Evolution of the distribution function and radiation spectrum for electrons in a magnetic field

The evolution of a system of electrons with a given initial distribution in an external magnetic field is considered. An equation describing the evolution of the electron distribution function in a uniform magnetic field is derived for the case of arbitrarily relativistic electrons, and an exact solution to this equation is found. Asymptotics of this solution corresponding to the cases of synchrotron radiation and relativistic dipole radiation are calculated, and the evolution of the radiation spectra for these limiting cases is analyzed. The curvature of the magnetic field lines is taken into account phenomenologically, which demonstrates the presence of an exponential dependence in the case of synchrotron radiation.     

The libration points for the motion of a star inside an elliptical galaxy

We consider the three-dimensional motion of a star inside an inhomogeneous, rotating, elliptical galaxy with a homothetic density distribution. The libration points inside a triaxial, rotating, inhomogeneous, gravitating ellipsoid are determined and their stability studied. We determine zero-velocity surfaces and regions of possible motion both inside and outside the galaxy. The motions are shown to be stable in the sense given by Hill. The obtained zero-velocity surfaces enable the construction of a Roche model for a galaxy in the form of either a triaxial ellipsoid or an oblate ellipsoid of rotation.     

Broadening of electron cyclotron maser emission lines in a nonuniform magnetic field

The formation of cyclotron maser emission lines in a non-uniform (regular or random) magnetic field is studied. In the presence of sufficiently small inhomogeneity, the line shape can be described by a broadened Gaussian profile. In the case of stronger inhomogeneity, the initial Gaussian profile splits into two Gaussian components, which could be observationally perceived as “harmonics.” A relation between the distribution of local magnetic trap sizes and the distribution of the spectral widths of solar radio spikes is derived. Possible applications of the results to the interpretation of solar radio spikes and related problems are discussed.     

The motion of a star in the vicinity of a globular cluster in an elliptical galaxy

The spatial motion of a star in the vicinity of a globular cluster located in an inhomogeneous, rotating elliptical galaxy (EG) is considered. Perturbations due to the gravitation of the galaxy are taken into account, taking it to be a two-layer system together with its halo: an inner ellipsoid, representing the lumious part of the galaxy, and a homeoid, representing space filled with dark matter between inner and outer ellipsoidal boundaries. The ellipsoids are taken to be homothetic and to have a common center, with the boundary of the outer ellipsoid coincident with the boundary of the galactic halo. The luminous part of the EG and the homeoid have different densities. The motion of the star near a globular cluster occurs outside the luminous part of the EG, but inside the homeoid. The concept of the “vicinity of the globular cluster” is concretized using the concept of a “sphere of influence” (and the gravitational sphere and Hill gravitational sphere). Stellar motions inside and outside the sphere of influence of the globular cluster are considered, and the region of possible motions is determined. A quasi-integral and surfaces of minimum energy are found, which under certain conditions can be transformed into an analog of the Jacobi integral and surfaces of zero velocity. The Lyapunov stability of the stationary solutions obtained is established. The results are applied to model EGs whose parameters coincide with those of NGC 4472 (M49), NGC 4636, and NGC 4374, which contain a large number of globular clusters, and are presented in the form of figures and tables. Using these galaxies as examples, it is shown that studying stellar motions, and also determining the libration points and establishing their stability, requires use of an exact, rather than an approximate, expression for the potential of the luminous part of the elliptical galaxy.     

The motion of a star with variable mass inside a layered inhomogeneous elliptical galaxy

We consider the motion of a variable-mass star inside a layered, inhomogeneous, rotating elliptical variable-mass galaxy. Under certain conditions, the differential equations of motion of a star inside the galaxy admit autonomization. The autonomized differential equations in this problem are similar to those for the motion of a constant-mass star. We have found analogs for the Jacobi integral and the Eddington-Jeans law for the variation of the density of the galaxy in its center and layers.     

