Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.Comment: 12 pages, 6 figure

Galaxy morphology rules out astrophysically relevant Hu-Sawicki f(R)f(R) gravity

$f(R)$ is a paradigmatic modified gravity theory that typifies extensions to General Relativity with new light degrees of freedom and hence screened fifth forces between masses. These forces produce observable signatures in galaxy morphology, caused by a violation of the weak equivalence principle due to a differential impact of screening among galaxies' mass components. We compile statistical datasets of two morphological indicators -- offsets between stars and gas in galaxies and warping of stellar disks -- and use them to constrain the strength and range of a thin-shell-screened fifth force. This is achieved by applying a comprehensive set of upgrades to past work (Desmond et al 2018a,b): we construct a robust galaxy-by-galaxy Bayesian forward model for the morphological signals, including full propagation of uncertainties in the input quantities and marginalisation over an empirical model describing astrophysical noise. Employing more stringent data quality cuts than previously we find no evidence for a screened fifth force of any strength $\Delta G/G_\text{N}$ in the Compton wavelength range $0.3-8$ Mpc, setting a $1\sigma$ bound of $\Delta G/G_\text{N}<0.8$ at $\lambda_C=0.3$ Mpc that strengthens to $\Delta G/G_\text{N}<3\times10^{-5}$ at $\lambda_C=8$ Mpc. These are the tightest bounds to date beyond the Solar System by over an order of magnitude. For the Hu-Sawicki model of $f(R)$ with $n=1$ we require a background scalar field value $f_{R0} < 1.4 \times 10^{-8}$, forcing practically all astrophysical objects to be screened. We conclude that this model can have no relevance to astrophysics or cosmology.Comment: 15 pages, 6 figures; minor revision, matches PRD accepted versio

A Bayesian approach to star-galaxy classification

Star-galaxy classification is one of the most fundamental data-processing tasks in survey astronomy, and a critical starting point for the scientific exploitation of survey data. For bright sources this classification can be done with almost complete reliability, but for the numerous sources close to a survey's detection limit each image encodes only limited morphological information. In this regime, from which many of the new scientific discoveries are likely to come, it is vital to utilise all the available information about a source, both from multiple measurements and also prior knowledge about the star and galaxy populations. It is also more useful and realistic to provide classification probabilities than decisive classifications. All these desiderata can be met by adopting a Bayesian approach to star-galaxy classification, and we develop a very general formalism for doing so. An immediate implication of applying Bayes's theorem to this problem is that it is formally impossible to combine morphological measurements in different bands without using colour information as well; however we develop several approximations that disregard colour information as much as possible. The resultant scheme is applied to data from the UKIRT Infrared Deep Sky Survey (UKIDSS), and tested by comparing the results to deep Sloan Digital Sky Survey (SDSS) Stripe 82 measurements of the same sources. The Bayesian classification probabilities obtained from the UKIDSS data agree well with the deep SDSS classifications both overall (a mismatch rate of 0.022, compared to 0.044 for the UKIDSS pipeline classifier) and close to the UKIDSS detection limit (a mismatch rate of 0.068 compared to 0.075 for the UKIDSS pipeline classifier). The Bayesian formalism developed here can be applied to improve the reliability of any star-galaxy classification schemes based on the measured values of morphology statistics alone.Comment: Accepted 22 November 2010, 19 pages, 17 figure

Parametric modelling of the 3.6um to 8um colour distributions of galaxies in the SWIRE Survey

We fit a parametric model comprising a mixture of multi-dimensional Gaussian functions to the 3.6 to 8um colour and optical photo-z distribution of galaxy populations in the ELAIS-N1 and Lockman Fields of SWIRE. For 16,698 sources in ELAIS-N1 we find our data are best modelled (in the sense of the Bayesian Information Criterion) by the sum of four Gaussian distributions or modes (C_a, C_b, C_c and C_d). We compare the fit of our empirical model with predictions from existing semi-analytic and phenomological models. We infer that our empirical model provides a better description of the mid-infrared colour distribution of the SWIRE survey than these existing models. This colour distribution test is thus a powerful model discriminator and complementary to comparisons of number counts. We use our model to provide a galaxy classification scheme and explore the nature of the galaxies in the different modes of the model. C_a consists of dusty star-forming systems such as ULIRG's. Low redshift late-type spirals are found in C_b, where PAH emission dominates at 8um. C_c consists of dusty starburst systems at intermediate redshifts. Low redshift early-type spirals and ellipticals dominate C_d. We thus find a greater variety of galaxy types than one can with optical photometry alone. Finally we develop a new technique to identify unusual objects, and find a selection of outliers with very red IRAC colours. These objects are not detected in the optical, but have very strong detections in the mid-infrared. These sources are modelled as dust-enshrouded, strongly obscured AGN, where the high mid-infrared emission may either be attributed to dust heated by the AGN or substantial star-formation. These sources have z_ph ~ 2-4, making them incredibly infrared luminous, with a L_IR ~ 10^(12.6-14.1) L_sun.Comment: 44 pages, 10 figures, 6 tables. Accepted for publication in the Astronomical Journa

