The non-thermal radiation–cluster merger connection

The paper presents an investigation of the self-focusing of Gaussian electromagnetic beams propagating in a strongly ionized plasma along a static magnetic field. The nonlinearity in the dielectric tensor of the plasma arises because of the heating and consequent redistribution of electrons along the wavefront. At low values of magnetic field the main source of electron energy dissipation is thermal conduction; for large magnetic fields the carrier mean free path becomes comparable to or greater than the Larmor radius of the electrons, and the collisional loss of energy becomes dominant. This investigation reveals that the length of self-focusing of the beam in the extraordinary as well as ordinary mode of propagation is reduced by the application of the magnetic field, for low values of the magnetic field (ωc double less-than sign ω). For higher values of the magnetic field the self-focusing of the extraordinary mode is further enhanced while that of the ordinary mode is reduced.

The present paper is based on the theory first proposed by Ginzburg and Shklovsky that all non-thermal, non-stellar, cosmic radio emission arises from synchrotron radiation by electrons. The electrons will be regarded as secondaries from nuclear collisions of cosmic rays with ambient gas. Evidence for this point of view can be adduced from the observed radio frequency spectra. The consequences of cosmic rays existing (i) in galaxies, (ii) in clusters of galaxies, (iii) in space generally, are examined, on the assumption that the cosmic-ray energy density is always ∼ 1 eV cm −3 . Apart from the introduction, the paper is divided into three parts : I. Weak emission from galaxies, clusters, and intergalactic space. II. Strong emission from extragalactic sources. III. Strong emission from galactic sources. Halo emission from spiral galaxies—from M31 and the Galaxy in particular—is considered in I. The cases of Cygnus A and NGC 1275 are investigated in II—a new class of optically non-visible source being also proposed in this part. The cases of the Crab Nebula, Casseiopeia A, and IC 443 are discussed in III. So far as strong sources are concerned, the argument depends in an important way on the conditions that develop at the shock front of a cloud expanding at great speed into an ambient medium. The present situation differs in a curious way from ordinary gas dynamics, in that the momentum and energy terms of the Rankine–Hugoniot relations are carried by quite different components of the assembly—the momentum by the material of the gas cloud and the ambient medium, and the energy by a reservoir of relativistic particles and by a magnetic field. To overcome the difficulty that the detailed physical processes that take place within the shock front itself are not well understood, a rule is proposed that receives strong empirical support from a wide range of observed phenomena, including such diverse cases as the radio emission of Cygnus A and the optical emission of the Crab Nebula. When the magnetic field dominates in the energy terms, the rule yields results that differ markedly from those given by the de Hoffman–Teller equations. The field does not preserve a uniform structure at the front, as in the de Hoffman–Teller case, but develops a highly wrapped, contorted structure—such as is suggested by the observed optical filaments of Casseiopeia A. If the rule were also applicable to cases where the energy and momentum were carried by different components, the momentum by a comparatively high-density, low-temperature gas and the energy by a low-density, high-temperature non-relativistic gas (the gas considered in the present paper is relativistic) a new process would be available for producing very high temperatures.

The physics of magnetic fields (B) and cosmic rays (CRs) have recently been included in simulations of galaxy formation. However, significant uncertainties remain in how these components affect galaxy evolution. To understand their common observational tracers, we analyse the magnetic fields in a set of high-resolution, magnetohydrodynamic, cosmological simulations of Milky-Way-like galaxies from the FIRE-2 project. We compare mock observables of magnetic field tracers for simulations with and without CRs to observations of Zeeman splitting and rotation/dispersion measures. We find reasonable agreement between simulations and observations in both the neutral and the ionized interstellar medium (ISM). We find that the simulated galaxies with CRs show weaker ISM |B| fields on average compared to their magnetic-field-only counterparts. This is a manifestation of the effects of CRs in the diffuse, low density inner circumgalactic medium (CGM). We find that equipartition between magnetic and cosmic ray energy densities may be valid at large (> 1 kpc) scales for typical ISM densities of Milky-Way-like galaxies, but not in their haloes. Within the ISM, the magnetic fields in our simulated galaxies follow a power-law scaling with gas density. The scaling extends down to neutral hydrogen number densities < 300 cm−3, in contrast to observationally derived models, but consistent with the observational measurements. Finally, we generate synthetic rotation measure (RM) profiles for projections of the simulated galaxies and compare to observational constraints in the CGM. While consistent with upper limits, improved data are needed to detect the predicted CGM RMs at 10–200 kpc and better constrain theoretical predictions.

The magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars (Beck 2005). The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ≈ 3 μG (Han et al. 2006). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars (Kronberg et al. 2008) suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain.Here we report a measurement of a magnetic field of B ≈ 84 μG in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 μG in the neutral interstellar gas of our Galaxy (Heiles et al. 2004). This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past, rather than stronger (Parker 1970).The full text of this paper was published in Nature (Wolfe et al. 2008).

The separation $\del$ between two peaks in the gamma-ray pulse profile is calculated as a function of energy for several polar cap models with curvature-radiation-induced cascades. The Monte Carlo results are interpreted with the help of analytical approximations and discussed in view of the recent data analysis for the Vela pulsar (Kanbach 1999). We find that the behaviour of $\del$ as a function of photon energy $\epsilon$ depends primarily on local values of the magnetic field, $B_{\rm local}$, in the region where electromagnetic cascades develop. For low values of $B_{\rm local}$ ($< 10^{12}$ G), $\del(\epsilon)$ is kept constant. However, for stronger magnetic fields ($\ga 10^{12}$ G) in the hollow-column model $\del$ decreases with increasing photon energy at a rate dependent on maximum energy of beam particles as well as on viewing geometry. There exists a critical photon energy $\et$ above which the relation $\del(\epsilon)$ changes drastically: for $\epsilon > \et$, in hollow-column models the separation $\del$ increases (whereas in filled-column model it decreases) rapidly with increasing $\epsilon$, at a rate of $\sim 0.28$ of the total phase per decade of photon energy. The existence of critical energy $\et$ is a direct consequence of one-photon magnetic absorption effects. In general, $\et$ is located close to the high-energy cutoff of the spectrum, thus photon statistics at $\et$ should be very low. That will make difficult to verify the existence of $\et$ in real gamma-ray pulsars. Spectral properties of the Vela pulsar would favour those models which use low values of magnetic field in the emission region ($B_{\rm local} \simless 10^{11}$ G) which in turn implies a constant value of the predicted $\del$ within EGRET range.

Galactic magnetic fields and cosmic rays are tightly bound up together. The fact that the energy density of cosmic rays in the local region of the Galaxy is approximately the same order of magnitude as the energy density of the magnetic field has led many authors to postulate that this is a universal phenomenon, i.e., that there is equipartition. Gamma ray observations of the Magellanic Clouds lead us to doubt the presence of such equipartition there, however. Doubt is raised, therefore, about the application of equipartition, and a fixed electron to proton ratio, by radio astronomers to observations of synchrotron radiation from galaxies in general.A consequence of the lack of equipartition may be that in some galaxies the cosmic ray intensity is increasing (or decreasing). The positive link between the strength of galactic magnetic fields and the star formation rate implies that dynamo action may not be the only source of galactic magnetic fields.

We discuss the pitch angle scattering of relativistic particles by self‐generated hydromagnetic waves. We show that in a hot background plasma, because of the resonant damping of short wavelength waves by thermal protons, cosmic rays need not slow down to a mean streaming speed which is of order the Alfven speed. We also discuss the effects of a high cosmic ray energy density upon the destabilized wave mode. Our recent work indicates that when the cosmic ray energy density is on the order of or exceeds the energy density in the ambient magnetic field, the velocity of the amplified waves is significantly greater than the Alfven speed. These effects have important implications for recent cosmic ray acceleration models and are important for studies of particle propagation in many astrophysical plasmas.

The presence of heavy particles in cosmic rays makes it plausible that cosmic radiation is generated by the acceleration of charged particles in extended electromagnetic fields. The energy density of cosmic rays ($3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\frac{M{c}^{2}}{{\mathrm{cm}}^{3}}$) would lead to very great total amounts of energy if one assumes that cosmic radiation extends throughout intergalactic or throughout interstellar space. This would require very efficient methods of cosmic-ray production. It is therefore of interest to investigate the possibility that cosmic rays are generated in the vicinity of the sun and are confined to the solar system by extended magnetic fields. The strength of these fields is estimated to be ${10}^{\ensuremath{-}5}$ gauss. According to this picture, cosmic rays circulate in the neighborhood of the planetary system for thousands of years, during which time the radiation becomes isotropic. The electron component of the radiation is eliminated by collisions with solar light quanta.

