A Transit Timing Analysis of Mine RISE Light Curves of the Exoplanet System TrES-3

We present nine newly observed transits of TrES-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. A Markov-Chain Monte Carlo analysis was used to determine the planet star radius ratio and inclination of the system, which were found to be R-p/R-star = 0.1664(-0.0018)(+0.0011) and i = 81.73(-0.04)(+0.13), respectively, consistent with previous results. The central transit times and uncertainties were also calculated, using a residual-permutation algorithm as an independent check on the errors. A re-analysis of eight previously published TrES-3 light curves was conducted to determine the transit times and uncertainties using consistent techniques. Whilst the transit times were not found to be in agreement with a linear ephemeris, giving chi(2) = 35.07 for 15 degrees of freedom, we interpret this to be the result of systematics in the light curves rather than a real transit timing variation. This is because the light curves that show the largest deviation from a constant period either have relatively little out-of-transit coverage or have clear systematics. A new ephemeris was calculated using the transit times and was found to be T-c(0) = 2454632.62610 +/- 0.00006 HJD and P = 1.3061864 +/- 0.0000005 days. The transit times were then used to place upper mass limits as a function of the period ratio of a potential perturbing planet, showing that our data are sufficiently sensitive to have probed sub-Earth mass planets in both interior and exterior 2:1 resonances, assuming that the additional planet is in an initially circular orbit.

IntCal09 and Marine09 radiocarbon age calibration curves, 0 - 50,000 years cal BP

The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the ¹⁴C and calendar timescales as established in 2002. No change was made to the curves from 0-12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org.

A transit timing analysis of seven RISE light curves of the exoplanet system HAT-P-3

We present seven light curves of the exoplanet system HAT-P-3, taken as part of a transit timing programme using the rapid imager to search for exoplanets instrument on the Liverpool Telescope. The light curves are analysed using a Markov chain Monte Carlo algorithm to update the parameters of the system. The inclination is found to be i = 86.75+0.22-0.21°, the planet-star radius ratio to be Rp/R* = 0.1098+0.0010-0.0012 and the stellar radius to be R* = 0.834+0.018-0.026Rsolar, consistent with previous results but with a significant improvement in the precision. Central transit times and uncertainties for each light curve are also determined, and a residual permutation algorithm is used as an independent check on the errors. The transit times are found to be consistent with a linear ephemeris, and a new ephemeris is calculated as Tc(0) = 2454856.70118 +/- 0.00018 HJD and P = 2.899738 +/- 0.000007 d. Model timing residuals are fitted to the measured timing residuals to place upper mass limits for a hypothetical perturbing planet as a function of the period ratio. These show that we have probed for planets with masses as low as 0.33 and 1.81 M? in the interior and exterior 2:1 resonances, respectively, assuming the planets are initially in circular orbits.

A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.