Cosmic ray diffusive acceleration at shock waves with finite upstream and downstream escape boundaries

In the present paper we discuss the modifications introduced into the first-order Fermi shock acceleration process due to a finite extent of diffusive regions near the shock or due to boundary conditions leading to an increased particle escape upstream and/or downstream the shock. In the considered simple example of the planar shock wave we idealize the escape phenomenon by imposing a particle escape boundary at some distance from the shock. Presence of such a boundary (or boundaries) leads to coupled steepening of the accelerated particle spectrum and decreasing of the acceleration time scale. It allows for a semi-quantitative evaluation and, in some specific cases, also for modelling of the observed steep particle spectra as a result of the first-order Fermi shock acceleration. We also note that the particles close to the upper energy cut-off are younger than the estimate based on the respective acceleration time scale. In Appendix A we present a new time-dependent solution for infinite diffusive regions near the shock allowing for different constant diffusion coefficients upstream and downstream the shock.Comment: LaTeX, 14 pages, 4 postscript figures; Solar Physics (accepted

The Density Spike in Cosmic-Ray-Modified Shocks: Formation, Evolution, and Instability

We examine the formation and evolution of the density enhancement (density spike) that appears downstream of strong, cosmic-ray-modified shocks. This feature results from temporary overcompression of the flow by the combined cosmic-ray shock precursor/gas subshock. Formation of the density spike is expected whenever shock modification by cosmic-ray pressure increases strongly. That occurence may be anticipated for newly generated strong shocks or for cosmic-ray-modified shocks encountering a region of higher external density, for example. The predicted mass density within the spike increases with the shock Mach number and with shocks more dominated by cosmic-ray pressure. We find this spike to be linearly unstable under a modified Rayleigh-Taylor instability criterion at the early stage of its formation. We confirm this instability numerically using two independent codes based on the two-fluid model for cosmic-ray transport. These two-dimensional simulations show that the instability grows impulsively at early stages and then slows down as the gradients of total pressure and gas density decrease. Observational discovery of this unstable density spike behind shocks, possibly through radio emission enhanced by the amplified magnetic fields would provide evidence for the existence of strongly cosmic-ray modified shock structures.Comment: 26 pages in Latex and 6 figures. Accepted to Ap

Probing Nearby CR Accelerators and ISM Turbulence with Milagro Hot Spots

Both the acceleration of cosmic rays (CR) in supernova remnant shocks and their subsequent propagation through the random magnetic field of the Galaxy deem to result in an almost isotropic CR spectrum. Yet the MILAGRO TeV observatory discovered a sharp ($\sim10^{\circ})$ arrival anisotropy of CR nuclei. We suggest a mechanism for producing a weak and narrow CR beam which operates en route to the observer. The key assumption is that CRs are scattered by a strongly anisotropic Alfven wave spectrum formed by the turbulent cascade across the local field direction. The strongest pitch-angle scattering occurs for particles moving almost precisely along the field line. Partly because this direction is also the direction of minimum of the large scale CR angular distribution, the enhanced scattering results in a weak but narrow particle excess. The width, the fractional excess and the maximum momentum of the beam are calculated from a systematic transport theory depending on a single scale $l$ which can be associated with the longest Alfven wave, efficiently scattering the beam. The best match to all the three characteristics of the beam is achieved at $l\sim1$pc. The distance to a possible source of the beam is estimated to be within a few 100pc. Possible approaches to determination of the scale $l$ from the characteristics of the source are discussed. Alternative scenarios of drawing the beam from the galactic CR background are considered. The beam related large scale anisotropic CR component is found to be energy independent which is also consistent with the observations.Comment: 2 figures, ApJ accepted version2 minor changes and correction

Self-Similar Collisionless Shocks

Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution, and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B \propto D^{s_B} with -1<s_B<=0, that the spectrum of accelerated particles is dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation function is \propto x^{2s_B} (for x>>D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing "thermal" particles. We argue that the latter may be considered as infinitely conducting, in which case s_B=0 and the scalings are completely determined (e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non- relativistic shocks such as in supernova remnants, if the upstream magnetic field can be neglected. Self-similarity has important implications for any model of particle acceleration and/or field generation. For example, we show that the diffusion function in the angle \mu of momentum p in diffusive shock acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(p/D), and that a previously suggested model for the generation of large scale magnetic fields through a hierarchical merger of current-filaments should be generalized. A numerical experiment testing our analysis is outlined (Abridged).Comment: 16 pages, 1 figure, accepted for publication in Ap

Late Miocene to Holocene high-resolution eastern equatorial Pacific carbonate records: stratigraphy linked by dissolution and paleoproductivity

