Thermal Structure of Titan's Troposphere and Middle Atmosphere

The thermal structure of Titan's atmosphere is reviewed, with particular emphasis on recent Cassini-Huygens results. Titan's has a similar troposphere-stratosphere-mesosphere pattern like Earth, but with a much more extended atmosphere, because of the weaker gravity, and also much lower temperatures, because of its greater distance from the sun. Titan's atmosphere exhibits an unusually large range in radiative relaxation times. In the troposphere, these are long compared to seasonal time scales, but in the stratosphere they are much shorter than a season. An exception is near the winter pole, where the stratospheric relaxation times at 100-170 km become comparable to the seasonal time scale; at the warm stratopause, they are comparable to a Titan day. Hence, seasonal behavior in the troposphere should be muted, but significant in the stratosphere. This is reflected in the small meridional contrast observed in temperatures in the troposphere and the large stratospheric contrasts noted above. A surprising feature of the vertical profiles of temperature is the abrupt transition between these regimes in at high northern latitudes in winter, where the temperatures in the lower stratosphere exhibit a sudden drop with increasing altitude. This could be a radiative effect, not associated with spatial variations in gaseous opacity, but rather from an optically thick condensate at thermal-infrared wavelengths. A curious aspect of Titan's middle atmosphere is that the axis of symmetry of the temperature field is tilted by several degrees relative to the rotational axis of the moon itself. Whether this is driven by solar heating or gravitational perturbations is not known. Titan's surface exhibits weak contrasts in temperature, approximately 3 K in the winter hemisphere. At low latitudes, there is evidence of a weak nocturnal boundary layer on the morning terminator, which is not radiatively controlled, but can be explained in terms of vertical mixing with a small eddy viscosity

Equatorial Oscillations in Jupiter's and Saturn's Atmospheres

Equatorial oscillations in the zonal-mean temperatures and zonal winds have been well documented in Earth's middle atmosphere. A growing body of evidence from ground-based and Cassini spacecraft observations indicates that such phenomena also occur in the stratospheres of Jupiter and Saturn. Earth-based midinfrared measurements spanning several decades have established that the equatorial stratospheric temperatures on Jupiter vary with a cycle of 4-5 years and on Saturn with a cycle of approximately 15 years. Spectra obtained by the Composite Infrared Spectrometer (CIRS) during the Cassini swingby at the end of 2000, with much better vertical resolution than the ground-based data, indicated a series of vertically stacked warm and cold anomalics at Jupiter's equator; a similar structurc was seen at Saturn's equator in CIRS limb measurements made in 2005, in the early phase of Cassini's orbital tour. The thermal wind equation implied similar patterns of mean zonal winds increasing and decreasing with altitude. On Saturn the peak-to-pcak amplitude of this variation was nearly 200 meters per second. The alternating vertical pattern of wanner and colder cquatorial tcmperatures and easterly and westerly tendencies of the zonal winds is seen in Earth's equatorial oscillations, where the pattern descends with time, The Cassini Jupiter and early Saturn observations were snapshots within a limited time interval, and they did not show the temporal evolution of the spatial patterns. However, more recent Saturn observations by CIRS (2010) and Cassini radio-occultation soundings (2009-2010) have provided an opportunity to follow the change of the temperature-zonal wind pattern, and they suggest there is descent, at a rate of roughly one scale height over four years. On Earth, the observed descent in the zonal-mean structure is associated with the absorption of a combination of vertically propagating waves with easlerly and westerly phase velocities. The peak-to-peak zonal wind amplitude in the oscillation pattern and the rate of descent constrain the absorbed wave flux of zonal momentum. On Saturn this is approximately 0.05 square meters per square seconds, which is comparable to if not greater than that associated with the terrestrial oscillations. We discuss possible candidates for the absorbed waves on Saturn. On Earth the wave forcing of the equatorial oscillation generales secondary circulations that can affcct the temperature and wind structure at latitudes well away from the equator, and we discuss possible evidence of that on Saturn

Can Vertical Profiles of Tropospheric Methane on Titan Be Derived from Radio-Occultation Soundings?

