Dynamic Screening and Thermonuclear Reaction Rates

We show that there are no dynamic screening corrections to the Salpeter's enhancement factor in the weak-screening limit.Comment: 7 pages LaTex, no figures, Submitted to Ap

Screening in Thermonuclear Reaction Rates in the Sun

We evaluate the effect of electrostatic screening by ions and electrons on low-Z thermonuclear reactions in the sun. We use a mean field formalism and calculate the electron density of the screening cloud using the appropriate density matrix equation of quantum statistical mechanics. Because of well understood physical effects that are included for the first time in our treatment, the calculated enhancement of reaction rates does not agree with the frequently used interpolation formulae. Our result does agree, within small uncertainties, with Salpeter's weak screening formula. If weak screening is used instead of the commonly employed screening prescription of Graboske et al., the predicted $^8$B neutrino flux is increased by 7% and the predicted chlorine rate is increased by 0.4 SNU.Comment: 15 pages, 1 figure, submitted to ApJ. Acknowledgments, a footnote, and an explanation added. Additional information at www.sns.ias.edu/~jn

Convection-Dominated Accretion Flows

Non-radiating, advection-dominated, accretion flows are convectively unstable. We calculate the two-dimensional (r-theta) structure of such flows assuming that (1) convection transports angular momentum inwards, opposite to normal viscosity and (2) viscous transport by other mechanisms (e.g., magnetic fields) is weak (alpha << 1). Under such conditions convection dominates the dynamics of the accretion flow and leads to a steady state structure that is marginally stable to convection. We show that the marginally stable flow has a constant temperature and rotational velocity on spherical shells, a net flux of energy from small to large radii, zero net accretion rate, and a radial density profile proportional to r^{-1/2}, flatter than the r^{-3/2} profile characteristic of spherical accretion flows. This solution accurately describes the full two-dimensional structure of recent axisymmetric numerical simulations of advection-dominated accretion flows.Comment: final version accepted by ApJ; discussion expanded, references adde

Photon acceleration in variable ultra-relativistic outflows and high-energy spectra of Gamma-Ray Bursts

MeV seed photons produced in shocks in a variable ultra-relativistic outflow gain energy by the Fermi mechanism, because the photons Compton scatter off relativistically colliding shells. The Fermi-modified high-energy photon spectrum has a non-universal slope and a universal cutoff. A significant increase in the total radiative efficiency is possible. In some gamma ray bursts, most of the power might be emitted at the high-energy cutoff for this mechanism, which would be close to 100 MeV for outflows with a mean bulk Lorentz factor of 100.Comment: 8 pages, submitted to ApJ

Turbulence and Particle Heating in Advection-Dominated Accretion Flows

We extend and reconcile recent work on turbulence and particle heating in advection-dominated accretion flows. For approximately equipartition magnetic fields, the turbulence primarily heats the electrons. For weaker magnetic fields, the protons are primarily heated. The division between electron and proton heating occurs between $\beta \sim 5$ and $\beta \sim 100$ (where $\beta$ is the ratio of the gas to the magnetic pressure), depending on unknown details of how Alfv\'en waves are converted into whistlers on scales of the proton Larmor radius. We also discuss the possibility that magnetic reconnection could be a significant source of electron heating.Comment: 17 pages (Latex), incl. 2 Figures; submitted to Ap

Graviton Mass or Cosmological Constant?

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local Lorentz-invariant mass terms Minkowski space is unstable. We start with the Pauli-Fierz (PF) term that is the only local mass term with no ghosts in the linearized approximation. We show that nonlinear completions of the PF Lagrangian give rise to instability of Minkowski space. We continue with the mass terms that are not of a PF type. Although these models are known to have ghosts in the linearized approximations, nonlinear interactions can lead to background change due to which the ghosts are eliminated. In the latter case, however, the graviton perturbations on the new background are not massive. We argue that a consistent theory of a massive graviton on flat space can be formulated in theories with extra dimensions. They require an infinite number of fields or non-local description from a 4D point of view.Comment: 16 pages; references and comments adde

Radiative Efficiency of Collisionless Accretion

Radiative efficiency of a slowly accreting black hole is estimated using a two-temperature model of accretion. The radiative efficiency depends on the magnetic field strength near the Schwarzschild radius. For weak magnetic fields (magnetic energy=equipartition/1000), the low efficiency 0.0001 assumed in some theoretical models might be achieved. For stronger fields, a significant fraction of viscous heat is dissipated by electrons and radiated away resulting in a larger efficiency. At equipartition magnetic fields, we estimate efficiency = of order 10%.Comment: 12 pages, Latex, Submitted to Ap

THE 7 Be ELECTRON CAPTURE RATE IN THE SUN

For solar conditions, we numerically integrate the density matrix equation for a thermal electron in the field of a 7Be ion and other plasma ions and smeared-out electrons. Our results are in agreement with previous calculations that are based on a different physical picture, a picture which postulates the existence of distinct continuum and bound state orbits for electrons. The density matrix calculation of the electron capture rate is independent of the nature of electron states in the solar plasma. To within a 1 % accuracy, the effects of screening can be described at high temperatures by a Salpeter-like factor of exp(−Ze2 /kTRD), which can be derived from the density matrix equation. The total theoretical uncertainty in the electron capture rate is about ±2%. Subject headings: nuclear reactions – 3