Nonrigid Structure-From-Motion From 2-D Images Using Markov Chain Monte Carlo

In this paper we present a new method for simultaneously determining three dimensional (3-D) shape and motion of a non-rigid object from uncalibrated two dimensional (2- D) images without assuming the distribution characteristics. A non-rigid motion can be treated as a combination of a rigid rotation and a non-rigid deformation. To seek accurate recovery of deformable structures, we estimate the probability distribution function of the corresponding features through random sampling, incorporating an established probabilistic model. The fitting between the observation and the projection of the estimated 3-D structure will be evaluated using a Markov chain Monte Carlo based expectation maximisation algorithm. Applications of the proposed method to both synthetic and real image sequences are demonstrated with promising results.

Radiocarbon peat chronologies and environmental change

Raised bog peat deposits form important archives for reconstructing past changes in climate. Precise and reliable age models are of vital importance for interpreting such archives. We propose enhanced, Markov chain Monte Carlo based methods for obtaining age models from radiocarbon-dated peat cores, based on the assumption of piecewise linear accumulation. Included are automatic choice of sections, a measure of the goodness of fit and outlier downweighting. The approach is illustrated by using a peat core from the Netherlands.

Updated parameters for the transiting exoplanet WASP-3b using RISE, a new fast camera for the Liverpool Telescope

Some of the first results are reported from RISE - a new fast camera mounted on the Liverpool Telescope primarily designed to obtain high time-resolution light curves of transiting extrasolar planets for the purpose of transit timing. A full and partial transit of WASP-3 are presented, and a Markov-Chain Monte Carlo analysis is used to update the parameters from the discovery paper. This results in a planetary radius of 1.29(-0.12)(+0.05) R-J and therefore a density of 0.82(-0.09)(+0.14) rho(J), consistent with previous results. The inclination is 85.06(-0.15)(+0.16) deg, in agreement (but with a significant improvement in the precision) with the previously determined value. Central transit times are found to be consistent with the ephemeris given in the discovery paper; however, a new ephemeris calculated using the longer baseline results in T-c(0) = 2 454 605.55915 +/- 0.00023 HJD and P = 1.846835 +/- 0.000002 days.

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.

WASP-10b: a 3M(J), gas-giant planet transiting a late-type K star

We report the discovery of WASP-10b, a new transiting extrasolar planet (ESP) discovered by the Wide Angle Search for Planets ( WASP) Consortium and confirmed using Nordic Optical Telescope FIbre-fed Echelle Spectrograph and SOPHIE radial velocity data. A 3.09-d period, 29 mmag transit depth and 2.36 h duration are derived for WASP-10b using WASP and high-precision photometric observations. Simultaneous fitting to the photometric and radial velocity data using a Markov Chain Monte Carlo procedure leads to a planet radius of 1.28R(J), a mass of 2.96M(J) and eccentricity of approximate to 0.06. WASP-10b is one of the more massive transiting ESPs, and we compare its characteristics to the current sample of transiting ESP, where there is currently little information for masses greater than approximate to 2M(J) and non-zero eccentricities. WASP-10's host star, GSC 2752-00114 (USNO-B1.0 1214-0586164) is among the fainter stars in the WASP sample, with V = 12.7 and a spectral type of K5. This result shows promise for future late-type dwarf star surveys.

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.

Tight constraints on the existence of additional planets around HD 189733†

We report a transit timing study of the transiting exoplanetary system HD 189733. In total, we observed 10 transits in 2006 and 2008 with the 2.6-m Nordic Optical Telescope, and two transits in 2007 with the 4.2-m William Herschel Telescope. We used Markov Chain Monte Carlo simulations to derive the system parameters and their uncertainties, and our results are in a good agreement with previously published values. We performed two independent analyses of transit timing residuals to place upper mass limits on putative perturbing planets. The results show no evidence for the presence of planets down to 1 Earth mass near the 1:2 and 2:1 resonance orbits, and planets down to 2.2 Earth masses near the 3:5 and 5:3 resonance orbits with HD 189733b. These are the strongest limits to date on the presence of other planets in this system. Based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. Based on observations made with the William Herschel Telescope operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. ‡

Ground-based detection of thermal emission from the exoplanet WASP-19b

We present an occultation of the newly discovered hot Jupiter system WASP-19, observed with the High Acuity Wide-field K-band Imager instrument on the VLT, in order to measure thermal emission from the planet's dayside at ~2µm. The light curve was analysed using a Markov Chain Monte Carlo method to find the eclipse depth and the central transit time. The transit depth was found to be 0.366 +/- 0.072 per cent, corresponding to a brightness temperature of 2540 +/- 180 K. This is significantly higher than the calculated (zero-albedo) equilibrium temperature and indicates that the planet shows poor redistribution of heat to the night side, consistent with models of highly irradiated planets. Further observations are needed to confirm the existence of a temperature inversion and possibly molecular emission lines. The central eclipse time was found to be consistent with a circular orbit.