The intensity of the received signal at Earth in the radio occultations of Titan is attenuated both by refractive defocusing and pressure-induced absorption from N2-N2 and CH4-N2 pairs. Because the absorption strength is different for the two sets of pairs, matching the retrieved absorptivity profile can in principle yield the vertical variation in gaseous methane in the troposphere. There are two factors that make this difficult. The first is the propagation of noise in the phase and amplitude of the received signal in the absorption retrieval. The phase data is first inverted to retrieve vertical profiles of refractivity, from which the refractive defocusing is calculated. This is then subtracted from the observed. intensity attenuation of the received signal to generate a profile of atmospheric absorption. The second problem is the uncertainty in the pressure-induced absorption coefficients. Laboratory data at radio wavelengths is only available near room temperature (see, e.g., [1] for N2-N2), and the extrapolation to the low temperatures in Titan's troposphere is not well established. Ab initio calculations by Borysow et al. [2, 3] provide absorption coefficients at low temperatures and long wavelengths, but their accuracy has come into question. We present examples from Cassini radio occultations of Titan to illustrate the difficulties. For methane mole fractions in the lower troposphere comparable to that inferred from the Huygens probe (approximately 0.05), it will be difficult to separate the contributions of N2-N2 collisions from those of N2-CH4, collisions to the retrieved absorption. However, higher concentrations of CH4 and/or a higher signal-to-noise ratio from a future uplink experiment could result in a successful separation of the two components. However, key to this are highly accurate estimates of the absorption from a combination of laboratory measurements at love temperatures and long wavelengths, and possibly improved theoretical calculations

Pulsar kicks from neutrino oscillations

Neutrino oscillations can explain the observed motion of pulsars. We show that two different models of neutrino emission from a cooling neutron star are in good quantitative agreement and predict the same order of magnitude for the pulsar kick velocity, consistent with the data.Comment: revtex; 4 page

Three Dimensional Numerical General Relativistic Hydrodynamics I: Formulations, Methods, and Code Tests

This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and convergence of our general relativistic hydrodynamic treatment and its coupling to the spacetime evolutions described by the full set of Einstein equations with a perfect fluid source. The numerical treatment of the general relativistic hydrodynamic equations is based on high resolution shock capturing schemes. These schemes rely on the characteristic information of the system. A spectral decomposition for general relativistic hydrodynamics suitable for a general spacetime metric is presented. Evolutions based on three different approximate Riemann solvers coupled to four different discretizations of the Einstein equations are studied and compared. The coupling between the hydrodynamics and the spacetime (the right and left hand side of the Einstein equations) is carried out in a treatment which is second order accurate in {\it both} space and time. Convergence tests for all twelve combinations with a variety of test beds are studied, showing consistency with the differential equations and correct convergence properties. The test-beds examined include shocktubes, Friedmann-Robertson-Walker cosmology tests, evolutions of self-gravitating compact (TOV) stars, and evolutions of relativistically boosted TOV stars. Special attention is paid to the numerical evolution of strongly gravitating objects, e.g., neutron stars, in the full theory of general relativity, including a simple, yet effective treatment for the surface region of the star (where the rest mass density is abruptly dropping to zero).Comment: 45 pages RevTeX, 34 figure

A New Algorithm for Supernova Neutrino Transport and Some Applications

We have developed an implicit, multi-group, time-dependent, spherical neutrino transport code based on the Feautrier variables, the tangent-ray method, and accelerated ${\bf \Lambda}$ iteration. The code achieves high angular resolution, is good to O($v/c$), is equivalent to a Boltzmann solver (without gravitational redshifts), and solves the transport equation at all optical depths with precision. In this paper, we present our formulation of the relevant numerics and microphysics and explore protoneutron star atmospheres for snapshot post-bounce models. Our major focus is on spectra, neutrino-matter heating rates, Eddington factors, angular distributions, and phase-space occupancies. In addition, we investigate the influence on neutrino spectra and heating of final-state electron blocking, stimulated absorption, velocity terms in the transport equation, neutrino-nucleon scattering asymmetry, and weak magnetism and recoil effects. Furthermore, we compare the emergent spectra and heating rates obtained using full transport with those obtained using representative flux-limited transport formulations to gauge their accuracy and viability. Finally, we derive useful formulae for the neutrino source strength due to nucleon-nucleon bremsstrahlung and determine bremsstrahlung's influence on the emergent $\nu_{\mu}$ and $\nu_{\tau}$ neutrino spectra.Comment: 58 pages, single-spaced LaTeX, 23 figures, revised title, also available at http://jupiter.as.arizona.edu/~burrows/papers, accepted for publication in the Ap.

