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

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

Decreasing Atmospheric CO2 During the Late Miocene Cooling

A pronounced late Miocene cooling (LMC) from ~7 to 5.7 Ma has been documented in extratropical and tropical sea surface temperature records, but to date, available proxy evidence has not revealed a significant pCO2 decline over this event. Here, we provide a new, high‐resolution pCO2 proxy record over the LMC based on alkenone carbon isotopic fractionation (εp) measured in sediments from the South Atlantic at Ocean Drilling Program (ODP) Site 1088. We apply a recent proxy calibration derived from a compilation of laboratory cultures, which more accurately reflects the proxy sensitivity to pCO2 changes during late Quaternary glacial‐interglacial cycles, together with new micropaleontological proxies to reconstruct past variations in algal growth rate, an important secondary influence on the εp. Our resulting pCO2 record suggests an approximately twofold to threefold decline over the LMC and confirms a strong coupling between climate and pCO2 through the late Miocene. Within this long‐term trend are pCO2 variations on sub‐myr timescales that may reflect 400‐kyr long‐eccentricity cycles, in which pCO2 minima coincide with several orbital‐scale maxima in published high‐resolution benthic δ18O records. These may correspond to ephemeral glaciations, potentially in the Northern Hemisphere. Our temperature and planktonic δ18O records from Site 1088 are consistent with substantial equatorward movement of Southern Ocean frontal systems during the LMC. This suggests that potential feedbacks between cooling, ocean circulation and deep ocean CO2 storage may warrant further investigation during the LMC

Ponderal Somatogram Analysis of Girth Measurements by Position in Division III College Football Players

Ponderal somatograms assessed body compositions in four groups of Division III collegiate football players: offensive line (OL), defensive line (DL), offensive backs (OB), and defensive backs (DB). Ponderal somatograms evaluate body size and shape by converting muscular (shoulders, chest, biceps, forearm, thigh, and calf) and nonmuscular (abdomen, hips knee, ankle, and wrist) girths into ponderal equivalent (PE) values. Anthropometric measurements, including stature, body mass, girths, and percent body fat by densitometry were collected in 82 players (22 OL, 12 DL, 20 OB, and 28 DB) during preseason camp. PE values were calculated for each girth as PE, kilograms = (girth, cm / k)sq. x stature, decimeters, where k=k constant from Behnke\u27s reference man. PE values were compared to body mass to indicate overdevelopment (PE greater than body mass) and underdevelopment (PE less than body mass). OL was significantly heavier than DL (+15.6 kg), OB (+25.2 kg), and DB (+22.4 kg). OL percent fat as significantly greater than DL (+5.9%), OB (+9.0%), and DB (+9.3%). Similar differences occurred in girths and PE values by position. Muscular components were generally overdeveloped, with the greatest overdevelopment in the biceps (OL + 16.0 kg, DL + 19 kg, OB + 14.2 kg, and DB + 16.2 kg). Nonmuscular abdomen, hips, and knee were generally overdeveloped, with the greatest overdevelopment in the OL abdomen (+19.3 kg). Nonmuscular ankle and wrist were underdeveloped. Ponderal somatograms provide a relatively quick and simple method to translate girth measurements into ponderal equivalent values that seem to be position-specific among offensive and defensive linemen and backs. Somatograms provide an appraisal of body composition that helps coaches and athletes monitor the effectiveness of strength and conditioning programs

Ponderal Somatograms Assess Changes in Anthropometric Measurements Over an Academic Year in Division III Collegiate Football Players

