To better understand the observed distributions of rotation rate and magnetic activity of sun-like and low-mass stars, we derive a physically motivated scaling for the dependence of the stellar-wind torque on Rossby number. The torque also contains a
n empirically-derived scaling with stellar mass (and radius), which provides new insight into the mass-dependence of stellar magnetic and wind properties. We demonstrate that this new formulation explains why the lowest mass stars are observed to maintain rapid rotation for much longer than solar-mass stars, and simultaneously, why older populations exhibit a sequence of slowly rotating stars, in which the low-mass stars rotate more slowly than solar-mass stars. The model also reproduces some previously unexplained features in the period-mass diagram for the Kepler field, notably: the particular shape of the upper envelope of the distribution, suggesting that ~95% of Kepler field stars with measured rotation periods are younger than ~4 Gyr; and the shape of the lower envelope, corresponding to the location where stars transition between magnetically saturated and unsaturated regimes.
The treatment of radiation transport in global circulation models (GCMs) is crucial to correctly describe Earth and exoplanet atmospheric dynamics processes. The two-stream approximation and correlated-k method are currently state-of-the-art approxim
ations applied in both Earth and hot Jupiter GCM radiation schemes to facilitate rapid calculation of fluxes and heating rates. Their accuracy have been tested extensively for Earth-like conditions, but verification of the methods applicability to hot Jupiter-like conditions is lacking in the literature. We are adapting the UK Met Office GCM, the Unified Model (UM), for the study of hot Jupiters, and present in this work the adaptation of the Edwards-Slingo radiation scheme based on the two-stream approximation and the correlated-k method. We discuss the calculation of absorption coefficients from high temperature line lists and highlight the large uncertainty in the pressure-broadened line widths. We compare fluxes and heating rates obtained with our adapted scheme to more accurate discrete ordinate (DO) line-by-line (LbL) calculations ignoring scattering effects. We find that, in most cases, errors stay below 10 % for both heating rates and fluxes using ~ 10 k-coefficients in each band and a diffusivity factor D = 1.66. The two-stream approximation and the correlated-k method both contribute non-negligibly to the total error. We also find that using band-averaged absorption coefficients, which have previously been used in radiative-hydrodynamical simulations of a hot Jupiter, may yield errors of ~ 100 %, and should thus be used with caution.
The determination of Saturns atmospheric noble gas abundances are critical to understanding the formation and evolution of Saturn, and giant planets in general. These measurements can only be performed with an entry probe. A Saturn probe will address
whether enhancement in heavy noble gases, as was found in Jupiter, are a general feature of giant planets, and their ratios will be a powerful constraint on how they form. The helium abundance will show the extent to which helium has phase separated from hydrogen in the planets deep interior. Jupiters striking neon depletion may also be tied to its helium depletion, and must be confirmed or refuted in Saturn. Together with Jupiters measured atmospheric helium abundance, a consistent evolutionary theory for both planets, including helium rain will be possible. We will then be able to calibrate the theory of the evolution of all giant planets, including exoplanets. In addition, high pressure H/He mixtures under giant planet conditions are an important area of condensed matter physics that are beyond the realm of experiment.
Despite the revolution in our knowledge resulting from the detection of planets around mature stars, we know almost nothing about planets orbiting young stars because rapid rotation and active photospheres preclude detection by radial velocities or t
ransits and because direct imaging has barely penetrated the requisite range of high contrast and angular resolution. Of the techniques presently under consideration for the coming decade, only space-based astrometry offers the prospect of discovering gas giants (100 to >> 300 Mearth), lower mass systems such as icy giants (10 to 100 Mearth), and even a few rocky, super-Earths 300 Mearth) orbiting stars ranging in age from 1 to 100 Myr. Astrometry will complement high contrast imaging which should be able to detect gas giants (1~10 MJup) in orbits from a few to a few hundred AU. An astrometric survey in combination with imaging data for a subsample of objects will allow a detailed physical understanding of the formation and evolution of young gas giant planets impossible to achieve by any one technique.
