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Physics of Eclipsing Binaries. Ii. Toward the Increased Model Fidelity A

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Physics of Eclipsing Binaries. Ii. Toward the Increased Model Fidelity A The Astrophysical Journal Supplement Series, 227:29 (20pp), 2016 December doi:10.3847/1538-4365/227/2/29 © 2016. The American Astronomical Society. All rights reserved. PHYSICS OF ECLIPSING BINARIES. II. TOWARD THE INCREASED MODEL FIDELITY A. Prša1, K. E. Conroy1,2, M. Horvat1,3, H. Pablo4, A. Kochoska1,3, S. Bloemen5, J. Giammarco6, K. M. Hambleton1,7, and P. Degroote8 1 Villanova University, Dept.of Astrophysics and Planetary Sciences, 800 E Lancaster Avenue, Villanova PA 19085, USA 2 Vanderbilt University, Dept.of Physics and Astronomy, 6301 Stevenson Center Lane, Nashville TN, 37235, USA 3 University of Ljubljana, Dept.of Physics, Jadranska 19, SI-1000 Ljubljana, Slovenia 4 Université de Montréal, Pavillon Roger-Gaudry, 2900, boul.Édouard-Montpetit Montréal QC H3T 1J4, Canada 5 Radboud University Nijmegen, Department of Astrophysics, IMAPP, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands 6 Eastern University, Dept.of Astronomy and Physics, 1300 Eagle Road, St.Davids, PA 19087, USA 7 Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1 2HE, UK 8 KU Leuven, Instituut voor Sterrenkunde, Celestijnenlaan 200D, B-3001 Heverlee, Belgium Received 2016 September 26; revised 2016 November 7; accepted 2016 November 8; published 2016 December 15 ABSTRACT The precision of photometric and spectroscopic observations has been systematically improved in the last decade, mostly thanks to space-borne photometric missions and ground-based spectrographs dedicated to finding exoplanets. The field of eclipsing binary stars strongly benefited from this development. Eclipsing binaries serve as critical tools for determining fundamental stellar properties (masses, radii, temperatures, and luminosities), yet the models are not capable of reproducing observed data well, either because of the missing physics or because of insufficient precision. This led to a predicament where radiative and dynamical effects, insofar buried in noise, started showing up routinely in the data, but were not accounted for in the models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an open source modeling code for computing theoretical light and radial velocity curves that addresses both problems by incorporating missing physics and by increasing the computational fidelity. In particular, we discuss triangulation as a superior surface discretization algorithm, meshing of rotating single stars, light travel time effects, advanced phase computation, volume conservation in eccentric orbits, and improved computation of local intensity across the stellar surfaces that includes thephoton-weighted mode, theenhanced limb darkening treatment, thebetter reflection treatment, and Doppler boosting. Here we present the concepts on which PHOEBE is builtand proofs of concept that demonstrate the increased model fidelity. Key words: binaries: close – binaries: eclipsing – methods: numerical – stars: fundamental parameters – techniques: photometric – techniques: spectroscopic 1. INTRODUCTION firehose of observations. However, from all the data currently available, Torres et al. (2010) find only ∼100 EBs with the Eclipsing binary stars (EBs) serve as cornerstones of stellar astrophysics. Their uniquely important role in determining uncertainties in the masses and radii smaller than 3%. For such fundamental stellar parameters (Popper 1980) anddistances benchmark objects, this number is several orders of magnitude (Pietrzyński et al. 2013),and providing rigorous tests for stellar too low. ( ) Having superb quality data in abundance has clear evolution models Torres et al. 2010 have been widely fi appreciated. While the underlying principles that govern the repercussions on our modeling capability. For the rst time, modeling of EBs are simple (Newtonian mechanics and we observe astrophysical objects in a near-uninterrupted straight-forward geometry considerations), a plethora of regime, with uncertainties that dip below 20 ppm. State-of- – complications arises from subtler effects: surface distortions, the-art models such as the renowned Wilson Devinney code ( intensity variations due to gravity darkening, limb darkening, Wilson & Devinney 1971; Wilson 1979, 2008; Wilson & Van ) ( ) reflection, and surface prominences. As the precision of the Hamme 2014 , ELC Orosz & Hauschildt 2000 , and PHOEBE ( š ) data increases, so does the number of subtleties that a reliable Pr a & Zwitter 2005a, paper I are showing systematics in the model needs to take into account. derived values of fundamental stellar parameters. This is partly This decade has provided us with a range of ground-breaking because of embedded approximations, partly because of the surveys and missions: MOST (Walker et al. 2003), CoRoT inconsistent use of physical units and constants (see the IAU (Baglin 2003), Kepler (Borucki et al. 2010), Pan-Starrs (Kaiser 2015 resolution B3; Prša et al. 2016) and partly because of the et al. 2002), Gaia (de Bruijne 2012), and LSST (Tyson & LSST missing and/or inadequate physics built into these models. The 2002), to name just a few. These yielded a vast number of EBs residuals of the best-fit models and observed data are no longer (Prša et al. 2011 estimated ∼7 million from LSST alone), Gaussian, and we cannot assume that these effects are buried in thousands to unprecedented quality (down to ∼20 ppm for noise; rather, we need to account for their signatures in light Kepler light curves; see Figure 1 for several examples of and radial velocity curves explicitly. attained precision). We are seeing phenomena that have been Furthermore, the codes provide minimization algorithms that up until recently only theorized, but now they are appearing fit model curves to the data. EB data fitting is a highly routinely: modern observations provide us with a glimpse into nonlinear problem that suffers from degenerate solutions: the the micromagnitude scale. With such a tremendous boost in right combination of the wrong parameters can often fit the both quantity and quality, the tools we use to reduce, analyze, observed data as well as the actual solution. The algorithms and interpret data need to be able to cope with this literal currently in use, namely differential corrections (DC), 1 The Astrophysical Journal Supplement Series, 227:29 (20pp), 2016 December Prša et al. Figure 1. Kepler time series (left) and phased light curves (right) of KIC 5513861 (P=1.51012 day, detached EB), KIC 8074045 (P=0.53638 day, semi-detached EB), and KIC 3127873 (P=0.67146 day, contact EB), top-to-bottom. Powell’s(1964)direction set method, Nelder & Mead’s constraining, enhanced reddening treatment, improvements to (1965)Simplex method (NMS), and genetic algorithms (Attia DC, introduction of the downhill simplex fitting method, the et al. 2009), have all met with success, but cannot be run built-in scripting backend, and a graphical user interface. robustly without experienced human intervention, making the Since PHOEBE inherited the underlying logic of WD, it also tools fully manual. inherited its limitations. These became apparent as ultra-precise In this paper, we discuss several deficiencies of our models photometric data became available: the model could no longer and present advancements in improving the reliability of binary produce adequate fits to light curves at Keplerʼs level of star solutions. The improvements result from including missing precision. In addition, a wealth of triple and multiple stellar instrumental and astrophysical phenomena in the model systems have been discovered that exhibit eclipse timing explicitly, thus reducing systematical errors in correlated variations due to the light travel time effect and dynamical parameters that no longer need to compensate for the missing effects, circumbinary planets and multiply eclipsing systems, aspects in the code. The paper is accompanied by the release of all of which render the old model unsuitable. To overcome the new version of the open source modeling code PHOEBE 2.0, available from http://phoebe-project.org, along these inherited limitations, the new version of PHOEBE with extensive documentation and tutorials. presented here has been rewritten from scratch. We present The layout of the paper is as follows. In Section 2, we all novel aspects of the model, benchmarks that prompted a provide background on the PHOEBE project; Section 3 redesign, and comparison between original and revised models. introduces the new triangulation scheme for surface discretiza- The rewrite of the code was initiated in 2011 but was limited tion; Section 4 focuses on dynamical and temporal aspects of by the lack of funding; the current release has been made the model; Section 5 gives the rationale for computing all local possible by the NSF support #1517474, which we gratefully quantities across the mesh; in Section 6, we discuss current acknowledge. limitations and provide concluding remarks. The version of PHOEBE presented here is 2.0. The code is not backwards-compatible to PHOEBE 1.0 because of the 2. REVISING THE PHOEBE MODEL complete redesign of the backend, but original PHOEBE fi ( š ) parameter les can be imported into the new version The original PHOEBE model Pr a & Zwitter 2005a was seamlessly. Versioning will follow the common semantic based on the Wilson–Devinney code (Wilson & Devin- versioning syntax (major.minor.patch) with any critical bug ney 1971, hereafter WD). The most important features of the fixes noted with an increment in the patch number (i.e., 2.0.1, model includean analytic description of binary star orbits, 2.0.2),
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