Sedov Solution Research Articles

ASCA Observations of the Supernova Remnant G156.2+5.7

We report on the ASCA X-ray spectra from the north rim and the center of the supernova remnant (SNR) G156.2+5.7. The spectra are found to comprise soft and hard X-ray components. No clear shell structure has been found, either in the soft or in the hard X-ray bands. The soft X-rays are attributable to a non-equilibrium ionization plasma with a temperature of 0.4 keV and an ionization timescale of 1011.0−11.2 cm−3s. A Sedov solution with an explosion energy of 1051 erg leads to an age of ∼ 1.5 × 104 yr and a density of ambient gas of ∼ 0.2 cm−3. The distance to G156.2+5.7 is estimated to be ∼ 1.3 kpc. The abundances of silicon and sulfur vary between the center and the north rim of the SNR, while the abundances of all other elements do not. The hard component can be modeled with either thermal emission of a temperature higher than a few keV or a non-thermal process with a power-law spectrum of photon index 1.5–1.8. Since the former model requires an uncomfortably high temperature, we favor a non-thermal model. We also discuss the nature of a point source found at the edge of the SNR.

Construction of piecewise-analytical gas flows joined through shock waves near the axis or center of symmetry

Analytical solutions of a quasilinear system of equations with partial derivatives are constructed in the case where the initial data for different functions are specified on different surfaces and the resultant problem has singularities of the form u/x and w/x. Conditions for existence and uniqueness of a solution in the form of formal power series for the problem posed and sufficient conditions for convergence of the series are indicated. A generalization of the problem considered is given. Results of the study are used to solve the problem of the focussing of a compression wave generated by a piston moving smoothly in a quiescent gas: a solution for t=0, including determination of the piston trajectory, and a solution for t 0. The solution of this problem is a generalization to the case of two independent variable self-similar Sedov's solutions.

A detailed X-ray and radio study of the supernova remnant W44

We analyze EXOSAT and Einstein Observatory X-ray spectra, an Einstein X-ray image, and a detailed VLA radio map of the SNR W44. The diffuse soft X-ray emission, which is only observed from the interior of the SNR, is shown to be largely of thermal origin. The absence of soft X-ray emission from the shell can be explained by the measured line-of-sight absorption, and provides an opportunity to study the SNR interior without confusion by bright shell emission. A deprojection of the interior X-ray surface brightness measured with the Einstein IPC is performed to derive density profiles which are relatively insensitive to the assumptions made. The density is found to decrease with radius by a factor of 3–4 between the center and a fractional radius of 0.8. The interior density profiles are completely inconsistent with those predicted by the Sedov solution for expansion into a uniform medium, but can be largely explained in terms of expansion into a cloudy interstellar medium in which most of the mass resides in a cool dense state. Shocked and compressed clouds of gas of size ≈ 0.4 to 8 pc in this state may be responsible for the numerous bright knots and filaments of radio emission revealed for the first time in our VLA map. A radio synchrotron nebula associated with the pulsar PSR 1853 + 01 may have been detected within the SNR. This proposed nebula is unusual because its position is offset from the pulsar, and in a direction consistent with motion of the pulsar away from the SNR centre.

Supernova remnant evolution in an interstellar medium with evaporating clouds

A new similarity solution that describes the evolution of an SNR expanding into a cloudy interstellar medium is expounded. The solution incorporates a reasonable model of the conductive evaporation of cold clouds embedded in the hot gas behind the shock. The model has two new parameters in addition to those describing the usual Sedov solution for a uniform interstellar medium. The X-ray, infrared, and optical luminosities of remnants with evaporating clouds are calculated, and some of the expected spectral characteristics in the various wavebands are discussed. The effects described may explain the class of remnants observed to have centrally peaked X-ray emission and shell-like radio emission. The total H-alpha luminosity from evaporating clouds predicted by this model is less than that observed for SNRs with centrally peaked thermal X-ray emission. A detailed calculation of the X-ray and optical line emission from evaporating clouds would be very useful in testing this model against the observations.

Instabilities Driven in Young Supernova Remnants by Electron Heat Conduction

Adiabatic models of supernova remnants (SNRs) show very large temperature gradients. The effect of thermal conduction on the Sedov solution was studied by a number of authors (Solinger et al., 1979; Cox and Edgar, 1983; Cowie, 1977).The observations show, however, that young SNRs such as SN 1006 (Hesser and van den Bergh, 1981) and SN 1572 (Strom, Goss and Shaver, 1982) are in an intermediate state between free expansion and the Sedov phase. In these cases stellar matter cannot be neglected. Following Chevalier (1982), the freely expanding ejecta of a Type I SNR can be modeled in such a way that the inner 4/7 of the mass have constant density and the outer 3/7 have a ρ∝r−7 profile (the "ramp"). The interaction of the ejecta with the uniform circumstellar medium (CSM) gives rise to a pair of shocks. As long as the reverse shock is within the r−7 part of the density profile, the interaction region is described by a self-similar solution (Chevalier, 1982). Such a solution holds for an adiabatic single fluid; the temperature gradient, however, is so large that it may give rise to a quite high heat flux.

