We present an improved and expanded simply parametrized phenomenological model of the broad-line region (BLR) in active galactic nuclei for modelling reverberation mapping data. By modelling ...reverberation mapping data directly, we can constrain the geometry and dynamics of the BLR and measure the black hole mass without relying on the normalization factor needed in the traditional analysis. For realistic simulated reverberation mapping data sets of high quality, we can recover the black hole mass to 0.05–0.25 dex uncertainty and distinguish between dynamics dominated by elliptical orbits and inflowing gas. While direct modelling of the integrated emission-line light curve allows for measurement of the mean time lag, other details of the geometry of the BLR are better constrained by the full spectroscopic data set of emission-line profiles. We use this improved model of the BLR to explore possible sources of uncertainty in measurements of the time lag using cross-correlation function (CCF) analysis and in measurements of the black hole mass using the virial product. Sampling the range of geometries and dynamics in our model of the BLR suggests that the theoretical uncertainty in black hole masses measured using the virial product is of the order of 0.25 dex. These results support the use of the CCF to measure time lags and the virial product to measure black hole masses when direct modelling techniques cannot be applied, provided the uncertainties associated with the interpretation of the results are taken into account.
Bayesian inference methods rely on numerical algorithms for both model selection and parameter inference. In general, these algorithms require a high computational effort to yield reliable estimates. ...One of the major challenges in phylogenetics is the estimation of the marginal likelihood. This quantity is commonly used for comparing different evolutionary models, but its calculation, even for simple models, incurs high computational cost. Another interesting challenge relates to the estimation of the posterior distribution. Often, long Markov chains are required to get sufficient samples to carry out parameter inference, especially for tree distributions. In general, these problems are addressed separately by using different procedures. Nested sampling (NS) is a Bayesian computation algorithm, which provides the means to estimate marginal likelihoods together with their uncertainties, and to sample fromthe posterior distribution at no extra cost. The methods currently used in phylogenetics for marginal likelihood estimation lack in practicality due to their dependence on many tuning parameters and their inability of most implementations to provide a direct way to calculate the uncertainties associated with the estimates, unlike NS. In this article, we introduce NS to phylogenetics. Its performance is analysed under different scenarios and compared to established methods. We conclude that NS is a competitive and attractive algorithm for phylogenetic inference. An implementation is available as a package for BEAST 2 under the LGPL licence, accessible at https://github.com/BEAST2-Dev/nested-sampling.
We present a general method to analyze reverberation (or echo) mapping data that simultaneously provides estimates for the black hole mass and for the geometry and dynamics of the broad-line region ...(BLR) in active galactic nuclei (AGNs). While previous methods yield a typical scale size of the BLR or a reconstruction of the transfer function, our method directly infers the spatial and velocity distribution of the BLR from the data, from which a transfer function can be easily derived. Previous echo mapping analysis requires an independent estimate of a scaling factor known as the virial coefficient to infer the mass of the black hole, but this is not needed in our more direct approach. We use the formalism of Bayesian probability theory and implement a Markov Chain Monte Carlo algorithm to obtain estimates and uncertainties for the parameters of our BLR models. Fitting of models to the data requires knowledge of the continuum flux at all times, not just the measured times. We use Gaussian Processes to interpolate and extrapolate the continuum light curve data in a fully consistent probabilistic manner, taking the associated errors into account. We illustrate our method using simple models of BLR geometry and dynamics and show that we can recover the parameter values of our test systems with realistic uncertainties that depend upon the variability of the AGN and the quality of the reverberation mapping observing campaign. With a geometry model we can recover the mean radius of the BLR to within ~0.1 dex random uncertainty for simulated data with an integrated line flux uncertainty of 1.5%, while with a dynamical model we can recover the black hole mass and the mean radius to within ~0.05 dex random uncertainty, for simulated data with a line profile average signal-to-noise ratio of 4 per spectral pixel. These uncertainties do not include modeling errors, which are likely to be present in the analysis of real data, and should therefore be considered as lower limits to the accuracy of the method.
