Ion acceleration and Alfvén wave generation at the Earth’s bow shock

The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10^?2–1 Hz and their spectral peak with a wave amplitude βB ～ B comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10^?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.     

Shock acceleration of solar cosmic rays

The solar cosmic ray (SCR) acceleration by the shocks driven by coronal mass ejections is studied by taking into account the generation of Alfvén waves by accelerated particles. Detailed numerical calculations of the SCR spectra produced during the shock propagation through the solar corona have been performed within a quasi-linear approach with a realistic set of coronal parameters. The resultant SCR energy spectrum is shown to include a power-law part N ∝ ?^-γ with an index γ = 1.7–3.5 that ends with an exponential tail. The maximum SCR energy lies within the range ? _max = 0.01–10 GeV, depending on the shock velocity V _S = 750–2500 km s^?1. The decrease of the shock Alfvénic Mach number due to the increase Alfvén velocity with heliocentric distance r leads to the end of the efficient SCR acceleration when the shock size reaches R _S ≈ 4R _⊙. In this case, the diffusive SCR propagation begins to exceed the shock velocity; as a result, SCRs escape intensively from the shock vicinity. The self-consistent generation of Alfvén waves by accelerated particles is accompanied by a steepening of the particle spectrum and an increase of their maximum energy. Comparison of the calculated SCR fluxes expected near the Earth’s orbit with the available experimental data shows that the theory explains the main observed features.     

Variations of microwave emission from solar active regions

Based on observational data obtained with the RT-22 Crimean Astrophysical Observatory radio telescope at frequencies of 8.6 and 15.4 GHz, we investigate the quasi-periodic variations of microwave emission from solar active regions with periods T_p<10 min. As follows from our wavelet analysis, the oscillations with periods of 3–5 min and 10–40 s have the largest amplitudes in the dynamic power spectra, while there are virtually no oscillations with T_p<10 s. Our analysis shows that acoustic modes with T_p?1 min strongly dissipate in the lower solar corona due to thermal conduction losses. The oscillations with T_p=10–40 s are associated with Alfvén disturbances. We analyze the influence of acoustic and Alfvén oscillations on the thermal mechanisms of microwave emission in terms of the homogeneous model. We discuss the probable coronal heating sources.     

Particle acceleration and Alfvén wave generation by an interplanetary shock

Based on the event observed by ISEE 3 near the Earth’s orbit at 01:21 UT on April 5, 1979, we investigate the diffusive shock acceleration of ions and the generation of Alfvén waves by accelerated particles near the quasi-parallel parts of interplanetary shock fronts within a quasi-linear approach. The theory is shown to give an excessively high level of Alfvén wave generation by accelerated particles at significant deflection angles of the interplanetary magnetic field from the normal to the shock front. At the Earth’s orbit, the Alfve´ n waves produced by accelerated ions are confined within the frequency range 5 × 10^?2?0.5 Hz, and their spectral peak with a wave amplitude δB ≤ B corresponds to a frequency ν = (1?2)×10^?2 Hz. The high-frequency part of the wave spectrum (ν ≥ 0.5 Hz) is subjected to damping on thermal protons. The calculated spectra of the accelerated ions and Alfvén waves generated by them reproduce the main features observed in experiments.     

Effects of boundary conditions and viscous energy dissipation on carbon burning in thermonuclear supernova models

Based on a one-dimensional hydrodynamic model, we investigate carbon burning in a thermonuclear type-Ia supernova in the approximation of unsteady convection. The relatively broad range of convective parameters, 1×10^?3≤α_c≤2×10^?3, in which delayed detonation from the edge takes place was found to be preserved only for cases with a low boundary temperature at the presupernova stage, T _b ^(PS) = 6.4 × 10⁶ K, and with a high envelope mass, m_ex ? 2 × 10^?3M_⊙. In cases with a more realistic temperature, T _b ^(PS) = 2 × 10⁸ K, which corresponds to helium burning in the shell source, and with a lower mass m_ex, delayed detonation from the edge takes place only at α_c = 2 × 10^?3, while at α_c = 1 × 10^?3, numerous model pulsations occur during t?500 s. Artificial viscosity is shown to give a determining contribution to the increase in entropy in outer model shells, which is caused by the generation of weak shock waves during pulsations. We also show that the entropies calculated by two independent methods are equal.     

