A temperate Earth-sized planet with tidal heating transiting an M6 star.

Temperate Earth-sized exoplanets around late-M dwarfs offer a rare opportunity to explore under which conditions planets can develop hospitable climate conditions. The small stellar radius amplifies the atmospheric transit signature, making even compact secondary atmospheres dominated by N2 or CO2 amenable to characterization with existing instrumentation1. Yet, despite large planet search efforts2, detection of low-temperature Earth-sized planets around late-M dwarfs has remained rare and the TRAPPIST-1 system, a resonance chain of rocky planets with seemingly identical compositions, has not yet shown any evidence of volatiles in the system3. Here we report the discovery of a temperate Earth-sized planet orbiting the cool M6 dwarf LP 791-18. The newly discovered planet, LP 791-18d, has a radius of 1.03 ± 0.04 R⊕ and an equilibrium temperature of 300-400 K, with the permanent night side plausibly allowing for water condensation. LP 791-18d is part of a coplanar system4 and provides a so-far unique opportunity to investigate a temperate exo-Earth in a system with a sub-Neptune that retained its gas or volatile envelope. On the basis of observations of transit timing variations, we find a mass of 7.1 ± 0.7 M⊕ for the sub-Neptune LP 791-18c and a mass of [Formula: see text] for the exo-Earth LP 791-18d. The gravitational interaction with the sub-Neptune prevents the complete circularization of LP 791-18d's orbit, resulting in continued tidal heating of LP 791-18d's interior and probably strong volcanic activity at the surface5,6.

A broadband thermal emission spectrum of the ultra-hot Jupiter WASP-18b.

Close-in giant exoplanets with temperatures greater than 2,000 K ('ultra-hot Jupiters') have been the subject of extensive efforts to determine their atmospheric properties using thermal emission measurements from the Hubble Space Telescope (HST) and Spitzer Space Telescope1-3. However, previous studies have yielded inconsistent results because the small sizes of the spectral features and the limited information content of the data resulted in high sensitivity to the varying assumptions made in the treatment of instrument systematics and the atmospheric retrieval analysis3-12. Here we present a dayside thermal emission spectrum of the ultra-hot Jupiter WASP-18b obtained with the NIRISS13 instrument on the JWST. The data span 0.85 to 2.85 µm in wavelength at an average resolving power of 400 and exhibit minimal systematics. The spectrum shows three water emission features (at >6σ confidence) and evidence for optical opacity, possibly attributable to H-, TiO and VO (combined significance of 3.8σ). Models that fit the data require a thermal inversion, molecular dissociation as predicted by chemical equilibrium, a solar heavy-element abundance ('metallicity', [Formula: see text] times solar) and a carbon-to-oxygen (C/O) ratio less than unity. The data also yield a dayside brightness temperature map, which shows a peak in temperature near the substellar point that decreases steeply and symmetrically with longitude towards the terminators.

A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level.

We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a dataset of questions from Massachusetts Institute of Technology (MIT)'s largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pretrained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8 to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work automatically solves university-level mathematics course questions at a human level and explains and generates university-level mathematics course questions at scale, a milestone for higher education.

An abundance of small exoplanets around stars with a wide range of metallicities.

The abundance of heavy elements (metallicity) in the photospheres of stars similar to the Sun provides a 'fossil' record of the chemical composition of the initial protoplanetary disk. Metal-rich stars are much more likely to harbour gas giant planets, supporting the model that planets form by accumulation of dust and ice particles. Recent ground-based surveys suggest that this correlation is weakened for Neptunian-sized planets. However, how the relationship between size and metallicity extends into the regime of terrestrial-sized exoplanets is unknown. Here we report spectroscopic metallicities of the host stars of 226 small exoplanet candidates discovered by NASA's Kepler mission, including objects that are comparable in size to the terrestrial planets in the Solar System. We find that planets with radii less than four Earth radii form around host stars with a wide range of metallicities (but on average a metallicity close to that of the Sun), whereas large planets preferentially form around stars with higher metallicities. This observation suggests that terrestrial planets may be widespread in the disk of the Galaxy, with no special requirement of enhanced metallicity for their formation.

