Effects of cosmic rays and density inhomogeneity of the circumstellar medium on the formation of a supernova shell

We consider the self-similar problem of a supernova explosion in a radially inhomogeneous medium by taking into account the generation of accelerated relativistic particles. The initial density of the medium is assumed to decrease with distance from the explosion center as a power law, ρ ₀ = A/r ^θ. We use a two-fluid approach in which the total pressure in the medium is the sum of the circumstellar gas pressure and the relativistic particle pressure. The relativistic particle pressure at the shock front is specified as an external parameter. This approach is applicable in the case where the diffusion coefficient of accelerated particles is small and the thickness of the shock front is much smaller than its radius. We have numerically solved a system of ordinary differential equations for the dimensionless quantities that describe the velocity and density behind the shock front as well as the nonrelativistic gas and relativistic particle pressures for various parameters of the inhomogeneity of the medium and various compression ratios of the medium at the shock front. We have established that the shock acceleration of cosmic rays affects most strongly the formation of a supernova shell (making it thinner) in a homogeneous circumstellar medium. A decrease in the circumstellar matter density with distance from the explosion center causes the effect of shock-accelerated relativistic particles on the supernova shell formation to weaken considerably. Inhomogeneity of the medium makes the shell thicker and less dense, while an increase in the compression ratio of the medium at the shock front causes the shell to become thinner and denser. As the relativistic particle density increases, the effect of circumstellar matter inhomogeneity on the shell formation becomes weaker.     

Influence of accelerated particles on the large-scale magnetic field in young supernova remnants

We offer a possible explanation for the observational data on the magnetic-field structure in young supernova remnants (SN 1006, Tycho, Kepler, Cas A) that have been obtained by analyzing the polarizations of electromagnetic radiation in the radio, infrared, and other wavelength ranges. The authors of observational works interpret these data as evidence that the ordered magnetic-field component is predominantly radial, but it can be much smaller in amplitude than the stochastic field component that accounts for the bulk of the total magnetic energy. We calculate the magnetic field in supernova remnants by taking into account the shock compression of the primary field and the generation of a large-scale magnetic field by the particles accelerated at the shock front. The assumption that the field in the supernova remnant is the explosion-compressed primary field near the star is inconsistent with observational data, because the tangential (relative to the shock front) field component perpendicular to the radius must prevail in this case. However, allowing for the generation of an additional magnetic field by the electric current of the particles accelerated by a strong shock front leads us to conclude that the field components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. Such a field configuration for uniform injection does not lead to the generation of an additional magnetic field, and, in this sense, it is stable. This explains the data on the radial direction of the ordered field component. As regards the stochastic field component, we show that it is effectively generated by accelerated particles if their injection into acceleration at the shock front is nonuniform along the front. Injection nonuniformity can be caused by upstream density nonuniformities. A relative density nonuniformity of the order of several percent is enough for an observable magnetic field with scales on the order of the density nonuniformity scales to be generated.     

Reverse shock wave in relativistic explosions

The dynamical evolution of a relativistic explosion in a homogeneous medium is studied by means of a time-dependent, hydrodynamic code. When the expanding velocity of the shock front reduces to the sound velocity in the relativistic fluid, the reverse shock wave propagating inward through the expanding material is generated. The radius of the turning point of the reverse shock wave is proportional to the explosion energy and hardly depends on the mass of the explosion products. In the case of the non-relativistic explosion, the reverse shock wave is generated just after the free expansion stage. The radius of the turning point of the reverse shock wave is proportional to the mass of the explosion products and little depends on the explosion energy. In both cases of the non-relativistic and relativistic explosion, the reverse shock wave is strong in a spherical explosion and weak in a cylindrical one. The plane symmetric explosion does not generate the reverse shock wave.     

Generation of magnetic fluctuations near a shock front in a partially ionized medium

We investigate the generation mechanism of long-wavelength Alfvénic disturbances near the front of a collisionless shock that propagates in a partially ionized plasma. The wave generation and dissipation rates are calculated in the linear approximation. The instability is attributable to a current of energetic particles upstream of the shock front. The generation of long-wavelength magnetic fluctuations is most pronounced for strong shocks, but the effect is retained for shocks with a moderate particle acceleration efficiency without any noticeable modification of the shock structure by the pressure of accelerated particles. The mode generation time for supernova remnants in a partially ionized interstellar medium is shown to be shorter than their age. Long-wavelength magnetic disturbances determine the limiting energies of the particles accelerated at a shock by the Fermimechanism. We discuss the application of the mechanism under consideration to explaining the observed properties of the SN 1006 remnant.     

Cosmic Rays and Nonthermal Radiation in Middle-Aged Supernova Remnants

A nonlinear model of cosmic-ray acceleration at the shock fronts in the supernova remnants W28, W44, and IC433 is investigated. The hydrodynamic evolution of a supernova remnant, including the shock modification by the pressure of accelerated particles and the streaming instability of particles upstream of the shock propagating in a partially ionized interstellar gas, is modeled. The electromagnetic radiation generated by accelerated particles is calculated and compared with observations in a wide range of photon energies.     

