The Limits of Inclination for Binary Star Partial Eclipses

Morris, Steven L.

doi:10.1086/307488

Cited by 3 publications

(4 citation statements)

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“…For strictly contact binaries, the minimum inclination angle for eclipses to occur is formally given as 34 • (see, e.g.,Morris 1999).8 The proof of this is simple to visualize. Project the kinematic trajectory of the spot over the course of a binary orbit onto a plane perpendicular to the line of sight and compare it to the trajectory of the highest projected point on the companion star.…”

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confidence: 90%

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THE ANTICORRELATED NATURE OF THE PRIMARY AND SECONDARY ECLIPSE TIMING VARIATIONS FOR THEKEPLERCONTACT BINARIES

Tran

Levine

Rappaport

et al. 2013

ApJ

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We report on a study of eclipse timing variations in contact binary systems, using long-cadence lightcurves in the Kepler archive. As a first step, 'observed minus calculated' (O − C) curves were produced for both the primary and secondary eclipses of some 2000 Kepler binaries. We find ∼390 shortperiod binaries with O − C curves that exhibit (i) random-walk like variations or quasi-periodicities, with typical amplitudes of ±200-300 seconds, and (ii) anticorrelations between the primary and secondary eclipse timing variations. We present a detailed analysis and results for 32 of these binaries with orbital periods in the range of 0.35 ± 0.05 days. The anticorrelations observed in their O − C curves cannot be explained by a model involving mass transfer, which among other things requires implausibly high rates of ∼0.01 M ⊙ yr −1 . We show that the anticorrelated behavior, the amplitude of the O − C delays, and the overall random-walk like behavior can be explained by the presence of a starspot that is continuously visible around the orbit and slowly changes its longitude on timescales of weeks to months. The quasi-periods of ∼50 − 200 days observed in the O − C curves suggest values for k, the coefficient of the latitude dependence of the stellar differential rotation, of ∼0.003−0.013.

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“…For strictly contact binaries, the minimum inclination angle for eclipses to occur is formally given as 34 • (see, e.g.,Morris 1999). 8 The proof of this is simple to visualize.…”

mentioning

confidence: 99%

THE ANTICORRELATED NATURE OF THE PRIMARY AND SECONDARY ECLIPSE TIMING VARIATIONS FOR THEKEPLERCONTACT BINARIES

Tran

Levine

Rappaport

et al. 2013

ApJ

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“…9 The latest member of the class of slowly pulsating B stars (periods of 1È5 days ; Aerts et al 1999a) is a member of the open cluster NGC 7652 (Choi et al 1999). 9 Concave stars havenÏt actually been observed, but the more massive component of some contact binaries must be so (Morris 1999). 9 The former Delta Scuti star V879 Aql is really a W UMa contact binary, whose discoverers had originally called it an RR Lyrae (Kopacki & Pigulski 1998).…”

Section: So Doth the Greater Glory Dim The Restmentioning

confidence: 99%

Astrophysics in 1999

Trimble

Aschwanden

2000

PUBL ASTRON SOC PAC

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ABSTRACT. The year 1999 saw the arrival of a star with three planets, a universe with three parameters, and a solar corona that could be heated at least three ways. In addition, there were at least three papers on every question that has ever been asked in astrophysics, from "" Will the Universe expand forever ? ÏÏ to "" Does mantle convection occur in one or two layers ? ÏÏ The answers generally were, "" Yes,ÏÏ "" No,ÏÏ and "" None of the above,ÏÏ to each of the questions. The authors have done their best to organize the richness around centers deÐned by objects, methods, and madnesses.

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“…Ground-based observatories on Earth have also utilised stellar occultations to constrain minor planet shape (Ortiz et al 2017) and ring particle size (e.g. Colwell et al 2018;Mentel et al 2018), but have difficulty distinguishing amongst grazing, partial and total eclipses in binary star systems (Morris 1999). For the external observers of solar system planets, Wells et al (2018) instead derived non-grazing transit visibility zones, whereas Heller & Pudritz (2016) focused on the Earth's transit visibility zone.…”

Section: Introductionmentioning

confidence: 99%

Explicit relations and criteria for eclipses, transits, and occultations

Veras

2018

Monthly Notices of the Royal Astronomical Society

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Solar system, exoplanet and stellar science rely on transits, eclipses and occultations for dynamical and physical insight. Often, the geometry of these configurations are modelled by assuming a particular viewpoint. Here, instead, I derive user-friendly formulae from first principles independent of viewpoint and in three dimensions. I generalise the results of Veras & Breedt (2017) by (i) characterising three-body systems which are in transit but are not necessarily perfectly aligned, and by (ii) incorporating motion. For a given snapshot in time, I derive explicit criteria to determine whether a system is in or out of transit, if an eclipse is total or annular, and expressions for the size of the shadow, including their extreme values and a condition for engulfment. These results are exact. For orbital motion, I instead obtain approximate results. By assuming fixed orbits, I derive a single implicit algebraic relation which can be solved to obtain the frequency and duration of transit events -including ingresses and egresses -for combinations of moons, planets and stars on arbitrarily inclined circular orbits; the eccentric case requires the solution of Kepler's equation but remains algebraic. I prove that a transit shadow -whether umbral, antumbral or penumbral -takes the shape of a parabolic cylinder, and finally present geometric constraints on Earth-based observers hoping to detect a three-body syzygy (or perfect alignment) -either in extrasolar systems or within the solar system -potentially as a double annular eclipse.

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The Limits of Inclination for Binary Star Partial Eclipses

Cited by 3 publications

References 3 publications

THE ANTICORRELATED NATURE OF THE PRIMARY AND SECONDARY ECLIPSE TIMING VARIATIONS FOR THEKEPLERCONTACT BINARIES

THE ANTICORRELATED NATURE OF THE PRIMARY AND SECONDARY ECLIPSE TIMING VARIATIONS FOR THEKEPLERCONTACT BINARIES

Astrophysics in 1999

Explicit relations and criteria for eclipses, transits, and occultations

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