Slow solar wind: Sources and components of the stream structure at the solar maximum

We study the sources and components of the solar-wind spatial stream structure at the maximum of the solar cycle 23. In our analysis, we use several independent sets of experimental data: radio-astronomical observations of scattered radiation from compact sources with the determination of the distance from the Sun to the inner boundary of the transonic-flow transition region (R_in); calculated data on the magnetic-field intensity and structure in the solar corona, in the solar-wind source region, obtained from optical measurements of the photospheric magnetic-field intensity at the Stanford Solar Observatory (USA); and observations of the white-light corona with the LASCO coronograph onboard the SOHO spacecraft. We show that at the solar maximum, low-speed streams with a transition region located far from the Sun dominate in the solar-wind structure. A correlation analysis of the location of the inner boundary R_in and the source-surface magnetic-field intensity |B _R | on a sphere R=2.5R_S (R_S is the solar radius) has revealed the previously unknown lowest-speed streams, which do not fit into the regular relationship between the parameters R_in and |B _R |. In the white-light corona, the sources of these streams are located near the dark strip, a coronal region with a greatly reduced density; the nonstandard parameters of the streams probably result from the interaction of several discrete sources of different types.     

Spectroscopy of the W Virginis star V1 (K 307 ) in the globular cluster M12

High-resolution CCD spectra have been obtained for the first time for the W Virginis star V1 (K 307) in the globular cluster M12 and its closest neighbor K 307b (m _pg=14^m; the angular distance from the W Vir star is δ<1 arcsec). We determined the fundamental parameters (T _eff=5600 K, logg=1.3, and T _eff=4200 K, logg=1.0 for the W Vir star and the neighboring star, respectively) and their detailed chemical composition. The derived metallicities of the two stars ([Fe/H]=?1.27 and ?1.22 relative to the solar value) are in good agreement with the metallicities of other cluster members. Changed CNO abundances were found in the atmosphere of the W Vir star: a small carbon overabundance, [C/Fe]=+0.30 dex, and a large nitrogen overabundance, [N/Fe]=+1.15 dex, with oxygen being underabundant, [O/Fe]≈?0.2 dex. The C/O ratio is ≥1. Na and the α-process elements Mg, Al, Si, Ca, and Ti are variously enhanced with respect to iron. We found an enhanced abundance of s-process metals relative to iron: [X/Fe]=+0.34 for Y, Zr, and Ba. The overabundance of the heavier metals La, Ce, and Nd with respect to iron is larger: [X/Fe]=+0.49. The largest overabundance was found for the r-process element europium, [Eu/Fe]=+0.82. The spectrum of the W Vir star exhibits the Hα and Hβ absorption-emission profiles and the He I λ5876 Å emission line, which are traditionally interpreted as a result of shock passage in the atmosphere. However, the radial velocities determined from absorption and emission features are in conflict with the formation pattern of a strong shock. The high luminosity log L/L _⊙ = 2.98, the chemica peculiarities, and the spectral peculiarity are consistent with the post-AGB evolution in the instability strip. The pattern of relative elemental abundances [X/Fe]in the atmosphere of the neighboring star K 307b is solar. Statistically significant differences were found only for sodium and α-process elements: the mean overabundance of light metals is [X/Fe]=+0.35.     