An ingress and a complete transit of HD80606 b

We have used four telescopes at different longitudes to obtain near-continuous light-curve coverage of the star HD80606 as it was transited by its ~4-MJup planet. The observations were performed during the predicted transit windows around 2008 October 25 and 2009 February 14. Our data set is unique in that it simultaneously constrains the duration of the transit and the planet's period. Our Markov Chain Monte Carlo analysis of the light curves, combined with constraints from radial-velocity data, yields system parameters consistent with previously reported values. We find a planet-to-star radius ratio marginally smaller than previously reported, corresponding to a planet radius of Rp = 0.921 +/- 0.036RJup.

WASP-21b: a hot-Saturn exoplanet transiting a thick disc star

We report the discovery of WASP-21b, a new transiting exoplanet discovered by the Wide Angle Search for Planets (WASP) Consortium and established and characterized with the FIES, SOPHIE, CORALIE and HARPS fiber-fed echelle spectrographs. A 4.3-d period, 1.1% transit depth and 3.4-h duration are derived for WASP-21b using SuperWASP-North and high precision photometric observations at the Liverpool Telescope. Simultaneous fitting to the photometric and radial velocity data with a Markov Chain Monte Carlo procedure leads to a planet in the mass regime of Saturn. With a radius of 1.07 RJup and mass of 0.30 MJup, WASP-21b has a density close to 0.24 ?Jup corresponding to the distribution peak at low density of transiting gaseous giant planets. With a host star metallicity [Fe/H] of -0.46, WASP-21b strengthens the correlation between planetary density and host star metallicity for the five known Saturn-like transiting planets. Furthermore there are clear indications that WASP-21b is the first transiting planet belonging to the thick disc.

Spin-orbit angle measurements for six southern transiting planets. New insights into the dynamical origins of hot Jupiters

Context. Several competing scenarios for planetary-system formation and evolution seek to explain how hot Jupiters came to be so close to their parent stars. Most planetary parameters evolve with time, making it hard to distinguish between models. The obliquity of an orbit with respect to the stellar rotation axis is thought to be more stable than other parameters such as eccentricity. Most planets, to date, appear aligned with the stellar rotation axis; the few misaligned planets so far detected are massive (> 2 MJ). Aims: Our goal is to measure the degree of alignment between planetary orbits and stellar spin axes, to search for potential correlations with eccentricity or other planetary parameters and to measure long term radial velocity variability indicating the presence of other bodies in the system. Methods: For transiting planets, the Rossiter-McLaughlin effect allows the measurement of the sky-projected angle ß between the stellar rotation axis and a planet's orbital axis. Using the HARPS spectrograph, we observed the Rossiter-McLaughlin effect for six transiting hot Jupiters found by the WASP consortium. We combine these with long term radial velocity measurements obtained with CORALIE. We used a combined analysis of photometry and radial velocities, fitting model parameters with the Markov Chain Monte Carlo method. After obtaining ß we attempt to statistically determine the distribution of the real spin-orbit angle ?. Results: We found that three of our targets have ß above 90°: WASP-2b: ß = 153°+11-15, WASP-15b: ß = 139.6°+5.2-4.3 and WASP-17b: ß = 148.5°+5.1-4.2; the other three (WASP-4b, WASP-5b and WASP-18b) have angles compatible with 0°. We find no dependence between the misaligned angle and planet mass nor with any other planetary parameter. All six orbits are close to circular, with only one firm detection of eccentricity e = 0.00848+0.00085-0.00095 in WASP-18b. No long-term radial acceleration was detected for any of the targets. Combining all previous 20 measurements of ß and our six and transforming them into a distribution of ? we find that between about 45 and 85% of hot Jupiters have ? > 30°. Conclusions: Most hot Jupiters are misaligned, with a large variety of spin-orbit angles. We find observations and predictions using the Kozai mechanism match well. If these observational facts are confirmed in the future, we may then conclude that most hot Jupiters are formed from a dynamical and tidal origin without the necessity to use type I or II migration. At present, standard disc migration cannot explain the observations without invoking at least another additional process.