Ponderal somatograms evaluate body size and shape by converting muscular (shoulders, chest, biceps, forearm, thigh, calf) and nonmuscular (abdomen, hips, knee, ankle, wrist) girths into ponderal equivalent (PE) values. Anthropometric measurements, including stature, body mass, girths, and percent body fat by densitometry were collected in 54 Division III football players in preseason camp (fall) and at the beginning (winter) and end (spring) of the team strength and conditioning program. PE values were calculated for each girth as PE, kg = (girth, cm / k) squared x stature, dm, where k = k constant from Behnke\u27s reference man. PE values were compared to body mass to indicate overdevelopment (PE is greater than body mass) and underdevelopment (PE is less than body mass) at specific girth sites. From fall to winter, body mass (+1.6 kg), percent fat (+1.3%), fat mass (+1.6 kg), nonmuscular abdominal and hip girths (+2.1 cm, +1.5 cm), and PE values (+5.3 kg, +2.6 kg) increased significantly (p is less than 0.05). From winter to spring, percent fat (-1.5%), fat mass (-1.4 kg), nonmuscular abdominal girth (-1.0 co), and PE value (-2.5 kg) decreased significantly (p is less than 0.05) from winter to spring. Fat-free mass (+1.5 kg), muscular biceps girth (+0.4 cm), and PE value (+2.6 kg) increased significantly (p is less than 0.05) from winter to spring. Ponderal somatograms muscular components were generally overdeveloped, with the greatest overdevelopment at the biceps in the fall (+14.7 kg), winter (+14.9 kg), and spring (+17.4 kg). Nonmuscular components generally were underdeveloped, except abdomen and hips that were overdeveloped. The abdomen remained the greatest nonmuscular overdevelopment in fall (+6.8 kg), winter (+10.5 kg), and spring (+7.9 kg). Ponderal somatograms provide a relatively simple, practical method to track specific changes in body size and shape over time

Nonthermal Emission from a Supernova Remnant in a Molecular Cloud

In evolved supernova remnants (SNRs) interacting with molecular clouds, such as IC 443, W44, and 3C391, a highly inhomogeneous structure consisting of a forward shock of moderate Mach number, a cooling layer, a dense radiative shell and an interior region filled with hot tenuous plasma is expected. We present a kinetic model of nonthermal electron injection, acceleration and propagation in that environment and find that these SNRs are efficient electron accelerators and sources of hard X- and gamma-ray emission. The energy spectrum of the nonthermal electrons is shaped by the joint action of first and second order Fermi acceleration in a turbulent plasma with substantial Coulomb losses. Bremsstrahlung, synchrotron, and inverse Compton radiation of the nonthermal electrons produce multiwavelength photon spectra in quantitative agreement with the radio and the hard emission observed by ASCA and EGRET from IC 443. We distinguish interclump shock wave emission from molecular clump shock wave emission accounting for a complex structure of molecular cloud. Spatially resolved X- and gamma- ray spectra from the supernova remnants IC 443, W44, and 3C391 as might be observed with BeppoSAX, Chandra XRO, XMM, INTEGRAL and GLAST would distinguish the contribution of the energetic lepton component to the gamma-rays observed by EGRET.Comment: 14 pages, 4 figure, Astrophysical Journal, v.538, 2000 (in press

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

Density and Richness of Benthic Invertebrate Populations in the North Sydenham River of Southwestern Ontario (1996-2000) Compared with Those of the St. Clair River (1990-1995)

Richness (the number of invertebrate families/sample site) and density (the number of invertebrates/sq m) of benthic populations in the North Sydenham River were measured and compared with similar estimates for the St. Clair River. Seventeen sample sites were examined from May to October over five consecutive years. At each sample site, particle size distribution of the sediment, sediment temperature, total phosphorous, total nitrogen, total carbon, and water flow rate were measured. Physical and chemical characteristics of the North Sydenham system over the 100 km run examined were less variable than those of the St. Clair. Statistically significant but weak multiple linear correlations were found for richness and density with several of the measured variables. Invertebrate populations in the North Sydenham River were less rich and less dense than those in the downstream reach of the St. Clair and exhibited a different distribution of abundance among the orders of organisms. As in the St. Clair River, some evidence of long term cycling of abundance in several families of invertebrates was found in the North Sydenham

Rayleigh-Taylor Instabilities in Young Supernova Remnants Undergoing Efficient Particle Acceleration

We employ hydrodynamic simulations to study the effects of high shock compression ratios, as expected for fast shocks with efficient particle acceleration, on the convective instability of driven waves in supernova remnants. We find that the instability itself does not depend significantly on the compression ratio, but because the width of the interaction region between the forward and reverse shocks can shrink significantly with increasing shock compression, we find that convective instabilities can reach all the way to the forward shock front if compression ratios are high enough.Comment: Submitted to The Astrophysical Journa