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David V. Martin

Publications and source records attributed to David V. Martin.

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Searching for Small Circumbinary Planets I. The STANLEY Automated Algorithm and No New Planets in Existing Systems

No circumbinary planets have been discovered smaller than 3 Earth radii, yet planets of this small size comprise over 75% of the discoveries around single stars. The observations do not prove the non-existence of small circumbinary planets, but rather they are much harder to find than around single stars, because their transit timing variations are much larger than the transit durations. We present STANLEY: an automated algorithm to find small circumbinary planets. It employs custom methods to detrend eclipsing binary light curves and stack shallow transits of variable duration and interval using N-body integrations. Applied to the Kepler circumbinaries, we recover all known planets, including the three planets of Kepler-47, and constrain the absence of additional planets of similar or smaller size. We also show that we could have detected < 3 Earth radii planets in half of the known systems. Our work will ultimately be applied to a broad sample of eclipsing binaries to (hopefully) produce new discoveries, and derive a circumbinary size distribution which can be compared to that for single stars.

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The EBLM project. VII. Spin-orbit alignment for the circumbinary planet host EBLM J0608-59 A/TOI-1338 A

A dozen short-period detached binaries are known to host transiting circumbinary planets. In all circumbinary systems so far, the planetary and binary orbits are aligned within a couple of degrees. However, the obliquity of the primary star, which is an important tracer of their formation, evolution, and tidal history, has only been measured in one circumbinary system until now. EBLM J0608-59/TOI-1338 is a low-mass eclipsing binary system with a recently discovered circumbinary planet identified by TESS. Here, we perform high-resolution spectroscopy during primary eclipse to measure the projected stellar obliquity of the primary component. The obliquity is low, and thus the primary star is aligned with the binary and planetary orbits with a projected spin-orbit angle $β= 2.8 \pm 17.1$ deg. The rotation period of $18.1 \pm 1.6$ days implied by our measurement of $v\sin{i_\star}$ suggests that the primary has not yet pseudo-synchronized with the binary orbit, but is consistent with gyrochronology and weak tidal interaction with the binary companion. Our result, combined with the known coplanarity of the binary and planet orbits, is suggestive of formation from a single disc. Finally, we considered whether the spectrum of the faint secondary star could affect our measurements. We show through simulations that the effect is negligible for our system, but can lead to strong biases in $v\sin{i_\star}$ and $β$ for higher flux ratios. We encourage future studies in eclipse spectroscopy test the assumption of a dark secondary for flux ratios $\gtrsim 1$ ppt.

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TOI-1338: TESS' First Transiting Circumbinary Planet

We report the detection of the first circumbinary planet found by TESS. The target, a known eclipsing binary, was observed in sectors 1 through 12 at 30-minute cadence and in sectors 4 through 12 at two-minute cadence. It consists of two stars with masses of 1.1 MSun and 0.3 MSun on a slightly eccentric (0.16), 14.6-day orbit, producing prominent primary eclipses and shallow secondary eclipses. The planet has a radius of ~6.9 REarth and was observed to make three transits across the primary star of roughly equal depths (~0.2%) but different durations -- a common signature of transiting circumbinary planets. Its orbit is nearly circular (e ~ 0.09) with an orbital period of 95.2 days. The orbital planes of the binary and the planet are aligned to within ~1 degree. To obtain a complete solution for the system, we combined the TESS photometry with existing ground-based radial-velocity observations in a numerical photometric-dynamical model. The system demonstrates the discovery potential of TESS for circumbinary planets, and provides further understanding of the formation and evolution of planets orbiting close binary stars.

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Circumbinary Planets -- The Next Steps

The Kepler mission opened the door to a small but bonafide sample of circumbinary planets. Some initial trends have been identified and used to challenge our theories of planet and binary formation. However, the Kepler sample is not only small but contains biases. I will present a circumbinary plan for the future. Specifically, I will cover the BEBOP radial velocity survey, the latest TESS transit mission and a new technique for digging out small circumbinary planets in archival Kepler photometry.

