arXiv subjects

Brendon J. Brewer

Publications and source records attributed to Brendon J. Brewer.

At least 55 records · Page 3Linked to original sources

arXiv2011

The Mass of the Black Hole in Arp 151 from Bayesian Modeling of Reverberation Mapping Data

Supermassive black holes are believed to be ubiquitous at the centers of galaxies. Measuring their masses is extremely challenging yet essential for understanding their role in the formation and evolution of cosmic structure. We present a direct measurement of the mass of a black hole in an active galactic nucleus (Arp 151) based on the motion of the gas responsible for the broad emission lines. By analyzing and modeling spectroscopic and photometric time series, we find that the gas is well described by a disk or torus with an average radius of 3.99 +- 1.25 light days and an opening angle of 68.9 (+21.4, -17.2) degrees, viewed at an inclination angle of 67.8 +- 7.8 degrees (that is, closer to face-on than edge-on). The black hole mass is inferred to be 10^(6.51 +- 0.28) solar masses. The method is fully general and can be used to determine the masses of black holes at arbitrary distances, enabling studies of their evolution over cosmic time.

astro-ph.CO↗

arXiv2011

Geometric and Dynamical Models of Reverberation Mapping Data

We present a general method to analyze reverberation mapping data that provides both estimates for the black hole mass and for the geometry and dynamics of the broad line region (BLR) in active galactic nuclei (AGN). Our method directly infers the spatial and velocity distribution of the BLR from the data, allowing us to easily derive a velocity-resolved transfer function and allowing for a self-consistent estimate of the black hole mass without a virial coefficient. We obtain estimates and reasonable uncertainties of the BLR model parameters by implementing a Markov Chain Monte Carlo algorithm using the formalism of Bayesian probability theory. We use Gaussian Processes to interpolate the the continuum light curve data and create mock light curves that can be fitted to the data. We test our method by creating simulated reverberation mapping data-sets with known true parameter values and by trying to recover these parameter values using our models. We are able to recover the parameters with realistic uncertainties that depend upon the variability of the AGN and the quality of the reverberation mapping campaign. With a geometry model we can recover the mean radius of the BLR to within ~0.1dex 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 ~0.05dex 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.

astro-ph.CO↗

arXiv2010

Modelling of the Complex CASSOWARY/SLUGS Gravitational Lenses

We present the first high-resolution images of CSWA 31, a gravitational lens system observed as part of the SLUGS (Sloan Lenses Unravelled by Gemini Studies) program. These systems exhibit complex image structure with the potential to strongly constrain the mass distribution of the massive lens galaxies, as well as the complex morphology of the sources. In this paper, we describe the strategy used to reconstruct the unlensed source profile and the lens galaxy mass profiles. We introduce a prior distribution over multi-wavelength sources that is realistic as a representation of our knowledge about the surface brightness profiles of galaxies and groups of galaxies. To carry out the inference computationally, we use Diffusive Nested Sampling, an efficient variant of Nested Sampling that uses Markov Chain Monte Carlo (MCMC) to sample the complex posterior distributions and compute the normalising constant. We demonstrate the efficacy of this approach with the reconstruction of the group-group gravitational lens system CSWA 31, finding the source to be composed of five merging spiral galaxies magnified by a factor of 13.

astro-ph.CO↗

arXiv2010

Diffusive Nested Sampling

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested probability distributions, each successive distribution occupying ~e^-1 times the enclosed prior mass of the previous distribution. While NS technically requires independent generation of particles, Markov Chain Monte Carlo (MCMC) exploration fits naturally into this technique. We illustrate the new method on a test problem and find that it can achieve four times the accuracy of classic MCMC-based Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup. An additional benefit is that more samples and a more accurate evidence value can be obtained simply by continuing the run for longer, as in standard MCMC.

stat.CO↗

arXiv2010

A comparison of Bayesian and Fourier methods for frequency determination in asteroseismology

Bayesian methods are becoming more widely used in asteroseismic analysis. In particular, they are being used to determine oscillation frequencies, which are also commonly found by Fourier analysis. It is important to establish whether the Bayesian methods provide an improvement on Fourier methods. We compare, using simulated data, the standard iterative sine-wave fitting method against a Markov Chain Monte Carlo (MCMC) code that has been introduced to infer purely the frequencies of oscillation modes (Brewer et al. 2007). A uniform prior probability distribution function is used for the MCMC method. We find the methods do equally well at determining the correct oscillation frequencies, although the Bayesian method is able to highlight the possibility of a misidentification due to aliasing, which can be useful. In general, we suggest that the least computationally intensive method is preferable.

astro-ph.IM↗

arXiv2010

AAOmega Observations of 47 Tucanae: Evidence for a Past Merger?

