On pulsar-driven isothermal blast-wave models of supernova remanants

We investigate the ‘equilibrium’ and stability of spherically-symmetric self-similar isothermal blast waves with a continuous post-shock flow velocity expanding into medium whose density varies asr ^?ω ahead of the blast wave, and which are powered by a central source (a pulsar) whose power output varies with time ast ^ω?3. We show that:

1. for ω<0, no physically acceptable self-similar solution exists;
2. for ω>3, no solution exists since the mass swept up by the blast wave is infinite;
3. ? must exceed zero in order that the blast wave expand with time, but ?<2 in order that the central source injects a finite total energy into the blast wave;
4. for 3>ω_min(?)>ω>ω_max(?)>0, where $$\begin{gathered} \omega _{\min } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} + {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} + {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \omega _{\max } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} - {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} - {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \end{gathered} $$ two critical points exist in the flow velocity versus position plane. The physically acceptable solution must pass through the origin with zero flow speed and through the blast wave. It must also pass throughboth critical points if \(\varphi > \tfrac{5}{3}\) , while if \(\varphi< \tfrac{5}{3}\) it must by-pass both critical points. It is shown that such a solution exists but a proper connection at the lower critical point (for ?>5/3) (through whichall solutions pass with thesame slope) has not been established;
5. for 3>ω>ω_min(?) it is shown that the two critical points of (iv) disappear. However a new pair of critical points form. The physically acceptable solution passing with zero flow velocity through the origin and also passing through the blast wave mustby-pass both of the new critical points. It is shown that the solution does indeed do so;
6. for 3>ω_min(?)>ω_max(?)>ω it is shown that the dependence of the self-similar solution on either ω or ? is non-analytic and therefore, inferences drawn from any solutions obtained in ω>ω_max(?) (where the dependence of the solutionis analytic on ω and ?) are not valid when carried over into the domain 3>ω_min(?)>ω_max(?)>ω;
7. all of the physically acceptable self-similar solutions obtained in 3>ω>0 are unstable to short wavelength, small amplitude but nonself-similar radial velocity perturbations near the origin, with a growth which is a power law in time;
8. the physical self-similar solutions are globally unstable in a fully nonlinear sense to radial time-dependent flow patterns. In the limit of long times, the nonlinear growth is a power law in time for 5<ω+2?, logarithmic in time for 5>ω+2?, and the square of the logarithm in time for 5=ω+2?.

The results of (vii) and (viii) imply that the memory of the system to initial and boundary values does not decay as time progresses and so the system does not tend to a self-similar form. These results strongly suggest that the evolution of supernova remnants is not according to the self-similar form.     

Isothermal self-similar blast wave theory of supernova remnants driven by relativistic gas pressure

We investigate the spherically symmetric, self-similar flow behind a blast wave from a point explosion in a medium whose density varies with distance asr ^– with the assumption that the flow is both isothermal and contains a relativistic component of pressure. A self-similar solution is shown to exist only if both the blast wave speed,u _s ,and the local sound speed,w, are constant. If [(1–w ²/c ²)] lies in 1>>0, there exists a critical point in the radial distance-flow velocity plane. To be physically acceptable, the solution must pass through the origin and through the critical point and then through to the blast front; solution branches between these points exist, although a proper connection at the critical point has not been demonstrated. If <0, a continuous single-valued solution does not exist. If 2>>1, the critical point is beyond the blast curve and the flow is subsonic everywhere. For 2<<3, the critical point disappears, but a new one arises. To be physically acceptable, the flow must by-pass this new critical point. It is shown that it does. The dependence of the solutions of is non-analytic for <1, so that interpolation between neighboring values of is not permitted. We investigate the stability of these isothermal blast waves to spherically symmetric but non-self-similar perturbations. If 3>>3/2 or 0<<1, the solutions are shown to be definitively linearly unstable against short wavelength disturbances near the blast front, they are also unstable there in 3/2>>1 unless the flow meets the blast front atprecisely the velocity (normalized) of (2–1)^1/2/(3–2)^1/2. The solutions are also unstable for all in 1>>0 near the critical point. Since there is no characteristic time scale in the system, all the instabilities grow as a power law in time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form. We conclude that isothermal self-similar blast waves do not provide a valid model for a supernova remnant driven by a relativistic gas pressure. Since the validity of the adiabatic blast wave models has elsewhere been shown to be questionable, it is doubtful whether the self-similar property can be involved at all in the case of supernova remnants. This raises serious questions of interpretation of quantities deduced for supernova remnants on the basis of the use of self-similar models.     

