A Time-Dependent Radiative Model of HD209458b

We present a time-dependent radiative model of the atmosphere of HD209458b and investigate its thermal structure and chemical composition. In a first step, the stellar heating profile and radiative timescales were calculated under planet-averaged insolation conditions. We find that 99.99% of the incoming stellar flux has been absorbed before reaching the 7 bar level. Stellar photons cannot therefore penetrate deeply enough to explain the large radius of the planet. We derive a radiative time constant which increases with depth and reaches about 8 hr at 0.1 bar and 2.3 days at 1 bar. Time-dependent temperature profiles were also calculated, in the limit of a zonal wind that is independent on height (i.e. solid-body rotation) and constant absorption coefficients. We predict day-night variations of the effective temperature of \~600 K, for an equatorial rotation rate of 1 km/s, in good agreement with the predictions by Showman &Guillot (2002). This rotation rate yields day-to-night temperature variations in excess of 600 K above the 0.1-bar level. These variations rapidly decrease with depth below the 1-bar level and become negligible below the ~5--bar level for rotation rates of at least 0.5 km/s. At high altitudes (mbar pressures or less), the night temperatures are low enough to allow sodium to condense into Na2S. Synthetic transit spectra of the visible Na doublet show a much weaker sodium absorption on the morning limb than on the evening limb. The calculated dimming of the sodium feature during planetary transites agrees with the value reported by Charbonneau et al. (2002).Comment: 9 pages, 8 figures, replaced with the revised versio

New Questions on Legal Education

Periodically, Cleveland-Marshall Law Review asks prominent legal educators for their views on current problems in legal education. Here are the responses to our most recent survey. The comments are not intended to be comprehensive or definitive, but they reflect significant attitudes of outstanding scholars on important educational issues

New Questions on Legal Education

Periodically, Cleveland-Marshall Law Review asks prominent legal educators for their views on current problems in legal education. Here are the responses to our most recent survey. The comments are not intended to be comprehensive or definitive, but they reflect significant attitudes of outstanding scholars on important educational issues

Satellite on-board processing for earth resources data

Results of a survey of earth resources user applications and their data requirements, earth resources multispectral scanner sensor technology, and preprocessing algorithms for correcting the sensor outputs and for data bulk reduction are presented along with a candidate data format. Computational requirements required to implement the data analysis algorithms are included along with a review of computer architectures and organizations. Computer architectures capable of handling the algorithm computational requirements are suggested and the environmental effects of an on-board processor discussed. By relating performance parameters to the system requirements of each of the user requirements the feasibility of on-board processing is determined for each user. A tradeoff analysis is performed to determine the sensitivity of results to each of the system parameters. Significant results and conclusions are discussed, and recommendations are presented

Satellite on-board processing for earth resources data

The feasibility was investigated of an on-board earth resources data processor launched during the 1980-1990 time frame. Projected user applications were studied to define the data formats and the information extraction algorithms that the processor must execute. Based on these constraints, and the constraints imposed by the available technology, on-board processor systems were designed and their feasibility evaluated. Conclusions and recommendations are given

Dark Stars: the First Stars in the Universe may be powered by Dark Matter Heating

A new line of research on Dark Stars is reviewed, which suggests that the first stars to exist in the universe were powered by dark matter heating rather than by fusion. Weakly Interacting Massive Particles, which may be there own antipartmers, collect inside the first stars and annihilate to produce a heat source that can power the stars. A new stellar phase results, a Dark Star, powered by dark matter annihilation as long as there is dark matter fuel.Comment: 6 pages, Eighth UCLA Symposium: Sources and Detection of Dark Matter and Dark Energy in the Universe, proceeding

Giant Planet Formation: A First Classification of Isothermal Protoplanetary Equilibria

We present a model for the equilibrium of solid planetary cores embedded in a gaseous nebula. From this model we are able to extract an idealized roadmap of all hydrostatic states of the isothermal protoplanets. The complete classification of the isothermal protoplanetary equilibria should improve the understanding of the general problem of giant planet formation, within the framework of the nucleated instability hypothesis. We approximate the protoplanet as a spherically symmetric, isothermal, self-gravitating classical ideal gas envelope in equilibrium, around a rigid body of given mass and density, with the gaseous envelope required to fill the Hill-sphere. Starting only with a core of given mass and an envelope gas density at the core surface, the equilibria are calculated without prescribing the total protoplanetary mass or nebula density. The static critical core masses of the protoplanets for the typical orbits of 1, 5.2, and 30 AU, around a parent star of 1 solar mass are found to be 0.1524, 0.0948, and 0.0335 Earth masses, respectively, for standard nebula conditions (Kusaka et al. 1970). These values are much lower than currently admitted ones primarily because our model is isothermal and the envelope is in thermal equilibrium with the nebula. For a given core, multiple solutions (at least two) are found to fit into the same nebula. We extend the concept of the static critical core mass to the local and global critical core mass. We conclude that the 'global static critical core mass' marks the meeting point of all four qualitatively different envelope regions.Comment: 13 pages, 15 figure

