We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of reaction network theory a
s a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.
We report the sky-projected orbital obliquity (spin-orbit angle) of WASP-84b, a 0.70-$M_{rm Jup}$ planet in a 8.52-day orbit around a G9V/K0V star, to be $lambda = 0.3 pm 1.7^circ$. We obtain a true obliquity of $psi = 14.8 pm 8.0^circ$ from a measur
ement of the inclination of the stellar spin axis with respect to the sky plane. Due to the young age and the weak tidal forcing of the system, we suggest that the orbit of WASP-84b is unlikely to have both realigned and circularised from the misaligned and/or eccentric orbit likely to have arisen from high-eccentricity migration. Therefore we conclude that the planet probably migrated via interaction with the protoplanetary disc. This would make it the first short-orbit, giant planet to have been shown to have migrated via this pathway. Further, we argue that the distribution of obliquities for planets orbiting cool stars ($T_{rm eff}$ < 6250 K) suggests that high-eccentricity migration is an important pathway for the formation of short-orbit, giant planets.
We report the discovery of the transiting exoplanets WASP-69b, WASP-70Ab and WASP-84b, each of which orbits a bright star ($Vsim10)$. WASP-69b is a bloated Saturn-mass planet (0.26 $M_{rm Jup}$, 1.06 $R_{rm Jup}$) in a 3.868-d period around an active
, $sim$1-Gyr, mid-K dwarf. ROSAT detected X-rays $60 pm 27$ from WASP-69. If the star is the source then the planet could be undergoing mass-loss at a rate of $sim$10$^{12}$ g s$^{-1}$. This is 1 to 2 orders of magnitude higher than the evaporation rate estimated for HD 209458b and HD 189733b, both of which have exhibited anomalously-large Lyman-$alpha$ absorption during transit. WASP-70Ab is a sub-Jupiter-mass planet (0.59 $M_{rm Jup}$, 1.16 $R_{rm Jup}$) in a 3.713-d orbit around the primary of a spatially-resolved, 9-to-10-Gyr, G4+K3 binary, with a separation of 3.3$$ ($geq$800 AU). WASP-84b is a sub-Jupiter-mass planet (0.69 $M_{rm Jup}$, 0.94 $R_{rm Jup)}$ in an 8.523-d orbit around an active, $sim$1-Gyr, early-K dwarf. Of the transiting planets discovered from the ground to date, WASP-84b has the third-longest period. For the active stars WASP-69 and WASP-84, we pre-whitened the radial velocities using a low-order harmonic series. We found this reduced the residual scatter more than did the oft-used method of pre-whitening with a fit between residual radial velocity and bisector span. The system parameters were essentially unaffected by pre-whitening.
We report the discovery of three extrasolar planets that transit their moderately bright (Vmag = 12-13) host stars. WASP-44b is a 0.89-MJup planet in a 2.42-day orbit around a G8V star. WASP-45b is a 1.03-MJup planet which passes in front of the limb
of its K2V host star every 3.13 days. Weak Ca II H+K emission seen in the spectra of WASP-45 suggests the star is chromospherically active. WASP-46b is a 2.10-MJup planet in a 1.43-day orbit around a G6V star. Rotational modulation of the light curves of WASP-46 and weak Ca II H+K emission in its spectra show the star to be photospherically and chromospherically active. We imposed circular orbits in our analyses as the radial velocity data are consistent with (near-)circular orbits, as could be expected from both empirical and tidal-theory perspectives for such short-period, Jupiter-mass planets. We discuss the impact of fitting for eccentric orbits for such planets when not supported by the data. The derived planetary and stellar radii depend on the fitted eccentricity and these parameters inform intense theoretical efforts concerning tidal circularisation and heating, bulk planetary composition and the observed systematic errors in planetary and stellar radii. As such, we recommend exercising caution in fitting the orbits of short period, Jupiter-mass planets with an eccentric model when there is no evidence of non-circularity.
