Sedov Stage Research Articles

Magneto-hydrodynamic simulations of young supernova remnants and their energy-conversion phase

ABSTRACT Supernova remnants (SNRs) can be rich sources of information on the parent SN (supernova) explosion. Thus, investigating the transition from the phase of SN to that of SNR can be crucial to link these two phases of evolution. Here, we aim to study the early development of SNR in more detail, paying the major attention to the transition from the early expansion stage to the Sedov stage and the role played by magnetic field in this transition. To this end, spherical magnetohydrodynamic simulations of SNRs have been performed to study the evolution of magnetic field in young SNRs and explore a sequence of the SNR evolutionary stages in the pre-radiative epoch. Remnants of three supernova types are considered, namely, SNIa, SNIc, and SNIIP, that covers a wide space of parameters relevant for SNRs. Changes in global characteristics and development of spatial distributions are analysed. It is shown that the radial component of magnetic field rapidly drops downstream of the forward shock. Therefore, the radially aligned polarization patterns observed in few young SNRs cannot be reproduced in the 1D MHD simulations. The period SNR takes for the transition from the earliest ejecta-driven phase to the Sedov phase is long enough, with its distinctive physical features, headed by the energy conversion from mostly kinetic one to a fixed ratio between the thermal and kinetic components. This transition worth to be distinguished as a phase in SNR evolutionary scheme. The updated sequence of stages in SNR evolution could be the free expansion (of gas) – energy conversion – Sedov–Taylor – post-adiabatic – radiative.

DYNAMICAL EVOLUTION OF SUPERNOVA REMNANTS BREAKING THROUGH MOLECULAR CLOUDS

We carry out three-dimensional hydrodynamic simulations of the supernova remnants (SNRs) produced inside molecular clouds (MCs) near their surface using the HLL code (Harten et al. 1983). We explore the dynamical evolution and the X-ray morphology of SNRs after breaking through the MC surface for ranges of the explosion depths below the surface and the density ratios of the clouds to the intercloud media (ICM). We find that if an SNR breaks out through an MC surface in its Sedov stage, the outermost dense shell of the remnant is divided into several layers. The divided layers are subject to the Rayleigh-Taylor instability and fragmented. On the other hand, if an SNR breaks through an MC after the remnant enters the snowplow phase, the radiative shell is not divided to layers. We also compare the predictions of previous analytic solutions for the expansion of SNRs in stratified media with our onedimensional simulations. Moreover, we produce synthetic X-ray surface brightness in order to research the center-bright X-ray morphology shown in thermal composite SNRs. In the late stages, a breakout SNR shows the center-bright X-ray morphology inside an MC in our results. We apply our model to the observational results of the X-ray morphology of the thermal composite SNR 3C 391.

Maximum energy of cosmic rays accelerated in supernova remnants

Amplification of the magnetic field in young supernova remnants leads to the corresponding increase in the maximum energy of particles approximately to the knee energy 3 × 1015 eV at the end of the free expansion stage. The knee in the spectrum of cosmic rays is due to the transition of the supernova remnant from the free expansion stage to the Sedov stage. The knee energy is calculated for different types of supernovae. The maximum energy of accelerated particles teaches Z × 1017 eV for the observed remnant expansion velocities.

Long‐Term Evolution of Supernova Remnants in Magnetized Interstellar Medium

The evolution of supernova remnants (SNRs) is studied, with particular attention to the effect of magnetic fields with axisymmetric two-dimensional magnetohydrodynamic simulations. We study the interaction of SNRs with a quiescent, magnetized ISM having uniform density, temperature, and magnetic field. The evolution of magnetic SNRs is the same as that of nonmagnetic ones in the adiabatic Sedov stage. After a thin shell is formed, the shell is driven by the pressure of the hot interior gas (bubble). Evolution in the pressure-driven snowplow phase is much affected by the magnetic field. The shell sweeping the magnetic field lines thickens owing to the magnetic pressure force. After 5 × 105 to 2 × 106 yr, the inner boundary of the thick shell begins to contract. This compresses the hot bubble radially and maintains its thermal pressure. Thus, the bubble forms a prolate spheroidal shape and becomes thinner and thinner, since it expands in a direction parallel to the magnetic field for B0 3 μG. Finally, the bubble contracts. The porosity of the hot low-density gas in the ISM is reduced, taking the effect of the magnetic field into account.