Thermodynamics of a system of leptons,photons and interacting nucleons

The thermodynamics of matter composed of interacting nucleons with an admixutre of leptons and photons is investigated in the density-temperature region relevant to the problem of supernova explosion. A quantum mechanical calculation is carried out using Skyrme effective interaction between nucleons. The equation of state is shown to soften below the nuclear density and suddenly stiffen in the transnuclear density region, a condition which is suitable for producing a strong bounce shock that is needed for effective supernova explosion and leaving a remnant neutron star behind.     

A nonlinear theory of stellar wind with allowance for the influence of relativistic particles

We solve the nonlinear problem of the dynamics of a steady-state, spherically symmetric stellar wind by taking into account particle acceleration to relativistic energies near the shock front. The particles are assumed to be accelerated through the Fermi mechanism, interacting with stellar-wind turbulence and crossing many times the shock front that separates the supersonic and subsonic stellar-wind regions. We take into account the influence of the accelerated particles on hydrodynamic plasma-flow parameters. Our method allows all hydrodynamic parameters of the shock front and plasma in the supersonic region to be determined in a self-consistent way and the accelerated-particle energy spectrum to be calculated. Our numerical and analytic calculations show that the plasma compression ratio at the shock front increases compared to the case where there are no relativistic particles and that the velocity profile in the supersonic region acquires a characteristic kink. The shape of the energy spectrum for the accelerated particles and their pressure near the front are essentially determined by the presumed dependence of the diffusion coefficient on particle energy, which, in turn, depends on the scale distribution of turbulent pulsations and other stellar-wind inhomogeneities.     

The motion of the cylindrical-symmetrical relativistic shock wave in the presence of an axial magnetic field

Some observed astrophysical phenomena, such as the blast of a supernova, suggest the necessity to study the motion of shock waves in a relativistic fluid flow in the presence of a magnetic field. This paper deals with the motion of a special relativistic shock wave which propagates from the center line outwardly after an explosion with the assumption that the magnetic field which has an axial component only. Similarity solutions which depend on the parameter =r/t are constructed. Two special cases are then studied in detail. In the first case, there is an ultrarelativistic fluid in front of the shock and in the second case, there is a cold fluid in front of the shock.     

Relativistic hydrodynamics of a free expansion and a shock wave in one-dimension

Dynamical evolution of a relativistic explosion resulting from a large amount of energy release in a homogenous medium is studied using the Khalatnikov equation describing relativistic, hydrodynamic, planar flow. The early phase of the explosion is idealized to two stages: a free expansion and a shock wave stage. By the hodograph transformation inverting the dependent and independent variables, the hydrodynamic equations for the relativistic flow are reduced to second-order linear equations in a velocity-enthalpy space and they are solved by the method of Laplace transformation. The propagation laws and flow structures of the relativistic expansion are obtained at each stage. In the free expansion stage, the flow with a sufficiently high sound velocity forms a thin shell of the energy density in the comoving frame at the front and accelerates the front. In the shock wave stage, the Lorentz factor of the shock front decreases logarithmically with time. The transition time from a free expansion to a shock wave stage suggests that the super-light expansion observed in extragalactic radio sources has no spherical geometry but must be confined to a narrow cone.     

A test for models of radio source evolution

Some observed astrophysical phenomena such as the blast of a supernova (cf. Zeldovich and Novikov, 1966; Blandfordet al., 1977; Shapiro, 1979) suggest the necessity of study of the motion of shock waves in a relativistic fluid flow in the presence of a magnetic field. This paper deals with the motion of special relativistic shock wave which propagates from the center line outwardly after an explosion with the assumption that the magnetic field which has an axial component only. Similarity solutions which depend on the parameter =r/t are constructed. Two special cases are then studied in detail. In the first case, there is an ultra-relativistic fluid in front of the shock and in the second case, there is a cold fluid in front of the shock.     

Efficient cosmic-ray production in supernova remnant G347.3–0.5

Broad-band models of the bright NW limb of G347.3–0.5 give convincing evidence that the forward shock of this supernova remnant is accelerating cosmic rays efficiently, placing >25% of the shock kinetic energy flux into relativistic ions. Despite this high efficiency, the maximum electron and proton energies are well below the observed ‘knee’ at ∼10¹⁵ eV in the Galactic cosmic-ray spectrum.     

On the escape of particles from cosmic ray modified shocks

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles,   p _max  , decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t , particles with momenta larger than   p _max( t )  leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.     

