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Register a new userTurbulence and Energetic Particles in Radiative Shock Waves in the Cygnus Loop I: Shock Properties
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We have obtained a contiguous set of long-slit spectra of a shock wave in the Cygnus Loop to investigate its structure, which is far from the morphology predicted by 1D models. Proper motions from Hubble Space Telescope images combined with the known distance to the Cygnus Loop provide an accurate shock speed. Earlier analyses of shock spectra estimated the shock speed, postshock density, temperature, and elemental abundances. In this paper we determine several more shock parameters: a more accurate shock speed, ram pressure, density, compression ratio, dust destruction efficiency, magnetic field strength, and vorticity in the cooling region. From the derived shock properties we estimate the emissivities of synchrotron emission in the radio and pion decay emission in the gamma rays. Both are consistent with the observations if we assume simple adiabatic compression of ambient cosmic rays as in the van der Laan mechanism. We also find that, although the morphology is far from that predicted by 1D models and the line ratios vary dramatically from point to point, the average spectrum is matched reasonably well by 1D shock models with the shock speed derived from the measured proper motion. A subsequent paper will analyze the development of turbulence in the cooling zone behind the shock.
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Radiative shock waves in the Cygnus Loop and other supernova remnants show different morphologies in [O III] and H{alpha} emission. We use HST spectra and narrowband images to study the development of turbulence in the cooling region behind a shock on the west limb of the Cygnus Loop. We refine our earlier estimates of shock parameters that were based upon ground-based spectra, including ram pressure, vorticity and magnetic field strength. We apply several techniques, including Fourier power spectra and the Rolling Hough Transform, to quantify the shape of the rippled shock front as viewed in different emission lines. We assess the relative importance of thermal instabilities, the thin shell instability, upstream density variations, and upstream magnetic field variations in producing the observed structure.
Observations of SN1006 have shown that ions and electrons in the plasma behind fast supernova remnant shock waves are far from equilibrium, with the electron temperature much lower than the proton temperature and ion temperatures approximately proportional to ion mass. In the ~360 km/s shock waves of the Cygnus Loop, on the other hand, electron and ion temperatures are roughly equal, and there is evidence that the oxygen kinetic temperature is not far from the proton temperature. In this paper we report observations of the He II lambda 1640 line and the C IV lambda 1550 doublet in a 360 km/s shock in the Cygnus Loop. While the best fit kinetic temperatures are somewhat higher than the proton temperature, the temperatures of He and C are consistent with the proton temperature and the upper limits are 0.5 and 0.3 times the mass-proportional temperatures, implying efficient thermal equilibration in this collisionless shock. The equilibration of helium and hydrogen affects the conversion between proton temperatures determined from H alpha line profiles and shock speeds, and that the efficient equilibration found here reduces the shock speed estimates and the distance estimate to the Cygnus Loop of Medina et al. (2014) to about 800 pc.
In this paper we analyze crowd turbulence from both classical and quantum perspective. We analyze various crowd waves and collisions using crowd macroscopic wave function. In particular, we will show that nonlinear Schr{o}dinger (NLS) equation is fundamental for quantum turbulence, while its closed-form solutions include shock-waves, solitons and rogue waves, as well as planar de Broglies waves. We start by modeling various crowd flows using classical fluid dynamics, based on Navier-Stokes equations. Then, we model turbulent crowd flows using quantum turbulence in Bose-Einstein condensation, based on modified NLS equation. Keywords: Crowd behavior dynamics, classical and quantum turbulence, shock waves, solitons and rogue waves
Upper limits on the shock speeds in supernova remnants can be combined with post-shock temperatures to obtain upper limits on the ratio of cosmic ray to gas pressure (P_CR / P_G) behind the shocks. We constrain shock speeds from proper motions and distance estimates, and we derive temperatures from X-ray spectra. The shock waves are observed as faint H-alpha filaments stretching around the Cygnus Loop supernova remnant in two epochs of the Palomar Observatory Sky Survey (POSS) separated by 39.1 years. We measured proper motions of 18 non-radiative filaments and derived shock velocity limits based on a limit to the Cygnus Loop distance of 576 +/- 61 pc given by Blair et al. for a background star. The PSPC instrument on-board ROSAT observed the X-ray emission of the post-shock gas along the perimeter of the Cygnus Loop, and we measure post-shock electron temperature from spectral fits. Proper motions range from 2.7 arcseconds to 5.4 arcseconds over the POSS epochs and post-shock temperatures range from kT ~ 100-200 eV. Our analysis suggests a cosmic ray to post-shock gas pressure consistent with zero, and in some positions P_CR is formally smaller than zero. We conclude that the distance to the Cygnus Loop is close to the upper limit given by the distance to the background star and that either the electron temperatures are lower than those measured from ROSAT PSPC X-ray spectral fits or an additional heat input for the electrons, possibly due to thermal conduction, is required.
Supersonic turbulence generates distributions of shock waves. Here, we analyse the shock waves in three-dimensional numerical simulations of uniformly driven supersonic turbulence, with and without magnetohydrodynamics and self-gravity. We can identify the nature of the turbulence by measuring the distribution of the shock strengths. We find that uniformly driven turbulence possesses a power law distribution of fast shocks with the number of shocks inversely proportional to the square root of the shock jump speed. A tail of high speed shocks steeper than Gaussian results from the random superposition of driving waves which decay rapidly. The energy is dissipated by a small range of fast shocks. These results contrast with the exponential distribution and slow shock dissipation associated with decaying turbulence. A strong magnetic field enhances the shock number transverse to the field direction at the expense of parallel shocks. A simulation with self-gravity demonstrates the development of a number of highly dissipative accretion shocks. Finally, we examine the dynamics to demonstrate how the power-law behaviour arises.
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