Equivalence problem for the orthogonal webs on the sphere

We solve the equivalence problem for the orthogonally separable webs on the three-sphere under the action of the isometry group. This continues a classical project initiated by Olevsky in which he solved the corresponding canonical forms problem. The solution to the equivalence problem together with the results by Olevsky forms a complete solution to the problem of orthogonal separation of variables to the Hamilton-Jacobi equation defined on the three-sphere via orthogonal separation of variables. It is based on invariant properties of the characteristic Killing two-tensors in addition to properties of the corresponding algebraic curvature tensor and the associated Ricci tensor. The result is illustrated by a non-trivial application to a natural Hamiltonian defined on the three-sphere.Comment: 32 page

Attributing scientific and technical progress: the case of holography

Holography, the three-dimensional imaging technology, was portrayed widely as a paradigm of progress during its decade of explosive expansion 1964–73, and during its subsequent consolidation for commercial and artistic uses up to the mid 1980s. An unusually seductive and prolific subject, holography successively spawned scientific insights, putative applications and new constituencies of practitioners and consumers. Waves of forecasts, associated with different sponsors and user communities, cast holography as a field on the verge of success—but with the dimensions of success repeatedly refashioned. This retargeting of the subject represented a degree of cynical marketeering, but was underpinned by implicit confidence in philosophical positivism and faith in technological progressivism. Each of its communities defined success in terms of expansion, and anticipated continual progressive increase. This paper discusses the contrasting definitions of progress in holography, and how they were fashioned in changing contexts. Focusing equally on reputed ‘failures’ of some aspects of the subject, it explores the varied attributes by which success and failure were linked with progress by different technical communities. This important case illuminates the peculiar post-World War II environment that melded the military, commercial and popular engagement with scientific and technological subjects, and the competing criteria by which they assessed the products of science

The McDonald Accelerating Stars Survey (MASS):Discovery of a Long-Period Substellar Companion Orbiting the Old Solar Analog HD 47127

Brown dwarfs with well-determined ages, luminosities, and masses provide rare but valuable tests of low-temperature atmospheric and evolutionary models. We present the discovery and dynamical mass measurement of a substellar companion to HD 47127, an old ($\approx$7-10 Gyr) G5 main sequence star with a mass similar to the Sun. Radial velocities of the host star with the Harlan J. Smith Telescope uncovered a low-amplitude acceleration of 1.93 $\pm$ 0.08 m s$^{-1}$ yr$^{-1}$ based on 20 years of monitoring. We subsequently recovered a faint ($\Delta H$=13.14 $\pm$ 0.15 mag) co-moving companion at 1.95$''$ (52 AU) with follow-up Keck/NIRC2 adaptive optics imaging. The radial acceleration of HD 47127 together with its tangential acceleration from Hipparcos and Gaia EDR3 astrometry provide a direct measurement of the three-dimensional acceleration vector of the host star, enabling a dynamical mass constraint for HD 47127 B (67.5-177 $M_\mathrm{Jup}$ at 95% confidence) despite the small fractional orbital coverage of the observations. The absolute $H$-band magnitude of HD 47127 B is fainter than the benchmark T dwarfs HD 19467 B and Gl 229 B but brighter than Gl 758 B and HD 4113 C, suggesting a late-T spectral type. Altogether the mass limits for HD 47127 B from its dynamical mass and the substellar boundary imply a range of 67-78 $M_\mathrm{Jup}$ assuming it is single, although a preference for high masses of $\approx$100 $M_\mathrm{Jup}$ from dynamical constraints hints at the possibility that HD 47127 B could itself be a binary pair of brown dwarfs or that another massive companion resides closer in. Regardless, HD 47127 B will be an excellent target for more refined orbital and atmospheric characterization in the future.Comment: Accepted to ApJ Letter

A Large and Variable Leading Tail of Helium in a Hot Saturn Undergoing Runaway Inflation

