Identifying terrestrial planets in the habitable zones (HZs) of other stars is one of the primary goals of ongoing radial velocity (RV) and transit exoplanet surveys and proposed future space missions. Most current estimates of the boundaries of the HZ are based on one-dimensional (1D), cloud-free, climate model calculations by Kasting et?al. However, this model used band models that were based on older HITRAN and HITEMP line-by-line databases. The inner edge of the HZ in the Kasting et?al. model was determined by loss of water, and the outer edge was determined by the maximum greenhouse provided by a CO2 atmosphere. A conservative estimate for the width of the HZ from this model in our solar system is 0.95-1.67?AU. Here an updated 1D radiative-convective, cloud-free climate model is used to obtain new estimates for HZ widths around F, G, K, and M stars. New H2O and CO2 absorption coefficients, derived from the HITRAN 2008 and HITEMP 2010 line-by-line databases, are important improvements to the climate model. According to the new model, the water-loss (inner HZ) and maximum greenhouse (outer HZ) limits for our solar system are at 0.99 and 1.70?AU, respectively, suggesting that the present Earth lies near the inner edge. Additional calculations are performed for stars with effective temperatures between 2600 and 7200?K, and the results are presented in parametric form, making them easy to apply to actual stars. The new model indicates that, near the inner edge of the HZ, there is no clear distinction between runaway greenhouse and water-loss limits for stars with T eff 5000?K, which has implications for ongoing planet searches around K and M stars. To assess the potential habitability of extrasolar terrestrial planets, we propose using stellar flux incident on a planet rather than equilibrium temperature. This removes the dependence on planetary (Bond) albedo, which varies depending on the host star's spectral type. We suggest that conservative estimates of the HZ (water-loss and maximum greenhouse limits) should be used for current RV surveys and Kepler mission to obtain a lower limit on ??, so that future flagship missions like TPF-C and Darwin are not undersized. Our model does not include the radiative effects of clouds; thus, the actual HZ boundaries may extend further in both directions than the estimates just given.

https://iopscience.iop.org/article/10.1088/0004-637X/765/2/131/pdf

Habitable Zones Around Main-Sequence Stars: New Estimates

At least two arguments suggest that the orbits of a large fraction of binary stars and extrasolar planets shrank by 1-2 orders of magnitude after formation: (1) the physical radius of a star shrinks by a large factor from birth to the main sequence, yet many main-sequence stars have companions orbiting only a few stellar radii away, and (2) in current theories of planet formation, the region within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many hot Jupiters are observed at such distances. We investigate orbital shrinkage by the combined effects of secular perturbations from a distant companion star (Kozai oscillations) and tidal friction. We integrate the relevant equations of motion to predict the distribution of orbital elements produced by this process. Binary stars with orbital periods of 0.1-10 days, with a median of ~2 days, are produced from binaries with much longer periods (10 to ~105 days), consistent with observations indicating that most or all short-period binaries have distant companions (tertiaries). We also make two new testable predictions: (1) For periods between 3 and 10 days, the distribution of the mutual inclination between the inner binary and the tertiary orbit should peak strongly near 40? and 140?. (2) Extrasolar planets whose host stars have a distant binary companion may also undergo this process, in which case the orbit of the resulting hot Jupiter will typically be misaligned with the equator of its host star.

https://iopscience.iop.org/article/10.1086/521702/pdf

Shrinking binary and planetary orbits by Kozai cycles with tidal friction

The Kepler mission is uniquely suited to study the frequencies of extrasolar planets. This goal requires knowledge of the incidence of false positives such as eclipsing binaries in the background of the targets, or physically bound to them, which can mimic the photometric signal of a transiting planet. We perform numerical simulations of the Kepler targets and of physical companions or stars in the background to predict the occurrence of astrophysical false positives detectable by the mission. Using real noise level estimates, we compute the number and characteristics of detectable eclipsing pairs involving main-sequence stars and non-main-sequence stars or planets, and we quantify the fraction of those that would pass the Kepler candidate vetting procedure. By comparing their distribution with that of the Kepler Objects of Interest (KOIs) detected during the first six quarters of operation of the spacecraft, we infer the false positive rate of Kepler and study its dependence on spectral type, candidate planet size, and orbital period. We find that the global false positive rate of Kepler is 9.4%, peaking for giant planets (6-22 R ⊕) at 17.7%, reaching a low of 6.7% for small Neptunes (2-4 R ⊕), and increasing again for Earth-size planets (0.8-1.25 R ⊕) to 12.3%. Most importantly, we also quantify and characterize the distribution and rate of occurrence of planets down to Earth size with no prior assumptions on their frequency, by subtracting from the population of actual Kepler candidates our simulated population of astrophysical false positives. We find that 16.5% ± 3.6% of main-sequence FGK stars have at least one planet between 0.8 and 1.25 R ⊕ with orbital periods up to 85 days. This result is a significant step toward the determination of eta-earth, the occurrence of Earth-like planets in the habitable zone of their parent stars. There is no significant dependence of the rates of planet occurrence between 0.8 and 4 Earth radii with spectral type. In the process, we also derive a prescription for the signal recovery rate of Kepler that enables a good match to both the KOI size and orbital period distribution, as well as their signal-to-noise distribution.

