening angle of $\sim20^\circ$, and was misaligned by $\sim41^\circ$ from our line of sight. The data are also consistent with a more collimated jet: $E_{\rm AG,\,iso}\sim10^{51}$~erg, $θ_{1/2,\,\rm jet}\sim5^\circ$, $θ_{\rm obs}\sim17^\circ$. This is the most conclusive detection of an off-axis GRB afterglow and the first associated with a BNSM-GW event to date. Assuming a uniform top-hat jet, we use the viewing angle estimates to infer the initial bulk Lorentz factor and true energy release of the burst.

astro-ph.HE↗

arXiv2016

Galaxy gas as obscurer: I. GRBs x-ray galaxies and find a N_H ~ M* relation

An important constraint for galaxy evolution models is how much gas resides in galaxies, in particular at the peak of star formation z=1-3. We attempt a novel approach by letting long-duration Gamma Ray Bursts (LGRBs) x-ray their host galaxies and deliver column densities to us. This requires a good understanding of the obscurer and biases introduced by incomplete follow-up observations. We analyse the X-ray afterglow of all 844 Swift LGRBs to date for their column density $N_H$. To derive the population properties we propagate all uncertainties in a consistent Bayesian methodology. The $N_H$ distribution covers the $10^{20-23}\mathrm{cm}^{-2}$ range and shows no evolutionary effect. Higher obscurations, e.g. Compton-thick columns, could have been detected but are not observed. The $N_H$ distribution is consistent with sources randomly populating a ellipsoidal gas cloud of major axis $N_H^\text{major}=10^{23}\mathrm{cm}^{-2}$ with 0.22 dex intrinsic scatter between objects. The unbiased SHOALS survey of afterglows and hosts allows us to constrain the relation between Spitzer-derived stellar masses and X-ray derived column densities $N_H$. We find a well-constrained powerlaw relation of $N_H=10^{21.7}\mathrm{cm}^{-2}\times\left(M_{\star}/10^{9.5}M_{\odot}\right)^{1/3}$, with 0.5 dex intrinsic scatter between objects. The Milky Way and the Magellanic clouds also follow this relation. From the geometry of the obscurer, its stellar mass dependence and comparison with local galaxies we conclude that LGRBs are primarily obscured by galaxy-scale gas. Ray tracing of simulated Illustris galaxies reveals a relation of the same normalisation, but a steeper stellar-mass dependence and mild redshift evolution. Our new approach provides valuable insight into the gas residing in high-redshift galaxies.

astro-ph.HE↗

arXiv2016

Galaxy gas as obscurer: II. Separating the galaxy-scale and nuclear obscurers of Active Galactic Nuclei

The "torus" obscurer of Active Galactic Nuclei (AGN) is poorly understood in terms of its density, substructure and physical mechanisms. Large X-ray surveys provide model boundary constraints, for both Compton-thin and Compton-thick levels of obscuration, as obscured fractions are mean covering factors $f_{\text{cov}}$. However, a major remaining uncertainty is host galaxy obscuration. In Paper I we discovered a relation of $N_H \propto M_{\star}^{1/3}$ for the obscuration of galaxy-scale gas. Here we apply this observational relation to the AGN population, and find that galaxy-scale gas is responsible for a luminosity-independent fraction of Compton-thin AGN, but does not produce Compton-thick columns. With the host galaxy obscuration understood, we present a model of the remaining, nuclear obscurer which is consistent with a range of observations. Our radiation-lifted torus model consists of a Compton-thick component ($f_{\text{cov}}\sim35\%$) and a Compton-thin component ($f_{\text{cov}}\sim40\%$), which depends on both black hole mass and luminosity. This provides a useful summary of observational constraints for torus modellers who attempt to reproduce this behaviour. It can also be employed as a sub-grid recipe in cosmological simulations which do not resolve the torus. We also investigate host-galaxy X-ray obscuration inside cosmological, hydro-dynamic simulations (EAGLE, Illustris). The obscuration from ray-traced galaxy gas can agree with observations, but is highly sensitive to the chosen feedback assumptions.