Atmospheric escape shapes the fate of exoplanets, with statistical evidence for transformative mass loss imprinted across the mass-radius-insolation distribution. Here we present transit spectroscopy of the highly irradiated, low-gravity, inflated hot Saturn HAT-P-67 b. The Habitable Zone Planet Finder (HPF) spectra show a detection of up to 10% absorption depth of the 10833 Angstrom Helium triplet. The 13.8 hours of on-sky integration time over 39 nights sample the entire planet orbit, uncovering excess Helium absorption preceding the transit by up to 130 planetary radii in a large leading tail. This configuration can be understood as the escaping material overflowing its small Roche lobe and advecting most of the gas into the stellar -- and not planetary -- rest frame, consistent with the Doppler velocity structure seen in the Helium line profiles. The prominent leading tail serves as direct evidence for dayside mass loss with a strong day-/night- side asymmetry. We see some transit-to-transit variability in the line profile, consistent with the interplay of stellar and planetary winds. We employ 1D Parker wind models to estimate the mass loss rate, finding values on the order of $2\times10^{13}$ g/s, with large uncertainties owing to the unknown XUV flux of the F host star. The large mass loss in HAT-P-67 b represents a valuable example of an inflated hot Saturn, a class of planets recently identified to be rare as their atmospheres are predicted to evaporate quickly. We contrast two physical mechanisms for runaway evaporation: Ohmic dissipation and XUV irradiation, slightly favoring the latter.Comment: Submitted to The Astronomical Journa

Radial Velocity Discovery of an Eccentric Jovian World Orbiting at 18 au

Based on two decades of radial velocity (RV) observations using Keck/High Resolution Echelle Spectrometer (HIRES) and McDonald/Tull, and more recent observations using the Automated Planet Finder, we found that the nearby star HR 5183 (HD 120066) hosts a 3 minimum mass planet with an orbital period of yr. The orbit is highly eccentric (e ≃ 0.84), shuttling the planet from within the orbit of Jupiter to beyond the orbit of Neptune. Our careful survey design enabled high cadence observations before, during, and after the planet\u27s periastron passage, yielding precise orbital parameter constraints. We searched for stellar or planetary companions that could have excited the planet\u27s eccentricity, but found no candidates, potentially implying that the perturber was ejected from the system. We did identify a bound stellar companion more than 15,000 au from the primary, but reasoned that it is currently too widely separated to have an appreciable effect on HR 5183 b. Because HR 5183 b\u27s wide orbit takes it more than 30 au (1\u27\u27) from its star, we also explored the potential of complimentary studies with direct imaging or stellar astrometry. We found that a Gaia detection is very likely, and that imaging at 10 μm is a promising avenue. This discovery highlights the value of long-baseline RV surveys for discovering and characterizing long-period, eccentric Jovian planets. This population may offer important insights into the dynamical evolution of planetary systems containing multiple massive planets

Radial Velocity Discovery of an Eccentric Jovian World Orbiting at 18 au

Based on two decades of radial velocity (RV) observations using Keck/High Resolution Echelle Spectrometer (HIRES) and McDonald/Tull, and more recent observations using the Automated Planet Finder, we found that the nearby star HR 5183 (HD 120066) hosts a 3 M_J minimum mass planet with an orbital period of 74(+43)_(-22) yr. The orbit is highly eccentric (e ≃ 0.84), shuttling the planet from within the orbit of Jupiter to beyond the orbit of Neptune. Our careful survey design enabled high cadence observations before, during, and after the planet's periastron passage, yielding precise orbital parameter constraints. We searched for stellar or planetary companions that could have excited the planet's eccentricity, but found no candidates, potentially implying that the perturber was ejected from the system. We did identify a bound stellar companion more than 15,000 au from the primary, but reasoned that it is currently too widely separated to have an appreciable effect on HR 5183 b. Because HR 5183 b's wide orbit takes it more than 30 au (1'') from its star, we also explored the potential of complimentary studies with direct imaging or stellar astrometry. We found that a Gaia detection is very likely, and that imaging at 10 μm is a promising avenue. This discovery highlights the value of long-baseline RV surveys for discovering and characterizing long-period, eccentric Jovian planets. This population may offer important insights into the dynamical evolution of planetary systems containing multiple massive planets

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

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms