Closed-form expressions for particle relative velocities induced by turbulence

In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much shorter than the large eddy overturn time) and are also surprisingly accurate in complete generality (that is, also apply for particles with stopping times comparable to, or much longer than, the large eddy overturn time). We note that some previous studies may have adopted previous simple expressions, which we find to be in error regarding the size dependence in the large particle regime.Comment: 8 pages, accepted as Research Note by A&

Colliding Particles in Highly Turbulent Flows

We discuss relative velocities and the collision rate of small particles suspended in a highly turbulent fluid. In the limit where the viscous damping is very weak, we estimate the relative velocities using the Kolmogorov cascade principle.Comment: 5 pages, no figures, v2 contains additional result

Gamma-ray emission expected from Kepler's SNR

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to investigate the properties of Kepler's SNR and, in particular, to predict the gamma-ray spectrum expected from this SNR. Observations of the nonthermal radio and X-ray emission spectra as well as theoretical constraints for the total supernova (SN) explosion energy E_sn are used to constrain the astronomical and particle acceleration parameters of the system. Under the assumption that Kepler's SN is a type Ia SN we determine for any given explosion energy E_sn and source distance d the mass density of the ambient interstellar medium (ISM) from a fit to the observed SNR size and expansion speed. This makes it possible to make predictions for the expected gamma-ray flux. Exploring the expected distance range we find that for a typical explosion energy E_sn=10^51 erg the expected energy flux of TeV gamma-rays varies from 2x10^{-11} to 10^{-13} erg/(cm^2 s) when the distance changes from d=3.4 kpc to 7 kpc. In all cases the gamma-ray emission is dominated by \pi^0-decay gamma-rays due to nuclear CRs. Therefore Kepler's SNR represents a very promising target for instruments like H.E.S.S., CANGAROO and GLAST. A non-detection of gamma-rays would mean that the actual source distance is larger than 7 kpc.Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics, minor typos correcte

Nonthermal Radiation from Type Ia Supernova Remnants

We present calculations of expected continuum emissions from Sedov-Taylor phase Type Ia supernova remnants (SNRs), using the energy spectra of cosmic ray (CR) electrons and protons from nonlinear diffusive shock acceleration (DSA) simulations. A new, general-purpose radiative process code, Cosmicp, was employed to calculate the radiation expected from CR electrons and protons and their secondary products. These radio, X-ray and gamma-ray emissions are generally consistent with current observations of Type Ia SNRs. The emissions from electrons in these models dominate the radio through X-ray bands. Decays of \pi^0 s from p-p collisions mostly dominate the gamma-ray range, although for a hot, low density ISM case (n_{ISM}=0.003 cm^{-3}), the pion decay contribution is reduced sufficiently to reveal the inverse Compton contribution to TeV gamma-rays. In addition, we present simple scalings for the contributing emission processes to allow a crude exploration of model parameter space, enabling these results to be used more broadly. We also discuss the radial surface brightness profiles expected for these model SNRs in the X-ray and gamma-ray bands.Comment: 37 pages, 7 figures, accepted in MNRA

Variable-range Projection Model for Turbulence-driven Collisions

We discuss the probability distribution of relative speed $\Delta V$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution $P(\Delta V) \sim \exp(-C |\Delta V|^{4/3})$ (for some constant $C$). Our conclusions are supported by numerical simulations and the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesised mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.Comment: 4 pages, 2 figure

Turbulence-induced magnetic fields and the structure of Cosmic Ray modified shocks

We propose a model for Diffusive Shock Acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray streaming instabilities; i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale cosmic ray streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to work are produced through the interactions of the pressure gradient of the cosmic ray precursor and density perturbations in the inflowing fluid. Our estimates show that this mechanism provides fast growth of magnetic field and is very generic. We argue that for supernovae shocks the mechanism is capable of generating upstream magnetic fields that are sufficiently strong for accelerating cosmic rays up to around 10^16 eV. No action of any other mechanism is necessary.Comment: 10 pages, 5 figures, ApJ accepte

Is the giant radio galaxy M 87 a TeV gamma-ray emitter?

For the first time an excess of photons above an energy threshold of 730 GeV from the giant radio galaxy M 87 has been measured at a significance level above 4 σ. The data have been taken during the years 1998 and 1999 with the HEGRA stereoscopic system of 5 imaging atmospheric Cherenkov telescopes. The excess of 107.4 ± 26.8 events above 730 GeV corresponds to an integral flux of 3.3% of the Crab flux or Nγ (E > 730 GeV) = (0.96 ± 0.23) × 10-12 phot cm-2 s-1. M 87 is located at the center of the Virgo cluster of galaxies at a relatively small redshift of z = 0.00436 and is a promising candidate among the class of giant radio galaxies for the emission of TeV γ-radiation. The detection of TeV γ-rays from M 87 - if confirmed - would establish a new class of extragalactic source in this energy regime since all other AGN detected to date at TeV energies are BL Lac type objects.F. A. Aharonian ...G. P. Rowell...et al

Shock Acceleration of Cosmic Rays - a critical review

Motivated by recent unsuccessful efforts to detect the predicted flux of TeV gamma-rays from supernova remnants, we present a critical examination of the theory on which these predictions are based. Three crucial problems are identified: injection, maximum achievable particle energy and spectral index. In each case significant new advances in understanding have been achieved, which cast doubt on prevailing paradigms such as Bohm diffusion and single-fluid MHD. This indicates that more realistic analytical models, backed by more sophisticated numerical techniques should be employed to obtain reliable predictions. Preliminary work on incorporating the effects of anomalous transport suggest that the resulting spectrum should be significantly softer than that predicted by conventional theory.Comment: 8 pages, invited review presented at the 17th ECRS, Lodz, July 2000; to appear in Journal of Physics G: Nuclear and Particle Physic

Tycho Brahe's 1572 supernova as a standard type Ia explosion revealed from its light echo spectrum

Type Ia supernovae (SNe Ia) are thermonuclear explosions of white dwarf stars in close binary systems. They play an important role as cosmological distance indicators and have led to the discovery of the accelerated expansion of the Universe. Among the most important unsolved questions are how the explosion actually proceeds and whether accretion occurs from a companion or via the merging of two white dwarfs. Tycho Brahe's supernova of 1572 (SN 1572) is thought to be one of the best candidates for a SN Ia in the Milky Way. The proximity of the SN 1572 remnant has allowed detailed studies, such as the possible identification of the binary companion, and provides a unique opportunity to test theories of the explosion mechanism and the nature of the progenitor. The determination of the yet unknown exact spectroscopic type of SN 1572 is crucial to relate these results to the diverse population of SNe Ia. Here we report an optical spectrum of Tycho Brahe's supernova near maximum brightness, obtained from a scattered-light echo more than four centuries after the direct light of the explosion swept past Earth. We find that SN 1572 belongs to the majority class of normal SNe Ia. The presence of a strong Ca II IR feature at velocities exceeding 20,000 km/s, which is similar to the previously observed polarized features in other SNe Ia, suggests asphericity in SN 1572.Comment: 15 pages, 3 figures - accepted for publication in Natur

Comparison of Different Methods for Nonlinear Diffusive Shock Acceleration

We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical, Monte Carlo and semi-analytical), even if based on different physical assumptions and implementations, for typical environmental parameters lead to very consistent results in terms of shock hydrodynamics, cosmic ray spectrum and also escaping flux spectrum and anisotropy. Strong points and limits of each approach are also discussed, as a function of the problem one wants to study.Comment: 26 pages, 4 figures, published version (references updated