Estimating the masses of extra-solar planets

All extra-solar planet masses that have been derived spectroscopically are lower limits since the inclination of the orbit to our line-of-sight is unknown except for transiting systems. In theory, however, it is possible to determine the inclination angle, i, between the rotation axis of a star and an observer's line-of-sight from measurements of the projected equatorial velocity (v sin i), the stellar rotation period (P(rot)) and the stellar radius (R(*)). For stars which host planetary systems this allows the removal of the sin i dependency of extra-solar planet masses derived from spectroscopic observations under the assumption that the planetary orbits lie perpendicular to the stellar rotation axis.
We have carried out an extensive literature search and present a catalogue of v sin i, P(rot) and R(*) estimates for stars hosting extra-solar planets. In addition, we have used Hipparcos parallaxes and the Barnes-Evans relationship to further supplement the R(*) estimates obtained from the literature. Using this catalogue, we have obtained sin i estimates using a Markov-chain Monte Carlo analysis. This technique allows proper 1 Sigma two-tailed confidence limits to be placed on the derived sin i's along with the transit probability for each planet to be determined.
While we find that a small proportion of systems yield sin i's significantly greater than 1, most likely due to poor P(rot) estimations, the large majority are acceptable. We are further encouraged by the cases where we have data on transiting systems, as the technique indicates inclinations of similar to 90 degrees and high transit probabilities. In total, we are able to estimate the true masses of 133 extra-solar planets. Of these 133 extra-solar planets, only six have revised masses that place them above the 13M(J) deuterium burning limit; four of those six extra-solar planet candidates were already suspected to lie above the deuterium burning limit before correcting their masses for the sin i dependency. Our work reveals a population of high-mass extra-solar planets with low eccentricities, and we speculate that these extra-solar planets may represent the signature of different planetary formation mechanisms at work. Finally, we discuss future observations that should improve the robustness of this technique.

A lower mass for the exoplanet WASP-21b

We present high-precision transit observations of the exoplanet WASP-21b, obtained with the Rapid Imager to Search for Exoplanets instrument mounted on the 2.0-m Liverpool Telescope. A transit model is fitted, coupled with a Markov chain Monte Carlo routine, to derive accurate system parameters. The two new high-precision transits allow us to estimate the stellar density directly from the light curve. Our analysis suggests that WASP-21 is evolving off the main sequence which led to a previous overestimation of the stellar density. Using isochrone interpolation, we find a stellar mass of 0.86 ± 0.04 Msun, which is significantly lower than previously reported (1.01 ± 0.03 Msun). Consequently, we find a lower planetary mass of 0.27 ± 0.01 MJup. A lower inclination (87?4 ± 0?3) is also found for the system than previously reported, resulting in a slightly larger stellar (R*= 1.10 ± 0.03 Rsun) and planetary radius (Rp= 1.14 ± 0.04 RJup). The planet radius suggests a hydrogen/helium composition with no core which strengthens the correlation between planetary density and host star metallicity. A new ephemeris is determined for the system, i.e. T0= 245 5084.519 74 ± 0.000 20 (HJD) and P= 4.322 5060 ± 0.000 0031 d. We found no transit timing variations in WASP-21b.

High-precision transit observations of the exoplanet WASP-13b with the RISE instrument

WASP-13b is a sub-Jupiter mass exoplanet orbiting a G1V type star with a period of 4.35 d.The current uncertainty in its impact parameter (0 < b < 0.46) results in poorly definedstellar and planetary radii. To better constrain the impact parameter, we have obtained highprecisiontransit observations with the rapid imager to search for exoplanets (RISE) instrumentmounted on 2.0-m Liverpool Telescope. We present four new transits which are fitted witha Markov chain Monte Carlo routine to derive accurate system parameters. We found anorbital inclination of 85. ◦ 2 ± 0. ◦ 3 resulting in stellar and planetary radii of 1.56 ± 0.04 Rand 1.39 ± 0.05RJup, respectively. This suggests that the host star has evolved off the mainsequence and is in the hydrogen-shell-burning phase.We also discuss how the limb darkeningaffects the derived system parameters.With a density of 0.17ρJ,WASP-13b joins the group oflow-density planets whose radii are too large to be explained by standard irradiation models.We derive a new ephemeris for the system, T0 = 245 5575.5136 ± 0.0016 (HJD) and P =4.353 011 ± 0.000 013 d. The planet equilibrium temperature (Tequ = 1500 K) and the brighthost star (V = 10.4mag) make it a good candidate for follow-up atmospheric studies.