Variable solar wind

The solar wind in the heliosphere is a variable phenomenon on all spatial and time scales. It has been shown that there are two basic types of solar wind by the Strouhal number S = L/VT, which characterizes relative variations in the main parameters of the solar wind on the given time interval T and linear scale L for velocity V, which is never zero. The first type is transient (S > 1), which is usually the basic type for sufficiently small values of T and large values of L. The second type is quasi-stationary, when 1 > S > 0. The constant solar wind is nonexistent. The extreme case of S = 0 is physically impossible, as is the case of S = ∞. It is always necessary to indicate and justify the range of applicability for a special quasi-stationary case 1 ? S > 0. Otherwise, to consider the case of S = 0 is incorrect. Regarding this, the widely-spread views on the stationary state of the solar wind are very conditional. They either lack physical sense, or have a very limited range of applicability for time T and scale L.     

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.     

Moments of inertia and the Chandlerian period for two-and three-layer models of the Galilean satellite Io

We consider two-layer (Fe-FeS core+silicate mantle) and three-layer (Fe-FeS core+silicate mantle+crust) models of the Galilean satellite Io. Two parameters are known from observations for the equilibrium figure of the satellite, the mean density ρ₀ and the Love number k₂. Previously, the Radau-Darwin formula was used to determine the mean moment of inertia. Using formulas of the Figure Theory, we calculated the principal moments of inertia A, B, and C and the mean moment of inertia I for the two-and three-layer models of Io using ρ₀ and k₂ as the boundary conditions. We concluded that when modeling the internal structure of Io, it is better to use the observed value of k₂ than the moment of inertia I derived from k₂ using the Radau-Darwin formula. For the models under consideration, we calculated the Chandlerian wobble periods of Io. For the three-layer model, this period is approximately 460 days.     

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.     

Two populations of sunspots and secular variations of their characteristics

We investigate the magnetic fields and total areas of mid- and low-latitude sunspots based on observations at the Greenwich and Kislovodsk (sunspot areas) and Mount Wilson, Crimean, Pulkovo, Ural, IMIS, Ussuriysk, IZMIRAN, and Shemakha (magnetic fields) observatories. We show that the coefficients in the linear form of the dependence of the logarithm of the total sunspot area S on its maximum magnetic field H change with time. Two distinct populations of sunspots are identified using the twodimensional H–log S occurrence histogram: small and large, separated by the boundaries log S = 1.6 (S = 40 MSH) and H = 2050 G. Analysis of the sunspot magnetic flux also reveals the existence of two lognormally distributed populations with the mean boundary between them Φ = 10²¹ Mx. At the same time, the positions of the flux occurrence maxima for the populations change on a secular time scale: by factors of 4.5 and 1.15 for small and large sunspots, respectively. We have confirmed that the sunspots form two physically distinct populations and show that the properties of these populations change noticeably with time. This finding is consistent with the hypothesis about the existence of two magnetic field generation zones on the Sun within the framework of a spatially distributed dynamo.     

On the MOND external field effect in the solar system

In the framework of the MOdified Newtonian Dynamics (MOND), the internal dynamics of a gravitating system s embedded in a larger one S is affected by the external background field E of S even if it is constant and uniform, thus implying a violation of the Strong Equivalence Principle: it is the so-called External Field Effect (EFE). In the case of the solar system, E would be A _cen≈10^?10 m?s^?2 because of its motion through the Milky Way: it is orders of magnitude smaller than the main Newtonian monopole terms for the planets. We address here the following questions in a purely phenomenological manner: are the Sun’s planets affected by an EFE as large as 10^?10 m?s^?2? Can it be assumed that its effect is negligible for them because of its relatively small size? Does E induce vanishing net orbital effects because of its constancy over typical solar system’s planetary orbital periods? It turns out that a constant and uniform acceleration, treated perturbatively, does induce non-vanishing long-period orbital effects on the longitude of the pericenter ? of a test particle. In the case of the inner planets of the solar system and with E≈10^?10 m?s^?2, they are 4–6 orders of magnitude larger than the present-day upper bounds on the non-standard perihelion precessions \(\Delta\dot{\varpi}\) recently obtained with by E.V. Pitjeva with the EPM ephemerides in the Solar System Barycentric frame. The upper limits on the components of E are E _x ≤1×10^?15 m?s^?2, E _y ≤2×10^?16 m?s^?2, E _z ≤3×10^?14 m?s^?2. This result is in agreement with the violation of the Strong Equivalence Principle by MOND. Our analysis also holds for any other exotic modification of the current laws of gravity yielding a constant and uniform extra-acceleration. If and when other corrections \(\Delta\dot{\varpi}\) to the usual perihelion precessions will be independently estimated with different ephemerides it will be possible to repeat such a test.     