astro-ph.HE↗

arXiv2016

The Sloan Digital Sky Survey Quasar Catalog: twelfth data release

We present the Data Release 12 Quasar catalog (DR12Q) from the Baryon Oscillation Spectroscopic Survey (BOSS) of the SDSS-III. This catalog includes all SDSS-III/BOSS objects that were spectroscopically targeted as quasar candidates during the full survey and that are confirmed as quasars via visual inspection of the spectra, have luminosities Mi[z=2]<-20.5 (in a LCDM cosmology with H_0 = 70 km/s/Mpc, Omega_M = 0.3, and Omega _L=0.7), and either display at least one emission line with a full width at half maximum (FWHM)larger than 500 km/s or, if not, have interesting/complex absorption features. The catalog also includes previously known quasars (mostly from SDSS-I and II) that were reobserved by BOSS. The catalog contains 297,301 quasars detected over 9,376 square degrees with robust identification and redshift measured by a combination of principal component eigenspectra. The number of quasars with z>2.15 is about an order of magnitude greater than the number of z>2.15 quasars known prior to BOSS. Redshifts and FWHMs are provided for the strongest emission lines (CIV, CIII], MgII). The catalog identifies 29,580 broad absorption line quasars and lists their characteristics. For each object, the catalog presents five-band (u, g, r, i, z) CCD-based photometry together with some information on the optical morphology and the selection criteria. When available, the catalog also provides information on the optical variability of quasars using SDSS and PTF multi-epoch photometry. The catalog also contains X-ray, ultraviolet, near-infrared, and radio emission properties of the quasars, when available, from other large-area surveys. The calibrated digital spectra, covering the wavelength region 3,600-10,500A at a spectral resolution in the range 1,300<R<2,500, can be retrieved from the SDSS Catalog Archive Server.

astro-ph.GA↗

arXiv2016

Global Dynamics, Blow-Up, and Bianchi Cosmology

Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of general relativity to quasilinear reaction-advection-diffusion equations of parabolic type. Specific questions concern the convergence to equilibria, the existence of periodic, homoclinic, and heteroclinic solutions, and the existence and geometric structure of global attractors. On the other hand, many solutions develop singularities in finite time. The singularities have to be analyzed in detail before attempting to extend solutions beyond their singularities, or to understand their geometry in conjunction with globally bounded solutions. In this context we have also aimed at global qualitative descriptions of blow-up and grow-up phenomena.

math.DS↗

arXiv2016

X-ray spectral properties of the AGN sample in the northern XMM-XXL field

In this paper we describe and publicly release a catalogue consisting of 8445 point-like X-ray sources detected in the XMM-XXL north survey. For the 2512 AGN which have reliable spectroscopy, we present the X-ray spectral fitting which has been computed with a Bayesian approach. We have also applied an X-ray spectral stacking method to different sub-samples. We confirm the well-known Iwasawa-Taniguchi effect in our luminosity-redshift sub-samples, and argue that such an effect is due to a decrease in the covering factor of a distant obscuring torus with increasing X-ray luminosity. By comparing the distribution of the reflection fraction, the ratio of the normalization of the reflected component to the direct radiation, we find that the low-luminosity, low-redshift sub-sample had systematically higher reflection fraction values than the high-redshift, high-luminosity one. On the other hand, no significant difference is found between samples having similar luminosity but different redshift, suggesting that the structure of the torus does not evolve strongly with redshift. Contrary to previous works, we do not find evidence for an increasing photon index at high Eddington ratio. This may be an indication that the structure of the accretion disc changes as the Eddington ratio approaches unity. Comparing our X-ray spectral analysis results with the optical spectral classification, we find that $\sim20$ per cent of optical type-1 AGN show an X-ray absorbing column density higher than $10^{21.5}\,\rm{cm^{-2}}$, and about 50 per cent of type-2 AGN have an X-ray absorbing column density less than $10^{21.5}\,\rm{cm^{-2}}$. We suggest that the excess X-ray absorption shown in the high-luminosity optical type-1 AGN can be due to small-scale dust-free gas within (or close to) the broad line region, while in the low-luminosity ones it can be due to a clumpy torus with a large covering factor.

