arXiv subjects

Michael P. Hobson

Publications and source records attributed to Michael P. Hobson.

At least 37 records · Page 2Linked to original sources

arXiv2016

Friedmann-Robertson-Walker models do not require zero active mass

The $R_h = ct$ cosmological model has received considerable attention in recent years owing to claims that it is favoured over the standard $Λ$ cold dark matter ($Λ$CDM) model by most observational data. A key feature of the $R_h = ct$ model is that the zero active mass condition $ρ+ 3p = 0$ holds at all epochs. Most recently, Melia has claimed that this condition is a requirement of the symmetries of the Friedmann-Robertson-Walker (FRW) spacetime. We demonstrate that this claim is false and results from a flaw in the logic of Melia's argument.

astro-ph.CO↗

arXiv2016

Spherically-symmetric solutions in general relativity

We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lemaître-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus 'physical' coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann-Robertson-Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-zero pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of 'Swiss cheese' model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and verify the validity of Birkhoff's theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called $R_h = ct$ cosmological model, which has recently received considerable attention. These considerations in turn illustrate the interesting behaviour of a number of 'horizons' in general cosmological models.

gr-qc↗

arXiv2016

AMI observations of ten CLASH galaxy clusters: SZ and X-ray data used together to determine cluster dynamical states

Using Arcminute Microkelvin Imager (AMI) SZ observations towards ten CLASH clusters we investigate the influence of cluster mergers on observational galaxy cluster studies. Although selected to be largely relaxed, there is disagreement in the literature on the dynamical states of CLASH sample members. We analyse our AMI data in a fully Bayesian way to produce estimated cluster parameters and consider the intrinsic correlations in our NFW/GNFW-based model. Varying pressure profile shape parameters, illustrating an influence of mergers on scaling relations, induces small deviations from the canonical self-similar predictions -- in agreement with simulations of Poole et al. 2007 who found that merger activity causes only small scatter perpendicular to the relations. We demonstrate this effect observationally using the different dependencies of SZ and X-ray signals to $n_{\rm e}$ that cause different sensitivities to the shocking and/or fractionation produced by mergers. Plotting $Y_{\rm X}$--$M_{\rm gas}$ relations (where $Y_{\rm X}=M_{\rm gas}T$) derived from AMI SZ and from $Chandra$ X-ray gives ratios of AMI and $Chandra$ $Y_{\rm X}$ and $M_{\rm gas}$ estimates that indicate movement of clusters \textit{along} the scaling relation, as predicted by Poole et al. 2007. Clusters that have moved most along the relation have the most discrepant $T_{\rm SZ}$ and $T_{\rm X}$ estimates: all the other clusters (apart from one) have SZ and X-ray estimates of $M_{\rm gas}$, $T$ and $Y_{\rm X}$ that agree within $r_{500}$. We use SZ vs X-ray discrepancies in conjunction with $Chandra$ maps and $T_{\rm X}$ profiles, making comparisons with simulated cluster merger maps in Poole et al. 2006, to identify disturbed members of our sample and estimate merger stages.

astro-ph.CO↗

arXiv2014

Bayesian estimation of non-Gaussianity in pulsar timing analysis

We introduce a method for performing a robust Bayesian analysis of non-Gaussianity present in pulsar timing data, simultaneously with the pulsar timing model, and additional stochastic parameters such as those describing red spin noise and dispersion measure variations. The parameters used to define the presence of non-Gaussianity are zero for Gaussian processes, giving a simple method of defining the strength of non-Gaussian behaviour. We use simulations to show that assuming Gaussian statistics when the noise in the data is drawn from a non-Gaussian distribution can significantly increase the uncertainties associated with the pulsar timing model parameters. We then apply the method to the publicly available 15 year Parkes Pulsar Timing Array data release 1 dataset for the binary pulsar J0437$-$4715. In this analysis we present a significant detection of non-Gaussianity in the uncorrelated non-thermal noise, but we find that it does not yet impact the timing model or stochastic parameter estimates significantly compared to analysis performed assuming Gaussian statistics. The methods presented are, however, shown to be of immediate practical use for current European Pulsar Timing Array (EPTA) and International Pulsar Timing Array (IPTA) datasets.

astro-ph.IM↗

arXiv2014

SKYNET: an efficient and robust neural network training tool for machine learning in astronomy