We present semi-analytical models of galactic outflows in high redshift galaxies driven by both hot thermal gas and non-thermal cosmic rays. Thermal pressure alone may not sustain a large scale outflow in low mass galaxies (i.e $M\sim 10^8$~M$_\odot$), in the presence of supernovae (SNe) feedback with large mass loading. We show that inclusion of cosmic ray pressure allows outflow solutions even in these galaxies. In massive galaxies for the same energy efficiency, cosmic ray driven winds can propagate to larger distances compared to pure thermally driven winds. On an average gas in the cosmic ray driven winds has a lower temperature which could aid detecting it through absorption lines in the spectra of background sources. Using our constrained semi-analytical models of galaxy formation (that explains the observed UV luminosity functions of galaxies) we study the influence of cosmic ray driven winds on the properties of the intergalactic medium (IGM) at different redshifts. In particular, we study the volume filling factor, average metallicity, cosmic ray and magnetic field energy densities for models invoking atomic cooled and molecular cooled halos. We show that the cosmic rays in the IGM could have enough energy that can be transferred to the thermal gas in presence of magnetic fields to influence the thermal history of the intergalactic medium. The significant volume filling and resulting strength of IGM magnetic fields can also account for recent $\gamma$-ray observations of blazars.

The antiferromagnetically ordered state of the monoclinic quasi-one-dimensional $S=1/2$ Heisenberg antiferromagnet ${\mathrm{CuSb}}_{2}{\mathrm{O}}_{6}$ was studied combining torque magnetometry with a phenomenological approach to magnetic anisotropy. This system is known to have a number of different twins in the monoclinic $\ensuremath{\beta}$ phase, which differ in the orientation of the two ${\mathrm{CuO}}_{6}$ octahedra in the unit cell resulting in different orientation of magnetic axes with respect to crystal axes for each twin. We performed torque measurements in magnetic fields $H\ensuremath{\le}0.8\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ on a sample where a certain type of twin was shown to be dominant by ESR spectroscopy. The measured data reveal that the easy axis is the crystallographic $b$ axis for this sample. Phenomenological magnetocrystalline anisotropy energy invariant to crystal symmetry operations was used to model the spin axis direction in zero and finite magnetic fields. Our model reproduces the value of the spin-flop field ${H}_{\mathrm{SF}}=1.25\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ found in literature. A combination of this approach with our torque results shows that the spin axis will flop in the direction of the maximal value of measured $\mathbf{g}$ tensor when the magnetic field $H&gt;{H}_{\mathrm{SF}}$ is applied along the easy axis direction. Our analysis of magnetocrystalline anisotropy energy predicts two possibilities for the easy axis direction in this system, $b$ or $a$, connected to different crystallographic twins that can be realized in ${\mathrm{CuSb}}_{2}{\mathrm{O}}_{6}$. These results offer a possibility to reconcile the different reports of easy axis direction found in literature for this system and also nicely demonstrate how a combination of torque magnetometry and a phenomenological approach to magnetic anisotropy can be used to determine the value of the spin-flop field and the direction of spin axis in antiferromagnets in both $H&lt;{H}_{\mathrm{SF}}$ and $H&gt;{H}_{\mathrm{SF}}$ by performing measurements in fields significantly smaller than ${H}_{\mathrm{SF}}$.

Using data from the Voyager and Pioneer spacecraft at distances up to 60 AU from the Sun to help define the effects of solar modulation, we have made a new estimate of the local interstellar cosmic-ray spectra and the associated energy density and ionization rate. The energy density, including the low-energy electron contribution, is ~1.80 eV cm-3, equivalent energetically to that in a 7 μG magnetic field. The ionization rate from this same cosmic-ray population, including a significant contribution from low-energy electrons, is (3-4) × 10-17 s-1 (H atom). This is most likely a minimum value and is not too different from estimates of the typical ionization rate required to heat the interstellar medium and maintain the diffuse ionized gas range from (3-30) × 10-17 s-1 (H atom) as a function of locale in the Galaxy. This suggests that cosmic rays could be a significant contributor to interstellar heating. The cosmic-ray ionization rate will be more or less uniform throughout the Galactic disk and also perpendicular to the disk according to the scale height of cosmic rays which may be ~1 kpc, thus providing a source of ionization at high Z values. The recent observation of low-energy particle acceleration at the heliospheric termination shock, which produces local ionization rates comparable to those due to Galactic cosmic rays, raises the interesting possibility that "hot spots," where the ionization rate due to locally accelerated particles may exceed 10-16 s-1 (H atom), may occur near massive stars with more powerful stellar winds.

The mechanism accelerating cosmic rays in the Milky Way Galaxy and galaxy clusters is identified and described. The acceleration of cosmic rays is a purely electrostatic process which operates up to the maximum energies of $10^{23}$ $eV$ in galaxy clusters. Galactic cosmic rays are accelerated in a pervasive electrostatic field active in the whole Galaxy except in restricted regions shielded by interstellar and stellar plasmas as, for instance, the region occupied by the solar system. It is proved that the energy spectrum of the cosmic radiation in the $Milky$ $Way$ $Galaxy$, in the region where the solar system resides, has a constant spectral index comprised between 2.64-2.68 and the maximum energies of Galactic protons are $3.0 \times 10^{19}$ $eV$. The agreement of these results with the experimental data is discussed in detail and underlined. The various physical processes that maintain the stability of the electrostatic structure in the $Milky$ $Way$ $Galaxy$ are the same that generate the Galactic magnetic field. Accordingly, the intensity, orientation and direction of the Galactic magnetic field are evaluated. The results of the calculation are compared with the observational data, optical and mostly radio astronomy data. The accord of the intensity, orientation and direction of the observed magnetic field with calculation is excellent.

