ROCHE: Analysis of Eclipsing Binary Multi-Dataset Observables
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1 ROCHE: Analysis of Eclipsing Binary Multi-Dataset Observables Theodor Pribulla Astronomical Institute of the Slovak Academy of Sciences, Tatranská Lomnica, SLOVAKIA IAUS 282 From Interacting Binaries to Exoplanets: Essential Modeling Tools July 18-22, 2011, Tatranská Lomnica, Slovakia
2 (very) Brief history Prior to 1969: rectified Russell-Merrill sphere-sphere models 1969: Lucy s common envelope model of contact binaries beginning of 1970-ties: first successful attempts to fit light curves of close binaries - Mochnacki, Wilson, Binnendijk, Linnell 1979: systems with eccentric orbits and asynchronous rotation since 80-ties: first attempts to model spotted systems 1995: modelling of radiation pressure Drechsel since 90-ties: eclipse mapping & Doppler tomography present: simultaneous analysis of light curves, radial velocity curves, polarimetric curves even astrometric data, use of HJDs instead of orbital phases, light-time effect Models computing radiation transfer, including accreation disk etc. (e.g. SHELLSPEC) EBAI artificial intelligence
3 Available software W&D, 1971, 1992 FOTEL (Hadrava, 1990) synthesis and modelling LC & RV curves, extensive input datasets PHOEBE (Prša & Zwitter, 2005) user-friendly interface to the W&D (2003) code + several improvements: e.g. SED, IS extinction, Simplex BM 2.0 & 3.0 (Bradstreet, 1993, 2005) LIGHT2 (Hill, 1979, Hill & Ruciński, 1993), pixels in the plane of sky, synthesis of RV, LC and BFs, ellipsoidal spots Nightfall (Wichmann, 1998; Hauschild, Allard & Baron, 1999) LCs, RVs & line profiles, circular & eccentric orbits, asynchronous rotation, spots, Simplex Binsyn (Linnell, 1984, 1993), Roche & polytropic model GDDSYN (Mochnacki & Hendry, 1992), uses geodetic spheres to produce similar surface elements, synthesis of LC, RV, line profiles Other: Djurasevi (1991), Binnendijk (1976).
4 Program ROCHE Goal: precise determination of fundamental parameters of stars
5 Model assumptions Roche surface geometry Eccentric orbits and asynchronous/differential rotation (rotation axes perpendicular to the orbital plane) Volume is preserved in eccentric orbits, no dynamical tides Circular surface spots (max. two spots optimised simultaneously) with constant temperature factor Third light stellar/free Linear/logarithmic LD, gravity darkening, mutual irradiation Model atmospheres to calculate surface passband-specific intensity Local BF strength depending on temperature Tested for stellar down to planetary mass ratios 3D model correct for ( < q < 1.0), practical for q > No accreation disks, no mass streams no dust
6 Surface grid (icosahedron) 20n 2 elements (detached) Rather simple to address points and faces of the surface grid Area of the elements equal to about 15% for spherical stars
7 Visibility & terminator terminator modeled by a broken line visibility tested by two different approaches (i) sampling over the line of sight (ii) finding potential maximum along the line of sight Problems in exoplanets with Rp/Rs < 1/20
8 Synthetized observables up to 7 passband-specific LCs two photocentric RV curves two barycentric RV curves up to 200 BFs (takes into account instrumental profile and exposure times) relative astrometric orbit UBVRIJHK apparent magnitudes (interferometric visibilities) absolute parameters of components
9 Input data HJD/phases up to 7 passband-specific LCs two photocentric RV curves up to 200 BFs, matrix with a constant phase step or individual relative orbit [, ] Errors average for a dataset/individual (interferometric visibilities)
10 New (?) tricks Using space symmetries of the 3D model Using phase symmetries (both circular and eccentric orbits) Interpolation in between 360 phase points Micro-stepping: adaptive grids in detached systems (i) eclipse or (ii) LC phase-derivative defined surface grid density equal/unequal for components optional computation without reflection effect.
11 Optimisation & dataset weighting Weighting of the data, data-sets, level-dependent weighting - shot noise, no normal points (up to 5000 points/lc) Optimising: Damped differential corrections method, requires 1st partial derivatives Automated grid search in inclination and/or mass ratio Automated interpolation of LD coefficients from tables of van Hamme (1993)
12 Accuracy of synthesis Transit in a totally eclipsing detached binary Accuracy in intensity is about for about 1000 faces
13 Programming & graphics ROCHE written in FORTRAN 77 M$ Windows/Linux Graphics plotted using the PGPLOT library (grwin with W7/XP) Plotting: 3D model, fits to all datasets or residuals Input data recreated after each optimisation step No nice interface as in PHEOBE or BM3
14 Why multidataset? Combination of different datasets results in more reliable parameters of components Typicaly LCs + RVs, better LCs + BFs (LSD profiles), even better LCs + BFs + visual orbit, possibly also LCs + BFs+LB visibilities, can include timing in multiple systems Problem: relative weighting of datasets
15 Interesting systems
16 Velorum Velorum (Vmax=1.96, = 40.9 mas) the brightest Southern eclipsing binary, member of visual binary triple system Interferometrically resolved eclipsing binary (Kellerer et al., 2007) Shows strong infrared excess probable result of a bowshock Complications: never detected as a SB, orbital days with eclipses lasting hours, eccentric orbit New data: SMEI photometry, OCA spectroscopy, VLTI interferometry Result: precise masses, orbit, detection of fast spin of components (2/3 of break-up), age about 400 My
17 Velorum Pribulla et al., 2011, A&A 528, 21, Merand et al, 2011, A&A in press
18 Velorum Global fit to 63 BFs (20 shown) and LC Pribulla et al., 2011, A&A 528, 21
19 Velorum Global fit BFs outside eclipses (limb-darkened rotational profiles), Pribulla et al., 2011, A&A 528, 21
20 Velorum Outer visual orbit of the triple system (Merand et al, 2011, A&A in press)
21 AW UMa vs. V566 Oph AW UMa: prototype contact binary LC solutions of AW UMa perfect agreement with the models of Lucy (1968) mass ratio q Results of ROCHE modelling: (i) sp. mass ratio does not agree with photom. ratio (ii) shapes of BFs do not conform the expectations of the Roche model (iii) probable equatorial belt encompassing the system (iv) contact-binary nature can be mimicked V566 (q 0.26): no complications seen!
22 AW UMa vs. V566 Oph Pribulla & Ruciński, 2007, MNRAS, 386, 377
23 VW LMi, 4xRVs + 1xLITE Simultaneous fit to 4 RV curves and one (O-C) curve VW LMi tightest quadruple known Two binaries orbiting in a tight, 355 days orbit
24 VW LMi BFs RVs (four RV curves) Pribulla et al., 2008, MNRAS, 390, 798
25 Prospects for future Better surface inhomogeneities modelling better optimisation methods Radiation pressure for OB-type systems (Drechsel et al., 1995) Free orientation of the rotation axis of either of the components in non-synchronously rotating systems Distance as one of the optimised (now UBVRIJHK magnitudes synthetised), including IS extinction Modelling of interferometric visibilities including prox. effects) Extending accurate modelling down to planet/star mass ratios (q < 0.01) [hot Jupiters very probably follow the Roche model!!!]
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