We present the first public release of our generic neural network training algorithm, called SkyNet. This efficient and robust machine learning tool is able to train large and deep feed-forward neural networks, including autoencoders, for use in a wide range of supervised and unsupervised learning applications, such as regression, classification, density estimation, clustering and dimensionality reduction. SkyNet uses a `pre-training' method to obtain a set of network parameters that has empirically been shown to be close to a good solution, followed by further optimisation using a regularised variant of Newton's method, where the level of regularisation is determined and adjusted automatically; the latter uses second-order derivative information to improve convergence, but without the need to evaluate or store the full Hessian matrix, by using a fast approximate method to calculate Hessian-vector products. This combination of methods allows for the training of complicated networks that are difficult to optimise using standard backpropagation techniques. SkyNet employs convergence criteria that naturally prevent overfitting, and also includes a fast algorithm for estimating the accuracy of network outputs. The utility and flexibility of SkyNet are demonstrated by application to a number of toy problems, and to astronomical problems focusing on the recovery of structure from blurred and noisy images, the identification of gamma-ray bursters, and the compression and denoising of galaxy images. The SkyNet software, which is implemented in standard ANSI C and fully parallelised using MPI, is available at http://www.mrao.cam.ac.uk/software/skynet/.

astro-ph.IM↗

arXiv2013

How to take the interstellar weather with you in pulsar timing analysis

Here we present a Bayesian method of including discrete measurements of dispersion measure due to the interstellar medium in the direction of a pulsar as prior information in the analysis of that pulsar. We use a simple simulation to show the efficacy of this method, where the inclusion of the additional measurements results in both a significant increase in the precision with which the timing model parameters can be obtained, and an improved upper limit on the amplitude of any red noise in the dataset. We show that this method can be applied where no multi-frequency data exists across much of the dataset, and where there is no simultaneous multi-frequency data for any given observing epoch. Including such information in the analysis of upcoming International Pulsar Timing Array (IPTA) and European Pulsar Timing Array (EPTA) data releases could therefore prove invaluable in obtaining the most constraining limits on gravitational wave signals within those datasets.

astro-ph.IM↗

arXiv2013

TempoNest: A Bayesian approach to pulsar timing analysis

A new Bayesian software package for the analysis of pulsar timing data is presented in the form of TempoNest which allows for the robust determination of the non-linear pulsar timing solution simultaneously with a range of additional stochastic parameters. This includes both red spin noise and dispersion measure variations using either power law descriptions of the noise, or through a model-independent method that parameterises the power at individual frequencies in the signal. We use TempoNest to show that at noise levels representative of current datasets in the European Pulsar Timing Array (EPTA) and International Pulsar Timing Array (IPTA) the linear timing model can underestimate the uncertainties of the timing solution by up to an order of magnitude. We also show how to perform Bayesian model selection between different sets of timing model and stochastic parameters, for example, by demonstrating that in the pulsar B1937+21 both the dispersion measure variations and spin noise in the data are optimally modelled by simple power laws. Finally we show that not including the stochastic parameters simultaneously with the timing model can lead to unpredictable variation in the estimated uncertainties, compromising the robustness of the scientific results extracted from such analysis.

astro-ph.IM↗

arXiv2013

Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data

A new model independent method is presented for the analysis of pulsar timing data and the estimation of the spectral properties of an isotropic gravitational wave background (GWB). We show that by rephrasing the likelihood we are able to eliminate the most costly aspects of computation normally associated with this type of data analysis. When applied to the International Pulsar Timing Array Mock Data Challenge data sets this results in speedups of approximately 2 to 3 orders of magnitude compared to established methods. We present three applications of the new likelihood. In the low signal to noise regime we sample directly from the power spectrum coefficients of the GWB signal realization. In the high signal to noise regime, where the data can support a large number of coefficients, we sample from the joint probability density of the power spectrum coefficients for the individual pulsars and the GWB signal realization. Critically in both these cases we need make no assumptions about the form of the power spectrum of the GWB, or the individual pulsars. Finally we present a method for characterizing the spatial correlation between pulsars on the sky, making no assumptions about the form of that correlation, and therefore providing the only truly general Bayesian method of confirming a GWB detection from pulsar timing data.

astro-ph.IM↗

arXiv2013

A joint analysis of AMI and CARMA observations of the recently discovered SZ galaxy cluster system AMI-CL J0300+2613

