We report here on the discovery of stellar occultations, observed with Kepler, that recur periodically at 15.685 hour intervals, but which vary in depth from a maximum of 1.3% to a minimum that can be less than 0.2%. The star that is apparently being occulted is KIC 12557548, a V = 16 magnitude K dwarf with T eff,s 4400 K. The out-of-occultation behavior shows no evidence for ellipsoidal light variations, indicating that the mass of the orbiting object is less than ∼3 M J (for an orbital period of 15.7 hr). Because the eclipse depths are highly variable, they cannot be due solely to transits of a single planet with a fixed size. We discuss but dismiss a scenario involving a binary giant planet whose mutual orbit plane precesses, bringing one of the planets into and out of a grazing transit. This scenario seems ruled out by the dynamical instability that would result from such a configuration. We also briefly consider an eclipsing binary, possibly containing an accretion disk, that either orbits KIC 12557548 in a hierarchical triple configuration or is nearby on the sky, but we find such a scenario inadequate to reproduce the observations. The much more likely explanation-but one which still requires more quantitative development-involves macroscopic particles escaping the atmosphere of a slowly disintegrating planet not much larger than Mercury in size. The particles could take the form of micron-sized pyroxene or aluminum oxide dust grains. The planetary surface is hot enough to sublimate and create a high-Z atmosphere; this atmosphere may be loaded with dust via cloud condensation or explosive volcanism. Atmospheric gas escapes the planet via a Parkertype thermal wind, dragging dust grains with it. We infer a mass loss rate from the observations of order 1 M ⊕ /Gyr, with a dust-to-gas ratio possibly of order unity. For our fiducial 0.1M ⊕ planet (twice the mass of Mercury), the evaporation timescale may be ∼0.2 Gyr. Smaller mass planets are disfavored because they evaporate still more quickly, as are larger mass planets because they have surface gravities too strong to sustain outflows with the requisite mass-loss rates. The occultation profile evinces an ingress-egress asymmetry that could reflect a comet-like dust tail trailing the planet; we present simulations of such a tail.

We critically examine the basic paradigm for the origin of the 2-3 hr period gap in cataclysmic variables (CVs), i.e., binary systems in which a white dwarf accretes from a relatively unevolved, low-mass donor star. The observed orbital period distribution for ∼ 300 CVs shows that these systems typically have orbital periods, P orb , in the range of ∼ 80 min to ∼ 8 hr, but a distinct dearth of systems with 2 ∼ < P orb (hr) ∼ < 3. This latter feature of the period distribution is often referred to as the "period gap". The conventional explanation for the period gap involves a thermal bloating of the donor star for P orb ∼ > 3 hr due to mass transfer rates which are enhanced over those which could be driven by gravitational radiation (GR) losses alone (e.g., magnetic braking). If for some reason the supplemental angular momentum losses become substantially reduced when P orb decreases below ∼ 3 hr, the donor star will relax thermally and shrink inside of its Roche lobe. This leads to a cessation of mass transfer until GR losses can bring the system into Roche-lobe contact again at P orb ∼ 2 hr.We carry out an extensive population synthesis study of CVs starting from ∼ 3 × 10 6 primordial binaries, and evolving some ∼ 2 × 10 4 surviving systems through their CV phase. In particular we study current-epoch distributions of CVs in theṀ −P orb , R 2 −P orb , M 2 −P orb , q−P orb , T ef f −P orb , and L 2 −P orb planes, whereṀ is the mass transfer rate, q is the mass ratio M 2 /M 1 , and M 2 , R 2 , T ef f , and L 2 are the donor star mass, radius, effective temperature, and luminosity, respectively. This work presents a new perspective on theoretical studies of the long-term evolution of CVs. In particular, we show that if the current paradigm is correct, the secondary masses in CVs just above the period gap should be as much as ∼ 50% lower than would be inferred if one assumes a main-sequence radius-mass relation for the donor star. We quantify the M 2 − P orb relations expected from models wherein the donor stars are thermally bloated. Finally, we propose specific observations, involving the determination of secondary masses in CVs, that would allow for a definitive test of the currently accepted model (i.e., interrupted thermal bloating) for the period gap in CVs.

We have computed an extensive grid of binary evolution tracks to represent low-and intermediate mass X-ray binaries (LMXBs and IMXBs). The grid includes 42,000 models which covers 60 initial donor masses over the range of 1 − 4 M ⊙ and, for each of these, 700 initial orbital periods over the range of 10 − 250 hours. These results can be applied to understanding LMXBs and IMXBs: those that evolve analogously to CVs; that form ultracompact binaries with P orb in the range of 6 − 50 minutes; and that lead to wide orbits with giant donors. We also investigate the relic binary recycled radio pulsars into which these systems evolve. To evolve the donor stars in this study, we utilized a newly developed stellar evolution code called "MESA" that was designed, among other things, to be able to handle very low-mass and degenerate donors. This first application of the results is aimed at an understanding of the newly discovered pulsar PSR J1614-2230 which has a 1.97 M ⊙ neutron star, P orb = 8.7 days, and a companion star of 0.5 M ⊙ . We show that (i) this system is a cousin to the LMXB Cyg X-2; (ii) for neutron stars of canonical birth mass 1.4 M ⊙ , the initial donor stars which produce the closest relatives to PSR J1614-2230 have a mass between 3.4 − 3.8 M ⊙ ; (iii) neutron stars as massive as 1.97 M ⊙ are not easy to produce in spite of the initially high mass of the donor star, unless they were already born as relatively massive neutron stars; (iv) to successfully produce a system like PSR J1614-2230 requires a minimum initial neutron star mass of at least 1.6 ± 0.1 M ⊙ , as well as initial donor masses and P orb of ∼4.25 ± 0.10 M ⊙ and ∼49 ± 2 hrs, respectively; and (v) the current companion star is largely composed of CO, but should have a surface H abundance of ∼10 − 15%.