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The binary mass ratios of circumbinary planet hosts

Almost a dozen circumbinary planets have been found transiting eclipsing binaries. For the first time the observational bias of this sample is calculated with respect to the mass ratio of the host binaries. It is shown that the mass ratio affects transit detection in multiple, sometimes subtle ways, through stability and dynamics of orbits, dilution of transit depths and the geometric transit and eclipse probabilities. Surprisingly though, it is found that these effects largely cancel out. Consequently, the transit detections in the Kepler mission are essentially unbiased with respect to mass ratio, and hence likely representative of the true underlying population. It is shown the mass ratio distribution of circumbinary hosts may be the same as field binaries, and hence roughly uniform, but more observations are needed to deduce any subtle differences. These results are discussed in the context of close binary formation and evolution, of which the mass ratio is believed to be a marker, and other surveys for circumbinary planets including TESS and BEBOP.

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Transits of Inclined Exomoons - Hide and Seek and an Application to Kepler-1625

A Neptune-sized exomoon candidate was recently announced by Teachey & Kipping, orbiting a 287 day gas giant in the Kepler-1625 system. However, the system is poorly characterized and needs more observations to be confirmed, with the next potential transit in 2019 May. In this Letter, we aid observational follow up by analyzing the transit signature of exomoons. We derive a simple analytic equation for the transit probability and use it to demonstrate how exomoons may frequently avoid transit if their orbit is larger than the stellar radius and sufficiently misaligned. The nominal orbit for the moon in Kepler-1625 has both of these characteristics, and we calculate that it may only transit roughly 40% of the time. This means that approximately six non-transits would be required to rule out the moon's existence at 95% confidence. When an exomoon's impact parameter is displaced off the star, the planet's impact parameter is displaced the other way, so larger planet transit durations are typically positively correlated with missed exomoon transits. On the other hand, strong correlations do not exist between missed exomoon transits and transit timing variations of the planet. We also show that nodal precession does not change an exomoon's transit probability and that it can break a prograde-retrograde degeneracy.

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The EBLM Project V. Physical properties of ten fully convective, very-low-mass stars

Measurements of the physical properties of stars at the lower end of the main sequence are scarce. In this context we report masses, radii and surface gravities of ten very-low-mass stars in eclipsing binary systems, with orbital periods of the order of several days. The objects probe the stellar mass-radius relation in the fully convective regime, $M_\star \lesssim 0.35$ M$_\odot$, down to the hydrogen burning mass-limit, $M_{\mathrm{HB}} \sim 0.07$ M$_\odot$. The stars were detected by the WASP survey for transiting extra-solar planets, as low-mass, eclipsing companions orbiting more massive, F- and G-type host stars. We use eclipse observations of the host stars (TRAPPIST, Leonhard Euler, SPECULOOS telescopes), and radial velocities of the host stars (CORALIE spectrograph), to determine physical properties of the low-mass companions. Companion surface gravities are derived from the eclipse and orbital parameters of each system. Spectroscopic measurements of the host star effective temperature and metallicity are used to infer the host star mass and age from stellar evolution models. Masses and radii of the low-mass companions are then derived from the eclipse and orbital parameters of each system. The objects are compared to stellar evolution models for low-mass stars, to test for an effect of the stellar metallicity and orbital period on the radius of low-mass stars in close binary systems. Measurements are in good agreement with stellar models; an inflation of the radii of low-mass stars with respect to model predictions is limited to 1.6 $\pm$ 1.2% in the fully convective regime. The sample of ten objects indicates a scaling of the radius of low-mass stars with the host star metallicity. No correlation between stellar radii and orbital periods of the binary systems is determined. A combined analysis with comparable objects from the literature is consistent with this result.