Investigation of the Coronal Magnetic Field Using a Type II Solar Radio Burst

The type II solar radio burst recorded on 13 June 2010 by the Hiraiso Solar Observatory Radio Spectrograph was employed to estimate the magnetic-field strength in the solar corona. The burst was characterized by a well-pronounced band splitting, which we used to estimate the density jump at the shock and Alfvén Mach number using the Rankine–Hugoniot relation. We convert the plasma frequency of the type II burst into height [R] in solar radii using an appropriate density model, and then we estimated the shock speed [V _s], coronal Alfvén velocity [V _A], and the magnetic-field strength at different heights. The relative bandwidth of the band splitting was found to be in the range 0.2?–?0.25, corresponding to a density jump of X=1.44?–?1.56, and an Alfvén Mach number of M _A=1.35?–?1.45. The inferred mean shock speed was on the order of V≈667 km?s^?1. From the dependencies V(R) and M _A(R) we found that the Alfvén speed slightly decreases at R≈1.3?–?1.5 R_⊙. The magnetic-field strength decreases from a value between 2.7 and 1.7 G at R≈1.3?–?1.5 R_⊙, depending on the coronal-density model employed. Our results are in good agreement with the empirical scaling by Dulk and McLean (Solar Phys. 57, 279, 1978) and Gopalswamy et al. (Astrophys. J. 744, 72, 2012). Our results show that the type II band-splitting method is an important tool for inferring the coronal magnetic field, especially when independent measurements are made from white-light observations.     

The toroidal iron atmosphere of a protoneutron star: Numerical solution

A numerical method presented by Imshennik et al. (2002) is used to solve the two-dimensional axisymmetric hydrodynamic problem on the formation of a toroidal atmosphere during the collapse of an iron stellar core and outer stellar layers. An evolutionary model from Boyes et al. (1999) with a total mass of 25M_⊙ is used as the initial data for the distribution of thermodynamic quantities in the outer shells of a high-mass star. Our computational region includes the outer part of the iron core (without its central part with a mass of 1M_⊙ that forms the embryo of a protoneutron star at the preceding stage of the collapse) and the silicon and carbon-oxygen shells with a total mass of (1.8–2.5)M_⊙. We analyze in detail the results of three calculations in which the difference mesh and the location of the inner boundary of the computational region are varied. In the initial data, we roughly specify an angular velocity distribution that is actually justified by the final result—the formation of a hydrostatic equilibrium toroidal atmosphere with reasonable total mass, M^tot=(0.117–0.122)M_⊙, and total angular momentum, J^tot=(0.445–0.472)×10⁵⁰ erg s, for the two main calculations. We compare the numerical solution with our previous analytical solution in the form of toroidal atmospheres (Imshennik and Manukovskii 2000). This comparison indicates that they are identical if we take into account the more general and complex equation of state with a nonzero temperature and self-gravitation effects in the atmosphere. Our numerical calculations, first, prove the stability of toroidal atmospheres on characteristic hydrodynamic time scales and, second, show the possibility of sporadic fragmentation of these atmospheres even after a hydrodynamic equilibrium is established. The calculations were carried out under the assumption of equatorial symmetry of the problem and up to relatively long time scales (～10 s).     

Reproducible characteristics of the solar wind acceleration

In experiments that were regularly carried out in 1999–2002 with Pushchino radio telescopes (Russian Academy of Sciences), the study of the radial dependence of the scattering of radio emission from compact natural sources was extended to regions of circumsolar plasma farther from the Sun. Based on a large body of data, we show that, apart from the standard transonic acceleration region located at distances of 10–40 R_⊙ from the Sun, there is a region of repeated acceleration at distances of 34–60 R_⊙ attributable to the equality between the solar wind velocity and the Alfvénic velocity. The repetition in the trans-Alfvénic region of the characteristic features of the radial stream structure observed in the transonic region (the existence of a precursor, a narrow region of reduced scattering that precedes a wide region of enhanced scattering) suggests that the main characteristic features of the resonant acceleration of solar wind streams are preserved up to distances of the order of 60 R_⊙.     

Effect of Coulomb collisions on the particle acceleration in collapsing magnetic traps

The problem of particle acceleration in collapsing magnetic traps in the solar corona has been solved by taking into account the particle scattering and braking in the high-temperature plasma of solar flares. The Coulomb collisions are shown to be weak in traps with lifetimes t _l < 10 s and strong for t _l > 100 s. In the approximation of strong collisions, collapsing magnetic traps are capable of confining up to 20% of the injected particles in the corona for a long time. In the collisionless approximation, this value exceeds 90%. The question about the observational manifestations of collisions is examined. For collision times comparable to t _l , the electron spectrumat energies above 10 keV is shown to be a double-power-law one. Such spectra were found by the RHESSI satellite in flares.     