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The false positive rate of kepler and the occurrence of planets

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the systems center of mass, are examined. From the results, empirical expressions are developed for both (1) the largest orbit around each of the stars and (2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10A4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0=e=0.7-0.8 and 0.1=mu=0.9 in both regions and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually interacting system of planets orbiting one star of a binary system is examined, though in less detail.

https://iopscience.iop.org/article/10.1086/300695/pdf

Long-Term Stability of Planets in Binary Systems

The basic geometry of the Solar System—the shapes, spacings, and orientations of the planetary orbits—has long been a subject of fascination as well as inspiration for planet-formation theories. For exoplanetary systems, those same properties have only recently come into focus. Here we review our current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multiplanet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems.

The Occurrence and Architecture of Exoplanetary Systems

Long-term Stability of Planets in Binary Systems

Analysis of video records of the Chelyabinsk superbolide of 15 February 2013 show that its orbit was sufficiently similar to the orbit of asteroid 86039 (1999 NC43) to suggest that the two were once part of the same object. The fireball that streaked across the skies above Chelyabinsk in Russia on 15 February 2013 is providing astronomers with a wealth of information. Two papers in this issue present detailed reconstructions of the Chelyabinsk event. From an analysis of videos, Jiři Borovicka et al. determined the trajectory and velocity of the superbolide with high precision. Its orbit was similar to that of the 2-kilometre-diameter asteroid 86039 (1999 NC43), suggesting that the two bodies may be part of the same asteroid family. And they show that it broke into small pieces between the altitudes of 45 and 30 kilometres. In the companion paper, Peter Brown et al. analysed the damage caused by the airburst which they estimate was equivalent in energy to the detonation of 400 to 600 kilotons of TNT. They suggest that the number of impactors with diameters of tens of metres was an order of magnitude higher than current estimates, shifting much of the residual impact risk to these sizes. Earth is continuously colliding with fragments of asteroids and comets of various sizes. The largest encounter in historical times occurred over the Tunguska river in Siberia in 1908, producing1,2 an airburst of energy equivalent to 5–15 megatons of trinitrotoluene (1 kiloton of trinitrotoluene represents an energy of 4.185 × 1012 joules). Until recently, the next most energetic airburst events occurred over Indonesia3 in 2009 and near the Marshall Islands4 in 1994, both with energies of several tens of kilotons. Here we report an analysis of selected video records of the Chelyabinsk superbolide5 of 15 February 2013, with energy equivalent to 500 kilotons of trinitrotoluene, and details of its atmospheric passage. We found that its orbit was similar to the orbit of the two-kilometre-diameter asteroid 86039 (1999 NC43), to a degree of statistical significance sufficient to suggest that the two were once part of the same object. The bulk strength—the ability to resist breakage—of the Chelyabinsk asteroid, of about one megapascal, was similar to that of smaller meteoroids6 and corresponds to a heavily fractured single stone. The asteroid broke into small pieces between the altitudes of 45 and 30 kilometres, preventing more-serious damage on the ground. The total mass of surviving fragments larger than 100 grams was lower than expected7.

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The trajectory, structure and origin of the Chelyabinsk asteroidal impactor

More than 200 years ago, mathematician Joseph-Louis Lagrange predicted the existence of what became known as Trojan asteroids — small bodies that can stably share the orbit of a planet if they remain near 'triangular points' 60° ahead of or behind it in its orbit. Jupiter has thousands of Trojans; Mars and Neptune have some too. Now Earth is shown to have a Trojan. A search of data collected by NASA's Wide-field Infrared Survey Explorer (WISE) satellite revealed the asteroid 2010 TK7 as a strong candidate, and subsequent optical observations confirm its status as a Trojan companion of Earth, oscillating around the L4 (leading) Lagrange triangular point. It was realized in 1772 that small bodies can stably share the same orbit as a planet if they remain near ‘triangular points’ 60° ahead of or behind it in the orbit1. Such ‘Trojan asteroids’ have been found co-orbiting with Jupiter2, Mars3 and Neptune4. They have not hitherto been found associated with Earth, where the viewing geometry poses difficulties for their detection5, although other kinds of co-orbital asteroid (horseshoe orbiters6 and quasi-satellites7) have been observed8. Here we report an archival search of infrared data for possible Earth Trojans, producing the candidate 2010 TK7. We subsequently made optical observations which established that 2010 TK7 is a Trojan companion of Earth, librating around the leading Lagrange triangular point, L4. Its orbit is stable over at least ten thousand years.

Paul Wiegert

Papers

Long-Term Stability of Planets in Binary Systems

Long-term Stability of Planets in Binary Systems

The trajectory, structure and origin of the Chelyabinsk asteroidal impactor

Earth’s Trojan asteroid

The Evolution of Long-Period Comets