We report the detection of thermal emission at 4.5 and 8 micron from the planet WASP-17b. We used Spitzer to measure the system brightness at each wavelength during two occultations of the planet by its host star. By combining the resulting light cur
ves with existing transit light curves and radial velocity measurements in a simultaneous analysis, we find the radius of WASP-17b to be 2.0 Rjup, which is 0.2 Rjup larger than any other known planet and 0.7 Rjup larger than predicted by the standard cooling theory of irradiated gas giant planets. We find the retrograde orbit of WASP-17b to be slightly eccentric, with 0.0012 < e < 0.070 (3 sigma). Such a low eccentricity suggests that, under current models, tidal heating alone could not have bloated the planet to its current size, so the radius of WASP-17b is currently unexplained. From the measured planet-star flux-density ratios we infer 4.5 and 8 micron brightness temperatures of 1881 +/- 50 K and 1580 +/- 150 K, respectively, consistent with a low-albedo planet that efficiently redistributes heat from its day side to its night side.
From WASP photometry and SOPHIE radial velocities we report the discovery of WASP-40b (HAT-P-27b), a 0.6 Mjup planet that transits its 12th magnitude host star every 3.04 days. The host star is of late G-type or early K-type and likely has a metallic
ity greater than solar ([Fe/H] = 0.14 +/- 0.11). The planets mass and radius are typical of the known hot Jupiters, thus adding another system to the apparent pileup of transiting planets with periods near 3 to 4 days. Our parameters match those of the recent HATnet announcement of the same planet, thus giving confidence in the techniques used. We report a possible indication of stellar activity in the host star.
We report the discovery of a 61-Jupiter-mass brown dwarf, which transits its F8V host star, WASP-30, every 4.16 days. From a range of age indicators we estimate the system age to be 1-2 Gyr. We derive a radius (0.89 +/- 0.02 RJup) for the companion t
hat is consistent with that predicted (0.914 RJup) by a model of a 1-Gyr-old, non-irradiated brown dwarf with a dusty atmosphere. The location of WASP-30b in the minimum of the mass-radius relation is consistent with the quantitative prediction of Chabrier & Baraffe (2000), thus confirming the theory.
We present the first ground-based detection of thermal emission from an exoplanet in the H-band. Using HAWK-I on the VLT, we observed an occultation of WASP-19b by its G8V-type host star. WASP-19b is a Jupiter-mass planet with an orbital period of on
ly 19 h, and thus, being highly irradiated, is expected to be hot. We measure an H-band occultation depth of (0.259 +0.046 -0.044) %, which corresponds to an H-band brightness temperature of T_H = 2580 +/- 125 K. A cloud-free model of the planets atmosphere, with no redistribution of energy from day-side to night-side, under predicts the planet/star flux density ratio by a factor of two. As the stellar parameters, and thus the level of planetary irradiation, are well-constrained by measurement, it is likely that our model of the planets atmosphere is too simple.
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled syste
m with mass-action kinetics admits a complex balanced equilibrium. Feinbergs deficiency zero theorem then implies that such a distribution exists so long as the corresponding chemical network is weakly reversible and has a deficiency of zero. The main parameter of the stationary distribution for the stochastically modeled system is a complex balanced equilibrium value for the corresponding deterministically modeled system. We also generalize our main result to some non-mass-action kinetics.
We report the discovery of WASP-5b, a Jupiter-mass planet orbiting a 12th-mag G-type star in the Southern hemisphere. The 1.6-d orbital period places WASP-5b in the class of very-hot Jupiters and leads to a predicted equilibrium temperature of 1750 K
. WASP-5b is the densest of any known Jovian-mass planet, being a factor seven denser than TrES-4, which is subject to similar stellar insolation, and a factor three denser than WASP-4b, which has a similar orbital period. We present transit photometry and radial-velocity measurements of WASP-5 (= USNO-B1 0487-0799749), from which we derive the mass, radius and density of the planet: M_P = 1.58 +0.13 -0.08 M_J, R_P = 1.090 +0.094 -0.058 R_J and Rho_P = 1.22 +0.19 -0.24 Rho_J. The orbital period is P = 1.6284296 +0.0000048 -0.0000037 d and the mid-transit epoch is T_C (HJD) = 2454375.62466 +0.00026 -0.00025.