Maximum energy of cosmic rays accelerated by supernova shocks

The expression for the cutoff momentum of CR, accelerated by the supernova blast wave is derived. Geometrical factors (finite increase with time shock size, slowing shock speed and CR adiabatic effect in the downstream region) are shown to determine the value of the cutoff momentum. These factors are stronger than the time restriction and have a significant dynamical effect: the supernova blast wave cannot be completely smoothed by the CR backreaction even at very high Mach numbers. The shock transition always includes a pure gas subshock which strongly influences CR acceleration and shock evolution. It is shown that maximum particle energy achievable during CR acceleration by supernova shock can be as large as _max ≈ Z × 10¹⁵ eV, if the diffusion coefficient is as small as the Bohm limit. Due to nonlinear effect and adiabatic heating in the downstream region in the free expansion phase the actual value of _max is an order of magnitude higher than that from previous estimates based on the plane-wave consideration and is high enough to consider CR diffusive acceleration in SNRs as a main source of galactic CR at least up to the knee energy 3 × 10¹⁵ eV.     

On the detection of subphotospheric convective velocities and temperature fluctuations

A procedure is outlined for estimating the influence of large-scale convective eddies on the wave patterns of five-minute oscillations of high degree. The method is applied to adiabatic oscillations, with frequency ω and wave number k, of a plane-parallel polytropic layer upon which is imposed a low-amplitude convective flow. The distortion to the k - ω relation has two constituents: one depends on the horizontal component of the convective velocity and has a sign which depends on the sign of ω/k; the other depends on temperature fluctuations and is independent of the sign of ω/k. The magnitude of the distortion is just at the limit of present observational sensitivity. Thus there is reasonable hope that it will be possible to reveal some aspects of the large-scale flow in the solar convection zone.     

The effect of wind on magnetized advection dominated accretion flows

We study the effects of winds on advection dominated accretion flows in the presence of a global magnetic field under a self-similar treatment. The disk gas is assumed to be isothermal. For a steady state structure of such accretion flows a set of self similar solutions are presented. We consider the wind in a general magnetic field with three components (r,φ,z) in advection-dominated accretion flows. The mass-accretion rate $\dot{M}$ decreases with radius r as $\dot{M}\propto r^{s+1/2}$ , where s is an arbitrary constant. We will see, by increasing the wind parameter s, radial and rotational velocities increase.     

Velocity shear effect on the longitudinal wave in a strongly coupled dusty plasma

The characteristics of longitudinal dust acoustic wave (DAW) in presence of velocity shear have been investigated in a strongly coupled dusty plasma using the generalized hydrodynamic (GH) model. In the hydrodynamic regime (ωτ _m ?1), i.e. when characteristic time τ _m is slower than inverse of wave frequency, the viscosity in the GH model plays the usual role of wave damping, whereas in the kinetic regime (ωτ _m ?1), i.e. when characteristic time τ _m is larger than inverse of wave frequency, viscosity shows energy storing property in the wave. In the kinetic regime, we have studied the longitudinal mode $\omega^{2}=k^{2} (c_{d}^{2}+c_{l}^{2})$ (where ω is the frequency, k is the wave number, c _d is the dust acoustic velocity and c _l is the longitudinal velocity that arises due to viscosity) in presence of velocity shear. It is shown that velocity shear can destabilize this mode. Both nonmodal and modal techniques are employed to demonstrate the growth rate of the instability.     

Similarity parameters for converging shock waves in non-ideal magnetogasdynamics by Landau-Stanyukovich rule

In present paper, I have studied second-kind self-similar solutions of converging cylindrical shock wave in non-ideal magnetogasdynamics. Two trial functions suggested by Singh et al. and the shooting method of Landau–Stanyukovich are used to determine the similarity exponent α for different values of specific heat ratio γ and the parameter k, where k∈(0,1] and internal volume $\tilde{b}$ in non-ideal magnetogasdynamics.     