We present CARMA observations of a massive galaxy cluster discovered in the AMI blind SZ survey. Without knowledge of the cluster redshift a Bayesian analysis of the AMI, CARMA and joint AMI & CARMA uv-data is used to quantify the detection significance and parameterise both the physical and observational properties of the cluster whilst accounting for the statistics of primary CMB anisotropies, receiver noise and radio sources. The joint analysis of the AMI & CARMA uv-data was performed with two parametric physical cluster models: the β-model; and the model described in Olamaie et al. 2012 with the pressure profile fixed according to Arnaud et al. 2010. The cluster mass derived from these different models is comparable but our Bayesian evidences indicate a preference for the β-profile which we, therefore, use throughout our analysis. From the CARMA data alone we obtain a Bayesian probability of detection ratio of 12.8:1 when assuming that a cluster exists within our search area; alternatively assuming that Jenkins et al. 2001 accurately predicts the number of clusters as a function of mass and redshift, the Bayesian probability of detection is 0.29:1. From the analysis of the AMI or AMI & CARMA data the probability of detection ratio exceeds 4.5x10^3:1. Performing a joint analysis of the AMI & CARMA data with a physical cluster model we derive the total mass internal to r200 as MT,200 = 4.1x10^14Msun. Using a phenomenological β-model to quantify the temperature decrement as a function of angular distance we find a central SZ temperature decrement of 170μK in the AMI & CARMA data. The SZ decrement in the CARMA data is weaker than expected and we speculate that this is a consequence of the cluster morphology. In a forthcoming study we will assess the impact of cluster morphology on the SZ decrements that are observed with interferometers such as AMI and CARMA.

astro-ph.CO↗

arXiv2013

SZ observations with AMI of the hottest galaxy clusters detected in the XMM-Newton Cluster Survey

We have obtained deep SZ observations towards 15 of the apparently hottest XMM Cluster Survey (XCS) clusters that can be observed with the Arcminute Microkelvin Imager (AMI). We use a Bayesian analysis to quantify the significance of our SZ detections. We detect the SZ effect at high significance towards three of the clusters and at lower significance for a further two clusters. Towards the remaining ten clusters, no clear SZ signal was measured. We derive cluster parameters using the XCS mass estimates as a prior in our Bayesian analysis. For all AMI-detected clusters, we calculate large-scale mass and temperature estimates while for all undetected clusters we determine upper limits on these parameters. We find that the large- scale mean temperatures derived from our AMI SZ measurements (and the upper limits from null detections) are substantially lower than the XCS-based core-temperature estimates. For clusters detected in the SZ, the mean temperature is, on average, a factor of 1.4 lower than temperatures from the XCS. For clusters undetected in SZ, the average 68% upper limit on the mean temperature is a factor of 1.9 below the XCS temperature.

astro-ph.CO↗

arXiv2013

AMI SZ observations and Bayesian analysis of a sample of six redshift-one clusters of galaxies

We present 16-GHz Sunyaev-Zel'dovich observations using the Arcminute Microkelvin Imager (AMI) and subsequent Bayesian analysis of six galaxy clusters at redshift ($z \approx 1$) chosen from an X-ray and Infrared selected sample from Culverhouse et al. (2010). In the subsequent analysis we use two cluster models, an isothermal β-model and a Dark Matter GNFW (DM-GNFW) model in order to derive a formal detection probability and the cluster parameters. We detect two clusters (CLJ1415+3612 & XMJ0830+5241) and measure their total masses out to a radius of 200 $\times$ the critical density at the respective cluster's redshift. For CLJ1415+3612 and XMJ0830+5241, we find M_{\mathrm{T},200} for each model, which agree with each other for each cluster. We also present maps before and after source subtraction of the entire sample and provide 1D and 2D posterior marginalised probability distributions for each fitted cluster profile parameter of the detected clusters. Using simulations which take into account the measured source environment from the AMI Large Array (LA), source confusion noise, CMB primordials, instrument noise, we estimate from low-radius X-ray data from Culverhouse et al. (2010), the detectability of each cluster in the sample and compare it with the result from the Small Array (SA) data. Furthermore, we discuss the validity of the assumptions of isothermality and constant gas mass fraction. We comment on the bias that these small-radius estimates introduce to large-radius SZ predictions. In addition, we follow-up the two detections with deep, single-pointed LA observations. We find a 3 sigma tentative decrement toward CLJ1415+3612 at high-resolution and a 5 sigma high-resolution decrement towards XMJ0830+5241.

