Neutrino transport in accretion disks

We test approximate approaches to solving a neutrino transport problem that presents itself in the analysis of some accretion-disk models. Approximation #1 consists of replacing the full, angular- dependent, distribution function by a two-stream simulation, where the streams are respectively outwardly and inwardly directed, with angles $\cos \theta=\pm 1/\sqrt{3}$ to the vertical. In this approximation the full energy dependence of the distribution function is retained, as are the energy and temperature dependences of the scattering rates. Approximation #2, used in recent works on the subject, replaces the distribution function by an intensity function and the scattering rates by temperature-energy-averaged quantities. We compare the approximations to the results of solving the full Boltzmann equation. Under some interesting conditions, approximation #1 passes the test; approximation #2 does not. We utilize the results of our analysis to construct a toy model of a disc at a temperature and density such that relativistic particles are more abundant than nucleons, and dominate both the opacity and pressure. The nucleons will still provide most of the energy density. In the toy model we take the rate of heat generation (which drives the radiative transfer problem) to be proportional to the nucleon density. The model allows the simultaneous solution of the neutrino transport and hydrostatic equilibrium problems in a disk in which the nucleon density decreases approximately linearly as one moves from the median plane of the disk upwards, reaching zero on the upper boundary.Comment: 8 pages, 5 figures Parentheses added in eqs. 10-1

Charge-conjugation violating neutrino interactions in supernovae

The well known charge conjugation violating interactions in the Standard Model increase neutrino- and decrease anti-neutrino- nucleon cross sections. This impacts neutrino transport in core collapse supernovae through "recoil" corrections of order the neutrino energy $k$ over the nucleon mass $M$. All $k/M$ corrections to neutrino transport deep inside a protoneutron star are calculated from angular integrals of the Boltzmann equation. We find these corrections significantly modify neutrino currents at high temperatures. This produces a large mu and tau number for the protoneutron star and can change the ratio of neutrons to protons. In addition, the relative size of neutrino mean free paths changes. At high temperatures, the electron anti-neutrino mean free path becomes {\it longer} than that for mu or tau neutrinos.Comment: 14 pages, 2 included ps figures, subm. to Phys. Rev.

Differential Neutrino Rates and Emissivities from the Plasma Process in Astrophysical Systems

The differential rates and emissivities of neutrino pairs from an equilibrium plasma are calculated for the wide range of density and temperature encountered in astrophysical systems. New analytical expressions are derived for the differential emissivities which yield total emissivities in full agreement with those previously calculated. The photon and plasmon pair production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are provided. The appropriate Legendre coefficients of these kernels, in forms suitable for multi-group flux-limited diffusion schemes are also computed.Comment: 27 pages and 10 figures. Submitted to Phys. Rev.

Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation

Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure

The photo-neutrino process in astrophysical systems

Explicit expressions for the differential and total rates and emissivities of neutrino pairs from the photo-neutrino process $e^\pm + \gamma \to e^\pm + \nu + \bar\nu$ in hot and dense matter are derived. Full information about the emitted neutrinos is retained by evaluating the squared matrix elements for this process which was hitherto bypassed through the use of Lenard's identity in obtaining the total neutrino emissivities. Accurate numerical results are presented for widely varying conditions of temperature and density. Analytical results helpful in understanding the qualitative behaviors of the rates and emissivities in limiting situations are derived. The corresponding production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are developed. The appropriate Legendre coefficients of these kernels, in forms suitable for multigroup flux-limited diffusion schemes are also provided.Comment: 26 pages and 7 figures. Version as accepted in Phys. Rev. D; three figures and related discussion revise

Human Adult Neurogenesis: Evidence and Remaining Questions

Renewed discussion about whether or not adult neurogenesis exists in the human hippocampus, and the nature and strength of the supporting evidence, has been reignited by two prominently published reports with opposite conclusions. Here, we summarize the state of the field and argue that there is currently no reason to abandon the idea that adult-generated neurons make important functional contributions to neural plasticity and cognition across the human lifespan