Structure of solar-wind streams at the maximum of solar cycle 23

We study the formation of solar-wind streams in the years of maximum solar activity 2000–2002. We use observations of the scattering of radio emission by solar-wind streams at distances of ～4–60R_S from the Sun, data on the magnetic field structure and strength in the source region (R ～ 2.5R_S), and observations with the LASCO coronagraph onboard the SOHO spacecraft. Analysis of these data allowed us to investigate the changes in the structure of circumsolar plasma streams during the solar maximum. We constructed radio maps of the solar-wind transition, transonic region in which the heliolatitudinal stream structure is compared with the structure of the white-light corona. We show that the heliolatitudinal structure of the white-light corona largely determines the structure of the solar-wind transition region. We analyze the correlation between the location of the inner boundary of the transition region R_in and the magnetic field strength on the source surface |B_R|. We discuss the peculiarities of the R_in = F(|B_R|) correlation diagrams that distinguish them from similar diagrams at previous phases of the solar cycle.     

Inverse problem of central configurations and singular curve in the collinear 4-body problem

In this paper, we consider the inverse problem of central configurations of n-body problem. For a given \({q=(q_1, q_2, \ldots, q_n)\in ({\bf R}^d)^n}\), let S(q) be the admissible set of masses denoted \({ S(q)=\{ m=(m_1,m_2, \ldots, m_n)| m_i \in {\bf R}^+, q}\) is a central configuration for m}. For a given \({m\in S(q)}\), let S _m (q) be the permutational admissible set about m = (m ₁, m ₂, . . . , m _n ) denoted

$S_m(q)=\{m^\prime | m^\prime\in S(q),m^\prime \not=m \, {\rm and} \, m^\prime\,{\rm is\, a\, permutation\, of }\, m \}.$

The main discovery in this paper is the existence of a singular curve \({\bar{\Gamma}_{31}}\) on which S _m (q) is a nonempty set for some m in the collinear four-body problem. \({\bar{\Gamma}_{31}}\) is explicitly constructed by a polynomial in two variables. We proved:

1. (1)
   If \({m\in S(q)}\), then either ^# S _m (q) = 0 or ^# S _m (q) = 1.
    
2. (2)
   ^#S _m (q) = 1 only in the following cases:

   1. (i)
      If s = t, then S _m (q) = {(m ₄, m ₃, m ₂, m ₁)}.
       
   2. (ii)
      If \({(s,t)\in \bar{\Gamma}_{31}\setminus \{(\bar{s},\bar{s})\}}\), then either S _m (q) = {(m ₂, m ₄, m ₁, m ₃)} or S _m (q) = {(m ₃, m ₁, m ₄, m ₂)}.
       
    

     

Plane Symmetric Dark Energy Models in the Form of Wet Dark Fluid in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) Gravity

In this paper, we have investigated the plane symmetric space-time with wet dark fluid (WDF), which is a candidate for dark energy, in the framework of f (R,T) gravity Harko et al. 2011, Phys. Rev. D, 84, 024020), where R and T denote the Ricci scalar and the trace of the energy–momentum tensor respectively. We have used the equation of state in the form of WDF for the dark energy component of the Universe. It is modeled on the equation of state p = ω(ρ ? ρ ^?). The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied. Also, we have discussed the well-known astrophysical phenomena, namely the look-back time, proper distance, the luminosity distance and angular diameter distance with red shift.     