Studying the influence of turbulent mixing on thermonuclear burning regimes during X-ray bursts of neutron stars using the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">ε</Emphasis></Subscript> model

We study the influence of turbulent mixing on the development of thermonuclear flashes in the surface layers of neutron stars. A simple K _ε model that includes various physical processes is used to describe the turbulent processes. In contrast to the widespread mixing-length theory, the K _ε model does not require using additional dimensional parameters, traces the development of turbulence in dynamics, describes the various turbulence development scenarios (gravitational and shear instabilities, convection, semiconvection, etc.) in a unified way, and can be used in multidimensional numerical simulations. Empirical constants of the model are chosen on the basis of experimental data and direct numerical simulations of typical processes. We have used the Era and Tigr-3T software packages to numerically simulate thermonuclear flashes in the accretion-renewable atmospheres of neutron stars. Turbulence is shown to accelerate significantly the transport of released energy to the stellar surface. Mixing equalizes the concentrations of matter components throughout the burning layer and increases the amount of matter involved in the thermonuclear burning during a flash.     

Radial pulsations of helium stars with masses from 1 to 10 <Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We present the results of our hydrodynamic calculations of radial pulsations in helium stars with masses 1 M_⊙ ≤ M ≤ 10 M_⊙, luminosity-to-mass ratios 1 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for mass fractions of helium Y=0.98 and heavy elements Z=0.02. We show that the lower boundary of the pulsation-instability region corresponds to L/M ～ 10³L_⊙/M_⊙ and that the instability region for L/M ? 5 × 10³L_⊙/M_⊙ is bounded by effective temperatures T_eff ? 3 × 10⁴ K. As the luminosity rises, the instability boundary moves into the left part of the Hertzsprung-Russell diagram and radial pulsations can arise in stars with effective temperatures T_eff ? 10⁵ K at L/M ? 7 × 10³L_⊙/M_⊙. The velocity amplitude for the outer boundary of the hydrodynamic model increases with L/M and lies within the range 200 ? ΔU ? 700 km s^?1 for the models under consideration. The periodic shock waves that accompany radial pulsations cause a significant change of the gas-density distribution in the stellar atmosphere, which is described by a dynamic scale height comparable to the stellar radius. The dynamic instability boundary that corresponds to the separation of the outer stellar atmospheric layers at a superparabolic velocity is roughly determined by a luminosity-to-mass ratio L/M ～ 3 × 10⁴L_⊙/M_⊙.     

A possible shock wave in the intergalactic medium of the cluster of galaxies A754

The cluster of galaxies A754 is undergoing a merger of several large structural units. X-ray observations show the nonequilibrium state of the central part of the cluster, in which a cloud of cold plasma ～500 kpc in size was identified amid the hotter cluster gas. The X-ray image of A754 exhibits a brightness discontinuity, which can be interpreted as a shock wave in front of a moving cloud of dense gas. The shock parameters are determined from the jump in intergalactic gas density using the ROSAT image. The estimated Mach number is M₁ = 1.71 _?0.24 ^+0.45 at a 68% confidence level.     

The hydrogen emission spectrum of a shock wave in a stellar atmosphere

Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M₁?10 and unperturbed gas densities σ₁=10^?10 g cm^?3, the Doppler shift is approximately one third of the shock velocity U₁. The FWHM of the emission-line profile δ _? is related to the shock velocity by δ _? ≈ k _? U₁, where k _? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.     

Radial pulsations of helium stars with masses from 10 to 50<Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We have performed hydrodynamic calculations of the radial pulsations of helium stars with masses 10M_⊙ ≤ M ≤ 50M_⊙, luminosity-to-mass ratios 5 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2.5 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for helium and heavy-element mass fractions of Y=0.98 and Z=0.02, respectively. We show that the high-temperature boundary of the instability region for radial pulsations at L/M ? 10⁴L_⊙/M_⊙ extends to T_eff≈10⁵ K. The amplitude of the velocity variations for outer layers is several hundred km s^?1, while the brightness variations in the B band of the UBV photometric system are within the range from several hundredths to half a magnitude. At constant luminosity-to-mass ratio, the radial pulsation period is determined only by the effective temperature of the star. In the ranges of luminosity-to-mass ratios 10⁴L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙ and effective temperatures 5 × 10⁴ K ≤ T_eff ≤ 9 × 10⁴ K, the periods of the radial modes are within 6 min ?Π?10³ min.     

