Explorations into the Viability of Coupled Radius-Orbit Evolutionary Models for Inflated Planets

The radii of some transiting extrasolar giant planets are larger than would be expected by the standard theory. We address this puzzle with the model of coupled radius-orbit tidal evolution developed by \citet{Ibgui_and_Burrows_2009}. The planetary radius is evolved self-consistently with orbital parameters, under the influence of tidal torques and tidal dissipation in the interior of the planet. A general feature of this model, which we have previously demonstrated in the generic case, is that a possible transient inflation of the planetary radius can temporarily interrupt its standard monotonic shrinking and can lead to the inflated radii that we observe. In particular, a bloated planet with even a circular orbit may still be inflated due to an earlier episode of tidal heating. We have modified our model to include an orbital period dependence of the tidal dissipation factor in the star, $Q'_{\ast} \propto P^{\gamma}$, $-1 \leqslant \gamma \leqslant 1$. With this model, we search, for a tidally heated planet, orbital and radius evolutionary tracks that fall within the observational limits of the radius, the semimajor axis, and the eccentricity of the planet in its current estimated age range. We find that, for some inflated planets (WASP-6b and WASP-15b), there are such tracks; for another (TrES-4), there are none; and for still others (WASP-4b and WASP-12b), there are such tracks, but our model might imply that we are observing the planets at a special time. Finally, we stress that there is a two to three order-of-magnitude timescale uncertainty of the inspiraling phase of the planet into its host star, arising from uncertainties in the tidal dissipation factor in the star $Q'_{\ast}$.Comment: Submitted to ApJ; 13 pages, 3 figures, 2 tables; (emulateapj format

Tidal Heating Models for the Radii of the Inflated Transiting Giant Planets WASP-4b, WASP-6b, WASP-12b, and TrES-4

In order to explain the inflated radii of some transiting extrasolar giant planets, we investigate a tidal heating scenario for the inflated planets WASP-4b, WASP-6b, WASP-12b, WASP-15b, and TrES-4. To do so, we assume that they retain a nonzero eccentricity, possibly by dint of continuing interaction with a third body. We calculate the amount of extra heating in the envelope that is then required to fit the radius of each planet, and we explore how this additional power depends on the planetary atmospheric opacity and on the mass of a heavy-element central core. There is a degeneracy between the core mass $M_{\rm core}$ and the heating $\dot{E}_{\rm heating}$. Therefore, in the case of tidal heating, there is for each planet a range of the couple $\{M_{\rm core},e^2/Q'_p\}$ that can lead to the same radius, where $Q'_p$ is the tidal dissipation factor and $e$ is the eccentricity. With this in mind, we also investigate the case of the non-inflated planet HAT-P-12b, which can admit solutions combining a heavy-element core and tidal heating. A substantial improvement of the measured eccentricities of such planetary systems could simplify this degeneracy by linking the two unknown parameters $\{M_{\rm core},Q'_p\}$. Further independent constraints on either of these parameters would, through our calculations, constrain the other.Comment: Accepted in ApJ; 17 pages, 3 figures, 6 tables (emulateapj format); expanded explanatory tex

Atmospheric Circulation of Eccentric Hot Neptune GJ436b

GJ436b is a unique member of the transiting extrasolar planet population being one of the smallest and least irradiated and possessing an eccentric orbit. Because of its size, mass and density, GJ436b could plausibly have an atmospheric metallicity similar to Neptune (20-60 times solar abundances), which makes it an ideal target to study the effects of atmospheric metallicity on dynamics and radiative transfer in an extrasolar planetary atmosphere. We present three-dimensional atmospheric circulation models that include realistic non-gray radiative transfer for 1, 3, 10, 30, and 50 times solar atmospheric metallicity cases of GJ436b. Low metallicity models (1 and 3 times solar) show little day/night temperature variation and strong high-latitude jets. In contrast, higher metallicity models (30 and 50 times solar) exhibit day/night temperature variations and a strong equatorial jet. Spectra and light curves produced from these simulations show strong orbital phase dependencies in the 50 times solar case and negligible variations with orbital phase in the 1 times solar case. Comparisons between the predicted planet/star flux ratio from these models and current secondary eclipse measurements support a high metallicity atmosphere (30-50 times solar abundances) with disequilibrium carbon chemistry at play for GJ436b. Regardless of the actual atmospheric composition of GJ436b, our models serve to illuminate how metallicity influences the atmospheric circulation for a broad range of warm extrasolar planets.Comment: 25 pages, 13 figure

Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces

In this article, we first extend several basic theorems of the operation of vector in 3-dimensional Euclidean spaces. Then three unit vectors: e1, e2, e3 and the definition of vector function in the same spaces are introduced. By dint of unit vector the main operation properties as well as the differentiation formulas of vector function are shown [12].Liang Xiquan - Qingdao University of Science and Technology, ChinaZhao Piqing - Qingdao University of Science and Technology, ChinaBai Ou - University of Science and Technology of China, Hefei, ChinaGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.Murray R. Spiegel. Vector Analysis and an Introduction to Tensor Analysis. McGraw-Hill Book Company, New York, 1959.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990

Review article: pathogenesis and clinical manifestations of gastrointestinal involvement in systemic sclerosis.

BACKGROUND: Gastrointestinal tract (GIT) involvement is a common cause of debilitating symptoms in patients with systemic sclerosis (SSc). There are no disease modifying therapies for this condition and the treatment remains symptomatic, largely owing to the lack of a clear understanding of its pathogenesis. AIMS: To investigate novel aspects of the pathogenesis of gastrointestinal involvement in SSc. To summarise existing knowledge regarding the cardinal clinical gastrointestinal manifestations of SSc and its pathogenesis, emphasising recent investigations that may be valuable in identifying potentially novel therapeutic targets. METHODS: Electronic (PubMed/Medline) and manual Google search. RESULTS: The GIT is the most common internal organ involved in SSc. Any part of the GIT from the mouth to the anus can be affected. There is substantial variability in clinical manifestations and disease course and symptoms are nonspecific and overlapping for a particular anatomical site. Gastrointestinal involvement can occur in the absence of cutaneous disease. Up to 8% of SSc patients develop severe GIT symptoms. This subset of patients display increased mortality with only 15% survival at 9 years. Dysmotiity of the GIT causes the majority of symptoms. Recent investigations have identified a novel mechanism in the pathogenesis of GIT dysmotility mediated by functional anti-muscarinic receptor autoantibodies. CONCLUSIONS: Despite extensive investigation, the pathogenesis of gastrointestinal involvement in systemic sclerosis remains elusive. Although treatment currently remains symptomatic, an improved understanding of novel pathogenic mechanisms may allow the development of potentially highly effective approaches including intravenous immunoglobulin and microRNA based therapeutic interventions

NIMBUS: The Near-Infrared Multi-Band Ultraprecise Spectroimager for SOFIA

We present a new and innovative near-infrared multi-band ultraprecise spectroimager (NIMBUS) for SOFIA. This design is capable of characterizing a large sample of extrasolar planet atmospheres by measuring elemental and molecular abundances during primary transit and occultation. This wide-field spectroimager would also provide new insights into Trans-Neptunian Objects (TNO), Solar System occultations, brown dwarf atmospheres, carbon chemistry in globular clusters, chemical gradients in nearby galaxies, and galaxy photometric redshifts. NIMBUS would be the premier ultraprecise spectroimager by taking advantage of the SOFIA observatory and state of the art infrared technologies. This optical design splits the beam into eight separate spectral bandpasses, centered around key molecular bands from 1 to 4 microns. Each spectral channel has a wide field of view for simultaneous observations of a reference star that can decorrelate time-variable atmospheric and optical assembly effects, allowing the instrument to achieve ultraprecise calibration for imaging and photometry for a wide variety of astrophysical sources. NIMBUS produces the same data products as a low-resolution integral field spectrograph over a large spectral bandpass, but this design obviates many of the problems that preclude high-precision measurements with traditional slit and integral field spectrographs. This instrument concept is currently not funded for development.Comment: 14 pages, 9 figures, SPIE Astronomical Telescopes and Instrumentation 201

