Cosmic Ray Pressure Research Articles

RE-ACCELERATION OF NON-THERMAL PARTICLES AT WEAK COSMOLOGICAL SHOCK WAVES

We examine diffusive shock acceleration (DSA) of the pre-exisiting as well as freshly injected populations of nonthermal, cosmic-ray (CR) particles at weak cosmological shocks. Assuming simple models for thermal leakage injection and Alfv\'enic drift, we derive analytic, time-dependent solutions for the two populations of CRs accelerated in the test-particle regime. We then compare them with the results from kinetic DSA simulations for shock waves that are expected to form in intracluster media and cluster outskirts in the course of large-scale structure formation. We show that the test-particle solutions provide a good approximation for the pressure and spectrum of CRs accelerated at these weak shocks. Since the injection is extremely inefficient at weak shocks, the pre-existing CR population dominates over the injected population. If the pressure due to pre-existing CR protons is about 5 % of the gas thermal pressure in the upstream flow, the downstream CR pressure can absorb typically a few to 10 % of the shock ram pressure at shocks with the Mach number $M \la 3$. Yet, the re-acceleration of CR electrons can result in a substantial synchrotron emission behind the shock. The enhancement in synchrotron radiation across the shock is estimated to be about a few to several for $M \sim 1.5$ and $10^2-10^3$ for $M \sim 3$, depending on the detail model parameters. The implication of our findings for observed bright radio relics is discussed.

COSMIC-RAY-DOMINATED AGN JETS AND THE FORMATION OF X-RAY CAVITIES IN GALAXY CLUSTERS

It is widely accepted that feedback from active galactic nuclei (AGN) plays a key role in the evolution of gas in groups and clusters of galaxies. Unequivocal evidence comes from quasi-spherical X-ray cavities observed near cluster centers having sizes ranging from a few to tens of kpc, some containing radio emission. Cavities apparently evolve from the interaction of AGN jets with the intracluster medium (ICM). However, in numerical simulations it has been difficult to create such fat cavities from narrow jets. Ultra-hot thermal jets dominated by kinetic energy typically penetrate deep into the ICM, forming radially elongated cavities at large radii unlike those observed. Here, we study very light jets dominated energetically by relativistic cosmic rays (CRs) with axisymmetric hydrodynamic simulations, investigating the jet evolution both when they are active and when they are later turned off. We find that, when the thermal gas density in a CR-dominated jet is sufficiently low, the jet has a correspondingly low inertia, and thus decelerates quickly in the ICM. Furthermore, CR pressure causes the jet to expand laterally, encounter and displace more decelerating ICM gas, naturally producing fat cavities near cluster centers similar to those observed. Our calculations of cavity formation imply that AGN jets responsible for creating fat X-ray cavities (radio bubbles) are very light, and dominated by CRs. This scenario is consistent with radio observations of Fanaroff-Riley I jets that appear to decelerate rapidly, produce strong synchrotron emission and expand typically at distances of a few kpc from the central AGN.

On the structure and scale of cosmic ray modified shocks

Strong astrophysical shocks, diffusively accelerating cosmic rays (CRs) ought to develop CR precursors. The length of such precursor Lp is believed to be set by the ratio of the CR mean free path λ to the shock speed, i.e. Lp ∼ cλ/Vsh ∼ crg/Vsh, which is formally independent of the CR pressure Pc. However, the x-ray observations of supernova remnant shocks suggest that the precursor scale may be significantly shorter than Lp which would question the above estimate unless the magnetic field is strongly amplified and the gyroradius rg is strongly reduced over a short (unresolved) spatial scale. We argue that while the CR pressure builds up ahead of the shock, the acceleration enters into a strongly nonlinear phase in which an acoustic instability, driven by the CR-pressure gradient, dominates other instabilities (at least in the case of low β plasma). In this regime the precursor steepens into a strongly nonlinear front whose size scales with the CR pressure as Lf ∼ Lp · (Ls/Lp)2(Pc/Pg)2, where Ls is the scale of the developed acoustic turbulence and Pc/Pg is the ratio of CR to gas pressure. Since Ls ≪ Lp, the precursor scale reduction may be strong in the case of even a moderate gas heating by the CRs through the acoustic and (possibly also) the other instabilities driven by the CRs.