The Evolution of Supernovae in Circumstellar Wind‐Blown Bubbles. I. Introduction and One‐Dimensional Calculations

Mass loss from massive stars (≳8 M☉) can result in the formation of circumstellar wind-blown cavities surrounding the star, bordered by a thin, dense, cold shell. When the star explodes as a core-collapse supernova (SN), the resulting shock wave will interact with this modified medium around the star, rather than the interstellar medium. In this work we first explore the nature of the circumstellar medium around massive stars in various evolutionary stages. This is followed by a study of the evolution of SNe within these wind-blown bubbles. The evolution depends primarily on a single parameter Λ, the ratio of the mass of the dense shell to that of the ejected material. We investigate the evolution for different values of this parameter. We also plot approximate X-ray surface brightness plots from the simulations. For very small values Λ ≪ 1 the effect of the shell is negligible, as one would expect. Values of Λ ≲ 1 affect the SN evolution, but the SN "forgets" about the existence of the shell in about 10 doubling times or so. The remnant density profile changes, and consequently the X-ray emission from the remnant will also change. The initial X-ray luminosity of the remnant is quite low, but interaction of the shock wave with the dense circumstellar shell can increase the luminosity by 2-3 orders of magnitude. As the reflected shock begins to move inward, X-ray images will show the presence of a double-shelled structure. Larger values result in more SN energy being expended to the shell. The resulting reflected shock moves quickly back to the origin, and the ejecta are thermalized rapidly. The evolution of the remnant is speeded up, and the entire remnant may appear bright in X-rays. If Λ ≫ 1, then a substantial amount of energy may be expended in the shell. In the extreme case the SN may go directly from the free expansion to the adiabatic stage, bypassing the Sedov stage. Our results show that in many cases the SNR spends a significant amount of time within the bubble. The low density within the bubble can delay the onset of the Sedov stage and may end up reducing the amount of time spent in the Sedov stage. The complicated density profile within the bubble makes it difficult to infer the mass-loss properties of the pre-SN star by studying the evolution of the resulting SNR.

On the spectrum of high-energy cosmic rays produced by supernova remnants in the presence of strong cosmic-ray streaming instability and wave dissipation

The cosmic-ray streaming instability creates strong magnetohydrodynamic turbulence in the precursor of a SN shock. The level of turbulence determines the maximum energy of cosmic-ray particles accelerated by the diffusive shock accelera- tion mechanism. In this paper we present the continuation of previous work (Ptuskin & Zirakashvili 2003). We assume that Kolmogorov type nonlinear wave interactions together with ion-neutral collisions restrict the amplitude of the random mag- netic field. As a result, the maximum energy of the accelerated particles strongly depends on the age of a SNR. The average spectrum of cosmic rays injected in the interstellar medium in the course of the adiabatic SNR evolution (the Sedov stage) is approximately Q(p)p 2 ∝ p −2 at energies larger than 10−30 GeV/nucleon and with a maximum particle energy that is close to the position of the knee in the cosmic-ray spectrum observed at ∼4 × 10 15 eV. At an earlier stage of SNR evolution - the ejecta-dominated stage described by the Chevalier-Nadyozhin solution, the particles are accelerated to higher energies and have a rather steep power-law distribution. These results suggest that the knee may mark the transition from the ejecta-dominated to the adiabatic evolution of SNR shocks which accelerate cosmic rays.

Limits on diffusive shock acceleration in supernova remnants in the presence of cosmic-ray streaming instability and wave dissipation

The instability in the cosmic-ray precursor of a supernova shock moving in interstellar medium is studied. The level of magnetohydrodynamic turbulence in this region determines the maximum energy of particles accelerated by the diffusive shock acceleration mechanism. The high efficiency of cosmic ray acceleration is accepted, and the consideration is not limited by the case of weak turbulence. It is assumed that Kolmogorov type nonlinear wave interactions together with the ion-neutral collisions restrict the amplitude of random magnetic field. As a result, the maximum energy of accelerated particles strongly depends on the age of supernova remnant. The maximum energy can be as high as $\sim10^{17}Z$ eV in young supernova remnants and falls down to about $\sim10^{10}Z$ eV at the end of Sedov stage. Thus the standard estimate of maximum particle energy based on the Bohm limit calculated for the interstellar magnetic field strength is not justified in this case. This finding may explain why the supernova remnants with the age more than a few thousand years are not prominent sources of very high energy gamma-rays.

Interaction of high-velocity pulsars with supernova remnant shells

Hydrodynamical simulations are presented of a pulsar wind emitted by a supersonically moving pulsar. The pulsar moves through the interstellar medium or, in the more interesting case, through the supernova remnant created at its birth event. In both cases there exists a three-fold structure consisting of the wind termination shock, contact discontinuity and a bow shock bounding the pulsar wind nebula. Using hydrodynamical simulations we study the behaviour of the pulsar wind nebula inside a supernova remnant, and in particular the interaction with the outer shell of swept up interstellar matter and the blast wave surrounding the remnant. This interaction occurs when the pulsar breaks out of the supernova remnant. We assume the remnant is in the Sedov stage of its evolution. Just before break-through, the Mach number associated with the pulsar motion equals ${\cal M}_{\rm psr} = 7/\sqrt{5}$, {\em independent} of the supernova explosion energy and pulsar velocity. The bow shock structure is shown to survive this break-through event.