The Structure and Dynamics of Titan's Middle Atmosphere and Troposphere

Titan, after Venus, is the second example in the solar system of an atmosphere with a global cyclostrophic circulation. The origin and maintenance of these superrotating atmospheres is not well understood, but Titan has a strong seasonal modulation in the middle atmosphere, and the seasonal changes in the winds may offer clues. The pole in winter and early spring is characterized by temperatures 20-30 K cooler at 140-170 km than those at low latitudes, and strong circumpolar winds as high as 190 m/s at 200- 250 km. At these levels the polar region is characterized by enhanced concentrations of several organic gases, and also detectable condensates. All this suggests that the polar vortex provides a mixing barrier between winter polar and lower-latitude air masses, analogous to the polar ozone holes on Earth. Because the concentrations of organic gases increase with altitude in the middle atmosphere, the observed enhancements suggest subsidence over the winter pole. Consistent with this are the observed temperatures approximately 200 K at the winter-polar stratopause (280 km), making it the warmest part of the atmosphere. The warm stratopause likely results from adiabatic heating associated with the subsidence. Recent observations in late northern winter and early spring indicate that the warm anomaly at the winter-polar stratopause is weakening;. In contrast to the middle atmosphere, latitude contrasts in tropospheric temperatures are muted. During the northern winter season, they were approximately 5 K at the tropopause and 3 K or less near the surface, being coldest at high northern latitudes. This is understandable in terms of the long radiative relaxation times in the troposphere, compared to times that are much shorter than a season in the upper stratosphere and higher. Curiously, the transition between the small meridional contrast (and presumably seasonal variations) in temperatures observed in the troposphere and the large variations observed at higher altitudes occurs abruptly above 80 km. Here the temperatures in the lower stratosphere, generally increasing with altitude, exhibit a sudden drop with increasing altitude at high northern latitudes, producing the contrast between low and high northern winter latitudes in the upper stratosphere described above. While the radiative relaxation time associated with infrared gaseous coolants decreases with altitude in the stratosphere, the abrupt transition suggests the presence of an optically thick condensate at thermal-infrared wavelengths. Near the surface, temperature lapse rates are adiabatic over the lowest 2 km, with the suggestion of a nocturnal stable inversion over the lowest 200 m in radio-occultation soundings near the morning terminator. At mid and high latitudes in both winter and summer hemispheres, the profiles are more statically stable (i.e., subadiabatic). This is most pronounced in the winter hemisphere

Titan's Winter Polar Vortex

Titan's atmosphere has provided an interesting study in contrasts and similarities with Earth's. While both have N$_2$ as the dominant constituent and comparable surface pressures $\sim1$ bar, Titan's next most abundant molecule is CH$_4$, not O$_2$, and the dissociative breakup of CH$_4$ and N$_2$ by sunlight and electron impact leads to a suite of hydrocarbons and nitriles, and ultimately the photochemical smog that enshrouds the moon. In addition, with a 15.95-day period, Titan is a slow rotator compared to Earth. While the mean zonal terrestrial winds are geostrophic, Titan's are mostly cyclostrophic, whipping around the moon in as little as 1 day. Despite the different dynamical regime, Titan's winter stratosphere exhibits several characteristics that should be familiar to terrestrial meteorologists. The cold winter pole near the 1 -mbar level is circumscribed by strong winds (up to 190 m/s) that act as a barrier to mixing with airmasses at lower latitudes. There is evidence of enhancement of several organic species over the winter pole, indicating subsidence. The adiabatic heating associated with this subsidence gives rise to a warm anomaly at the 0.01-mbar level, raising the stratopause two scale heights above its location at equatorial latitudes. Condensate ices have been detected in Titan's lower stratosphere within the winter polar vortex from infrared spectra. Although not always unambiguously identified, their spatial distribution exhibits a sharp gradient, decreasing precipitously across the vortex away from the winter pole. The interesting question of whether there is important heterogeneous chemistry occurring within the polar vortex, analogous to that occurring in the terrestrial polar stratospheric clouds in the ozone holes, has not been addressed. The breakup of Titan's winter polar vortex has not yet been observed. On Earth, the polar vortex is nonlinearly disrupted by interaction with large-amplitude planetary waves. Large-scale waves have not been identified in Titan's atmosphere, so the decay of its polar vortex may be more gradual than on Earth. Observations from an extended Cassini mission into late northern spring should provide critical data indicating whether the vortex goes away with a bang or just fades away