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The BEBOP radial-velocity survey for circumbinary planets I. Eight years of CORALIE observations of 47 single-line eclipsing binaries and abundance constraints on the masses of circumbinary planets

We introduce the BEBOP radial velocity survey for circumbinary planets. We initiated this survey using the CORALIE spectrograph on the Swiss Euler Telescope at La Silla, Chile. An intensive four year observing campaign commenced in 2013, targeting 47 single-lined eclipsing binaries drawn from the EBLM survey for low mass eclipsing binaries. Our specific use of binaries with faint M dwarf companions avoids spectral contamination, providing observing conditions akin to single stars. By combining new BEBOP observations with existing ones from the EBLM programme, we report on the results of 1519 radial velocity measurements over timespans as long as eight years. For the best targets we are sensitive to planets down to 0.1 Jupiter masses, and our median sensitivity is 0.4 Jupiter masses. In this initial survey we do not detect any planetary mass companions. Nonetheless, we present the first constraints on the abundance of circumbinary companions, as a function of mass and period. A comparison of our results to Kepler's detections indicates a dispersion of planetary orbital inclinations less than ~10 degrees.

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Populations of planets in multiple star systems

Astronomers have discovered that both planets and binaries are abundant throughout the Galaxy. In combination, we know of over 100 planets in binary and higher-order multi-star systems, in both circumbinary and circumstellar configurations. In this chapter we review these findings and some of their implications for the formation of both stars and planets. Most of the planets found have been circumstellar, where there is seemingly a ruinous influence of the second star if sufficiently close (<50 AU). Hosts of hot Jupiters have been a particularly popular target for binary star studies, showing an enhanced rate of stellar multiplicity for moderately wide binaries (>100 AU). This was thought to be a sign of Kozai-Lidov migration, however recent studies have shown this mechanism to be too inefficient to account for the majority of hot Jupiters. A couple of dozen circumbinary planets have been proposed around both main sequence and evolved binaries. Around main sequence binaries there are preliminary indications that the frequency of gas giants is as high as those around single stars. There is however a conspicuous absence of circumbinary planets around the tightest main sequence binaries with periods of just a few days, suggesting a unique, more disruptive formation history of such close stellar pairs.

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The EBLM Project IV. Spectroscopic orbits of over 100 eclipsing M dwarfs masquerading as transiting hot-Jupiters

We present 2271 radial velocity measurements taken on 118 single-line binary stars, taken over eight years with the CORALIE spectrograph. The binaries consist of F/G/K primaries and M-dwarf secondaries. They were initially discovered photometrically by the WASP planet survey, as their shallow eclipses mimic a hot-Jupiter transit. The observations we present permit a precise characterisation of the binary orbital elements and mass function. With modelling of the primary star this mass function is converted to a mass of the secondary star. In the future, this spectroscopic work will be combined with precise photometric eclipses to draw an empirical mass/radius relation for the bottom of the mass sequence. This has applications in both stellar astrophysics and the growing number of exoplanet surveys around M-dwarfs. In particular, we have discovered 34 systems with a secondary mass below $0.2 M_\odot$, and so we will ultimately double the known number of very low-mass stars with well characterised mass and radii. We are able to detect eccentricities as small as 0.001 and orbital periods to sub-second precision. Our sample can revisit some earlier work on the tidal evolution of close binaries, extending it to low mass ratios. We find some binaries that are eccentric at orbital periods < 3 days, while our longest circular orbit has a period of 10.4 days. By collating the EBLM binaries with published WASP planets and brown dwarfs, we derive a mass spectrum with twice the resolution of previous work. We compare the WASP/EBLM sample of tightly-bound orbits with work in the literature on more distant companions up to 10 AU. We note that the brown dwarf desert appears wider, as it carves into the planetary domain for our short-period orbits. This would mean that a significantly reduced abundance of planets begins at $\sim 3M_{\rm Jup}$, well before the Deuterium-burning limit. [abridged]

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The EBLM project III. A Saturn-size low-mass star at the hydrogen-burning limit

