We investigate the physical characteristics of the solar system’s proposed Planet Nine using modeling tools with a heritage of studying Uranus and Neptune. For a range of plausible masses and interior structures, we find upper limits on the intrinsic T eff , from ∼35 to 50 K for masses of 5–20 M _⊕, and we also explore lower T eff values. Possible planetary radii could readily span from 2.7 to 6 R _⊕, depending on the mass fraction of any H/He envelope. Given its cold atmospheric temperatures, the planet encounters significant methane condensation, which dramatically alters the atmosphere away from simple Neptune-like expectations. We find that the atmosphere is strongly depleted in molecular absorption at visible wavelengths, suggesting a Rayleigh scattering atmosphere with a high geometric albedo approaching 0.75. We highlight two diagnostics for the atmosphere’s temperature structure: (1) the value of the methane mixing ratio above the methane cloud and (2) the wavelength at which cloud scattering can be seen, which yields the cloud-top pressure. Surface reflection may be seen if the atmosphere is thin. Due to collision-induced opacity of H₂ in the infrared, the planet would be extremely blue instead of red in the shortest wavelength WISE colors if methane is depleted and would, in some cases, exist on the verge of detectability by WISE. For a range of models, thermal fluxes from ∼3 to 5 μm are ∼20 orders of magnitude larger than blackbody expectations. We report a search of the AllWISE Source Catalog for Planet Nine, but find no detection.

The far-ultraviolet magnitudes of late-F, G and early-K dwarfs with (B − V) ⩾ 0.50 as measured by the GALEX satellite are shown to correlate with soft X-ray luminosity. This result indicates that line and continuum emission from stellar active regions make significant contributions to the flux in the GALEX FUV band for late-F, G and K dwarfs. By contrast, detection of a correlation between FUV brightness and soft X-ray luminosity among early-F dwarfs requires subtraction of the photospheric component from the FUV flux. The range in (B − V) among F and G dwarfs over which a correlation between uncorrected FUV magnitude and X-ray luminosity is detected coincides with the range in colour over which coronal and chromospheric emission correlates with stellar rotation.

Implicit in the RNA world hypothesis is that prebiotic RNA synthesis, despite occurring in an environment without biochemical catalysts, produced the long RNA polymers which are essential to the formation of life. In order to investigate the prebiotic formation of long RNA polymers, we consider a general solution of functionally identical monomer units that are capable of bonding to form linear polymers by a step-growth process. Under the assumptions that (1) the solution is well-mixed and (2) bonding/unbonding rates are independent of polymerization state, the concentration of each length of polymer follows the geometric Flory-Schulz distribution. We consider the rate dynamics that produce this equilibrium; connect the rate dynamics, Gibbs free energy of bond formation, and the bonding probability; solve the dynamics in closed form for the representative special case of a Flory-Schulz initial condition; and demonstrate the effects of imposing a maximum polymer length. Afterwards, we derive a lower bound on the error introduced by truncation and compare this lower bound to the actual error found in our simulation. Finally, we suggest methods to connect these theoretical predictions to experimental results.

Implicit in the RNA world hypothesis is that prebiotic RNA synthesis, despite occurring in an environment without biochemical catalysts, produced the long RNA polymers which are essential to the formation of life. In order to investigate the prebiotic formation of long RNA polymers, we consider a general solution of functionally identical monomer units that are capable of bonding to form linear polymers by a step-growth process. Under the assumptions that (1) the solution is well-mixed and (2) bonding/unbonding rates are independent of polymerization state, the concentration of each length of polymer follows the geometric Flory-Schulz distribution. We consider the rate dynamics that produce this equilibrium; connect the rate dynamics, Gibbs free energy of bond formation, and the bonding probability; solve the dynamics in closed form for the representative special case of a Flory-Schulz initial condition; and demonstrate the effects of imposing a maximum polymer length. Afterwards, we derive a lower bound on the error introduced by truncation and compare this lower bound to the actual error found in our simulation. Finally, we suggest methods to connect these theoretical predictions to experimental results.