Optical and X-ray Transients from Planet-Star Mergers

We evaluate the prompt observational signatures of the merger between a massive close-in planet (a `hot Jupiter') and its host star, events with an estimated Galactic rate of ~0.1-1/yr. Depending on the ratio of the mean density of the planet rho_p to that of the star rho_star, a merger results in three possible outcomes. If rho_p/rho_star > 5, then the planet directly plunges below the stellar atmosphere before being disrupted by tidal forces. Dissipation of orbital energy creates a hot wake behind the planet, producing a EUV/soft X-ray transient as the planet sinks below the stellar surface. The peak luminosity L_X ~ 1e36 erg/s is achieved weeks-months prior to merger, after which the stellar surface is enshrouded by an outflow. The final inspiral is accompanied by an optical transient powered by the recombination of hydrogen in the outflow, which peaks at L~1e37-38 erg/s on a timescale ~days. If instead rho_planet/rho_star < 5, then Roche Lobe overflow occurs above the stellar surface. For rho_p/rho_star < 1, mass transfer is stable, resulting the planet being accreted on a relatively slow timescale. However, for 1 < rho_p/rho_star < 5, mass transfer may instead be unstable, resulting in the planet being dynamically disrupted into an accretion disk around the star. Super-Eddington outflows from the disk power an optical transient with L~1e37-38 erg/s and characteristic duration ~week-months. The disk itself becomes visible once the accretion rate become sub-Eddington, resulting in a bolometric brightening and spectral shift to the UV. Optical transients from planet merger events may resemble classical novae, but are distinguished by lower ejecta mass and velocity ~100s km/s, and by hard pre- and post-cursor emission, respectively. Promising search strategies include combined optical, UV, and X-ray surveys of nearby massive galaxies with cadences from days to months.Comment: 20 pages, 11 figures, 2 tables, submitted to MNRA

Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential

We consider a system of particles interacting via a screened Newtonian potential and study phase transitions between homogeneous and inhomogeneous states in the microcanonical and canonical ensembles. Like for other systems with long-range interactions, we obtain a great diversity of microcanonical and canonical phase transitions depending on the dimension of space and on the importance of the screening length. We also consider a system of particles in Newtonian interaction in the presence of a ``neutralizing background''. By a proper interpretation of the parameters, our study describes (i) self-gravitating systems in a cosmological setting, and (ii) chemotaxis of bacterial populations in the original Keller-Segel model

Disequilibrium Carbon, Oxygen, and Nitrogen Chemistry in the Atmospheres of HD 189733b and HD 209458b

We have developed 1-D photochemical and thermochemical kinetics and diffusion models for the transiting exoplanets HD 189733b and HD 209458b to study the effects of disequilibrium chemistry on the atmospheric composition of "hot Jupiters." Here we investigate the coupled chemistry of neutral carbon, hydrogen, oxygen, and nitrogen species, and we compare the model results with existing transit and eclipse observations. We find that the vertical profiles of molecular constituents are significantly affected by transport-induced quenching and photochemistry, particularly on cooler HD 189733b; however, the warmer stratospheric temperatures on HD 209458b can help maintain thermochemical equilibrium and reduce the effects of disequilibrium chemistry. For both planets, the methane and ammonia mole fractions are found to be enhanced over their equilibrium values at pressures of a few bar to less than a mbar due to transport-induced quenching, but CH4 and NH3 are photochemically removed at higher altitudes. Atomic species, unsaturated hydrocarbons (particularly C2H2), some nitriles (particularly HCN), and radicals like OH, CH3, and NH2 are enhanced overequilibrium predictions because of quenching and photochemistry. In contrast, CO, H2O, N2, and CO2 more closely follow their equilibrium profiles, except at pressures < 1 microbar, where CO, H2O, and N2 are photochemically destroyed and CO2 is produced before its eventual high-altitude destruction. The enhanced abundances of HCN, CH4, and NH3 in particular are expected to affect the spectral signatures and thermal profiles HD 189733b and other, relatively cool, close-in transiting exoplanets. We examine the sensitivity of our results to the assumed temperature structure and eddy diffusion coefficientss and discuss further observational consequences of these models.Comment: 40 pages, 16 figures, accepted for publication in Astrophysical Journa