New characteristics of the solar cycle and dynamo theory

Based on an analysis of the observational data for solar cycles 12–23 (Royal Greenwich Observatory-USAF/NOAA Sunspot Data), we have studied various parameters of the “Maunder butterflies.” Based on the observational data for cycles 16–23, we have found that BT/Land S depend linearly on each other, where B is the mean magnetic field of the cycle, T is the cycle duration, S is the cycle strength, and L is the mean sunspot latitude in the cycle (the arithmetic mean of the absolute values of the mean latitudes in the north and south). The connection of the observed quantities with the α-ω-dynamo theory is discussed.     

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_⊙.     

Parameters of the classical type-IIP supernova SN 1999em

Based on observations of SN 1999em, we determined the physical parameters of this supernova using hydrodynamic calculations including nonequilibrium radiative transfer. Taking the distance to SN 1999em estimated by the expanding photosphere method (EPM) to be D = 7.5 Mpc, we found the parameters of the presupernova: radius R = 450R_⊙, mass M = 15M_⊙, and explosion energy E = 7 × 10⁵⁰ erg. For the distance D = 12 Mpc determined from Cepheids, R, M, and E must be increased to the following values: R = 1000R_⊙, M = 18M_⊙, and E = 10⁵¹ erg. We show that one cannot restrict oneself to using the simple analytical formulas relating the supernova and presupernova parameters to obtain reliable parameters for type-IIP presupernovae.     

HI content in galactic disks: The role of gravitational instability

We examine the dependence of the total hydrogen mass M _HI in late-type star-forming galaxies on rotation velocity V _rot and optical size D ₂₅ or radial scale length R ₀ of the disk for two samples of galaxies: (i) isolated galaxies (AMIGA) and (ii) galaxies with edge-on disks (flat galaxies according to Karachentsev et al.). M _HI given in the HYPERLEDA database for flat galaxies have turned out to be, on average, overestimated by ~0.2 dex compared to isolated galaxies with similar V _rot or D ₂₅, which is apparently due to an overestimation of the self-absorption in the HI line. The hydrogen mass in the galaxies of both samples closely correlates with the total specific angular momentum of the galactic disk J, which is proportional to V _rot D ₂₅ or V _rot R ₀, with the low-surface-brightness galaxies lying along the common V _rot R ₀ sequence. We discuss the possibility of explaining the relationship between M _HI and V _rot D ₂₅ by assuming that the gas mass in the disk is regulated by the marginal gravitational stability condition for the gas layer. Comparison of the observed and theoretically expected dependences leads us to conclude that either the gravitational stability corresponds to higher values of the Toomre parameter than is usually assumed, or the threshold stability condition formost galaxies was fulfilled only in the past, when the gasmass in the disks was a factor of 2–4 higher than that at present (except for the galaxies with an anomalously high observed HI content). The latter condition requires that for most galaxies the conversion of gas into stars be not compensated by the external accretion of gas onto the disk.     

Dynamics of the earth radiation belts during strong magnetic storms based on <Emphasis Type="Italic">CORONAS-F</Emphasis> data

The results of an experimental study of the variations in the intensity of the fluxes of the Earth radiation belt (ERB) particles in 0.3–6 and 1–50 MeV energy intervals for electrons and protons, respectively, are reported. ERBs were studied during strong magnetic storms from August 2001 through November 2003. The results of the CORONAS-F mission obtained during the magnetic storms of November 6 (D _st = ?257 nT) and November 24, 2001 (D _st = ?221 nT), October 29–30 (D _st = ?400 nT) and November 20, 2003 (D _st = ?465 nT) are analyzed. The electron flux is found to decrease abruptly in the outer radiation belt during the main phase of the magnetic storms under consideration. During the recovery phase, the outer radiation belt is found to recover much closer to Earth, near the boundary of the penetration of solar electrons during the main phase of the magnetic storm. We associate the decrease in the electron flux with the abrupt decrease of the size of the magnetosphere during the main phase of the storm. Note that, in all cases studied, the Earth radiation belts exhibited rather long (several days) variations. In those cases where solar cosmic-ray fluxes were observed during the storm, protons with energies 1–5 MeV could be trapped to form an additional maximum of protons with such energies at L >2.     