The rotation of the Sun as a star from the green-line emission of the entire corona

A new representation for the database created by J. Sykora on the 5303 Å Fe XIV line emission observed from 1939 to 2001 is proposed. Observations of the corona at an altitude of 60″ above the limb reduced to a uniform photometric scale provide estimates of the emission of the entire visible solar surface. It is proposed to use the resulting series of daily measurements as a new index of the solar activity, GLSun (The Green-Line Sun). This index is purely observational and is free of the model-dependent limitations imposed on other indices of coronal activity. GLSun describeswell both the cyclic activity and the rotational modulation of the brightness of the corona of the Sun as a star. The GLSun series was subject to a wavelet analysis similar to that applied to long-term variability in the chromospheric emission of late-type active stars. We obtain that the brightness inhomogeneities in the solar corona rotate more slowly during epochs of high activity than their average rotational rate over the entire time observations. The time interval of slower rotation of the inhomogeneities is close to the epoch when the Sun’s field represents a horizontal magnetic dipole in each activity cycle, but is somewhat longer than the duration of the polarity reversal in both hemispheres. The difference between the periods for the slower and mean rotation exceeds three days, as is typical for some stars with higher but less regular activity than solar one. The importance of these findings for dynamo theory for the origin and evolution of the magnetic fields of the Sun and other late-type stars is briefly discussed.     

Curvature and non-resonance Compton gamma-ray emission of a radio pulsar with a non-dipolar magnetic field

We consider the influence of a non-dipolar magnetic field on the gamma-ray emission from the polar regions of a radio pulsar. The pulsar is treated in a Goldreich-Julian model with a free flow of charge from the surface of the neutron star. When finding the intensity of the gamma-ray radiation of the pulsar tube, both curvature gamma-ray radiation from the primary electrons and non-resonance inverse Compton scattering of thermal photons from the polar cap on primary electrons are taken into account. When finding the height of the upper plate of the pulsar diode, we included only positrons created by the curvature radiation of primary electrons. We assumed that the polar cap is heated by the return positron current. The influence on the gamma-ray emission of variations in both the radius of curvature of the magnetic force lines and in the electric field due to the non-dipolarity of the magnetic field were taken into account. The presence of even weak non-dipolarity of the magnetic field leads to a sharp decrease in the intensity of the gamma-ray emission from the pulsar tube at energies 1–100 MeV, while the intensity of the inverse Compton radiation (at energies 1–100 GeV) varies only relatively weakly.     

The solar cycle from data on the large-scale surface magnetic field and solar-dynamo theory

Latitude-time (butterfly) diagrams of the large-scale solar magnetic field differ appreciably from the butterfly diagrams for sunspots. Tilted features corresponding to waves propagating from the middle latitudes to the equator are virtually absent from the diagrams for the large-scale magnetic field. The latitude-time diagram of the 22-year solar cycle based on data for the large-scale surface field appears as a checkerboard pattern rather than a traveling wave. Solutions describing similar behavior for the poloidal magnetic field are found for Parker’s solar-dynamo equations. These solutions agree with observations especially well if meridional circulation is added to the two sources generating the magnetic-field in this dynamo-differential rotation and mirror-asymmetric convection.     

Equilibrium of a star cluster in the tidal field of the Galaxy

The tensor virial theorem is used to analyze the conditions for the existence of an equilibrium cluster moving in a circular orbit in a stationary axisymmetric galaxy. A general necessary condition is derived, which, for uniform models, coincides with the Bok stability condition. Generalized Mineur ellipsoids are constructed for nonuniform systems with anisotropic velocity distributions. The Hill stability of the cluster is analyzed.     

Stability of toroidal magnetic fields in the radiation zone of a star

The stability of a toroidal magnetic field in the rotating radiation zone of a star is analyzed to estimate the maximum possible magnitude of relic fields. Equations for small perturbations are obtained taking into account the finite diffusivity and the stabilizing effect of the subadiabatic stratification. The numerical solution of the eigenvalue problem indicates that the threshold field strength for the onset of instability in the radiation zone of the Sun is about 600 G. This figure sets an upper bound for the strength of the relic field. The assumption that magnetic instabilities are present in the solar radiation zone disagrees with the observed abundance of lithium. Our analysis of joint stability of toroidal field and nonuniform rotation shows that two-dimensional MHD solutions for the solar tachocline are stable against three-dimensional perturbations.     

