Detecting Differential Rotation and Starspot Evolution on the M dwarf GJ 1243 with Kepler

We present an analysis of the starspots on the active M4 dwarf GJ 1243, using four years of time series photometry from Kepler. A rapid $P = 0.592596\pm0.00021$ day rotation period is measured due to the $\sim$2.2\% starspot-induced flux modulations in the light curve. We first use a light curve modeling approach, using a Monte Carlo Markov Chain sampler to solve for the longitudes and radii of the two spots within 5-day windows of data. Within each window of time the starspots are assumed to be unchanging. Only a weak constraint on the starspot latitudes can be implied from our modeling. The primary spot is found to be very stable over many years. A secondary spot feature is present in three portions of the light curve, decays on 100-500 day timescales, and moves in longitude over time. We interpret this longitude shearing as the signature of differential rotation. Using our models we measure an average shear between the starspots of 0.0047 rad day$^{-1}$, which corresponds to a differential rotation rate of $\Delta\Omega = 0.012 \pm 0.002$ rad day$^{-1}$. We also fit this starspot phase evolution using a series of bivariate Gaussian functions, which provides a consistent shear measurement. This is among the slowest differential rotation shear measurements yet measured for a star in this temperature regime, and provides an important constraint for dynamo models of low mass stars.Comment: 13 pages, 7 figures, ApJ Accepte

Absence of a metallicity effect for ultra-short-period planets

Ultra-short-period (USP) planets are a newly recognized class of planets with periods shorter than one day and radii smaller than about 2 Earth radii. It has been proposed that USP planets are the solid cores of hot Jupiters that lost their gaseous envelopes due to photo-evaporation or Roche lobe overflow. We test this hypothesis by asking whether USP planets are associated with metal-rich stars, as has long been observed for hot Jupiters. We find the metallicity distributions of USP-planet and hot-Jupiter hosts to be significantly different ($p = 3\times 10^{-4}$), based on Keck spectroscopy of Kepler stars. Evidently, the sample of USP planets is not dominated by the evaporated cores of hot Jupiters. The metallicity distribution of stars with USP planets is indistinguishable from that of stars with short-period planets with sizes between 2--4~$R_\oplus$. Thus it remains possible that the USP planets are the solid cores of formerly gaseous planets smaller than Neptune.Comment: AJ, in pres

Reflection Positivity and Monotonicity

We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality $C_D \leq C_N$ between Dirichlet and Neumann covariance operators on a manifold with a reflection.Comment: 11 page

A Search for Planets Transiting the M Dwarf Debris Disk Host, AU Microscopii

We present high cadence, high precision multi-band photometry of the young, M1Ve, debris disk star, AU Microscopii. The data were obtained in three continuum filters spanning a wavelength range from 4500\AA to 6600\AA, plus H$\alpha$, over 28 nights in 2005. The lightcurves show intrinsic stellar variability due to starspots with an amplitude in the blue band of 0.051 magnitudes and a period of 4.847 days. In addition, three large flares were detected in the data which all occur near the minimum brightness of the star. We remove the intrinsic stellar variability and combine the lightcurves of all the filters in order to search for transits by possible planetary companions orbiting in the plane of the nearly edge-on debris disk. The combined final lightcurve has a sampling of 0.35 minutes and a standard deviation of 6.8 millimags (mmag). We performed Monte Carlo simulations by adding fake transits to the observed lightcurve and find with 95% significance that there are no Jupiter mass planets orbiting in the plane of the debris disk on circular orbits with periods, P $\le 5$ days. In addition, there are no young Neptune-like planets (with radii 2.5$\times$ smaller than the young Jupiter) on circular orbits with periods, P $\le 3$ days.Comment: accepted to MNRA