Algorithms for approximate Bayesian inference with applications to astronomical data analysis

Bayesian inference is a theoretically well-founded and conceptually simple approach to data analysis. The computations in practical problems are anything but simple though, and thus approximations are almost always a necessity. The topic of this thesis is approximate Bayesian inference and its applications in three intertwined problem domains. Variational Bayesian learning is one type of approximate inference. Its main advantage is its computational efficiency compared to the much applied sampling based methods. Its main disadvantage, on the other hand, is the large amount of analytical work required to derive the necessary components for the algorithm. One part of this thesis reports on an effort to automate variational Bayesian learning of a certain class of models. The second part of the thesis is concerned with heteroscedastic modelling which is synonymous to variance modelling. Heteroscedastic models are particularly suitable for the Bayesian treatment as many of the traditional estimation methods do not produce satisfactory results for them. In the thesis, variance models and algorithms for estimating them are studied in two different contexts: in source separation and in regression. Astronomical applications constitute the third part of the thesis. Two problems are posed. One is concerned with the separation of stellar subpopulation spectra from observed galaxy spectra; the other is concerned with estimating the time-delays in gravitational lensing. Solutions to both of these problems are presented, which heavily rely on the machinery of approximate inference

Untangling the physical components of galaxies using infrared spectra

The two main physical processes that underpin galaxy evolution are star formation and accretion of mass in active galactic nuclei (AGN). Understanding how contributions from these processes vary across cosmic time requires untangling their relative contributions. The infrared part of the electromagnetic spectrum contains a number of AGN and star formation diagnostics e.g. emission lines from ionised gas or polyaromatic hydrocarbons (PAHs), and the shape of the continuum. Despite the higher resolution of data from Spitzer’s IRS spectrograph, separating out emission from star formation and AGN is carried out using limited spectral features or simplistic templates. In the first part of this thesis, I show how sophisticated data analysis techniques can make full use of the wealth of spectral data. I demonstrate how the popular multivariate technique, Principal Component Analysis (PCA), can classify different types of ultra luminous infrared galaxies (ULIRGs), whilst providing a simple set of spectral components that provide better fits than state-of-the art radiative transfer models. I show how an alternative multivariate technique, Non-Negative Matrix Factorisation (NMF) is more appropriate by applying it to over 700 extragalactic spectra from the CASSIS database and demonstrating its capability in producing spectral components that are physically intuitive, allowing the processes of star formation and AGN activity to be clearly untangled. Finally, I show how rotational transition lines from carbon monoxide and water, observed by the Herschel Space Observatory, provides constraints on the physical conditions within galaxies. By coupling the radiative transfer code, RADEX, with the nested sampling routine, Multinest, I carry out Bayesian inference on the CO spectral line energy distribution ladder of the nearby starburst galaxy, IC342. I also show that water emission lines provide important constraints the conditions of the ISM of on one of the most distant starburst galaxies ever detected, HFLS3

Color gradients and half-mass radii of galaxies out to z=2z=2 in the CANDELS/3D-HST fields: further evidence for important differences in the evolution of mass-weighted and light-weighted sizes

Recent studies have indicated that the ratio between half-mass and half-light radii, $r_{\rm mass} / r_{\rm light}$, varies significantly as a function of stellar mass and redshift, complicating the interpretation of the ubiquitous $r_{\rm light}- M_*$ relation. To investigate, in this study we construct the light and color profiles of $\sim 3000$ galaxies at $1<z<2$ with $\log\, M_*/M_\odot > 10.25$ using $\texttt{imcascade}$, a Bayesian implementation of the Multi-Gaussian expansion (MGE) technique. $\texttt{imcascade}$ flexibly represents galaxy profiles using a series of Gaussians, free of any a-priori parameterization. We find that both star-forming and quiescent galaxies have on average negative color gradients. For star forming galaxies, we find steeper gradients that evolve with redshift and correlate with dust content. Using the color gradients as a proxy for gradients in the $M/L$ ratio we measure half mass radii for our sample of galaxies. There is significant scatter in individual $r_{\rm mass} / r_{\rm light}$ ratios, which is correlated with variation in the color gradients. We find that the median $r_{\rm mass} / r_{\rm light}$ ratio evolves from 0.75 at $z=2$ to 0.5 at $z=1$, consistent with previous results. We characterize the $r_{\rm mass}- M_*$ relation and we find that it has a shallower slope and shows less redshift evolution than the $r_{\rm light} - M_*$ relation. This applies both to star-forming and quiescent galaxies. We discuss some of the implications of using $r_{\rm mass}$ instead of $r_{\rm light}$, including an investigation of the size-inclination bias and a comparison to numerical simulations.Comment: Submitted to ApJ: Please find catalog of size and color gradient measurements here: https://raw.githubusercontent.com/tbmiller-astro/tbmiller-astro.github.io/main/assets/Miller2022_morph_CANDELs.tx