On the Relation Between Hot Jupiters & the Roche Limit

Many of the known extrasolar planets are ``hot Jupiters,'' giant planets with orbital periods of just a few days. We use the observed distribution of hot Jupiters to constrain the location of its inner edge in the mass--period diagram. If we assume a slope corresponding to the classical Roche limit, then we find that the edge corresponds to a separation close to_twice_ the Roche limit, as expected if the planets started on highly eccentric orbits that were later circularized. In contrast, any migration scenario would predict an inner edge right at the Roche limit, which applies to planets approaching on nearly circular orbits. However, the current sample of hot Jupiters is not sufficient to provide a precise constraint simultaneously on both the location and slope of the inner edge.Comment: 10 pages, 3 figures, to appear in ApJ

Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets

The Kepler Mission has discovered thousands of planets with radii $<4\ R_\oplus$, paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-to-Neptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-to-one relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass-radius relationship (M-R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M-R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that$M/M_\oplus=2.7(R/R_\oplus)^{1.3}$, a scatter in mass of$1.9\ M_\oplus$, and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M-R relation for the sample of RV-measured transiting sub-Neptunes ($R_{pl}<4\ R_\oplus$). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.Comment: 14 pages, 5 figures, 2 tables. Accepted to the Astrophysical Journal on April 28, 2016. Select posterior samples and code to use them to compute the posterior predictive mass distribution are available at https://github.com/dawolfgang/MRrelatio

Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps

The variability of the Crab Nebula in radio: No radio counterpart to gamma-ray flares

We present new Jansky Very Large Array (VLA) radio images of the Crab Nebula at 5.5 GHz, taken at two epochs separated by 6 days about two months after a gamma-ray flare in 2012 July. We find no significant change in the Crab's radio emission localized to a region of <2 light-months in radius, either over the 6-day interval between our present observations or between the present observations and ones from 2001. Any radio counterpart to the flare has a radio luminosity of <~ $2 \times 10^{-4}$ times that of the nebula. Comparing our images to one from 2001, we do however find changes in radio brightness, up to 10% in amplitude, which occur on decade timescales throughout the nebula. The morphology of the changes is complex suggesting both filamentary and knotty structures. The variability is stronger, and the timescales likely somewhat shorter, nearer the centre of the nebula. We further find that even with the excellent uv~coverage and signal-to-noise of the VLA, deconvolution errors are much larger than the noise, being up to 1.2% of peak brightness of the nebula in this particular case.Comment: Accepted to MNRAS; 13 pages, 6 figure