Revision of Earth-sized Kepler Planet Candidate Properties with High Resolution Imaging by Hubble Space Telescope

We present the results of our Hubble Space Telescope program and describe how our analysis methods were used to re-evaluate the habitability of some of the most interesting Kepler planet candidates. Our program observed 22 Kepler Object of Interest (KOI) host stars, several of which were found to be multiple star systems unresolved by Kepler. We use our high-resolution imaging to spatially resolve the stellar multiplicity of Kepler-296, KOI-2626, and KOI-3049, and develop a conversion to the Kepler photometry (Kp) from the F555W and F775W filters on WFC3/UVIS. The binary system Kepler-296 (5 planets) has a projected separation of 0.217" (80AU); KOI-2626 (1 planet candidate) is a triple star system with a projected separation of 0.201" (70AU) between the primary and secondary components and 0.161" (55AU) between the primary and tertiary; and the binary system KOI-3049 (1 planet candidate) has a projected separation of 0.464" (225AU). We use our measured photometry to fit the separated stellar components to the latest Victoria-Regina Stellar Models with synthetic photometry to conclude that the systems are coeval. The components of the three systems range from mid-K dwarf to mid-M dwarf spectral types. We solved for the planetary properties of each system analytically and via an MCMC algorithm using our independent stellar parameters. The planets range from ~1.6R_Earth to ~4.2R_Earth, mostly Super Earths and mini-Neptunes. As a result of the stellar multiplicity, some planets previously in the Habitable Zone are, in fact, not, and other planets may be habitable depending on their assumed stellar host.Comment: 16 pages, 10 figures, ApJ, 804, 9

On the "Causality Argument" in Bouncing Cosmologies

We exhibit a situation in which cosmological perturbations of astrophysical relevance propagating through a bounce are affected in a scale-dependent way. Involving only the evolution of a scalar field in a closed universe described by general relativity, the model is consistent with causality. Such a specific counter-example leads to the conclusion that imposing causality is not sufficient to determine the spectrum of perturbations after a bounce provided it is known before. We discuss consequences of this result for string motivated scenarios.Comment: 4 pages, 1 figure, ReVTeX, to appear in Phys. Rev. Let

Stochastic mechanics and the Feynman integral

The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author

Hubble Space Telescope High Resolution Imaging of Kepler Small and Cool Exoplanet Host Stars

High resolution imaging is an important tool for follow-up study of exoplanet candidates found via transit detection with the Kepler Mission. We discuss here HST imaging with the WFC3 of 23 stars that host particularly interesting Kepler planet candidates based on their small size and cool equilibrium temperature estimates. Results include detections, exclusion of background stars that could be a source of false positives for the transits, and detection of physically-associated companions in a number of cases providing dilution measures necessary for planet parameter refinement. For six KOIs, we find that there is ambiguity in which star hosts the transiting planet(s), with potentially strong implications for planetary characteristics. Our sample is evenly distributed in G, K, and M spectral types. Albeit with a small sample size, we find that physically-associated binaries are more common than expected at each spectral type, reaching a factor of 10 frequency excess at M. We document the program detection sensitivities, detections, and deliverables to the Kepler follow-up program archive.Comment: Accepted for the Astronomical Journal; 13 pages with 9 figure

The \^G Search for Extraterrestrial Civilizations with Large Energy Supplies. IV. The Signatures and Information Content of Transiting Megastructures

Arnold (2005), Forgan (2013), and Korpela et al. (2015) noted that planet-sized artificial structures could be discovered with Kepler as they transit their host star. We present a general discussion of transiting megastructures, and enumerate ten potential ways their anomalous silhouettes, orbits, and transmission properties would distinguish them from exoplanets. We also enumerate the natural sources of such signatures. Several anomalous objects, such as KIC 12557548 and CoRoT-29, have variability in depth consistent with Arnold's prediction and/or an asymmetric shape consistent with Forgan's model. Since well motivated physical models have so far provided natural explanations for these signals, the ETI hypothesis is not warranted for these objects, but they still serve as useful examples of how nonstandard transit signatures might be identified and interpreted in a SETI context. Boyajian et al. 2015 recently announced KIC 8462852, an object with a bizarre light curve consistent with a "swarm" of megastructures. We suggest this is an outstanding SETI target. We develop the normalized information content statistic $M$ to quantify the information content in a signal embedded in a discrete series of bounded measurements, such as variable transit depths, and show that it can be used to distinguish among constant sources, interstellar beacons, and naturally stochastic or artificial, information-rich signals. We apply this formalism to KIC 12557548 and a specific form of beacon suggested by Arnold to illustrate its utility.Comment: 25 pages, 10 figures. Accepted to Ap

A CLT for Plancherel representations of the infinite-dimensional unitary group

We study asymptotics of traces of (noncommutative) monomials formed by images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process that can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields. The limiting process has previously arisen via the global scaling limit of spectra for submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere.Comment: 12 page

From simplicial Chern-Simons theory to the shadow invariant II

This is the second of a series of papers in which we introduce and study a rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected compact structure groups G. More precisely, we introduce, for general links L in M, a rigorous simplicial version WLO_{rig}(L) of the corresponding Wilson loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson (Nucl. Phys. B408(2):345-390, 1993). For a simple class of links L we then evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement with Turaev's shadow invariant |L|.Comment: 53 pages, 1 figure. Some minor changes and corrections have been mad

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page