Integrated characteristics of the radial magnetic field in solar active regions during quiet and flare-productive phases of their evolution

This paper presents a statistical study of various integrated parameters of solar active regions, such as the distance between the polarity centroids, the inclination of the magnetic axis, the flux imbalance between the polarities, and the interosculation parameter of the magnetic fluxes of opposite polarities. The study is based on observations of the longitudinal photospheric magnetic field. We analyze ten active regions for which an appreciable volume of data with good spatial resolution are available. The distributions of the above parameters with field strength are very different for quiet and flare-productive active regions and for quiet and flare-active evolutionary phases of the same active region. Some distributions exhibit substantial and characteristic variations during the development of certain flare processes. The first moments of the distributions reflect specific features in the configuration of the photospheric magnetic fields and are correlated with the level of eruptive processes in the active regions.     

Radio synchrotron emission by protons and electrons in pulsars and the nuclei of quasars

Relations enabling estimation of the limiting brightness temperature of synchrotron radiation subject to self-absorption and inverse Compton scattering are presented for the case of relativistic electrons (positrons) and protons. Analogous expressions are presented for relativistic particles moving along curved magnetic lines of force (curvature radiation) and coherent radiation by relativistic particles. These relations can be used to determine the brightness temperatures expected for the central regions of active galactic nuclei, neutron stars, and other objects that produce relativistic particles. Radiation by relativistic protons yields higher intensities, and could be a source of the highest-energy cosmic rays.     

滇西大理至瑞丽铁路沿线地温场特征及其工程地质意义

在整理、分析云南大理至瑞丽拟建铁路沿线及其邻区现今地温场分布特征的基础上,进一步总结前人的资料,综合研究、探讨了该区地温场与岩浆活动、活动构造、地震活动、区域深部构造的关系。结果表明,该区中高温温泉（中高地温场）的空间分布与地表岩浆岩的出露、地表主要活动断裂带的分布都具有较好的对应关系。综合研究后认为,该区的中高温温泉可归结为岩浆热源型、断裂深循环型和岩浆热源叠加断裂深循环作用型3种基本成因类型。同时还发现,该区的温泉分布与区域地震活动空间上也存在密切的关系,并据此将区内划分为4个地震区带。研究结果表明,本区地表温泉分布所反映出的地温场特征对本区的工程稳定性评价具有重要的指示意义。     

The theory of atmospheric disturbances induced by gravity field inhomogeneities

For the first time, we analytically calculated the linear disturbances induced by inhomogeneities of the gravity force field in a stratified rotating medium. The interaction of a geostrophic current with gravity force anomalies in the model considered here can lead to notable generation of eddy disturbances. We analyzed the physical mechanism of the generation of these disturbances.     

滇西大理至瑞丽铁路沿线地温场特征及其 工程地质意义

在整理、分析云南大理至瑞丽拟建铁路沿线及其邻区现今地温场分布特征的基础上,进一步总结前人的资料,综合研究、探讨了该区地温场与岩浆活动、活动构造、地震活动、区域深部构造的关系。结果表明,该区中高温温泉（中高地温场）的空间分布与地表岩浆岩的出露、地表主要活动断裂带的分布都具有较好的对应关系。综合研究后认为,该区的中高温温泉可归结为岩浆热源型、断裂深循环型和岩浆热源叠加断裂深循环作用型3种基本成因类型。同时还发现,该区的温泉分布与区域地震活动空间上也存在密切的关系,并据此将区内划分为4个地震区带。研究结果表明,本区地表温泉分布所反映出的地温场特征对本区的工程稳定性评价具有重要的指示意义。     

滇西大理至瑞丽铁路沿线地温场特征及其工程地质意义

在整理、分析云南大理至瑞丽拟建铁路沿线及其邻区现今地温场分布特征的基础上,进一步总结前人的资料,综合研究、探讨了该区地温场与岩浆活动、活动构造、地震活动、区域深部构造的关系。结果表明,该区中高温温泉（中高地温场）的空间分布与地表岩浆岩的出露、地表主要活动断裂带的分布都具有较好的对应关系。综合研究后认为,该区的中高温温泉可归结为岩浆热源型、断裂深循环型和岩浆热源叠加断裂深循环作用型3种基本成因类型。同时还发现,该区的温泉分布与区域地震活动空间上也存在密切的关系,并据此将区内划分为4个地震区带。研究结果表明,本区地表温泉分布所反映出的地温场特征对本区的工程稳定性评价具有重要的指示意义。     

The structure of the global solar magnetic field excited by the turbulent dynamo mechanism