Phenomenological explanation for the shape of the spectrum of cosmic rays with energies <Emphasis Type="Italic">E</Emphasis> > 10 GeV

Assuming that the energy gain by cosmic-ray (CR) particles is a stochastic process with stationary increments, we derive expressions for the shape of their energy spectrum up to energies E ～ 10¹⁸ eV. In the ultrarelativistic case under study, the energy is proportional to the momentum, whose time derivative is the force. According to the Fermi mechanism, a particle accelerates when it passes through a system of shock waves produced by supernova explosions. Since these random forces act on time scales much shorter than the particle lifetime, we assume them to be delta-correlated in time. In this case, due to the linear energy-momentum relationship, the mean square of the energy (increments) is proportional to the differential scale τ(E) ～ Eτ(≥E), where τ (≥E) is the cumulative time it takes for a particle to gain an energy ≥E. The probability of finding a particle with energy ≥E somewhere in the system is inversely proportional to the time it takes to gain the energy E. To estimate an upper limit for the space number density of CR particles, we use estimates of the CR volume energy density, a quantity known for our Galaxy. It is taken to be constant in the range 10 GeV ≤ E ≤ 3 × 10⁶ GeV, where the index of the energy spectrum was found to be ?8/3 ≈ ?2.67 against its empirical value of ?2.7. In the range 3 × 10⁶ GeV ≤ E < 10⁹ GeV, the upper limit for the volume energy density is estimated by using the results from the previous range to be ?28/9 ≈ ?3.11 against its empirical value of ?3.1. The numerical coefficients in the suggested shapes of the spectrum can be determined by comparison with observational data. Thus, the CR energy spectrumis the result of the random walks of ultrarelativistic particles in energy/momentum space caused by the Fermi mechanism.     

A theory of the equilibrium figure and gravitational field of the Galilean satellite Io: The second approximation

We construct a theory of the equilibrium figure and gravitational field of the Galilean satellite Io to within terms of the second order in the small parameter α. We show that to describe all effects of the second approximation, the equation for the figure of the satellite must contain not only the components of the second spherical function, but also the components of the third and fourth spherical functions. The contribution of the third spherical function is determined by the Love number of the third order h₃, whose model value is 1.6582. Measurements of the third-order gravitational moments could reveal the extent to which the hydrostatic equilibrium conditions are satisfied for Io. These conditions are J₃=C₃₂=0 and C₃₁/C₃₃=?6. We have calculated the corrections of the second order of smallness to the gravitational moments J₂ and C₂₂. We conclude that when modeling the internal structure of Io, it is better to use the observed value of k₂ than the moment of inertia derived from k₂. The corrections to the lengths of the semiaxes of the equilibrium figure of Io are all positive and equal to ～64.5, ～26, and ～14 m for the a, b, and c axes, respectively. Our theory allows the parameters of the figure and the fourth-order gravitational moments that differ from zero to be calculated. For the homogeneous model, their values are:\(s_4 = \frac{{885}}{{224}}\alpha ^2 ,s_{42} = - \frac{{75}}{{224}}\alpha ^2 ,s_{44} = \frac{{15}}{{896}}\alpha ^2 ,J_4 = - \frac{{885}}{{224}}\alpha ^2 ,C_{42} = \frac{{75}}{{224}}\alpha ^2 ,C_{44} = \frac{{15}}{{896}}\alpha ^2 \).     