THE RELATION BETWEEN POST-SHOCK TEMPERATURE, COSMIC-RAY PRESSURE, AND COSMIC-RAY ESCAPE FOR NON-RELATIVISTIC SHOCKS

Supernova remnants are thought to be the dominant source of Galactic cosmic rays. This requires that at least 5% of the available energy is transferred to cosmic rays, implying a high cosmic-ray pressure downstream of supernova remnant shocks. Recently, it has been shown that the downstream temperature in some remnants is low compared to the measured shock velocities, implying that additional pressure support by accelerated particles is present. Here we use a two-fluid thermodynamic approach to derive the relation between post-shock fractional cosmic-ray pressure and post-shock temperature, assuming no additional heating beyond adiabatic heating in the shock precursor and with all non-adiabatic heating occurring at the subshock. The derived relations show that a high fractional cosmic-ray pressure is only possible, if a substantial fraction of the incoming energy flux escapes from the system. Recently a shock velocity and a downstream proton temperature were measured for a shock in the supernova remnant RCW 86. We apply the two-fluid solutions to these measurements and find that the the downstream fractional cosmic-ray pressure is at least 50% with a cosmic-ray energy flux escape of at least 20%. In general, in order to have 5% of the supernova energy go into accelerating cosmic rays, on average the post-shock cosmic-ray pressure needs to be 30% for an effective cosmic-ray adiabatic index of 4/3.

DIFFUSIVE SHOCK ACCELERATION IN TEST-PARTICLE REGIME

We examine the test-particle solution for diffusive shock acceleration, based on simple models for thermal leakage injection and Alfv'enic drift. The critical injection rate, \xi_c, above which the cosmic ray (CR) pressure becomes dynamically significant, depends mainly on the sonic shock Mach number, M, and preshock gas temperature, T_1. In the hot-phase interstellar medium (ISM) and intracluster medium, \xi_c < 10^{-3} for shocks with M < 5, while \xi_c ~ 10^{-4}(T_1/10^6 K)^{1/2} for shocks with M > 10. For T_1=10^6 K, for example, the test-particle solution would be valid if the injection momentum, p_{inj} > 3.8 p_{th}. This leads to the postshock CR pressure less than 10% of the shock ram pressure. If the Alfv'en speed is comparable to the sound speed in the preshock flow, as in the hot-phase ISM, the power-law slope of CR spectrum can be significantly softer than the canonical test-particle slope. Then the CR spectrum at the shock can be approximated by the revised test-particle power-law with an exponential cutoff at the highest accelerated momentum, p_{max}(t). An analytic form of the exponential cutoff is also suggested.

EFFECTS OF NEUTRAL PARTICLES ON MODIFIED SHOCKS AT SUPERNOVA REMNANTS

H-alpha emission from supernova remnants (SNRs) implies the existence of neutral hydrogens in the ambient medium. In the precursor of an SNR shock modified by cosmic rays (CRs), upstream plasmas are pushed by the CR pressure, but neutral particles are not, so that the relative velocity appears and some neutral particles become pickup ions by the charge exchange process in the precursor. We investigate how the pickup ions generated in the precursor affect the shock structure and the particle acceleration. If the CR pressure is larger than 20% of the shock ram pressure, the compression of the subshock becomes smaller than that without pickup ions because of the pressure of the pickup ions. Moreover, even if the shock is modified by CRs, the total compression ratio can be smaller than 4. In addition, the pickup ions play an important role for the injection into the particle acceleration. If the shock is a quasi-perpendicular shock and if the the multiply reflected ion acceleration occurs, the CR spectrum can be harder than that of the test particle diffusive shock acceleration below GeV.