The globular cluster 47 Tucanae is well studied but it has many characteristics that are unexplained, including a significant rise in the velocity dispersion profile at large radii, indicating the exciting possibility of two distinct kinematic populations. In this Letter we employ a Bayesian approach to the analysis of the largest available spectral dataset of 47 Tucanae to determine whether this apparently two-component population is real. Assuming the two models were equally likely before taking the data into account, we find that the evidence favours the two-component population model by a factor of ~3x10^7. Several possible explanations for this result are explored, namely the evaporation of low-mass stars, a hierarchical merger, extant remnants of two initially segregated populations, and multiple star formation epochs. We find the most compelling explanation for the two-component velocity distribution is that 47 Tuc formed as two separate populations arising from the same proto-cluster cloud which merged <7.3 +/- 1.5 Gyr ago. This may also explain the extreme rotation, low mass-to-light ratio and mixed stellar populations of this cluster.

astro-ph.GA↗

arXiv2009

Entropic Priors and Bayesian Model Selection

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst cosmologists: is dark energy a cosmological constant, or has it evolved with time in some way? And how shall we decide, when the data are in?

physics.data-an↗

arXiv2009

Gaussian Process Modelling of Asteroseismic Data

The measured properties of stellar oscillations can provide powerful constraints on the internal structure and composition of stars. To begin this process, oscillation frequencies must be extracted from the observational data, typically time series of the star's brightness or radial velocity. In this paper, a probabilistic model is introduced for inferring the frequencies and amplitudes of stellar oscillation modes from data, assuming that there is some periodic character to the oscillations, but that they may not be exactly sinusoidal. Effectively we fit damped oscillations to the time series, and hence the mode lifetime is also recovered. While this approach is computationally demanding for large time series (> 1500 points), it should at least allow improved analysis of observations of solar-like oscillations in subgiant and red giant stars, as well as sparse observations of semiregular stars, where the number of points in the time series is often low. The method is demonstrated on simulated data and then applied to radial velocity measurements of the red giant star xi Hydrae, yielding a mode lifetime between 0.41 and 2.65 days with 95% posterior probability. The large frequency separation between modes is ambiguous, however we argue that the most plausible value is 6.3 microHz, based on the radial velocity data and the star's position in the HR diagram.

astro-ph.SR↗

arXiv2008

Applications of Bayesian Probability Theory in Astrophysics

Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a series of papers that have been published in various astronomical journals during the years 2005-2008. The unifying thread running through the papers is the use of Bayesian Inference to solve underdetermined inverse problems in astrophysics. Firstly, a methodology is developed to solve a question in gravitational lens inversion - using the observed images of gravitational lens systems to reconstruct the undistorted source profile and the mass profile of the lensing galaxy. A similar technique is also applied to the task of inferring the number and frequency of modes of oscillation of a star from the time series observations that are used in the field of asteroseismology. For these complex problems, many of the required calculations cannot be done analytically, and so Markov Chain Monte Carlo algorithms have been used. Finally, probabilistic reasoning is applied to a controversial question in astrobiology: does the fact that life formed quite soon after the Earth constitute evidence that the formation of life is quite probable, given the right macroscopic conditions?

astro-ph↗

arXiv2008

The Implications of the Early Formation of Life on Earth

One of the most interesting unsolved questions in science today is the question of life on other planets. At the present time it is safe to say that we do not have much of an idea as to whether life is common or exceedingly rare in the universe, and this will probably not be solved for certain unless definitive evidence of extraterrestrial life is found in the future. Our presence on Earth is just as consistent with the hypothesis that life is extremely rare as it is with the hypothesis that it is common, since if there was only one planet with intelligent life, we would find ourselves on it. However, we have more information than this, such as the the surprisingly short length of time it took for life to arise on Earth. Previous authors have analysed this information, concluding that it is evidence that the probability of abiogenesis is moderate ($>$ 13% with 95% probability) and cannot be extremely small. In this paper I use simple probabilistic model to show that this conclusion was based more on an unintentional assumption than on the data. While the early formation of life on Earth provides some evidence in the direction of life being common, it is far from conclusive, and in particular does not rule out the possibility that abiogenesis has only occurred once in the history of the universe.