Modeling the linear polarization of optical emission from red giants

We present the results of solving the radiative transfer equation for the Stokes vector in the case of light scattering by spherical forsterite dust particles in an axisymmetric circumstellar envelope of a red giant. We have assumed that the surfaces of constant scattering-particle density are prolate or oblate spheroids, the particle density decreases with radius as N _d ∝ r ⁻², and the dust particles at the inner boundary of the envelope are in thermal equilibrium with the stellar emission at solid-phase evaporation temperature T _ev = 800 K. In the wavelength range 0.27 μm ≤ λ ≤ 1 μm, particles with radii 0.03 μm ≲ a ≲ 0.2 μm make a major contribution to the linear polarization of the stellar emission. The increase in scattering efficiency factor with decreasing wavelength λ is mainly responsible for the growth of polarization toward the short wavelengths known from observations. However, at a mean number of scatterings 1.2 ≤ N _sca ≤ 1.6, the polarization ceases to grow due to depolarization effects and decreases rapidly as the wavelength decreases further. The wavelength of the polarization maximum is determined mainly by two quantities: the particle radius and the mass loss rate. The upper limits for the degree of linear polarization in the case of light scattering in circumstellar dust envelopes with the geometries of prolate and oblate spheroids are p ≈ 3 and 5%, respectively. The polarization for light scattering by enstatite particles is higher than that for light scattering by forsterite particles approximately by 0.3%. Original Russian Text ? Yu.A. Fadeyev, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 2, pp. 123–133.     

Laplace series for the level ellipsoid of revolution

The outer gravitational potential V of the level ellipsoid of revolution T is uniquely determined by two quantities: the eccentricity \(\varepsilon \) of the ellipsoid and Clairaut parameter q, proportional to the angular velocity of rotation squared and inversely proportional to the mean density of the ellipsoid. Quantities \(\varepsilon \) and q are independent, though they lie in a rather strict two-dimensional domain. It follows that Stokes coefficients \(I_n\) of Laplace series representing the outer potential of T are uniquely determined by \(\varepsilon \) and q. In this paper, we have found explicit expressions for Stokes coefficients via \(\varepsilon \) and q, as well as their asymptotics when \(n\rightarrow \infty \). If T does not coincide with a Maclaurin ellipsoid, then \(|I_n|\sim B\varepsilon ^n/n\) with a certain constant B. Let us compare this asymptotics with one of \(I_n\) for ellipsoids constrained by the only condition of increasing (even nonstrict) of oblateness from the centre to the periphery: \(|I_n|\sim \bar{B}\varepsilon ^n/(n^2)\). Hence, level ellipsoids with ellipsoidal equidensites do not exist. The only exception represents Maclaurin ellipsoids. It should be recalled that we confine ourselves by ellipsoids of revolution.     

Irregular dwarf galaxy KK 230: A relatively young galaxy at the periphery of the local group?

We present some results of the photometric analysis of the stellar population of the irregular dwarf galaxy KK 230 on the basis of the archive database of the Hubble space telescope. The color index-magnitude diagram for KK 230 gets to magnitude 27 ^m in the V and I bands, and it comprises stellar populations of various ages. The age of the youngest main-sequence stars is 3.2 × 10⁷ yr. These stars are distributed along the north-south direction in the picture plane, and this fact can be linked to the observed kinematics of the neutral gas in the galaxy. Older blue and red supergiants are no less than 1.6 × 10⁸ years old, and such an age implies that the star formation was episodic over the last several hundreds of millions of years. As judged from the position of the tip of the red giant branch, the distance modulus for KK 230 is m ? M = 26.5 ^m . The corresponding distance is D = 2 Mpc. Based on the average absolute magnitude M _I,RC and color index (V ? I)_I,RC of the red clump, we conclude that the majority of KK 230 stars have an age of no more than (2–3) × 10⁹ yr, their metallicity being Z ≈ 0.0004.