Neutrino emission of Fermi supernova remnants

The Fermi γ-ray space telescope reported the observation of several Galactic supernova remnants recently, with the γ-ray spectra well described by hadronic pp collisions. The possible neutrino emissions from these Fermi detected supernova remnants are discussed in this work, assuming the hadronic origin of the γ-ray emission. The muon event rates induced by the neutrinos from these supernova remnants on typical km³ neutrino telescopes, such as the IceCube and the KM3NeT, are calculated. The results show that for most of these supernova remnants the neutrino signals are too weak to be detected by the on-going or up-coming neutrino experiment. Only for the TeV bright sources RX J1713.7-3946 and possibly W28 the neutrino signals can be comparable with the atmospheric background in the TeV region, if the protons can be accelerated to very high energies. The northern hemisphere based neutrino telescope might detect the neutrinos from these two sources.     

X-ray detection of the monoceros supernova remnant

The Monoceros nebula is seen in the optical and in radio as a 3°.5 degree diameter ring. It is believed to be an old supernova remnant. Here is reported the detection of X-rays from the Monoceros nebula, confirming its supernova remnant nature.Einstein imaging proportional counter observations of 0.2 to 5 keV X-rays were analyzed to produce a surface brightness map. Preliminary modeling of the Monoceros supernova remnant yields an age of 50 000 years. A large age is expected for such a large remnant. However, the remnant is found to still be in the adiabatic blast wave stage of evolution.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

The stability of differential rotation with non-axisymmetric perturbations

A plane-wave analysis on a simplified scheme based on the Boussinesq approximation and shallow convection is used to establish the necessary conditions for stability of a differentiallyrotating, compressible flow between two coaxial cylinders subject to non-axisymmetric perturbations. To test the adequateness of this simplification, the sufficient conditions for stability are again established which agree with those obtained by a normal-mode analysis on an exact scheme in an earlier paper by the author. This model is applicable to stellar models with rotation Ω=Ω(ω), where ω is the radial distance from the axis of rotation (thez-axis). A necessary condition for stability, in the non-dissipative case, is found to be that $$\frac{1}{\varrho }G_\varpi S_\varpi + \frac{{k_z^2 }}{M}\Phi - \frac{1}{4}\frac{{m^2 }}{M}\left( {D\Omega } \right)^2 \geqslant 0$$ everywhere. Here,m andk _z are the wave numbers in the ø- andz-direction, \(M \equiv k_z^2 + m^2 /\varpi ^2 ,D \equiv d/d\varpi ,G_\varpi \equiv - \varrho ^{ - 1} Dp,\varrho \) the density,p the pressure,S _ω and Φ the Schwarzschild and the Rayleigh discriminants defined as \(S_\varpi \equiv \left( {\gamma p/\varrho } \right)^{ - 2} Dp - D\varrho and \Phi \equiv ^{ - 3} d\left( {\varpi ^4 \Omega ^2 } \right)/d\varpi \) respectively, γ the ratio of specific heats. This condition is also a sufficient one. Some conjectures regarding the stabilizing influence of uniform rotation and the destabilizing influence of differential rotation are also verified. The most striking instability mechanism introduced by shear forces and by radiative dissipation is the excitation of the stable motion of small oscillations into that of oscillations with growing amplitude, i. e., overstability. In the case of radiative dissipation and axisymmetric perturbations, the Goldreich-Schubert criterion is only necessary but not sufficient for stability. Instability sets in as soon as the Schwarzschild criterion is violated. When the perturbations are non-axisymmetric, instability always sets in as overstability as long as rotation is differential. This may explain the convective turbulence in the upper atmosphere where the radiation is active.     

