A Bayesian Analysis of HAT-P-7b Using the EXONEST Algorithm

The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, HAT-P-7b. EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Model Selection, which is implemented with the MultiNest algorithm. These models take into account planetary effects, such as reflected light and thermal emissions, as well as the effect of the planetary motion on the host star, such as Doppler beaming, or boosting, of light from the reflex motion of the host star, and photometric variations due to the planet-induced ellipsoidal shape of the host star. By calculating model evidences, one can determine which model best describes the observed data, thus identifying which effects dominate the planetary system. Presented are parameter estimates and model evidences for HAT-P-7b.Comment: Submitted to the conference proceedings for MaxEnt 2014, to be published by AI

The X-ray Variability of AGN and its Implications for Observations of Galaxy Clusters

The detection of new clusters of galaxies or the study of known clusters of galaxies in X-rays can be complicated by the presence of X-ray point sources, the majority of which will be active galactic nuclei (AGN). This can be addressed by combining observations from a high angular resolution observatory (such as Chandra) with deeper data from a more sensitive observatory that may not be able to resolve the AGN (like XMM). However, this approach is undermined if the AGN varies in flux between the epochs of the observations. To address this we measure the characteristic X-ray variability of serendipitously detected AGN in 70 pairs of Chandra observations, separated by intervals of between one month and thirteen years. After quality cuts, the full sample consists of 1511 sources, although the main analysis uses a subset of 416 sources selected on the geometric mean of their flux in the pairs of observations, which eliminates selection biases. We find a fractional variability that increases with increasing interval between observations, from about 0.25 for observations separated by tens of days up to about 0.45 for observations separated by $\sim 10$ years. As a rule of thumb, given the precise X-ray flux of a typical AGN at one epoch, its flux at a second epoch some years earlier or later can be predicted with a precision of about $60\%$ due to its variability (ignoring any statistical noise). This is larger than the characteristic variability of the population by a factor of $\sqrt{2}$ due to the uncertainty on the mean flux of the AGN due to a single prior measurement. The precision can thus be improved with multiple prior flux measurements (reducing the $\sqrt{2}$ factor), or by reducing the interval between observations to reduce the characteristic variability.Comment: 13 pages, 7 figures; accepted for publication in the Open Journal of Astrophysics; full data table included with source files; comments welcom

Randomizations of models as metric structures

The notion of a randomization of a first order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original first order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete first order theory is a complete theory in continuous logic that admits elimination of quantifiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable

On theories of random variables

We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type

On probabilistic analog automata

We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy environment suggested by Maass and Orponen, and Maass and Sontag. Our main result is a generalization of Rabin's reduction theorem that implies that under very mild conditions, the computational power of the automaton is limited to regular languages

Combining Photometry From Kepler and TESS to Improve Short-Period Exoplanet Characterization

Planets emit thermal radiation and reflect incident light that they recieve from their host stars. As a planet orbits it's host star the photometric variations associated with these two effects produce very similar phase curves. If observed through only a single bandpass this leads to a degeneracy between certain planetary parameters that hinder the precise characterization of such planets. However, observing the same planet through two different bandpasses gives one much more information about the planet. Here, we develop a Bayesian methodology for combining photometry from both \emph{Kepler} and the Transiting Exoplanet Survey Satellite (TESS). In addition, we demonstrate via simulations that one can disentangle the reflected and thermally emitted light from the atmosphere of a hot-Jupiter as well as more precisely constrain both the geometric albedo and dayside temperature of the planet. This methodology can further be employed using various combinations of photometry from the James Webb Space Telescope (JWST), the Characterizing ExOplanet Satellite (CHEOPS), or the PLATO mission.Comment: Submitted to PAS

Governing urban wetlands for green growth in the Western Region Megapolis of Sri Lanka

The Western Region Megapolis (WRM) of Sri Lanka, the conurbation associated with Greater Colombo and covering the entire Western Province, is the thriving economic center of the country. According to the State of Sri Lankan Cities 2018 report (GoSL 2018), the city accounts for 40% of Sri Lanka’s gross domestic product (GDP), 30% of its population and is the nation’s administrative center. The WRM is also endowed with wetlands of international importance. This includes the Bellanwila-Attidiya marshes: a 370-ha freshwater marsh in southern Colombo rich in biodiversity (Box 1); the Colombo Flood Detention Area: a 400-ha network of marshes and canals that traverse the DISCUSSION BRIEF An aerial view of the city of Colombo in Sri Lanka with its network of wetlands supporting urban dwellers - A hub for green growth. Photo: Martin Seemungal city; and the Muthurajawela marsh: a 2,500-ha saltwater marsh in northern Colombo, which is the largest saline peat bog in Sri Lanka (IUCN and CEA 2006). The aim of this brief is to support the efforts of the Government of Sri Lanka to leverage the WRM wetlands to foster green growth. Green growth promotes economic development alongside environmental sustainability, and is gaining traction as a model to achieve sustainable urban development globally (Hammer et al. 2011). According to OECD (2013: 9), governments promote green growth “to create jobs and attract firms and investment, while improving local environmental quality and addressing global environmental challenges, particularly climate change.

A universal density slope - velocity anisotropy relation

One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection between velocity anisotropy and density slope, the \alpha-\beta relation. The first (phase-space density v.s. radius) has been analysed through several different simulations, however the second (\alpha-\beta relation) has not been quantified yet. We perform a large set of numerical experiments in order to quantify the slope and zero-point of the \alpha-\beta relation. When combined with the assumption of phase-space being a power-law in radius this allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy, central density slope of \alpha_0 = -0.8, and outer anisotropy of approximately \beta_\infinity = 0.5.Comment: 4 pages, 1 figure, to appear in the XXIst IAP Colloquium "Mass Profiles and Shapes of Cosmological Structures", Paris 4-9 July 2005, France, (Eds.) G. Mamon, F. Combes, C. Deffayet, B. Fort, EAS Publications Serie

EXONEST: Bayesian Model Selection Applied to the Detection and Characterization of Exoplanets Via Photometric Variations

EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian Inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian Model Selection, a unique aspect of EXONEST is the capability to distinguish between reflective and thermal contributions to the light curve. A case-study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the non-transiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically-relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.Comment: Accepted for publication in The Astrophysical Journa