On the possible observational manifestation of the impact of a supernova shock on the neutron star magnetosphere

The impact of a supernova explosion on the magnetosphere of a neutron star in a massive binary system is considered. The supernova shock impact on a plasma-filled neutron star magnetosphere can give rise to a long magnetospheric tail with a considerable store of magnetic energy. Magnetic reconnection in the formed current sheet can transform the magnetic energy stored in the tail into the kinetic energy of charged particles. The plasma instabilities excited by beams of accelerated relativistic particles can lead to the formation of a short pulse of coherent radio emission with parameters similar to those measured for the bright extragalactic millisecond radio burst detected in 2007.     

Synchrotron X-ray emission from supernova remnants. Exponential cut-off in the electron spectrum

We present a model which describes the evolution of the energy spectrum of relativistic electrons in supernova remnants, with radiation losses of electrons taken into account. The model can be used to calculate the synchrotron X-ray emission from supernova remnants in the uniform interstellar medium and in the uniform interstellar magnetic field. The importance of various factors in the variations of spatial distributions of nonthermal electrons and their synchrotron emissive capacity is demonstrated. We analyze the errors which arise in the magnetic field strength when it is estimated with the use of the models which ignore the detailed pattern of the evolution of the magnetic field and the electron spectrum behind the shock front in the remnant. The evolution of synchrotron emission spectrum and the ratio between the synchrotron radio and X-ray fluxes from supernova remnants are calculated.     

Acceleration of a Young Supernova Remnant by an Associated Pulsar

We present a numerical model of the action of a pulsar on its associated supernova remnant. The expansion of the blast wave in the progenitor star has first been considered until radiation pressure within the ejected material becomes negligible due to expansion. By assuming that expansion is ballistic and that the ejecta is opaque to the pulsar 's magnetodipole radiation, the model produces a radiation-filled cavity which grows around the pulsar and contributes to power the dynamics of the forming supernova remnant. The interface between the cavity and the ejecta has been modelled as a thin shell which, depending on the initial spin frequency of the pulsar, can sweep through the ejecta and reach the blast wave. Results for the evolution of the shell indicate that it may strike the front most part of the shocked gas some 60 years after the explosion. Such pulsar-supernova remnant interactions are proposed to form the base of a new subclassification of pulsar-filled supernova remnants. This revised version was published online in July 2006 with corrections to the Cover Date.     

Association of the supernova remnant G 65.3+5.7 with ambient neutral hydrogen and a possible nature of the remnant

The neutral hydrogen at 21 cm has been investigated with the RATAN-600 radio telescope around the supernova remnant G 65.3+5.7, which has the largest angular sizes in the group of shell remnants. An expanding HI shell left after an old supernova explosion with an energy of ∼10⁵¹ erg and an age of 440 000 yr coincident in coordinates with the radio and optical remnant has been discovered. Since an X-ray emission from a much younger (27 000 yr) supernova remnant is observed in the same region and the shells detected by nebular lines have probably intermediate ages, we suggest that several successive supernova explosions have occurred here.     

Self-similar propagation of axisymmetric radiative magnetogasdynamic shocks with increasing energy,II

In this paper self-similar solutions have been investigated for the propagation of axisymmetric radiative gasdynamic shocks caused by an explosion into an inhomogeneous ideal gas permeated by a current free azimuthal magnetic field. The effects of radiation flux and magnetic field together have been seen in the region of interest on the other flow variables. The total energy of the flow between the inner expanding surface and the shock is taken to be dependent on shock radius obeying a power law. The radiative pressure and energy have been neglected.     

Acceleration of relativistic charged particles by supersonic hydromagnetic turbulence

The acceleration of relativistic particles is considered during their intersection with hydromagnetic shock fronts in the presence of randomly distributed large-scale magnetic fields. In a series of astronomical objects, the Larmor radius of the relativistic particles exceeds the width of the shock front. In this case there is a change in the adiabatic invariant which results in an increase in the energy of the particle when it crosses the front in any direction. We have proved that the adiabatic part of the energy change will be partially or completely compensated by its reverse change in the weaker regions of the magnetic field. The acceleration mechanism considered is found to be more effective than the Fermi mechanism.If the mean free path of the particles is much less than the distance between the shock fronts, magnetic small-scale fluctuations cause further scattering of the particles. In this case the particles following and crossing the front will return to it. After reversed crossing, a fraction of the particles-defined by the ratio of the front speed to the particle velocity or of the distance between the fronts to the free path — will not return to the front. It is proved that for both large and small free paths the rates at which the particle gains energy are nearly the same.     

A possible mechanism of jet formation in the nuclei of radio galaxies

A hypothesis is being put forward that the formation of jets in the nuclei of radio galaxies is due to a high-speed energy excretion (explosion) in the accretion disk around a massive black hole. The explosion can be induced, for example, by a fall of the star into the black hole. For the accretion disk featuring an exponential high-density distribution, an asymmetrical explosion can be obtained: the shock front moves in the direction of decreasing the density accelerately and achieves the relativistic velocity swiftly, carrying away the most fraction of the explosion energy. Radio emission of the jet involves synchrotron radiation of relativistic electrons which are accelerated by such shock wave in the magnetic field driven up by the shock front.