Factors Affecting the Radii of Close-in Transiting Exoplanets

The radius of an exoplanet may be affected by various factors, including irradiation, planet mass and heavy element content. A significant number of transiting exoplanets have now been discovered for which the mass, radius, semi-major axis, host star metallicity and stellar effective temperature are known. We use multivariate regression models to determine the dependence of planetary radius on planetary equilibrium temperature T_eq, planetary mass M_p, stellar metallicity [Fe/H], orbital semi-major axis a, and tidal heating rate H_tidal, for 119 transiting planets in three distinct mass regimes. We determine that heating leads to larger planet radii, as expected, increasing mass leads to increased or decreased radii of low-mass (<0.5R_J) and high-mass (>2.0R_J) planets, respectively (with no mass effect on Jupiter-mass planets), and increased host-star metallicity leads to smaller planetary radii, indicating a relationship between host-star metallicity and planet heavy element content. For Saturn-mass planets, a good fit to the radii may be obtained from log(R_p/R_J)=-0.077+0.450 log(M_p/M_J)-0.314[Fe/H]+0.671 log(a/AU)+0.398 log(T_eq/K). The radii of Jupiter-mass planets may be fit by log(R_p/R_J)=-2.217+0.856 log(T_eq/K)+0.291 log(a/AU). High-mass planets' radii are best fit by log(R_p/R_J)=-1.067+0.380 log(T_eq/K)-0.093 log(M_p/M_J)-0.057[Fe/H]+0.019 log(H_tidal/1x10^{20}). These equations produce a very good fit to the observed radii, with a mean absolute difference between fitted and observed radius of 0.11R_J. A clear distinction is seen between the core-dominated Saturn-mass (0.1-0.5M_J) planets, whose radii are determined almost exclusively by their mass and heavy element content, and the gaseous envelope-dominated Jupiter-mass (0.5-2.0M_J) planets, whose radii increase strongly with irradiating flux, partially offset by a power-law dependence on orbital separation.Comment: 14 pages, 14 figures, accepted in A&

Turbulent Molecular Cloud Cores: Rotational Properties

The rotational properties of centrally condensed, turbulent molecular cloud cores with velocity fields that are characterized by Gaussian random fields are investigated. It is shown that the observed line width-size relationship can be reproduced if the velocity power spectrum is a power-law with P(k)=k**n and n=-3 to -4. The line-of-sight velocity maps of these cores show velocity gradients that can be interpreted as rotation. For n=-4, both, the deduced values of the angular velocity Omega=1.6 km/s/pc * (R/0.1 pc)**0.5 and the scaling relations between Omega and the core radius R are in very good agreement with the observations. As a result of the dominance of long wavelength modes, the cores also have a net specific angular momentum with an average value of j=7*(10**20)*(R/0.1 pc)**(1.5) cm**2/s with a large spread. Their internal dimensionless rotational parameter is beta=0.03, independent of the scale radius R. In general, the line-of-sight velocity gradient of an individual turbulent core does not provide a good estimate of its internal specific angular momentum. We find however that the distribution of the specific angular momenta of a large sample of cores which are described by the same power spectrum can be determined very accurately from the distribution of their line-of-sight velocity gradients Omega using the simple formula j=p*Omega*R*R where p depends on the density distribution of the core and has to be determined from a Monte-Carlo study. Our results show that for centrally condensed cores the intrinsic angular momentum is overestimated by a factor of 2-3 if p=0.4 is used.Comment: 23 pages, 7 figures, Astrophysical Journal, in pres

Structure and evolution of the first CoRoT exoplanets: Probing the Brown Dwarf/Planet overlapping mass regime

We present detailed structure and evolution calculations for the first transiting extrasolar planets discovered by the space-based CoRoT mission. Comparisons between theoretical and observed radii provide information on the internal composition of the CoRoT objects. We distinguish three different categories of planets emerging from these discoveries and from previous ground-based surveys: (i) planets explained by standard planetary models including irradiation, (ii) abnormally bloated planets and (iii) massive objects belonging to the overlapping mass regime between planets and brown dwarfs. For the second category, we show that tidal heating can explain the relevant CoRoT objects, providing non-zero eccentricities. We stress that the usual assumption of a quick circularization of the orbit by tides, as usually done in transit light curve analysis, is not justified a priori, as suggested recently by Levrard et al. (2009), and that eccentricity analysis should be carefully redone for some observations. Finally, special attention is devoted to CoRoT-3b and to the identification of its very nature: giant planet or brown dwarf ? The radius determination of this object confirms the theoretical mass-radius predictions for gaseous bodies in the substellar regime but, given the present observational uncertainties, does not allow an unambiguous identification of its very nature. This opens the avenue, however, to an observational identification of these two distinct astrophysical populations, brown dwarfs and giant planets, in their overlapping mass range, as done for the case of the 8 Jupiter-mass object Hat-P-2b. (abridged)Comment: 6 pages, 5 figures, accepted for publication in Astronomy and Astrophysic