physics.pop-ph↗

arXiv2008

Unlensing HST Observations of the Einstein Ring 1RXS J1131-1231: A Bayesian Analysis

We present a source and lens reconstruction for the optical Einstein ring gravitational lens system RXS J1131-1231. We resolve detail in the source, which is the host galaxy of a $z=0.658$ quasar, down to a resolution of 0.045 arc seconds (this is the size of the smallest conclusively resolved structures, rather than the pixel scale), using a Bayesian technique with a realistic model for the prior information. The source reconstruction reveals a substantial amount of complex structure in the host galaxy, which is $\sim$ 8 kpc in extent and contains several bright compact substructures, with the quasar source residing in one of these bright substructures. Additionally, we recover the mass distribution of the lensing galaxy, assuming a simply-parameterised model, using information from both the quasar images and the extended images. This allows a direct comparison of the amount of information about the lens that is provided by the quasar images in comparison to the extended images. In this system, we find that the extended images provide significantly more information about the lens than the quasar images alone, especially if we do not include prior constraints on the central position of the lens.

astro-ph↗

arXiv2008

A Molecular Einstein Ring at z=4.12: Imaging the Dynamics of a Quasar Host Galaxy Through a Cosmic Lens

We present high-resolution (0.3") Very Large Array (VLA) imaging of the molecular gas in the host galaxy of the high redshift quasar PSS J2322+1944 (z=4.12). These observations confirm that the molecular gas (CO) in the host galaxy of this quasar is lensed into a full Einstein ring, and reveal the internal dynamics of the molecular gas in this system. The ring has a diameter of ~1.5", and thus is sampled over ~20 resolution elements by our observations. Through a model-based lens inversion, we recover the velocity gradient of the molecular reservoir in the quasar host galaxy of PSS J2322+1944. The Einstein ring lens configuration enables us to zoom in on the emission and to resolve scales down to ~1 kpc. From the model-reconstructed source, we find that the molecular gas is distributed on a scale of 5 kpc, and has a total mass of M(H2)=1.7 x 10^10 M_sun. A basic estimate of the dynamical mass gives M_dyn = 4.4 x 10^10 (sin i)^-2 M_sun, that is, only ~2.5 times the molecular gas mass, and ~30 times the black hole mass (assuming that the dynamical structure is highly inclined). The lens configuration also allows us to tie the optical emission to the molecular gas emission, which suggests that the active galactic nucleus (AGN) does reside within, but not close to the center of the molecular reservoir. Together with the (at least partially) disturbed structure of the CO, this suggests that the system is interacting. Such an interaction, possibly caused by a major `wet' merger, may be responsible for both feeding the quasar and fueling the massive starburst of 680 M_sun/yr in this system, in agreement with recently suggested scenarios of quasar activity and galaxy assembly in the early universe.

astro-ph↗

arXiv2008

Getting Your Eye In: A Bayesian Analysis of Early Dismissals in Cricket

A Bayesian Survival Analysis method is motivated and developed for analysing sequences of scores made by a batsman in test or first class cricket. In particular, we expect the presence of an effect whereby the distribution of scores has more probability near zero than a geometric distribution, due to the fact that batting is more difficult when the batsman is new at the crease. A Metropolis-Hastings algorithm is found to be efficient at estimating the proposed parameters, allowing us to quantify exactly how large this early-innings effect is, and how long a batsman needs to be at the crease in order to ``get their eye in''. Applying this model to several modern players shows that a batsman is typically only playing at about half of their potential ability when they first arrive at the crease, and gets their eye in surprisingly quickly. Additionally, some players are more ``robust'' (have a smaller early-innings effect) than others, which may have implications for selection policy.

stat.AP↗

arXiv2007

Solar-like oscillations in the G2 subgiant beta Hydri from dual-site observations