We report the discovery of an eclipsing binary system with mass-ratio q $\sim$ 0.07. After identifying a periodic photometric signal received by WASP, we obtained CORALIE spectroscopic radial velocities and follow-up light curves with the Euler and TRAPPIST telescopes. From a joint fit of these data we determine that EBLM J0555-57 consists of a sun-like primary star that is eclipsed by a low-mass companion, on a weakly eccentric 7.8-day orbit. Using a mass estimate for the primary star derived from stellar models, we determine a companion mass of $85 \pm 4 M_{\rm Jup}$ ($0.081M_{\odot}$) and a radius of $0.84^{+0.14}_{-0.04} R_{\rm Jup}$ ($0.084 R_{\odot}$) that is comparable to that of Saturn. EBLM J0555-57Ab has a surface gravity $\log g_\mathrm{2} = 5.50^{+0.03}_{-0.13}$ and is one of the densest non-stellar-remnant objects currently known. These measurements are consistent with models of low-mass stars.

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Transit probability of precessing circumstellar planets in binaries and exomoons

Over two decades of exoplanetology have yielded thousands of discoveries, yet some types of systems are yet to be observed. Circumstellar planets around one star in a binary have been found, but not for tight binaries (< 5 AU). Additionally, extra-solar moons are yet to be found. This paper motivates finding both types of three-body system by calculating analytic and numerical probabilities for all transit configurations, accounting for any mutual inclination and orbital precession. The precession and relative three-body motion can increase the transit probability to as high as tens of per cent, and make it inherently time-dependent over a precession period as short as 5-10 yr. Circumstellar planets in such tight binaries present a tempting observational challenge: enhanced transit probabilities but with a quasi-periodic signature that may be difficult to identify. This may help explain their present non-detection, or maybe they simply do not exist. Whilst this paper considers binaries of all orientations, it is demonstrated how eclipsing binaries favourably bias the transit probabilities, sometimes to the point of being guaranteed. Transits of exomoons exhibit a similar behaviour under precession, but unfortunately only have one star to transit rather than two.

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Circumbinary planets II - when transits come and go

Circumbinary planets are generally more likely to transit than equivalent single-star planets, but practically the geometry and orbital dynamics of circumbinary planets make the chance of observing a transit inherently time-dependent. In this follow-up paper to Martin & Triaud (2015), the time-dependence is probed deeper by analytically calculating when and for how long the binary and planet orbits overlap, allowing for transits to occur. The derived equations are applied to the known transiting circumbinary planets found by Kepler to predict when future transits will occur, and whether they will be observable by upcoming space telescopes TESS, CHEOPS and PLATO. The majority of these planets spend less than 50% of their time in a transiting configuration, some less than 20%. From this it is calculated that the known Kepler eclipsing binaries likely host an additional ~ 17 - 30 circumbinary planets that are similar to the ten published discoveries, and they will ultimately transit some day, potentially during the TESS and PLATO surveys.

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Kozai-Lidov cycles towards the limit of circumbinary planets

In this paper we answer a simple question: can a misaligned circumbinary planet induce Kozai-Lidov cycles on an inner stellar binary? We use known analytic equations to analyse the behaviour of the Kozai-Lidov effect as the outer mass is made small. We demonstrate a significant departure from the traditional symmetry, critical angles and amplitude of the effect. Aside from massive planets on near-polar orbits, circumbinary planetary systems are devoid of Kozai-Lidov cycles. This has positive implications for the existence of highly misaligned circumbinary planets: an observationally unexplored and theoretically important parameter space.

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No circumbinary planets transiting the tightest Kepler binaries - a possible fingerprint of a third star

The Kepler mission has yielded the discovery of eight circumbinary systems, all found around eclipsing binaries with periods greater than 7 d. This is longer than the typical eclipsing binary period found by Kepler, and hence there is a dearth of planets around the closest binaries. In this paper we suggest how this dearth may be explained by the presence of a distant stellar tertiary companion, which shrunk the inner binary orbit by the process of Kozai cycles and tidal friction, a mechanism that has been implicated for producing most binaries with periods below 7 d. We show that the geometry and orbital dynamics of these evolving triple-star systems are highly restrictive for a circumbinary planet, which is subject itself to Kozai modulation, on one hand, and can shield the two inner stars from their Kozai cycle and subsequent shrinking, on the other hand. Only small planets on wide and inclined orbits may form, survive and allow for the inner binary shrinkage. Those are difficult to detect.