THERMAL INSTABILITY WITH ANISOTROPIC THERMAL CONDUCTION AND ADIABATIC COSMIC RAYS: IMPLICATIONS FOR COLD FILAMENTS IN GALAXY CLUSTERS

Observations of the cores of nearby galaxy clusters show H$\alpha$ and molecular emission line filaments. We argue that these are the result of {\em local} thermal instability in a {\em globally} stable galaxy cluster core. We present local, high resolution, two-dimensional magnetohydrodynamic simulations of thermal instability for conditions appropriate to the intracluster medium (ICM); the simulations include thermal conduction along magnetic field lines and adiabatic cosmic rays. Thermal conduction suppresses thermal instability along magnetic field lines on scales smaller than the Field length ($\gtrsim$10 kpc for the hot, diffuse ICM). We show that the Field length in the cold medium must be resolved both along and perpendicular to the magnetic field in order to obtain numerically converged results. Because of negligible conduction perpendicular to the magnetic field, thermal instability leads to fine scale structure in the perpendicular direction. Filaments of cold gas along magnetic field lines are thus a natural consequence of thermal instability with anisotropic thermal conduction. Nonlinearly, filaments of cold ($\sim 10^4$ K) gas should have lengths (along the magnetic field) comparable to the Field length in the cold medium $\sim 10^{-4}$ pc! Observations show, however, that the atomic filaments in clusters are far more extended, $\sim 10$ kpc. Cosmic ray pressure support (or a small scale turbulent magnetic pressure) may resolve this discrepancy: even a small cosmic ray pressure in the diffuse ICM, $\sim 10^{-4}$ of the thermal pressure, can be adiabatically compressed to provide significant pressure support in cold filaments. This is qualitatively consistent with the large population of cosmic rays invoked to explain the atomic and molecular line ratios observed in filaments.

COSMIC-RAY ACCELERATION EFFICIENCY VERSUS TEMPERATURE EQUILIBRATION: THE CASE OF SNR 0509-67.5

We study the 0509-67.5 supernova remnant in the Large Magellanic Cloud with the VLT/FORS2 spectrograph. We detect a broad component in the H-alpha emission with a FWHM of 2680 \pm 70 km/s and 3900 \pm 800 km/s for the southwest (SW) and northeast (NE) shocks respectively. For the SW, the proton temperature appears to be too low for the shock velocity, which we attribute to a cosmic-ray pressure behind the shock front of at least 20% of the total pressure. For the NE, the post-shock proton temperature and the shock velocity are compatible, only if the plasma behind the shock front has a degree of thermal equilibrium of over 20%, which is at odds with current models for temperature equilibration behind fast shocks, which do not accelerate cosmic rays. If we assume the electron temperature to be less than 10% of the proton temperature, we find a post-shock cosmic-ray pressure of at least 7%.

On the influence of non-thermal pressure on the mass determination of galaxy clusters

(Abridged) The main purpose of this paper is to consider the contribution of all three non-thermal components to total mass measurements of galaxy clusters: cosmic rays, turbulence and magnetic pressures. To estimate the thermal pressure we used public XMM-\textit{Newton} archival data of 5 Abell clusters. To describe the magnetic pressure, we assume a radial distribution for the magnetic field, $B(r) \propto \rho_{g}^{\alpha}$, to seek generality we assume $\alpha$ within the range of 0.5 to 0.9, as indicated by observations and numerical simulations. For the turbulent component, we assumed an isotropic pressure, $P_{\rm turb} = {1/3}\rho_{\rm g}(\sigma_{r}^{2}+\sigma_{t}^{2})$. We also consider the contribution of cosmic ray pressure, $P_{cr}\propto r^{-0.5}$. It follows that a consistent description for the non-thermal component could yield variation in mass estimates that vary from 10% up to $\sim$30%. We verified that in the inner parts of cool-core clusters the cosmic ray component is comparable to the magnetic pressure, while in non cool-core cluster the cosmic ray component is dominant. For cool-core clusters the magnetic pressure is the dominant component, contributing with more than 50% of total mass variation due to non-thermal pressure components. However, for non cool-core clusters, the major influence comes from the cosmic ray pressure that accounts with more than 80% of total mass variation due to non-thermal pressure effects. For our sample, the maximum influence of the turbulent component to total mass variation can be almost 20%. We show that this analysis can be regarded as a starting point for a more detailed and refined exploration of the influence of non-thermal pressure in the intra-cluster medium (ICM).