Coherent variation in CaCO3 burial is a feature of the Cenozoic eastern equatorial Pacific. Nevertheless, there has been a long-standing ambiguity in whether changes in CaCO3 dissolution or changes in equatorial primary production might cause the variability. Since productivity and dissolution leave distinctive regional signals, a regional synthesis of data using updated age models and high-resolution stratigraphic correlation is an important constraint to distinguish between dissolution and production as factors that cause low CaCO3. Furthermore, the new chronostratigraphy is an important foundation for future paleoceanographic studies. The ability to distinguish between primary production and dissolution is also important to establish a regional carbonate compensation depth (CCD). We report late Miocene to Holocene time series of XRF-derived (X-ray fluorescence) bulk sediment composition and mass accumulation rates (MARs) from eastern equatorial Pacific Integrated Ocean Drilling Program (IODP) sites U1335, U1337, and U1338 and Ocean Drilling Program (ODP) site 849, and we also report bulk-density-derived CaCO3 MARs at ODP sites 848, 850, and 851. We use physical properties, XRF bulk chemical scans, and images along with available chronostratigraphy to intercorrelate records in depth space. We then apply a new equatorial Pacific age model to create correlated age records for the last 8 Myr with resolutions of 1–2 kyr. Large magnitude changes in CaCO3 and bio-SiO2 (biogenic opal) MARs occurred within that time period but clay deposition has remained relatively constant, indicating that changes in Fe deposition from dust is only a secondary feedback to equatorial productivity. Because clay deposition is relatively constant, ratios of CaCO3 % or biogenic SiO2 % to clay emulate changes in biogenic MAR. We define five major Pliocene–Pleistocene low CaCO3 % (PPLC) intervals since 5.3 Ma. Two were caused primarily by high bio-SiO2 burial that diluted CaCO3 (PPLC-2, 1685–2135 ka, and PPLC-5, 4465–4737 ka), while three were caused by enhanced dissolution of CaCO3 (PPLC-1, 51–402 ka, PPLC-3, 2248–2684 ka, and PPLC-4, 2915–4093 ka). Regional patterns of CaCO3 % minima can distinguish between low CaCO3 caused by high diatom bio-SiO2 dilution versus lows caused by high CaCO3 dissolution. CaCO3 dissolution can be confirmed through scanning XRF measurements of Ba. High diatom production causes lowest CaCO3 % within the equatorial high productivity zone, while higher dissolution causes lowest CaCO3 percent at higher latitudes where CaCO3 production is lower. The two diatom production intervals, PPLC-2 and PPLC-5, have different geographic footprints from each other because of regional changes in eastern Pacific nutrient storage after the closure of the Central American Seaway. Because of the regional variability in carbonate production and sedimentation, the carbonate compensation depth (CCD) approach is only useful to examine large changes in CaCO3 dissolution

On the mechanism for breaks in the cosmic ray spectrum

The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on full consistency of the CR acceleration theory with the observations; direct proof is impossible because of the orbit stochasticity of CR particles. Recent observations of a number of galactic SNR strongly support the SNR-CR connection in general and the Fermi mechanism of CR acceleration, in particular. However, many SNR expand into weakly ionized dense gases, and so a significant revision of the mechanism is required to fit the data. We argue that strong ion-neutral collisions in the remnant surrounding lead to the steepening of the energy spectrum of accelerated particles by \emph{exactly one power}. The spectral break is caused by a partial evanescence of Alfven waves that confine particles to the accelerator. The gamma-ray spectrum generated in collisions of the accelerated protons with the ambient gas is also calculated. Using the recent Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that the parent proton spectrum is a classical test particle power law $\propto E^{-2}$, steepening to $E^{-3}$ at $E_{br}\approx7GeV$.Comment: APS talk to appear in PoP, 4 figure

Kinetic approaches to particle acceleration at cosmic ray modified shocks

Kinetic approaches provide an effective description of the process of particle acceleration at shock fronts and allow to take into account the dynamical reaction of the accelerated particles as well as the amplification of the turbulent magnetic field as due to streaming instability. The latter does in turn affect the maximum achievable momentum and thereby the acceleration process itself, in a chain of causality which is typical of non-linear systems. Here we provide a technical description of two of these kinetic approaches and show that they basically lead to the same conclusions. In particular we discuss the effects of shock modification on the spectral shape of the accelerated particles, on the maximum momentum, on the thermodynamic properties of the background fluid and on the escaping and advected fluxes of accelerated particles.Comment: 22 pages, 7 figures, accepted for publication in MNRA