Numerical Evolution of General Relativistic Voids

In this paper, we study the evolution of a relativistic, superhorizon-sized void embedded in a Friedmann-Robertson-Walker universe. We numerically solve the spherically symmetric general relativistic equations in comoving, synchronous coordinates. Initially, the fluid inside the void is taken to be homogeneous and nonexpanding. In a radiation- dominated universe, we find that radiation diffuses into the void at approximately the speed of light as a strong shock---the void collapses. We also find the surprising result that the cosmic collapse time (the $1^{\rm st}$-crossing time) is much smaller than previously thought, because it depends not only on the radius of the void, but also on the ratio of the temperature inside the void to that outside. If the ratio of the initial void radius to the outside Hubble radius is less than the ratio of the outside temperature to that inside, then the collapse occurs in less than the outside Hubble time. Thus, superhorizon-sized relativistic void may thermalize and homogenize relatively quickly. These new simulations revise the current picture of superhorizon-sized void evolution after first-order inflation.Comment: 37 pages plus 12 figures (upon request-- [email protected]) LaTeX, FNAL-PUB-93/005-

General Relativistic Effects in the Core Collapse Supernova Mechanism

We apply our recently developed code for spherically symmetric, fully general relativistic (GR) Lagrangian hydrodynamics and multigroup flux-limited diffusion neutrino transport to examine the effects of GR on the hydrodynamics and transport during collapse, bounce, and the critical shock reheating phase of core collapse supernovae. Comparisons of models computed with GR versus Newtonian hydrodynamics show that collapse to bounce takes slightly less time in the GR limit, and that the shock propagates slightly farther out in radius before receding. After a secondary quasistatic rise in the shock radius, the shock radius declines considerably more rapidly in the GR simulations than in the corresponding Newtonian simulations. During the shock reheating phase, core collapse computed with GR hydrodynamics results in a substantially more compact structure from the center out to the stagnated shock. The inflow speed of material behind the shock is also increased. Comparisons also show that the luminosity and rms energy of any neutrino flavor during the shock reheating phase increases when switching from Newtonian to GR hydrodynamics, and decreases when switching from Newtonian to GR transport. This latter decrease in neutrino luminosities and rms energies is less in magnitude than the increase that arise when switching from Newtonian to GR hydrodynamics, with the result that a fully GR simulation gives higher neutrino luminosities and harder neutrino spectra than a fully Newtonian simulation of the same precollapse model.Comment: 35 pages, 23 figure

Neutrino - nucleon reaction rates in the supernova core in the relativistic random phase approximation

In view of the application to supernova simulations, we calculate neutrino reaction rates with nucleons via the neutral and charged currents in the supernova core in the relativistic random phase approximation (RPA) and study their effects on the opacity of the supernova core. The formulation is based on the Lagrangian employed in the calculation of nuclear equation of state (EOS) in the relativistic mean field theory (RMF). The nonlinear meson terms are treated appropriately so that the consistency of the density correlation derived in RPA with the thermodynamic derivative obtained from EOS by RMF is satisfied in the static and long wave length limit. We employ pion and rho meson exchange interactions together with the phenomenological Landau-Migdal parameters for the isospin-dependent nuclear interactions. We find that both the charged and neutral current reaction rates are suppressed from the standard Bruenn's approximate formula considerably in the high density regime. In the low density regime, on the other hand, the vector current contribution to the neutrino-nucleon scattering rate is enhanced in the vicinity of the boundary of the liquid-gas phase transition, while the other contributions are moderately suppressed there also. In the high temperature regime or in the regime where electrons have a large chemical potential, the latter of which is important only for the electron capture process and its inverse process, the recoil of nucleons cannot be neglected and further reduces the reaction rates with respect to the standard approximate formula which discards any energy transfer in the processes. These issues could have a great impact on the neutrino heating mechanism of collapse-driven supernovae.Comment: 16pages, 19figures, submitted to PR