The secular behavior of X-ray and radio emission from supernova remnants

General models for the secular behavior of the radio and X-ray emission from supernova remnants are examined and compared with the observations. Hot plasma and synchrotron models for the X-ray emission are considered. Among other things, it is concluded that (1) the total kinetic energy released in most supernova outbursts is probably less than about 10⁵¹ ergs; (2) continuous injection probably occurs for at least 10 yr in every case and about 1000 yr in most supernova remnants, in which case the supernova remnants 3C392, W28, Pup A and IC443 should produce 1–10 keV X-ray fluxes 10^–10 ergs/cm² sec; and (3) the X-ray sources in the Crab Nebula, Cas A and Tycho can be explained in terms of a model wherein continuous injection occurs for 300 yr for the Crab Nebula, much less than 250 yr for Cas A and much longer than 400 yr for Tycho. Finally, it is shown that if Tycho and Cas A contain an X-ray star such as NP0532, it is quite possible that the X-ray emission from those sources is predominantly due to the X-ray star.Supported by the Air Force Office of Scientific Research under Contract No. F44620-67-C-0065.     

Dynamic evolution model of isothermal voids and shocks

We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and construct all types of possible void solutions without or with shocks in surrounding envelopes. We examine properties of void boundaries and outer envelopes. Voids without shocks are all bounded by overdense shells and either inflows or outflows in the outer envelope may occur. These solutions, referred to as type void solutions, are further divided into subtypes and according to their characteristic behaviours across the sonic critical line (SCL). Void solutions with shocks in envelopes are referred to as type voids and can have both dense and quasi-smooth edges. Asymptotically, outflows, breezes, inflows, accretions and static outer envelopes may all surround such type voids. Both cases of constant and varying temperatures across isothermal shock fronts are analyzed; they are referred to as types and void shock solutions. We apply the ‘phase net matching procedure’ to construct various self-similar void solutions. We also present analysis on void generation mechanisms and describe several astrophysical applications. By including self-gravity, gas pressure and shocks, our isothermal self-similar void (ISSV) model is adaptable to various astrophysical systems such as planetary nebulae, hot bubbles and superbubbles in the interstellar medium as well as supernova remnants.      

Investigating the Astrophysical Applicability of Radiative and Non-Radiative Blast wave Structure in Cluster Media

We describe experiments that investigate the capability of an experimental platform, based on laser-driven blast waves created in a medium of atomic clusters, to produce results that can be scaled to astrophysical situations. Quantitative electron density profiles were obtained for blast waves produced in hydrogen, argon, krypton and xenon through the interaction of a high intensity (I ≈ 10¹⁷ Wcm⁻²), sub-ps laser pulse. From this we estimate the local post-shock temperature, compressibility, shock strength and adiabatic index for each gas. Direct comparisons between blast wave structures for consistent relative gas densities were achieved through careful gas jet parameter control. From these we investigate the applicability of different radiative and Sedov-Taylor self-similar solutions, and therefore the (ρ,T) phase space that we can currently access.     

SNR Surface Density Distribution in Nearby Galaxies

Since supernova remnants (SNRs) are believed to be the primary sources of Galactic cosmic rays (CRs), their distribution in galaxies is an important basis for modelling and understanding the distribution of the CRs and their γ-ray spectrum. We analysed the radial surface density of X-ray and radio selected SNRs in the Large Magellanic Cloud (LMC) and M 33. Both in X-rays and in radio, the surface densities of the SNRs are in excellent agreement in both galaxies, showing an exponential decay in radius. The results were compared to the SNR distribution in the spiral galaxies M 31 and NGC 6946 as well. The radial scale length of the distribution is $\frac{1} {4} $ ? $\frac{1} {3} $ of the radius of the galaxies, fully consistent with values derived for the Milky Way, the LMC, and M 33. Therefore, not only the radio SNRs, but also the X-ray detected SNR sample can be interpreted to be representative for the CR sources within a galaxy.     

Coronal Mass Ejections as Expanding Force-Free Structures

We model solar coronal mass ejections (CMEs) as expanding force-free magnetic structures and find the self-similar dynamics of configurations with spatially constant ??, where J=?? B, in spherical and cylindrical geometries, expanding spheromaks and Lundquist fields, respectively. The field structures remain force-free, under the conventional non-relativistic assumption that the dynamical effects of the inductive electric fields can be neglected. While keeping the internal magnetic field structure of the stationary solutions, expansion leads to complicated internal velocities and rotation, caused by inductive electric fields. The structure depends only on overall radius R(t) and rate of expansion $\dot{R}(t)$ measured at a given moment, and thus is applicable to arbitrary expansion laws. In case of cylindrical Lundquist fields, magnetic flux conservation requires that both axial and radial expansion proceed with equal rates. In accordance with observations, the model predicts that the maximum magnetic field is reached before the spacecraft reaches the geometric center of a CME.     

