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Relativistic radiative transfer problems require the calculation of photon trajectories in curved spacetime. Programmed in Fortran, Geokerr uses a novel technique for rapid and accurate calculation of null geodesics in the Kerr metric. The equations of motion from the Hamilton-Jacobi equation are reduced directly to Carlson's elliptic integrals, simplifying algebraic manipulations and allowing all coordinates to be computed semi-analytically for the first time.
We have constructed a grid of non-LTE disk models for a wide range of black hole mass and mass accretion rate, for several values of viscosity parameter alpha, and for two extreme values of the black hole spin: the maximum-rotation Kerr black hole, and the Schwarzschild (non-rotating) black hole. Our procedure calculates self-consistently the vertical structure of all disk annuli together with the radiation field, without any approximations imposed on the optical thickness of the disk, and without any ad hoc approximations to the behavior of the radiation intensity. The total spectrum of a disk is computed by summing the spectra of the individual annuli, taking into account the general relativistic transfer function. The grid covers nine values of the black hole mass between M = 1/8 and 32 billion solar masses with a two-fold increase of mass for each subsequent value; and eleven values of the mass accretion rate, each a power of 2 times 1 solar mass/year. The highest value of the accretion rate corresponds to 0.3 Eddington. We show the vertical structure of individual annuli within the set of accretion disk models, along with their local emergent flux, and discuss the internal physical self-consistency of the models. We then present the full disk-integrated spectra, and discuss a number of observationally interesting properties of the models, such as optical/ultraviolet colors, the behavior of the hydrogen Lyman limit region, polarization, and number of ionizing photons. Our calculations are far from definitive in terms of the input physics, but generally we find that our models exhibit rather red optical/UV colors. Flux discontinuities in the region of the hydrogen Lyman limit are only present in cool, low luminosity models, while hotter models exhibit blueshifted changes in spectral slope.
Occultation and microlensing are different limits of the same phenomena of one body passing in front of another body. We derive a general exact analytic expression which describes both microlensing and occultation in the case of spherical bodies with a source of uniform brightness and a non-relativistic foreground body. We also compute numerically the case of a source with quadratic limb-darkening. In the limit that the gravitational deflection angle is comparable to the angular size of the foreground body, both microlensing and occultation occur as the objects align. Such events may be used to constrain the size ratio of the lens and source stars, the limb-darkening coefficients of the source star, and the surface gravity of the lens star (if the lens and source distances are known). Application of these results to microlensing during transits in binaries and giant-star microlensing are discussed. These results unify the microlensing and occultation limits and should be useful for rapid model fitting of microlensing, eclipse, and "microccultation" events.
Transit light curves for stellar continua have only one minimum and a "U" shape. By contrast, transit curves for optically thin chromospheric emission lines can have a "W" shape because of stellar limb-brightening. We calculate light curves for an optically thin shell of emission and fit these models to time-resolved observations of Si IV absorption by the planet HD209458b. We find that the best fit Si IV absorption model has R_p,SIV/R_*= 0.34+0.07-0.12, similar to the Roche lobe of the planet. While the large radius is only at the limit of statistical significance, we develop formulae applicable to transits of all optically thin chromospheric emission lines.
We present an IDL graphical user interface-driven software package designed for the analysis of extrasolar planet transit light curves. The Transit Analysis Package (TAP) software uses Markov Chain Monte Carlo (MCMC) techniques to fit light curves using the analytic model of Mandel and Agol (2002). The package incorporates a wavelet based likelihood function developed by Carter and Winn (2009) which allows the MCMC to assess parameter uncertainties more robustly than classic chi-squared methods by parameterizing uncorrelated "white" and correlated "red" noise. The software is able to simultaneously analyze multiple transits observed in different conditions (instrument, filter, weather, etc). The graphical interface allows for the simple execution and interpretation of Bayesian MCMC analysis tailored to a user's specific data set and has been thoroughly tested on ground-based and Kepler photometry. AutoKep provides a similar GUI for the preparation of Kepler MAST archive data for analysis by TAP or any other analysis software. This paper describes the software release and provides instructions for its use.
We present EXOFAST, a fast, robust suite of routines written in IDL which is designed to fit exoplanetary transits and radial velocity variations simultaneously or separately, and characterize the parameter uncertainties and covariances with a Differential Evolution Markov Chain Monte Carlo method. Our code self-consistently incorporates both data sets to simultaneously derive stellar parameters along with the transit and RV parameters, resulting in consistent, but tighter constraints on an example fit of the discovery data of HAT-P-3b that is well-mixed in under two minutes on a standard desktop computer. EXOFAST has an easy-to-use online interface for several basic features of our transit and radial velocity fitting.
TTVFast efficiently calculates transit times for n-planet systems and the corresponding radial velocities. The code uses a symplectic integrator with a Keplerian interpolator for the calculation of transit times (Nesvorny et al. 2013); it is available in both C and Fortran.
The self-lensing binary code with Markov chain code was used to analyze the self-lensing binary system KOI-3278. It includes the MCMC modeling and the key figures.
TTVFaster implements analytic formulae for transit time variations (TTVs) that are accurate to first order in the planet–star mass ratios and in the orbital eccentricities; the implementations are available in several languages, including IDL, Julia, Python and C. These formulae compare well with more computationally expensive N-body integrations in the low-eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems.
QATS detects transiting extrasolar planets in time-series photometry. It relaxes the usual assumption of strictly periodic transits by permitting a variable, but bounded, interval between successive transits.
celerite provides fast and scalable Gaussian Process (GP) Regression in one dimension and is implemented in C++, Python, and Julia. The celerite API is designed to be familiar to users of george and, like george, celerite is designed to efficiently evaluate the marginalized likelihood of a dataset under a GP model. This is then be used alongside a non-linear optimization or posterior inference library for the best results.