A self-similar solution for a supernova explosion with allowance for accelerated relativistic particles

A self-similar solution to Sedov’s problem of a strong explosion in a homogeneous medium is generalized to the case of relativistic-particle generation in a supernova remnant; the particles are accelerated by Fermi’s mechanism at the shock front and in the perturbed post-shock region. Self-similarity takes place if the thickness of the prefront is small compared to its radius and if the pressure ratio of the relativistic and nonrelativistic components at the shock front is kept constant. In the presence of relativistic particles, the time dependence of the shock-front radius remains the same as that in their absence, but the plasma parameters in the inner perturbed region change appreciably. The shell of the matter raked up by the explosion is denser and thinner than that in the nonrelativistic case, the relativistic-particle pressure in the central region remains finite, and the nonrelativistic-gas pressure at the explosion center approaches zero. The influence of relativistic particles on the transition to the radiative phase of expansion of the supernova remnant and on its dynamics is studied. It is shown that relativistic particles can decrease several-fold the remnant radius at which the transition to the radiative phase occurs.     

A massive circumstellar envelope around the type-IIn supernova SN 1995G

We model the interaction of the supernova SN 1995G with a dense circumstellar (CS) gas in a thin-shell approximation. A model fit to the observed bolometric light curve combined with data on the supernova expansion velocity gives estimates for the density, mass (≈1 M_⊙), and age (≈8 yr) of the CS envelope. The determined CS-envelope density is shown to be virtually independent of the assumed mass of the supernova envelope because of the high CS-gas density at which the forward shock wave is essentially radiative. The derived CS-envelope density is consistent with the Hα luminosity and with the presence of distinct Thomson scattering in the red wing of this line. The mass of the CS envelope together with its expansion velocity and age indicate that the CS envelope was ejected by the presupernova eight years before the supernova explosion through violent energy release (～6×10⁴⁸ erg).     

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.     

Massive stars exploding in a He-rich circumstellar medium – III. SN 2006jc: infrared echoes from new and old dust in the progenitor CSM

We present near- (NIR) and mid-infrared (MIR) photometric data of the Type Ibn supernova (SN) 2006jc obtained with the United Kingdom Infrared Telescope (UKIRT), the Gemini North Telescope and the Spitzer Space Telescope between days 86 and 493 post-explosion. We find that the IR behaviour of SN 2006jc can be explained as a combination of IR echoes from two manifestations of circumstellar material. The bulk of the NIR emission arises from an IR echo from newly condensed dust in a cool dense shell (CDS) produced by the interaction of the ejecta outward shock with a dense shell of circumstellar material ejected by the progenitor in a luminous blue variable (LBV)-like outburst about two years prior to the SN explosion. The CDS dust mass reaches a modest  3.0 × 10⁻⁴ M_⊙  by day 230. While dust condensation within a CDS formed behind the ejecta inward shock has been proposed before for one event (SN 1998S), SN 2006jc is the first one showing evidence for dust condensation in a CDS formed behind the ejecta outward shock in the circumstellar material. At later epochs, a substantial and growing contribution to the IR fluxes arises from an IR echo from pre-existing dust in the progenitor wind. The mass of the pre-existing circumstellar medium (CSM) dust is at least  ∼8 × 10⁻³ M_⊙  . This paper therefore adds to the evidence that mass-loss from the progenitors of core-collapse SNe could be a major source of dust in the Universe. However, yet again, we see no direct evidence that the explosion of an SN produces anything other than a very modest amount of dust.     

Neutral hydrogen in the vicinity of the supernova remnant HB 9

The neutral hydrogen emission at 21 cm has been investigated with the RATAN-600 radio telescope in the vicinity of the supernova remnant HB9. A clumpyHI shell with radial motions surrounding the remnant has been detected. Its measured parameters contradict the connection with a shock wave from a supernova explosion. The shell formation under the action of a wind from a star that exploded as a supernova at the end of its evolution seems more realistic. The characteristics of the star obtained from the observed shell parameters are the following: a wind power of 0.5 × 10³⁸ erg s^?1, a mass-loss rate of 3.7 × 10^?5 M _⊙ yr^?1, and an age of 3 × 10⁶ yr. Given the measurement errors, the mass of the star is estimated to be >8M _⊙.     

Nonresonant generation of MHD disturbances during supernova explosions in an inhomogeneous interstellar medium

We analyze the nonresonant generation of large-scale magnetic inhomogeneities near a shock front by accelerated particles. The MHD disturbances are generated by the electric current excited by relativistic particles in the preshock medium in the presence of weak large-scale density inhomogeneities. The MHD modes considered can be amplified by other resonant and nonresonant mechanisms related to the presence of relativistic particles. We estimate the magnetic fields and the energies to which charged particles can be accelerated in different phases of the interstellar medium by taking into account the random magnetic fields generated by the mechanism considered.     

The origin of the high-velocity circumstellar gas around SN 1998S

Modelling of high-resolution Balmer line profiles in the early-time spectra of SN 1998S shows that the inferred fast (≈400 km s⁻¹) circumstellar (CS) gas on days 23 and 42 post-explosion is confined to a narrow, negative velocity gradient shell just above the photosphere. This gas may be identified with a slow  (v<40 km s⁻¹)  progenitor wind accelerated at the ejecta–wind interface. In this scenario, the photosphere coincides with a cool dense shell formed in the reverse shock. Acceleration by radiation from the supernova or by a shock-accelerated relativistic particle precursor are both possible explanations for the observed fast CS gas. An alternative, equally plausible scenario is that the fast CS gas is accelerated within shocked clouds engulfed by the outer shock, as it propagates through the intercloud wind.     

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.     

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.     

Influence of a strong magnetic field on the neutrino heating of a supernova shock

Based on the magnetorotational model of a supernova explosion with core collapse, we investigate the significant processes of neutrino heating of the supernova shock. These processes should be taken into account in self-consistent modeling, since the neutrino heating mechanism is capable of increasing the explosion efficiency. We show that, even in the presence of a strong magnetic field (B ～ 10¹⁵ G) in the shock formation region, the heating rate is determined with good accuracy by the absorption and emission of neutrinos in direct URCA processes. Moreover, the influence on them of a magnetic field is reduced to insignificant corrections.     

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.     

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.     

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.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

Cosmic-ray energetics in the supernova remnant Cassiopeia A

Based on the observed radio spectrum for the supernova remnant Cassiopeia A, we have established that it represents synchrotron radiation of relativistic electrons with a nonpower-law energy spectrum in the form of Kaplan-Tsytovich’s standard distribution. The total density of relativistic electrons is 10^?3 cm^?3, only 20% of which form the radio spectrum. The particle number ratio of the proton-nuclear and electron cosmicray components inside the shell differs significantly from the mean Galactic ratio (100) and probably does not exceed unity.     

Supernovae in dense winds

An overview of the optical effects caused by a supernova explosion in a dense circumstellar wind is presented. Some unclear points and difficulties of the conventional models are pointed out and additional processes suggested, namely, thermal conductivity between the shocked wind and fragmented shocked ejecta, interaction of the wind with a relativistic precursor, and emission from accelerated fragments of shocked wind clouds. A simple model is proposed for cloud formation in the pre-supernova wind.     

The Crab Nebula: Interpretation of Chandra observations

We interpret the observed X-ray morphology of the central part of the Crab Nebula (torus + jets) in terms of the standard theory by Kennel and Coroniti (1984). The only new element is the inclusion of anisotropy in the energy flux from the pulsar in the theory. In the standard theory of relativistic winds, the Lorentz factor of the particles in front of the shock that terminates the pulsar relativistic wind depends on the polar angle as γ = γ₀ + γ _m sin² θ, where γ₀∼200 and γ_m∼4.5×10⁶. The plasma flow in the wind is isotropic. After the passage of the pulsar wind through the shock, the flow becomes subsonic with a roughly constant (over the plerion volume) pressure P=1/3;n∈ where n is the plasma particle density and ∈ is the mean particle energy. Since ∈∼γmc ², a low-density region filled with the most energetic electrons is formed near the equator. A bright torus of synchrotron radiation develops here. Jet-like regions are formed along the pulsar rotation axis, where the particle density is almost four orders of magnitude higher than that in the equatorial plane, because the particle energy there is four orders of magnitude lower. The energy of these particles is too low to produce detectable synchrotron radiation. However, these quasijets become comparable in brightness to the torus if additional particle acceleration takes place in the plerion. We also present the results of our study of the hydrodynamic interaction between an anisotropic wind and the interstellar medium. We compare the calculated and observed distributions of the volume emissivity of X-ray radiation.