Self-Similar Evolution of Remnants With Conductively Driven Mass-Loading

We present self-similar solutions for remnants that are mass-loaded by conductively driven evaporation. This work extends the earlier results of Chièze and Lazareff through the inclusion of the explicit dependence of the mass-loading rate on position as well as temperature, and the treatment of cylindrically symmetric as well as spherically symmetric cases. The latter case is relevant to an individual supernova remnant in its adiabatic phase expanding into a clumpy interstellar medium. The former case may be relevant to the evolution of the outflow from a young galaxy in which a nearly simultaneous burst of star formation occurs as the density increases on its axis of symmetry. This revised version was published online in July 2006 with corrections to the Cover Date.     

Supernova remnants in the starburst galaxy M82

We have used the enhanced MERLIN at 1.5 and 5 GHz to image the central 700pc of the nearby starburst galaxy M82. Of order 40 discrete sources are detected and it appears that most of these sources are supernova remnants. Not only do many show shell structure and have a non-thermal radio spectrum, but they also follow a surface brightness/diameter relation consistent with that found in the LMC and Galactic supernova remnants. The detected M82 remnants are more compact and brighter than Galactic remnants which implies that they must be less than a few hundred years old and hence supernova rates are of order 0.05 per year. The 1.5 GHz measurements have shown that many of the remnants have low-frequency spectral turnovers which are probably due to free-free absorption in localised ionised gas with emission measures > 10⁶ pc cm^–6.     

On the relationship between pulsars and supernova remnants

We propose that single stars in the mass range 4–6·5M _⊙, that explode as Supernovae of Type I, are totally disrupted by the explosion and form shell-type remnants. More massive single stars which explode as Supernovae of Type II also give rise to shell-type remnants, but in this case a neutron star or a black hole is left behind. The first supernova explosion in a close binary also gives rise to a shell-type supernova remnant. The Crab-like filled-centre supernova remnants are formed by the second supernova explosion in a close binary. The hybrid supernova remnants, consisting of a filled centre surrounded by a shell, are formed if there is an active neutron star inside the shell.     

A search for compact decametric radio sources in supernova remnants using the interplanetary scintillation technique

Interplanetary scintillation observations of eleven supernova remnants and the pulsar J1939+2134, around which the existence of a supernova remnant remains obscure, were carried out with the largest in the world decameter radio telescope UTR-2 at 20, 25 and 30 MHz to determine if any of them contain compact radio sources with the angular size θ<5″. The sample included the young Galactic remnants and the other powerful SNRs. The interplanetary scintillations of the compact radio source in the Crab Nebula associated with the well-known pulsar J0534+2200 and the pulsar J1939+2134 were observed. Apart from the Crab Nebula, we have not detected a compact radio source in supernova remnants with the angular size θ<5″ and the flux density more than 10 Jy. The observations do not confirm the existence of the low frequency compact source in Cassiopeia A that has remained controversial.     

Systematic search for molecular clouds near supernova remnants as sources of very-high-energy γ-ray emission

Supernova remnants accelerate particles up to energies of at least 100 TeV as established by observations in very-high-energy γ-ray astronomy. Molecular clouds in their vicinity provide an increased amount of target material for proton-proton interaction and subsequent neutral pion decay into γ-rays of accelerated hadrons escaping the remnant. Therefore, these molecular clouds are potential γ-ray sources. The γ-ray emission from these clouds provides a unique environment to derive information on the propagation of very-high-energy particles through the interstellar medium as well as on the acceleration of hadrons in supernova remnants. Current Imaging Atmospheric Cherenkov Telescope systems are suitable to explore a large parameter space of the propagation properties depending on the age of the supernova remnant and the distance between the remnant and the nearby molecular cloud.In this paper we present our strategy and results of a systematic search for γ-ray emitting molecular clouds near supernova remnants which are potentially detectable with current experiments in the TeV energy range and explore the prospects of future experiments.