ABSTRACT
The Cosmological Principle, that the Universe is homogeneous and isotropic on sufficiently large scales, underpins the standard model of cosmology. However, a recent analysis of 1.36 million ...infrared-selected quasars has identified a significant tension in the amplitude of the number-count dipole compared to that derived from the cosmic microwave background (CMB), thus challenging the Cosmological Principle. Here, we present a Bayesian analysis of the same quasar sample, testing various hypotheses using the Bayesian evidence. We find unambiguous evidence for the presence of a dipole in the distribution of quasars with a direction that is consistent with the dipole identified in the CMB. However, the amplitude of the dipole is found to be 2.7 times larger than that expected from the conventional kinematic explanation of the CMB dipole, with a statistical significance of 5.7σ. To compare these results with theoretical expectations, we sharpen the ΛCDM predictions for the probability distribution of the amplitude, taking into account a number of observational and theoretical systematics. In particular, we show that the presence of the Galactic plane mask causes a considerable loss of dipole signal due to a leakage of power into higher multipoles, exacerbating the discrepancy in the amplitude. By contrast, we show using probabilistic arguments that the source evolution of quasars improves the discrepancy, but only mildly so. These results support the original findings of an anomalously large quasar dipole, independent of the statistical methodology used.
We present dynamical modelling of the broad-line region (BLR) for a sample of five Seyfert 1 galaxies using reverberation mapping data taken by the Lick AGN Monitoring Project in 2008. By modelling ...the AGN continuum light curve and Hβ line profiles directly, we are able to constrain the geometry and kinematics of the BLR and make a measurement of the black hole mass that does not depend upon the virial factor, f, needed in traditional reverberation mapping analysis. We find that the geometry of the BLR is generally a thick disc viewed close to face-on. While the Hβ emission is found to come preferentially from the far side of the BLR, the mean size of the BLR is consistent with the lags measured with cross-correlation analysis. The BLR kinematics are found to be consistent with either inflowing motions or elliptical orbits, often with some combination of the two. We measure black hole masses of
$\log _{10}(M_{\rm \,BH}/\mathrm{M}_{\odot })=6.62^{+0.10}_{-0.13}$
for Arp 151,
$7.42^{+0.26}_{-0.27}$
for Mrk 1310,
$7.59^{+0.24}_{-0.21}$
for NGC 5548,
$6.37^{+0.21}_{-0.16}$
for NGC 6814, and
$6.99^{+0.32}_{-0.25}$
for SBS 1116+583A. The f factors measured individually for each AGN are found to correlate with inclination angle, although not with M
BH, L
5100, or FWHM/σ of the emission line profile.
ABSTRACT Based upon the kinematics of 10 globular clusters, it has recently been claimed that the ultra-diffuse galaxy, NGC 1052-DF2, lacks a significant quantity of dark matter. Dynamical analyses ...have generally assumed that this galaxy is pressure supported, with the relatively small velocity dispersion of the globular cluster population indicating the deficit of dark matter. However, the presence of a significant rotation of the globular cluster population could substantially modify this conclusion. Here, we present the discovery of such a signature of rotation in the kinematics of NGC 1052-DF2’s globular clusters, with a velocity amplitude of ${\sim}12.44^{+4.40}_{-5.16}$ km s−1, which, through Bayesian model comparison, represents a marginally better fit to the available kinematic data; note that this rotation is distinct from, and approximately perpendicular to, the recently identified rotation of the stellar component of NGC 1052-DF2. Assuming this truly represents an underlying rotation, it is shown that the determined mass depends upon the inclination of the rotational component and, with a moderate inclination, the resultant mass-to-light ratio can exceed M/L ∼ 10.