Structure of radio sources at wavelengths 10.5 and 12.0 cm from observations of the Solar eclipse on March 29, 2006

The eclipse observations were performed at the Laboratory of Radio Astronomy of the CrAO in Katsiveli with stationary instrumentation of the Solar Patrol at wavelengths of 10.5 and 12.0 cm. The data obtained were used to determine the brightness temperature of the undisturbed Sun at solar activity minimum between 11-year cycles 23 and 24: T _d10.5 = (43.7 ± 0.5) × 10³ K at 10.5 cm and T _d12.0 = (51.8 ± 0.5) × 10³ K at 12.0 cm. The radio brightness distribution above the limb group of sunspots NOAA 0866 was calculated. It shows that at both wavelengths the source consisted of a compact bright nucleus about 50 × 10³ km in size with temperatures T _b10.5 = 0.94 × 10⁶ K and T _b12.0 = 2.15 × 10⁶ K located, respectively, at heights h _10.5 = 33.5 × 10³ km and h _12.0 = 43.3 × 10³ km above the sunspot and an extended halo with a temperature T _b = (230–300) × 10³ K stretching to a height of 157 × 10³ km above the photosphere. The revealed spatial structure of the local source is consistent with the universally accepted assumption that the radiation from the bright part of the source is generated by electrons in the sunspot magnetic fields at the second-third cyclotron frequency harmonics and that the halo is the bremsstrahlung of thermal electrons in the coronal condensation forming an active region. According to the eclipse results, the electron density near the upper boundary of the condensation was N _e ≈ 2.3 × 10⁸ cm^?3, while the optical depth was τ ≈ 0.1 at an electron temperature T _e ≈ 10⁶ K. Thus, the observations of the March 29, 2006 eclipse have allowed the height of the coronal condensation at solar activity minimum to be experimentally determined and the physical parameters of the plasma near its upper boundary to be estimated.     

Magnetic configurations of streamer structures in the solar atmosphere

We consider two types of streamer structures observed in the solar atmosphere. Structures of the first type are medium-scale configurations with scale lengths comparable to the scale height in the corona, kT/mg = 100 thousand km, which appear as characteristic plasma structures in the shape of a dome surrounding the active region with thin streamers emanating from its top. In configurations of this type, gravity plays no decisive role in the mass distribution. The plasma density is constant on magnetic surfaces. Accordingly, the structure of the configurations is defined by the condition ψ = const, where ψ is the flux function of the magnetic field. Structures of the second type are large-scale configurations (coronal helmets, loops, and streamers), which differ from the above structures in that their scale lengths exceed the scale height in the corona. For them, gravity plays a decisive role; as a result, instead of the magnetic surfaces, the determining surface is BgradΦ = 0. We constructed three-dimensional images of these structures. Some of the spatial curves called “visible contours” of the B_r = 0 surface are shown to be brightest in the corona. We assume that the helmet boundaries and polar plumes are such curves.     

Fundamental parameters and intrinsic colors of F,G, and K supergiants and classical cepheids

We used high-resolution echelle spectra with high signal-to-noise ratio to determine with a high degree of accuracy some atmospheric parameters (T _eff, log g and [Fe/H]) for 68 non-variable supergiants of types F, G, and K and 26 classical Cepheids in 302 pulsation phases. Very accurate effective temperatures, with errors of only 10–30 K, were determined by the line-depth ratio method. We found that the observed intrinsic color indices (B ? V)₀ can be related to these parameters: (B ? V)₀ = 57.984? 10.3587(log T _eff)² + 1.67572(log T _eff)³ ? 3.356 log g+ 0.321 V _t + 0.2615[Fe/H] + 0.8833log g(log T _eff). With this empirical relation, the intrinsic colors of individual supergiants and classical Cepheids of spectral types F0-K0 and of luminosity classes I and II can be estimated with an accuracy as high as 0.05 ^m , which is comparable to the accuracy of the most elaborate photometric procedures. In view of large distances to supergiants, the method we propose here allows a large-scale mapping of interstellar extinction with an accuracy of 0.1–0.2 ^m in a quite large region of the Galaxy.