Distances to the remnants of historical Type I supernovae

For supernova remnants in the adiabatic phase, the well-known Sedov solution can be used to express the shock radius as a function of age, initial energy and ambient density. Consequently, the relative distances of adiabatic remnants can be expressed in terms of these parameters and the angular dimensions. For Type energy released, the relative distance depends only upon age, density and angular size. There exist reliable determinations of these parameters for the remnants of the Type I supernovae of AD 185, 1006, 1572 and 1604. After considering what is known about each object in some detail, their relative distances have been determined (assuming equal energies) with an estimated uncertainty of about 10 per cent. The values have been compared with a variety of absolute distance determinations (excluding the peak visual magnitude) to obtain the following distances: SN 185, 1.2 kpc; SN 1006, 1.4 kpc; SN 1572, 2.5 kpc; SN 1604, 4.2 kpc. For three of the four, the average MV = 19.7 ± 0.5, while for SN 1572 MV = − 17.6 ± 0.5. It is suggested that this and other evidence points to SN 1572 (Tycho) having been a subluminous Type Ib event. Other properties of the remnants are briefly discussed, as is a way of dropping the equal-energy assumption thereby permitting SNR of Type II to be included. A possible extension of the technique to adiabatic remnants of unknown age is considered. The solid theoretical foundation upon which the technique rests provides obvious advantages over the traditional Σ–D) method, especially as it should produce reliable distances for young remnants, and can help tie down the distances of nearby remnants where traditional methods result in large fractional uncertainties.

Cosmological self-similar shock waves and galaxy formation

view Abstract Citations (84) References (28) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Cosmological self-similar shock waves and galaxy formation Bertschinger, E. Abstract Similarity solutions are found which are valid for times long compared to the Hubble time for adiabatic shock waves in open and Einstein-de Sitter Friedmann universes. The fluid equations and boundary conditions are given and integrals of the motion are derived from similarity arguments. Initially the shock wave formed satisfied the Sedov solution for adiabatic evolution in a constant medium, but it is modified by the cosmological expansion to form a self-similar thin dense shell which cools by adiabatic expansion and is unstable to gravitational fragmentation and collapse. The shock solution is applied to the explosive amplification model of galaxy formation of Ostriker and Cowie (1981). One generation of explosive amplification from an initial seed galaxy produces a shell of about 300 billion solar masses in galaxies, with radius and velocity dispersion typical of small groups. Publication: The Astrophysical Journal Pub Date: May 1983 DOI: 10.1086/160925 Bibcode: 1983ApJ...268...17B Keywords: Big Bang Cosmology; Galactic Clusters; Galactic Evolution; Relativity; Shock Wave Interaction; Adiabatic Flow; Astronomical Models; Cooling; Gravitational Collapse; Intergalactic Media; Jeans Theory; Mass Distribution; Red Shift; Similarity Theorem; Astrophysics full text sources ADS |

Radial distribution of forbidden Fe XIV emission in the Cygnus Loop

The one dimensional distribution of Fe 14 emission has been determined along a radius of the Cygnus Loop through the use of a tilting filter photometer. The observed emission extends at least 5 arc minutes outside the optical filaments. A simple Sedov solution model of the temperature and density distribution behind the shock agrees with the observations for parameters in reasonable agreement with X-ray maps and optical radial velocities.

The early evolution of supernova remnants in a homogeneous medium - The effects of electron thermal conduction

The role of electron thermal conduction in the evolution of supernova remnants may be fully understood only in the context of a two-fluid model, in which electron and ion temperatures are distinguished. During the early stages of supernova remnant evolution, high electron temperatures within the remnant imply that time scales for energy exchange by Coulomb collisions are long. Within the blast wave shock, electron and ion temperatures may be equalized by plasma instabilities, but in the interior of the remnant they may differ substantially. Only electron temperature profiles are fully smoothed by thermal conduction; ion temperatures in the interior of the remnant may remain high.Electron thermal conduction through the blast wave shock itself may be suppressed by magnetic field effects and by plasma instabilities. We suggest that this is required if the remnant is to maintain approximate spherical symmetry while expanding in an ordered magnetic field.We present two-fluid numerical simulations of remnant evolution in a homogeneous medium which illustrate the importance of these effects. Density profiles within the remnant are intermediate in form between those of nonconductive one-fluid simulations and those obtained in the isothermal blast wave similarity solution of Solinger et al. The radius of the remnant differs frommore » that of the Sedov solution by less than a factor of 1.08. We briefly discuss the applicability of theory to observed remnants and discuss some possible tests. We emphasize that the discovery of iron emission lines in young remnants does not necessarily imply that the spectra should be interpreted as bremsstrahlung from a Maxwellianized electron distribution, but may be due instead to a suprathermal electron population.« less

