MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \emph{different} Markov (or other stochastic) processes to remain equal for as long as possible, when started in the \emph{same} state. We refer to this "un-coupling" or "maximal agreement" construction as \emph{MEXIT}, standing for "maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit \MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of \MEXIT for Brownian motions with two different constant drifts.Comment: 28 page

Measuring the mass of a sterile neutrino with a very short baseline reactor experiment

An analysis of the world's neutrino oscillation data, including sterile neutrinos, (M. Sorel, C. M. Conrad, and M. H. Shaevitz, Phys. Rev. D 70, 073004) found a peak in the allowed region at a mass-squared difference $\Delta m^2 \cong 0.9$ eV$^2$. We trace its origin to harmonic oscillations in the electron survival probability $P_{ee}$ as a function of L/E, the ratio of baseline to neutrino energy, as measured in the near detector of the Bugey experiment. We find a second occurrence for $\Delta m^2 \cong 1.9$ eV$^2$. We point out that the phenomenon of harmonic oscillations of $P_{ee}$ as a function of L/E, as seen in the Bugey experiment, can be used to measure the mass-squared difference associated with a sterile neutrino in the range from a fraction of an eV$^2$ to several eV$^2$ (compatible with that indicated by the LSND experiment), as well as measure the amount of electron-sterile neutrino mixing. We observe that the experiment is independent, to lowest order, of the size of the reactor and suggest the possibility of a small reactor with a detector sitting at a very short baseline.Comment: 4 pages, 2 figure

Time resolved spectroscopy of dust and gas from extrasolar planetesimals orbiting WD 1145+017

Multiple long and variable transits caused by dust from possibly disintegrating asteroids were detected in light curves of WD 1145+017. We present time-resolved spectroscopic observations of this target with QUCAM CCDs mounted in the Intermediate dispersion Spectrograph and Imaging System at the 4.2-m William Herschel Telescope in two different spectral arms: the blue arm covering 3800-4025 {\AA} and the red arm covering 7000-7430 {\AA}. When comparing individual transits in both arms, our observations show with 20 {\sigma} significance an evident colour difference between the in- and out-of-transit data of the order of 0.05-0.1 mag, where transits are deeper in the red arm. We also show with > 6 {\sigma} significance that spectral lines in the blue arm are shallower during transits than out-of-transit. For the circumstellar lines it also appears that during transits the reduction in absorption is larger on the red side of the spectral profiles. Our results confirm previous findings showing the u'-band excess and a decrease in line absorption during transits. Both can be explained by an opaque body blocking a fraction of the gas disc causing the absorption, implying that the absorbing gas is between the white dwarf and the transiting objects. Our results also demonstrate the capability of EMCCDs to perform high-quality time resolved spectroscopy of relatively faint targets.Comment: 9 pages, 5 figures. Accepted to MNRA

The orbital motion, absolute mass, and high-altitude winds of exoplanet HD209458b

For extrasolar planets discovered using the radial velocity method, the spectral characterization of the host star leads to a mass-estimate of the star and subsequently of the orbiting planet. In contrast, if also the orbital velocity of the planet would be known, the masses of both star and planet could be determined directly using Newton's law of gravity, just as in the case of stellar double-line eclipsing binaries. Here we report on the detection of the orbital velocity of extrasolar planet HD209458b. High dispersion ground-based spectroscopy during a transit of this planet reveals absorption lines from carbon monoxide produced in the planet atmosphere, which shift significantly in wavelength due to the change in the radial component of the planet orbital velocity. These observations result in a mass determination of the star and planet of 1.00+-0.22 Msun and 0.64+-0.09 Mjup respectively. A ~2 km/sec blueshift of the carbon monoxide signal with respect to the systemic velocity of the host star suggests the presence of a strong wind flowing from the irradiated dayside to the non-irradiated nightside of the planet within the 0.01-0.1 mbar atmospheric pressure range probed by these observations. The strength of the carbon monoxide signal suggests a CO mixing ratio of 1-3x10-3 in this planet's upper atmosphere.Comment: 11 Pages main article and 6 pages suppl. information: A final, edited version appears in the 24 May 2010 issue of Natur

A new form of the rotating C-metric

In a previous paper, we showed that the traditional form of the charged C-metric can be transformed, by a change of coordinates, into one with an explicitly factorizable structure function. This new form of the C-metric has the advantage that its properties become much simpler to analyze. In this paper, we propose an analogous new form for the rotating charged C-metric, with structure function G(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), where r_\pm are the usual locations of the horizons in the Kerr-Newman black hole. Unlike the non-rotating case, this new form is not related to the traditional one by a coordinate transformation. We show that the physical distinction between these two forms of the rotating C-metric lies in the nature of the conical singularities causing the black holes to accelerate apart: the new form is free of torsion singularities and therefore does not contain any closed timelike curves. We claim that this new form should be considered the natural generalization of the C-metric with rotation.Comment: 13 pages, LaTe