We present models of the Hβ-emitting broad-line region (BLR) in seven Seyfert 1 galaxies from the Lick AGN Monitoring Project 2011 sample, drawing inferences on the BLR structure and dynamics as well ...as the mass of the central supermassive black hole. We find that the BLR is generally a thick disk, viewed close to face-on, with preferential emission back toward the ionizing source. The dynamics in our sample range from near-circular elliptical orbits to inflowing or outflowing trajectories. We measure black hole masses of for PG 1310−108, for Mrk 50, for Mrk 141, for Mrk 279, for Mrk 1511, for NGC 4593, and for Zw 229−015. We use these black hole mass measurements along with cross-correlation time lags and line widths to recover the scale factor f used in traditional reverberation mapping measurements. Combining our results with other studies that use this modeling technique, which brings our sample size to 16, we calculate a scale factor that can be used for measuring black hole masses in other reverberation mapping campaigns. When using the root-mean-square (rms) spectrum and using the line dispersion to measure the line width, we find pred = 0.57 0.19. Finally, we search for correlations between f and other AGN and BLR parameters and find marginal evidence that f is correlated with MBH and the BLR inclination angle, but no significant evidence of a correlation with the AGN luminosity or Eddington ratio.
Abstract We present the second iteration of the caramel-gas code, an empirical model of the broad-line region (BLR) gas density field. Building on the initial development and testing of caramel-gas , ...we expand the meaning of the model parameter α , which initially represented only the power-law index of the dependency of emissivity on radial distance. In this work, we test a more generalized radial power-law index, α , that also includes a description of the effective emitting size(s) of the BLR structure as a function of radial distance. We select a sample of 10 active galactic nuclei (AGN) from three different Lick AGN Monitoring Project campaigns to further validate the caramel-gas code and test the generalized radial power-law index, α . Our results confirm that the caramel-gas results are in general agreement with the published results determined using the original caramel code, further demonstrating that our forward modeling method is robust. We find that a positive radial power-law index is generally favored and propose three possible scenarios: (i) the BLR structure has increasing effective emitting size(s) at larger radial distances from the central source, (ii) emission is concentrated at the outer edges of the BLR, and (iii) stronger theoretical assumptions are needed to break the degeneracies inherent to the interpretation of reverberation mapping data in terms of underlying gas properties.
AMORPH utilizes a new Bayesian statistical approach to interpreting X-ray diffraction results of samples with both crystalline and amorphous components. AMORPH fits X-ray diffraction patterns with a ...mixture of narrow and wide components, simultaneously inferring all of the model parameters and quantifying their uncertainties. The program simulates background patterns previously applied manually, providing reproducible results, and significantly reducing inter- and intra-user biases. This approach allows for the quantification of amorphous and crystalline materials and for the characterization of the amorphous component, including properties such as the centre of mass, width, skewness, and nongaussianity of the amorphous component. Results demonstrate the applicability of this program for calculating amorphous contents of volcanic materials and independently modeling their properties in compositionally variable materials.
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•AMORPH utilizes a new statistical approach to analysing XRD data.•AMORPH calculates crystallinity in mixed crystalline-amorphous (X-ray) materials.•AMORPH provides quantifiable characterization of amorphous materials.•The application is tested on terrestrial volcanics and Martian sediments.•Statistical variations of amorphous materials correlate to composition changes.
Summary
We present theoretical and practical properties of the affine‐invariant ensemble sampler Markov Chain Monte Carlo method. In high dimensions, the sampler's ‘stretch move’ has unusual and ...undesirable properties. We demonstrate this with an n‐dimensional correlated Gaussian toy problem with a known mean and covariance structure, and a multivariate version of the Rosenbrock problem. Visual inspection of a trace plots suggests the burn‐in period is short. Upon closer inspection, we discover the mean and the variance of the target distribution do not match the known values, and the chain takes a very long time to converge. This problem becomes severe as n increases beyond 50. We also applied different diagnostics adapted to be applicable to ensemble methods to determine any lack of convergence. The diagnostics include the Gelman–Rubin method, the Heidelberger–Welch test, the integrated autocorrelation and the acceptance rate. The trace plot of individual walkers appears to be useful as well. We therefore conclude that the stretch move should be used with caution in moderate to high dimensions. We also present some heuristic results explaining this behaviour.
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