Use of similarity hypotheses for solving the problem of homogeneous turbulence decay: PMM vol. 37, n≗5, 1973, pp. 864–881

The feasibility of defining a homogeneous, and in particular, an isotropic turbulence, using only the hypotheses of similarity of spectral, correlation, or structural functions is considered. Hypotheses of similarity (“self-preservation”) of correlation functions were used in [1] and in many subsequent works in conjunction with other assumptions. Sedov [2], using only these hypotheses for analyzing the problem of decay of homogeneous and isotropic turbulent motions of a viscous incompressible fluid, had shown possible alternatives: either the energy of turbulent velocity pulsations decrease in inverse proportion to time and the linear scale increases in proportion to the square root of time, when the determination of dimensionless correlation functions requires additional assumptions; or the complete solution can be derived (and was derived by Sedov) without having to resort to supplementary assumptions. It is shown here that this solution is in good agreement with experimental data on the decay of turbulent motions of air and water downstream of a grid. With the use of the hypothesis of self-preservation of spectral tensors Sedov's solution is extended to homogeneous nonisotropic turbulence, and with the use of hypotheses of self-preservation of structural functions isotropic turbulence. In both cases alternatives similar to those of Sedov were obtained.

Propagation of a blast wave in uniform or non-uniform media: a uniformly valid analytic solution

The shock propagation theory of Brinkley & Kirkwood (1947) is extended to provide a uniformly valid analytic solution of point-explosion problems both when the undisturbed medium is uniform and when it is stratified. This is achieved mainly by selecting the parameter expressing a similarity restraint in this theory such that initially it gives precisely the Taylor–Sedov solution, while asymptotically, in the weak regime, still retaining the well-known Landau–Whitham–Sedov form of the solution for shock overpressure. The shock overpressure, as calculated by the present method for spherical and cylindrical blast waves in the entire regime from the point of explosion to where they have become very weak, shows excellent agreement with that from the exact numerical solutions of Lutzky & Lehto (1968) and Plooster (1970). The solution for a spherical shock propagating in an exponential atmosphere stratified by a constant acceleration due to gravity also shows a good agreement with the exact numerical solution of Lutzky & Lehto.

Theory of the Explosion in M82 II.

view Abstract Citations (7) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Theory of the Explosion in M82 II. Solinger, Alan B. Abstract A hydrodynamic blast-wave model provides a theoretical basis for understanding observed features of the explosion in M82. A. B. Solinger (Astron. J. 71, 872,1966) has pointed out that a self-similar Sedov solution predicts the flow observed, and the blast is a more suitable heating mechanism for excitation of the Ha in the filaments than the synchrotron process. Evidence is presented here that the polarized continuum observed is due to Thomson scattering of light from a Seyfert-like uucleu~not synchrotron emission. Analysis of the data (Elvius, A., Bull. Lowell Obs. 5, 281, 1963; IAU Symp. No. 29, Armen?an SSSR, 1966, to be published) shows that polarization increases and intensity decreases with increasing central distance. Models based on the similarity solution are quantitatively fitted to these data. The parameters are shock position, electron density, bremsstrahlung intensity, and luminosity of the nucleus. All parameters are evaluated within a factor of 4. The luminosity of the nucleus is 1.5 X 10~~ erg/sec-about that of a typical Seyfert nucleus; the energy of the explosion, 4.5 X 10~~ erg, released 7.5 X 10~ yr ago; average shock radius, 1.9 X 10~ pc; and the post-shock electron density, 8.5 cm-3. This implies the existence of a circumgalactic density of about 2 cm-3. The expected bright Seyfert-like nucleus may be unobserved for either of two reasons: the large quantities of observed dust may obscure it, in which case it should be detectable in the infrared; or the nucleus may have ceased radiating as much as 300 yr ago. Because of the large light travel time, one would still observe the scattering. We suggest that M82 is/was a Seyfert galaxy, seen edge-on. If similar explosions occur in other Seyfert galaxies, polarization due to electron scattering should also be observed in them. Publication: The Astronomical Journal Pub Date: October 1967 DOI: 10.1086/110518 Bibcode: 1967AJ.....72R.830S full text sources ADS |