We have observed oscillations in the nearby G2 subgiant star beta Hyi using high-precision velocity observations obtained over more than a week with the HARPS and UCLES spectrographs. The oscillation frequencies show a regular comb structure, as expected for solar-like oscillations, but with several l=1 modes being strongly affected by avoided crossings. The data, combined with those we obtained five years earlier, allow us to identify 28 oscillation modes. By scaling the large frequency separation from the Sun, we measure the mean density of beta Hyi to an accuracy of 0.6%. The amplitudes of the oscillations are about 2.5 times solar and the mode lifetime is 2.3 d. A detailed comparison of the mixed l=1 modes with theoretical models should allow a precise estimate of the age of the star.

astro-ph↗

arXiv2006

Bayesian Inference from Observations of Solar-Like Oscillations

Stellar oscillations can provide a wealth of information about a star, which can be extracted from observed time series of the star's brightness or radial velocity. In this paper we address the question of how to extract as much information as possible from such a dataset. We have developed a Markov Chain Monte Carlo (MCMC) code that is able to infer the number of oscillation frequencies present in the signal and their values (with corresponding uncertainties), without having to fit the amplitudes and phases. Gaps in the data do not have any serious consequences for this method; in cases where severe aliasing exists, any ambiguity in the frequency determinations will be reflected in the results. It also allows us to infer parameters of the frequency pattern, such as the large separation Delta nu. We have previously applied this method to the star nu Indi (Bedding et al 2006), and here we describe the method fully and apply it to simulated datasets, showing that the code is able to give correct results even when some of the model assumptions are violated. In particular, the non-sinusoidal nature of the individual oscillation modes due to stochastic excitation and damping has no major impact on the usefulness of our approach.

astro-ph↗

arXiv2006

The Einstein Ring 0047-2808 Revisited: A Bayesian Inversion

In a previous paper, we outlined a new Bayesian method for inferring the properties of extended gravitational lenses, given data in the form of resolved images. This method holds the most promise for optimally extracting information from the observed image, whilst providing reliable uncertainties in all parameters. Here, we apply the method to the well studied optical Einstein ring 0047-2808. Our results are in broad agreement with previous studies, showing that the density profile of the lensing galaxy is aligned within a few degrees of the light profile, and suggesting that the source galaxy (at redshift 3.6) is a binary system, although its size is only of order 1-2 kpc. We also find that the mass of the elliptical lensing galaxy enclosed by the image is (2.91$\pm$0.01)$\times10^{11}$ M$_{\sun}$. Our method is able to achieve improved resolution for the source reconstructions, although we also find that some of the uncertainties are greater than has been found in previous analyses, due to the inclusion of extra pixels and a more general lens model.

astro-ph↗

arXiv2006

Solar-like oscillations in the metal-poor subgiant nu Indi: constraining the mass and age using asteroseismology

Asteroseismology is a powerful method for determining fundamental properties of stars. We report the first application to a metal-poor object, namely the subgiant star nu Ind. We measured precise velocities from two sites, allowing us to detect oscillations and infer a large frequency separation of Delta_nu = 24.25 +/- 0.25 microHz. Combining this value with the location of the star in the H-R diagram and comparing with standard evolutionary models, we were able to place constraints on the stellar parameters. In particular, our results indicate that nu Ind has a low mass (0.85 +/- 0.04 M_sun) and is at least 9 Gyr old.

astro-ph↗

arXiv2005

Strong Gravitational Lens Inversion: A Bayesian Approach

If an extended source, such as a galaxy, is gravitationally lensed by a massive object in the foreground, the lensing distorts the observed image. It is straightforward to simulate what the observed image would be for a particular lens and source combination. In practice, one observes the lensed image on the sky, but blurred by atmospheric and telescopic effects and also contaminated with noise. The question that then arises is, given this incomplete data, what combinations of lens mass distribution and source surface brightness profile could plausibly have produced this image? This is a classic example of an inverse problem, and the method for solving it is given by the framework of Bayesian inference. In this paper we demonstrate the application of Bayesian inference to the problem of gravitational lens reconstruction, and illustrate the use of Markov Chain Monte Carlo simulations which can be used when the analytical calculations become too difficult. Previous methods for performing gravitational lens inversion are seen in a new light, as special cases of the general approach presented in this paper. Thus, we are able to answer, at least in principle, lingering questions about the uncertainties in the reconstructed source and lens parameters, taking into account all of the data and any prior information we may have.

astro-ph↗