Zeeman Splitting in the Diffuse ISM

AbstractMany Zeeman-spitting measurements in the diffuse Galactic Interstellar Medium have been made of the 21-cm line in both absorption and emission. Typical field strength is about 6 μG, with enhancement in shocked regions; the magnetic, turbulent, and cosmic-ray pressures are comparable and considerably larger than the thermal gas pressure. For PhotoDissociation Regions, Carbon recombination lines show intriguing results for single-dish measurements. OH Megamasers in Ultra-Luminous Infrared Galaxies show easily detectable fields whose strength ranges up to at least 20 mG. Upper limits for several damped Ly-α systems range down to a few μG. The z=0.692 system against 3C286 was reported in the literature to have a large field strength, but this result is wrong.

Metal enrichment of the intra-cluster medium by thermally and cosmic-ray driven galactic winds

<i>Aims. <i/>We investigate the efficiency and time-dependence of thermally and cosmic ray driven galactic winds for the metal enrichment of the intra-cluster medium (ICM) using a new analytical approximation for the mass outflow. The spatial distribution of the metals are studied using radial metallicity profiles and 2D metallicity maps of the model clusters as they would be observed by X-ray telescopes like XMM-Newton.<i>Methods. <i/>Analytical approximations for the mass loss by galactic winds driven by thermal and cosmic ray pressure are derived from the Bernoulli equation and implemented in combined <i>N<i/>-body/hydrodynamic cosmological simulations with a semi-analytical galaxy formation model. Observable quantities like the mean metallicity, metallicity profiles, and 2D metal maps of the model clusters are derived from the simulations.<i>Results. <i/>We find that galactic winds alone cannot account for the observed metallicity of the ICM. At redshift the model clusters have metallicities originating from galactic winds which are almost a factor of 10 lower than the observed values. For massive, relaxed clusters we find, as in previous studies, a central drop in the metallicity due to a suppression of the galactic winds by the pressure of the ambient ICM. Combining ram-pressure stripping and galactic winds we find radial metallicity profiles of the model clusters which agree qualitatively with observed profiles. Only in the inner parts of massive clusters the observed profiles are steeper than in the simulations. Also the combination of galactic winds and ram-pressure stripping yields too low values for the ICM metallicities. The slope of the redshift evolution of the mean metallicity in the simulations agrees reasonably well with recent observations.

Thermal instability and the effects of cosmic-ray diffusion

We study the dynamical effects of cosmic rays (CRs) on thermal instability in the linear regime. CRs and the thermal plasma are treated as two different interacting fluids, in which CRs can diffuse along the magnetic field lines. We show that the growth rate of the magnetothermal condensation mode is reduced because of the existence of CRs, and this stabilizing effect depends on the diffusion coefficient and the ratio of CR pressure to gas pressure. Thus, a slower rate of structure formation via thermal instability is predicted when CRs are considered.