astro-ph.CO↗

arXiv2012

AMI Galactic Plane Survey at 16 GHz: I -- Observing, mapping and source extraction

The AMI Galactic Plane Survey (AMIGPS) is a large area survey of the outer Galactic plane to provide arcminute resolution images at milli-Jansky sensitivity in the centimetre-wave band. Here we present the first data release of the survey, consisting of 868 deg^2 of the Galactic plane, covering the area 76 deg \lessapprox l \lessapprox 170 deg between latitudes of |b| \lessapprox 5 deg, at a central frequency of 15.75 GHz (1.9 cm). We describe in detail the drift scan observations which have been used to construct the maps, including the techniques used for observing, mapping and source extraction, and summarise the properties of the finalized datasets. These observations constitute the most sensitive Galactic plane survey of large extent at centimetre-wave frequencies greater than 1.4 GHz.

astro-ph.GA↗

arXiv2012

Detailed SZ study of 19 LoCuSS galaxy clusters: masses and temperatures out to the virial radius

We present 16-GHz AMI SZ observations of 19 clusters with L_X >7x10^37 W (h50=1) selected from the LoCuS survey (0.142<z<0.295) and of A1758b, in the FoV of A1758a. We detect 17 clusters with 5-23sigma peak surface brightnesses. Cluster parameters are obtained using a Bayesian cluster analysis. We fit isothermal beta-models to our data and assume the clusters are virialized (with all the kinetic energy in gas internal energy). Our gas temperature, T_AMI, is derived from AMI SZ data, not from X-ray spectroscopy. Cluster parameters internal to r500 are derived assuming HSE. We find: (i) Different gNFW parameterizations yield significantly different parameter degeneracies. (ii) For h70 = 1, we find the virial radius r200 to be typically 1.6+/-0.1 Mpc and the total mass M_T(r200) typically to be 2.0-2.5xM_T(r500).(iii) Where we have found M_T X-ray (X) and weak-lensing (WL) values in the literature, there is good agreement between WL and AMI estimates (with M_{T,AMI}/M_{T,WL} =1.2^{+0.2}_{-0.3} and =1.0+/-0.1 for r500 and r200, respectively). In comparison, most Suzaku/Chandra estimates are higher than for AMI (with M_{T,X}/M_{T,AMI}=1.7+/-0.2 within r500), particularly for the stronger mergers.(iv) Comparison of T_AMI to T_X sheds light on high X-ray masses: even at large r, T_X can substantially exceed T_AMI in mergers. The use of these higher T_X values will give higher X-ray masses. We stress that large-r T_SZ and T_X data are scarce and must be increased. (v) Despite the paucity of data, there is an indication of a relation between merger activity and SZ ellipticity. (vi) At small radius (but away from any cooling flow) the SZ signal (and T_AMI) is less sensitive to ICM disturbance than the X-ray signal (and T_X) and, even at high r, mergers affect n^2-weighted X-ray data more than n-weighted SZ, implying significant shocking or clumping or both occur even in the outer parts of mergers.

astro-ph.CO↗

arXiv2012

Sunyaev-Zel'dovich observations of LoCuSS clusters with the Arcminute Microkelvin Imager: moderate X-ray luminosity sample

We present 16-GHz observations using the Arcminute Microkelvin Imager (AMI) of 11 clusters with 7 x 10^{37}W < L_X < 11 x 10^{37}W (h_{50}=1.0) selected from the Local Cluster Substructure Survey (LoCuSS) and compare them to X-ray data. We use a fast, Bayesian cluster analysis to explore the high-dimensional parameter space of the cluster-plus-sources model and obtain robust cluster parameter estimates in the presence of radio point sources, receiver noise and primordial CMB anisotropy. Our analysis fits a spherical, isothermal beta-model to our data and assumes the cluster follows the theoretical mass-temperature relation. Large-scale cluster parameters internal to r_{500} are derived under the assumption of hydrostatic equilibrium. Posterior distributions for the large-scale parameters of 8 of our clusters are given; SZ effects towards Abell 1704 and Zw0857.9+2107 were not detected and our spherical beta-profile was found to be an inadequate fit to the decrement on our map for Abell 2409.