Transiting circumbinary planets Kepler-34 b and Kepler-35 b.

Most Sun-like stars in the Galaxy reside in gravitationally bound pairs of stars (binaries). Although long anticipated, the existence of a 'circumbinary planet' orbiting such a pair of normal stars was not definitively established until the discovery of the planet transiting (that is, passing in front of) Kepler-16. Questions remained, however, about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we report two additional transiting circumbinary planets: Kepler-34 (AB)b and Kepler-35 (AB)b, referred to here as Kepler-34 b and Kepler-35 b, respectively. Each is a low-density gas-giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 b orbits two Sun-like stars every 289 days, whereas Kepler-35 b orbits a pair of smaller stars (89% and 81% of the Sun's mass) every 131 days. The planets experience large multi-periodic variations in incident stellar radiation arising from the orbital motion of the stars. The observed rate of circumbinary planets in our sample implies that more than ∼1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.

A 15.65-solar-mass black hole in an eclipsing binary in the nearby spiral galaxy M 33.

Stellar-mass black holes are found in X-ray-emitting binary systems, where their mass can be determined from the dynamics of their companion stars. Models of stellar evolution have difficulty producing black holes in close binaries with masses more than ten times that of the Sun (>10; ref. 4), which is consistent with the fact that the most massive stellar black holes known so far all have masses within one standard deviation of 10. Here we report a mass of (15.65 +/- 1.45) for the black hole in the recently discovered system M 33 X-7, which is located in the nearby galaxy Messier 33 (M 33) and is the only known black hole that is in an eclipsing binary. To produce such a massive black hole, the progenitor star must have retained much of its outer envelope until after helium fusion in the core was completed. On the other hand, in order for the black hole to be in its present 3.45-day orbit about its (70.0 +/- 6.9) companion, there must have been a 'common envelope' phase of evolution in which a significant amount of mass was lost from the system. We find that the common envelope phase could not have occurred in M 33 X-7 unless the amount of mass lost from the progenitor during its evolution was an order of magnitude less than what is usually assumed in evolutionary models of massive stars.

TESS DISCOVERY OF A TRANSITING SUPER-EARTH IN THE π MENSAE SYSTEM.

We report the detection of a transiting planet around π Men (HD 39091), using data from the Transiting Exoplanet Survey Satellite (TESS). The solar-type host star is unusually bright (V = 5.7) and was already known to host a Jovian planet on a highly eccentric, 5.7-year orbit. The newly discovered planet has a size of 2.04 ± 0.05 R ⊕ and an orbital period of 6.27 days. Radial-velocity data from the HARPS and AAT/UCLES archives also displays a 6.27-day periodicity, confirming the existence of the planet and leading to a mass determination of 4.82±0.85 M ⊕. The star's proximity and brightness will facilitate further investigations, such as atmospheric spectroscopy, asteroseismology, the Rossiter-McLaughlin effect, astrometry, and direct imaging.

Kepler-47: a transiting circumbinary multiplanet system.

We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, 18 transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet's orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical "habitable zone," where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems.

Kepler-16: a transiting circumbinary planet.

We report the detection of a planet whose orbit surrounds a pair of low-mass stars. Data from the Kepler spacecraft reveal transits of the planet across both stars, in addition to the mutual eclipses of the stars, giving precise constraints on the absolute dimensions of all three bodies. The planet is comparable to Saturn in mass and size and is on a nearly circular 229-day orbit around its two parent stars. The eclipsing stars are 20 and 69% as massive as the Sun and have an eccentric 41-day orbit. The motions of all three bodies are confined to within 0.5° of a single plane, suggesting that the planet formed within a circumbinary disk.