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Circumbinary planets - why they are so likely to transit

Transits on single stars are rare. The probability rarely exceeds a few per cent. Furthermore, this probability rapidly approaches zero at increasing orbital period. Therefore transit surveys have been predominantly limited to the inner parts of exoplanetary systems. Here we demonstrate how circumbinary planets allow us to beat these unfavourable odds. By incorporating the geometry and the three-body dynamics of circumbinary systems, we analytically derive the probability of transitability, a configuration where the binary and planet orbits overlap on the sky. We later show that this is equivalent to the transit probability, but at an unspecified point in time. This probability, at its minimum, is always higher than for single star cases. In addition, it is an increasing function with mutual inclination. By applying our analytical development to eclipsing binaries, we deduce that transits are highly probable, and in some case guaranteed. For example, a circumbinary planet revolving at 1 AU around a 0.3 AU eclipsing binary is certain to eventually transit - a 100% probability - if its mutual inclination is greater than 0.6 deg. We show that the transit probability is generally only a weak function of the planet's orbital period; circumbinary planets may be used as practical tools for probing the outer regions of exoplanetary systems to search for and detect warm to cold transiting planets.

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Gaia's potential for the discovery of circumbinary planets

The abundance and properties of planets orbiting binary stars - circumbinary planets - are largely unknown because they are difficult to detect with currently available techniques. Results from the Kepler satellite and other studies indicate a minimum occurrence rate of circumbinary giant planets of ~10 %, yet only a handful are presently known. Here, we study the potential of ESA's Gaia mission to discover and characterise extrasolar planets orbiting nearby binary stars by detecting the binary's periodic astrometric motion caused by the orbiting planet. We expect that Gaia will discover hundreds of giant planets around binaries with FGK dwarf primaries within 200 pc of the Sun, if we assume that the giant planet mass distribution and abundance are similar around binaries and single stars. If on the other hand all circumbinary gas giants have masses lower than two Jupiter masses, we expect only four detections. Gaia is critically sensitive to the properties of giant circumbinary planets and will therefore make the detailed study of their population possible. Gaia's precision is such that the distribution in mutual inclination between the binary and planetary orbital planes will be obtained. It also possesses the capacity to establish the frequency of planets across the H-R diagram, both as a function of mass and of stellar evolutionary state from pre-main sequence to stellar remnants. Gaia's discoveries can reveal whether a second epoch of planetary formation occurs after the red-giant phase.

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Planets Transiting Non-Eclipsing Binaries

The majority of binary stars do not eclipse. Current searches for transiting circumbinary planets concentrate on eclipsing binaries, and are therefore restricted to a small fraction of potential hosts. We investigate the concept of finding planets transiting non-eclipsing binaries, whose geometry would require mutually inclined planes. Using an N-body code we explore how the number and sequence of transits vary as functions of observing time and orbital parameters. The concept is then generalised thanks to a suite of simulated circumbinary systems. Binaries are constructed from RV surveys of the solar neighbourhood. They are then populated with orbiting gas giants, drawn from a range of distributions. The binary population is shown to be compatible with the Kepler eclipsing binary catalogue, indicating that the properties of binaries may be as universal as the initial mass function. These synthetic systems produce transiting circumbinary planets occurring on both eclipsing and non-eclipsing binaries. Simulated planets transiting eclipsing binaries are compared with published Kepler detections. We obtain 1) that planets transiting non-eclipsing binaries probably exist in the Kepler data, 2) that observational biases alone cannot account for the observed over-density of circumbinary planets near the stability limit, implying a physical pile-up, and 3) that the distributions of gas giants orbiting single and binary stars are likely different. Estimating the frequency of circumbinary planets is degenerate with the spread in mutual inclination. Only a minimum occurrence rate can be produced, which we find to be compatible with 9%. Searching for inclined circumbinary planets may significantly increase the population of known objects and will test our conclusions. Their existence, or absence, will reveal the true occurrence rate and help develop circumbinary planet formation theories.

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