astro-ph.CO↗

arXiv2012

The effect of an expanding universe on massive objects

We present some astrophysical consequences of the metric for a point mass in an expanding universe derived in Nandra, Lasenby & Hobson, and of the associated invariant expression for the force required to keep a test particle at rest relative to the central mass. We focus on the effect of an expanding universe on massive objects on the scale of galaxies and clusters. Using Newtonian and general-relativistic approaches, we identify two important time-dependent physical radii for such objects when the cosmological expansion is accelerating. The first radius, $r_F$, is that at which the total radial force on a test particle is zero, which is also the radius of the largest possible circular orbit about the central mass $m$ and where the gas pressure and its gradient vanish. The second radius, $r_S$, which is \approx r_F/1.6$, is that of the largest possible stable circular orbit, which we interpret as the theoretical maximum size for an object of mass $m$. In contrast, for a decelerating cosmological expansion, no such finite radii exist. Assuming a cosmological expansion consistent with a $Λ$CDM concordance model, at the present epoch we find that these radii put a sensible constraint on the typical sizes of both galaxies and clusters at low redshift. For galaxies, we also find that these radii agree closely with zeroes in the radial velocity field in the neighbourhood of nearby galaxies, as inferred by Peirani & Pacheco from recent observations of stellar velocities. We then consider the future effect on massive objects of an accelerating cosmological expansion driven by phantom energy, for which the universe is predicted to end in a `Big Rip' at a finite time in the future at which the scale factor becomes singular. In particular, we present a novel calculation of the time prior to the Big Rip that an object of a given mass and size will become gravitationally unbound.

gr-qc↗

arXiv2012

The effect of a massive object on an expanding universe

A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics describing a point mass in a spatially-flat, open and closed expanding universe respectively. In the spatially-flat case, a simple coordinate transformation relates the metric to the corresponding one derived by McVittie. Nonetheless, our use of non-comoving (`physical') coordinates greatly facilitates physical interpretation. For the open and closed universes, our metrics describe different spacetimes to the corresponding McVittie metrics and we believe the latter to be incorrect. In the closed case, our metric possesses an image mass at the antipodal point of the universe. We calculate the geodesic equations for the spatially-flat metric and interpret them. For radial motion in the Newtonian limit, the force acting on a test particle consists of the usual $1/r^2$ inwards component due to the central mass and a cosmological component proportional to $r$ that is directed outwards (inwards) when the expansion of the universe is accelerating (decelerating). For the standard $Λ$CDM concordance cosmology, the cosmological force reverses direction at about $z\approx 0.67$. We also derive an invariant fully general-relativistic expression, valid for arbitrary spherically-symmetric systems, for the force required to hold a test particle at rest relative to the central point mass.

gr-qc↗

arXiv2012

AMI radio continuum observations of young stellar objects with known outflows

We present 16 GHz (1.9 cm) deep radio continuum observations made with the Arcminute Microkelvin Imager (AMI) of a sample of low-mass young stars driving jets. We combine these new data with archival information from an extensive literature search to examine spectral energy distributions (SEDs) for each source and calculate both the radio and sub-mm spectral indices in two different scenarios: (1) fixing the dust temperature (Td) according to evolutionary class; (2) allowing Td to vary. We use the results of this analysis to place constraints on the physical mechanisms responsible for the radio emission. From AMI data alone, as well as from model fitting to the full SED in both scenarios, we find that 80 per cent of the objects in this sample have spectral indices consistent with free-free emission. We find an average spectral index in both Td scenarios consistent with free-free emission. We examine correlations of the radio luminosity with bolometric luminosity, envelope mass, and outflow force and find that these data are consistent with the strong correlation with envelope mass seen in lower luminosity samples. We examine the errors associated with determining the radio luminosity and find that the dominant source of error is the uncertainty on the opacity index, beta. We examine the SEDs for variability in these young objects, and find evidence for possible radio flare events in the histories of L1551 IRS 5 and Serpens SMM 1.

astro-ph.SR↗

arXiv2012

BAMBI: blind accelerated multimodal Bayesian inference

In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network (NN) to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. We begin by demonstrating, with a few toy examples, the ability of a NN to learn complicated likelihood surfaces. BAMBI's ability to decrease running time for Bayesian inference is then demonstrated in the context of estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe and other observations. We show that valuable speed increases are achieved in addition to obtaining NNs trained on the likelihood functions for the different model and data combinations. These NNs can then be used for an even faster follow-up analysis using the same likelihood and different priors. This is a fully general algorithm that can be applied, without any pre-processing, to other problems with computationally expensive likelihood functions.

astro-ph.IM↗