BUOYANCY INSTABILITIES IN GALAXY CLUSTERS: CONVECTION DUE TO ADIABATIC COSMIC RAYS AND ANISOTROPIC THERMAL CONDUCTION

Using a linear stability analysis and two and three-dimensional nonlinear simulations, we study the physics of buoyancy instabilities in a combined thermal and relativistic (cosmic ray) plasma, motivated by the application to clusters of galaxies. We argue that cosmic ray diffusion is likely to be slow compared to the buoyancy time on large length scales, so that cosmic rays are effectively adiabatic. If the cosmic ray pressure $p_{cr}$ is $\gtrsim 25 %$ of the thermal pressure, and the cosmic ray entropy ($p_{\rm cr}/\rho^{4/3}$; $\rho$ is the thermal plasma density) decreases outwards, cosmic rays drive an adiabatic convective instability analogous to Schwarzschild convection in stars. Global simulations of galaxy cluster cores show that this instability saturates by reducing the cosmic ray entropy gradient and driving efficient convection and turbulent mixing. At larger radii in cluster cores, the thermal plasma is unstable to the heat flux-driven buoyancy instability (HBI), a convective instability generated by anisotropic thermal conduction and a background conductive heat flux. Cosmic-ray driven convection and the HBI may contribute to redistributing metals produced by Type 1a supernovae in clusters. Our calculations demonstrate that adiabatic simulations of galaxy clusters can artificially suppress the mixing of thermal and relativistic plasma; anisotropic thermal conduction allows more efficient mixing, which may contribute to cosmic rays being distributed throughout the cluster volume.

Saturated magnetic field amplification at supernova shocks

Cosmic-ray streaming instabilities at supernova shocks are discussed in the quasilinear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the nonresonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear growth rate is calculated using kinetic theory for a streaming distribution. We show that the nonresonant instability is actually driven by a compensating current in the background plasma. The nonresonant instability can develop into a nonlinear regime generating turbulence. The saturation of the amplified magnetic fields due to particle diffusion in the turbulence is derived analytically. It is shown that the evolution of parallel and perpendicular cosmic-ray pressures is predominantly determined by nonresonant diffusion. However, the saturation is determined by resonant diffusion which tends to reduce the streaming motion through pitch angle scattering. The saturated level can exceed the mean background magnetic field.

Radio emission and nonlinear diffusive shock acceleration of cosmic rays in the supernova SN 1993J

The extensive observations of the supernova SN 1993J at radio wavelengths make this object a unique target for the study of particle acceleration in a supernova shock. To describe the radio synchrotron emission we use a model that couples a semianalytic description of nonlinear diffusive shock acceleration with self-similar solutions for the hydrodynamics of the supernova expansion. The synchrotron emission, which is assumed to be produced by relativistic electrons propagating in the postshock plasma, is worked out from radiative transfer calculations that include the process of synchrotron self-absorption. The model is applied to explain the morphology of the radio emission deduced from high-resolution VLBI imaging observations and the measured time evolution of the total flux density at six frequencies. Both the light curves and the morphology of the radio emission indicate that the magnetic field was strongly amplified in the blast wave region shortly after the explosion, possibly via the nonresonant regime of the cosmic-ray streaming instability operating in the shock precursor. The turbulent magnetic field was not damped behind the shock but carried along by the plasma flow in the downstream region. Cosmic-ray protons were efficiently produced by diffusive shock acceleration at the blast wave. We find that during the first ~8.5 years after the explosion, about 19% of the total energy processed by the forward shock was converted to cosmic-ray energy. However, the shock remained weakly modified by the cosmic-ray pressure. The high magnetic field amplification implies that protons were rapidly accelerated to energies well above 1 PeV. The results obtained for this supernova support the scenario that massive stars exploding into their former stellar wind are a major source of high-energy Galactic cosmic rays.

PARKER/BUOYANCY INSTABILITIES WITH ANISOTROPIC THERMAL CONDUCTION, COSMIC RAYS, AND ARBITRARY MAGNETIC FIELD STRENGTH

We report the results of a local stability analysis for a magnetized, gravitationally stratified plasma containing cosmic rays. We account for cosmic-ray diffusion and thermal conduction parallel to the magnetic field and allow beta to take any value, where p is the plasma pressure and B is the magnetic field strength. We take the gravitational acceleration to be in the -z-direction and the equilibrium magnetic field to be in the y-direction, and we derive the dispersion relation for small-amplitude instabilities and waves in the large-|k_x| limit. We use the Routh-Hurwitz criterion to show analytically that the necessary and sufficient criterion for stability in this limit is n k_B dT/dz + dp_cr/dz + (1/8pi)dB^2/dz > 0, where T is the temperature, n is the number density of thermal particles, and p_cr is the cosmic-ray pressure. We present approximate analytical solutions for the normal modes in the low- and high-diffusivity limits, show that they are consistent with the derived stability criterion, and compare them to numerical results obtained from the full, unapproximated, dispersion relation. Our results extend earlier analyses of buoyancy instabilities in galaxy-cluster plasmas to the beta <= 1 regime. Our results also extend earlier analyses of the Parker instability to account for anisotropic thermal conduction, and show that the interstellar medium is more unstable to the Parker instability than was predicted by previous studies in which the thermal plasma was treated as adiabatic.