astro-ph.HE↗

arXiv2015

A Spectroscopic Survey of X-ray Selected AGN in the Northern XMM-XXL Field

This paper presents a survey of X-ray selected active galactic nuclei (AGN) with optical spectroscopic follow-up in a $\sim 18\, \rm{deg^2}$ area of the equatorial XMM-XXL north field. A sample of 8445 point-like X-ray sources detected by XMM-Newton above a limiting flux of $F_{\rm 0.5-10\, keV} > 10^{-15} \rm\,erg\, cm^{-2}\, s^{-1}$ was matched to optical (SDSS) and infrared (WISE) counterparts. We followed up 3042 sources brighter than $r=22.5$ mag with the SDSS BOSS spectrograph. The spectra yielded a reliable redshift measurement for 2578 AGN in the redshift range $z=0.02-5.0$, with $0.5-2\rm\, keV$ luminosities ranging from $10^{39}-10^{46}\rm\,erg\,s^{-1}$. This is currently the largest published spectroscopic sample of X-ray selected AGN in a contiguous area. The BOSS spectra of AGN candidates show a bimodal distribution of optical line widths allowing a separation between broad- and narrow-emission line AGN. The former dominate our sample (70 per cent) due to the relatively bright X-ray flux limit and the optical BOSS magnitude limit. We classify the narrow emission line objects (22 per cent of full sample) using standard BPT diagnostics: the majority have line ratios indicating the dominant source of ionization is the AGN. A small number (8 per cent of full sample) exhibit the typical narrow line ratios of star-forming galaxies, or only have absorption lines in their spectra. We term the latter two classes "elusive'' AGN. We also compare X-ray, optical and infrared color AGN selections in this field. X-ray observations reveal, the largest number of AGN. The overlap between the selections, which is a strong function of the imaging depth in a given band, is also remarkably small. We show using spectral stacking that a large fraction of the X-ray AGN would not be selectable via optical or IR colours due to host galaxy contamination.

astro-ph.GA↗

arXiv2015

Obscuration-dependent evolution of Active Galactic Nuclei

We aim to constrain the evolution of AGN as a function of obscuration using an X-ray selected sample of $\sim2000$ AGN from a multi-tiered survey including the CDFS, AEGIS-XD, COSMOS and XMM-XXL fields. The spectra of individual X-ray sources are analysed using a Bayesian methodology with a physically realistic model to infer the posterior distribution of the hydrogen column density and intrinsic X-ray luminosity. We develop a novel non-parametric method which allows us to robustly infer the distribution of the AGN population in X-ray luminosity, redshift and obscuring column density, relying only on minimal smoothness assumptions. Our analysis properly incorporates uncertainties from low count spectra, photometric redshift measurements, association incompleteness and the limited sample size. We find that obscured AGN with $N_{H}>{\rm 10^{22}\, cm^{-2}}$ account for ${77}^{+4}_{-5}\%$ of the number density and luminosity density of the accretion SMBH population with $L_{\rm X}>10^{43}\text{ erg/s}$, averaged over cosmic time. Compton-thick AGN account for approximately half the number and luminosity density of the obscured population, and ${38}^{+8}_{-7}\%$ of the total. We also find evidence that the evolution is obscuration-dependent, with the strongest evolution around $N_{H}\thickapprox10^{23}\text{ cm}^{-2}$. We highlight this by measuring the obscured fraction in Compton-thin AGN, which increases towards $z\sim3$, where it is $25\%$ higher than the local value. In contrast the fraction of Compton-thick AGN is consistent with being constant at $\approx35\%$, independent of redshift and accretion luminosity. We discuss our findings in the context of existing models and conclude that the observed evolution is to first order a side-effect of anti-hierarchical growth.

astro-ph.HE↗

arXiv2014

A statistical test for Nested Sampling algorithms

Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood threshold. Thus, the problem of drawing from a space above a certain likelihood value arises naturally in nested sampling, making algorithms that solve this problem a key ingredient to the nested sampling framework. If the drawn points are distributed uniformly, the removal of a point shrinks the volume in a well-understood way, and the integration of nested sampling is unbiased. In this work, I develop a statistical test to check whether this is the case. This "Shrinkage Test" is useful to verify nested sampling algorithms in a controlled environment. I apply the shrinkage test to a test-problem, and show that some existing algorithms fail to pass it due to over-optimisation. I then demonstrate that a simple algorithm can be constructed which is robust against this type of problem. This RADFRIENDS algorithm is, however, inefficient in comparison to MULTINEST.

stat.CO↗