One aspect of the quantum nature of spacetime is its foaminess at very small scales. Many models for spacetime foam are defined by the accumulation power $alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase
shifts they produce) may accumulate over large path-lengths. Here $alpha$ is defined by theexpression for the path-length fluctuations, $delta ell$, of a source at distance $ell$, wherein $delta ell simeq ell^{1 - alpha} ell_P^{alpha}$, with $ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {em Chandra} to set the constraint $alpha gtrsim 0.58$, which rules out the random walk model (with $alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $alpha gtrsim 0.67$ and $alpha gtrsim 0.72$, respectively. These limits on $alpha$ seem to rule out $alpha = 2/3$, the model of some physical interest.
We present an analysis and interpretation of the Kepler binary system KOI 1224. This is the fourth binary found with Kepler that consists of a thermally bloated, hot white dwarf in a close orbit with a more or less normal star of spectral class A or
F. As we show, KOI 1224 contains a white dwarf with Teff = 14400 +/- 1100 K, mass = 0.20 +/- 0.02 Msun, and radius = 0.103 +/- 0.004 Rsun, and an F-star companion of mass = 1.59 +/- 0.07 Msun that is somewhat beyond its terminal-age main sequence. The orbital period is quite short at 2.69802 days. The ingredients that are used in the analysis are the Kepler binary light curve, including the detection of the Doppler boosting effect; the NUV and FUV fluxes from the Galex images of this object; an estimate of the spectral type of the F-star companion; and evolutionary models of the companion designed to match its effective temperature and mean density. The light curve is modelled with a new code named Icarus which we describe in detail. Its features include the full treatment of orbital phase-resolved spectroscopy, Doppler boosting, irradiation effects and transits/eclipses, which are particularly suited to irradiated eclipsing binaries. We interpret the KOI 1224 system in terms of its likely evolutionary history. We infer that this type of system, containing a bloated hot white dwarf, is the direct descendant of an Algol-type binary. In spite of this basic understanding of the origin of KOI 1224, we discuss a number of problems associated with producing this type of system with this short of an short orbital period.
Among the initial results from Kepler were two striking lightcurves, for KOI 74 and KOI 81, in which the relative depths of the primary and secondary eclipses showed that the more compact, less luminous object was hotter than its stellar host. That r
esult became particularly intriguing because a substellar mass had been derived for the secondary in KOI 74, which would make the high temperature challenging to explain; in KOI 81, the mass range for the companion was also reported to be consistent with a substellar object. We re-analyze the Kepler data and demonstrate that both companions are likely to be white dwarfs. We also find that the photometric data for KOI 74 show a modulation in brightness as the more luminous star orbits, due to Doppler boosting. The magnitude of the effect is sufficiently large that we can use it to infer a radial velocity amplitude accurate to 1 km/s. As far as we are aware, this is the first time a radial-velocity curve has been measured photometrically. Combining our velocity amplitude with the inclination and primary mass derived from the eclipses and primary spectral type, we infer a secondary mass of 0.22+/-0.03 Msun. We use our estimates to consider the likely evolutionary paths and mass-transfer episodes of these binary systems.
Galaxy-scale strong gravitational lenses with measured stellar velocity dispersions allow a test of the weak-field metric on kiloparsec scales and a geometric measurement of the cosmological distance-redshift relation, provided that the mass-dynamica
l structure of the lensing galaxies can be independently constrained to a sufficient degree. We combine data on 53 galaxy-scale strong lenses from the Sloan Lens ACS Survey with a well-motivated fiducial set of lens-galaxy parameters to find (1) a constraint on the post-Newtonian parameter gamma = 1.01 +/- 0.05 and (2) a determination of Omega_Lambda = 0.75 +/- 0.17 under the assumption of a flat universe. These constraints assume that the underlying observations and priors are free of systematic error. We evaluate the sensitivity of these results to systematic uncertainties in (1) total mass-profile shape, (2) velocity anisotropy, (3) light-profile shape, and (4) stellar velocity dispersion. Based on these sensitivities, we conclude that while such strong-lens samples can in principle provide an important tool for testing general relativity and cosmology, they are unlikely to yield precision measurements of gamma and Omega_Lambda unless the properties of the lensing galaxies are independently constrained with substantially greater accuracy than at present.