Numerical Simulations of Buoyancy Instabilities in Galaxy Cluster Plasmas with Cosmic Rays and Anisotropic Thermal Conduction

In clusters of galaxies, the specific entropy of intracluster plasma increases outwards. Nevertheless, a number of recent studies have shown that the intracluster medium is subject to buoyancy instabilities due to the effects of cosmic rays and anisotropic thermal conduction. In this paper, we present a new numerical algorithm for simulating such instabilities. This numerical method treats the cosmic rays as a fluid, accounts for the diffusion of heat and cosmic rays along magnetic field lines, and enforces the condition that the temperature and cosmic-ray pressure remain positive. We carry out several tests to ensure the accuracy of the code, including the detailed matching of analytic results for the eigenfunctions and growth rates of linear buoyancy instabilities. This numerical scheme will be useful for simulating convection driven by cosmic-ray buoyancy in galaxy cluster plasmas and may also be useful for other applications, including fusion plasmas, the interstellar medium, and supernovae remnants.

Cosmic ray acceleration by a supernova shock in a dense circumstellar plasma

Cosmic ray acceleration may occur at a supernova shock expanding into a circumstellar wind sustaining a Parker spiral magnetic field. Cosmic rays drift to the poles producing a large cosmic ray pressure which can generate polar density cavities through which cosmic rays escape upstream of the shock. This may be relevant to gamma-ray bursts accompanying shock breakout.

Gamma-ray probe of cosmic ray pressure in galaxy clusters and cosmological implications

Cosmic rays produced in cluster accretion and merger shocks provide pressure to the intracluster medium (ICM) and affect the mass estimates of galaxy clusters. Although direct evidence for cosmic-ray ions in the ICM is still lacking, they produce gamma-ray emission through the decay of neutral pions produced in their collisions with ICM nucleons. We investigate the capability of the Gamma-ray Large Area Space Telescope (GLAST) and imaging atmospheric Cerenkov telescopes (IACTs) for constraining the cosmic-ray pressure contribution to the ICM. We show that GLAST can be used to place stringent upper limits, a few per cent for individual nearby rich clusters, on the ratio of pressures of the cosmic rays and thermal gas. We further show that it is possible to place tight (<~10%) constraints for distant (z <~ 0.25) clusters in the case of hard spectrum, by stacking signals from samples of known clusters. The GLAST limits could be made more precise with the constraint on the cosmic-ray spectrum potentially provided by IACTs. Future gamma-ray observations of clusters can constrain the evolution of cosmic-ray energy density, which would have important implications for cosmological tests with upcoming X-ray and Sunyaev-Zel'dovich effect cluster surveys.

The Eddington Limit in Cosmic Rays: An Explanation for the Observed Faintness of Starbursting Galaxies

We show that the luminosity of a star forming galaxy is capped by the production and subsequent expulsion of cosmic rays from its interstellar medium. By defining an Eddington luminosity in cosmic rays, we show that the star formation rate of a given galaxy is limited by its mass content and the cosmic ray mean free path. When the cosmic ray luminosity and pressure reaches a critical value as a result of vigorous star formation, hydrostatic balance is lost, a cosmic ray-driven wind develops, and star formation is choked off. Cosmic ray pressure-driven winds are likely to produce wind velocities significantly in excess of the galactic escape velocity. It is possible that cosmic ray feedback results in the Faber-Jackson relation for a plausible set of input parameters that describe cosmic ray production and transport, which are calibrated by observations of the Milky Way's interstellar cosmic rays as well as other galaxies.