New microwave nonreciprocal properties are investigated in “ferrite plate – grating of resonant elements” metasandwiches arranged along the axis of a rectangular waveguide in a transverse constant magnetic field. Giant nonreciprocity in the transmission is observed at the ferromagnetic resonance frequencies at certain values of the magnetic field under conditions of a mutual influence between the ferromagnetic and the grating resonances. In addition, nonreciprocal splitting of the resonance in grating elements is observed under small magnetic field, which is much less than the field necessary to the ferromagnetic resonance excitation. The nonreciprocal transmission does not take place in the case of free ferrite in the absence of a grating. Sign reversal of the nonreciprocity is observed, when ferrite transfers to the opposite side of a grating as well as under certain values of the constant magnetic field, when the sign reversal of difference between frequencies of the ferromagnetic resonance and the grating resonance takes place. Nonreciprocal effects are explained by the interaction between precessing spins in ferrite and a magnetic field of the surface wave, formed by a grating, and by coupling between the resonances of grating elements. It has been shown theoretically that microwaves in waveguide with bianisotropic layer, simulating a grating of resonant elements, are elliptically or circularly polarized with frequency and spatially – dependent rotating sense of the microwave magnetic field. The nonreciprocal effects have been observed for different grating elements: for both electric dipoles and chiral elements.

Nonthermal radiation from supernova remnants (SNRs) provides observational evidence and constraints on the diffusive shock acceleration (DSA) hypothesis for the origins of Galactic cosmic rays (CRs). Recently it has been recognized that a variety of plasma wave-particle interactions operate at astrophysical shocks and the detailed outcomes of DSA are governed by their complex and nonlinear interrelationships. Here we calculate the energy spectra of CR protons and electrons accelerated at Type Ia SNRs, using time-dependent, DSA simulations with phenomenological models for magnetic field amplification due to CR streaming instabilities, Alf<TEX>$\acute{e}$</TEX>enic drift, and free escape boundary. We show that, if scattering centers drift with the Alf<TEX>$\acute{e}$</TEX>en speed in the amplified magnetic fields, the CR energy spectrum is steepened and the acceleration efficiency is significantly reduced at strong CR modified SNR shocks. Even with fast Afv<TEX>$\acute{e}$</TEX>nic drift, DSA can still be efficient enough to develop a substantial shock precursor due to CR pressure feedback and convert about 20-30% of the SN explosion energy into CRs. Since the high energy end of the CR proton spectrum is composed of the particles that are injected in the early stages, in order to predict nonthermal emissions, especially in X-ray and <TEX>${\gamma}-ray$</TEX> bands, it is important to follow the time dependent evolution of the shock dynamics, CR injection process, magnetic field amplification, and particle escape. Thus it is crucial to understand the details of these plasma interactions associated with collisionless shocks in successful modeling of nonlinear DSA.

Motivated by the suggestion of Kang, Ryu \& Jones (1996) that particles can be accelerated to high energies via diffusive shock acceleration process at the accretion shocks formed by the infalling flow toward the clusters of galaxies, we have calculated the expected particle flux from a cosmological ensemble of clusters. We use the observed temperature distribution of local clusters and assume a simple power-law evolutionary model for the comoving density of the clusters. The shock parameters such as the shock radius and velocity are deduced from the ICM temperature using the self-similar solutions for secondary infall onto the clusters. The magnetic field strength is assume to be in equipartition with the postshock thermal energy behind the accretion shock. We also assume that the injected energy spectrum is a power-law with the exponential cutoff at the maximum energy which is calculated from the condition that the energy gain rate for diffusive shock acceleration is balanced by the loss rate due to the interactions with the cosmic background radiation. In contrast to the earlier paper we have adopted here the description of the cosmic ray diffusion by Jokipii (1987) which leads to considerably higher particle energies. Finally the injected particle spectrum at the clusters is integrated over the cosmological distance to earth by considering the energy loss due to the interactions with the cosmic background radiation. Our calculations show that the expected spectrum of high-energy protons from the cosmological ensemble of the cluster accretion shocks could match well the observed cosmic ray spectrum near $10^{19}$eV with reasonable parameters and models if about $10^{-4}$ of the infalling kinetic energy can be injected into the intergalactic space as the high energy particles.