A mixing-length approximation is used to calculate Kλ for a Parker dynamo wave excited by the dynamo mechanism near the base of the solar convection zone (K is the wave number of the dynamo wave and λ the extent of the dynamo region). In a turbulent-dynamo model, this number characterizes the modes of the global magnetic field generated by a mechanism based on the joint action of the mean helical turbulence and solar differential rotation. Estimates are obtained for the helicity and radial angular-velocity gradient using the most recent helioseismological measurements at the growth phase of solar cycle 23. These estimates indicate that the dynamo mechanism most efficiently excites the fundamental antisymmetric (odd), dipole, mode of the poloidal field (Kλ≈?7) at low latitudes, while the conditions at latitudes above 50° are more favorable for the excitation of the lowest symmetric (even), quadrupole, mode (Kλ≈+8). The resulting north-south asymmetry of the poloidal field can explain the magnetic anomaly (“monopole” structure) of the polar fields observed near solar-cycle maxima. The effect of α quenching increases the calculated period of the dynamo-wave propagation from middle latitudes to the equator to about seven years, in rough agreement with the observed duration of the solar cycle.     

The magnetic fields and density of relativistic electrons in the nucleus of NGC 1052

We analyze observations of the compact GHZ-peaked-spectrum radio source in the nucleus of the weakly active galaxy NGC 1052, assuming that the low-frequency turnover in its spectrum is due to synchrotron self-absorption. The analysis is based on a model for an inhomogeneous source of synchrotron radiation. It is shown that the magnetic field is not uniform, but the change in the field strength from the center to the edge of the compact radio source does not exceed an order of magnitude. The maximum magnetic-field strength in the nucleus of NGC 1052 is 20 G < H _⊥ < 200 G, and the density of relativistic electrons is 0.018 cm⁻³ < n _e < 0.18 cm⁻³ on scales of 0.1 pc; everywhere in the radio source, the energy density of the magnetic field exceeds the energy density of the relativistic electrons. The physical conditions are similar to those in the nuclei of the nearby radio galaxies 3C 111 and 3C 465, and differ strongly from those in the nucleus of the radio galaxy 0108+388, which is a compact GHz-peaked-spectrum source (these three galaxies were studied by the authors earlier using the same method).     

Fast magnetic reconnection and particle acceleration in the non-equilibrium magnetosphere of a relativistic star

A scenario for hard impulsive flares due to magnetic reconnection and particle acceleration in cosmic plasma is proposed. The properties of fast reconnection in an appreciably non-equilibrium nagnetosphere of a compact relativistic object, such as a neutron star, magnetar, or white dwarf, are discussed. Such a magnetosphere could form as the result of the action of a relativistic shock on the strong magnetic field of the star. An analytical solution is presented for the generalized, two-dimensional structure, shape, and boundaries of the magnetosphere, together with the magnitudes of the direct and reverse currents in the reconnecting current layer. The uncompensated magnetic force acting on the reverse current is determined. The characteristic parameters of the non-equilibrium magnetospheres of compact stellar objects are estimated. The excess magnetic energy of the magnetosphere is comparable to the mechanical energy carried by the shock at the time of impact. The possible acceleration of particles to gigantic energies is discussed.     

The magnetic field of the pulsating subdwarf Balloon 090100001

We have analyzed polarization observations of the subdwarf Bal 09, which is one of a group of hybrid sdB stars that display simultaneously both short- and long-period pulsations. Certain properties previously unknown for subdwarfs have been established for Bal 09, such as variations of the pulsation amplitude of the main oscillation mode, rotational splitting of multiplets, and variations of this splitting. Information about the stellar magnetic field must be considered if we wish to explain these properties. New observational data enabling estimation of the longitudinal magnetic field of Bal 09 have been obtained on the main stellar spectrograph of the 6-m telescope of the Special Astrophysical Observatory. Studies of the longitudinal component of the magnetic field 〈B _z 〉 were carried out using a regression analysis. This method simultaneously yields estimates of the uncertainty in 〈B _z 〉. Test measurements of 〈B _z 〉 were carried out using the same method. For the star HD 158974, which has zero total magnetic field, the estimated longitudinal magnetic field is 〈B _z 〉 = −4 ± 5 G. The standard magnetic field for the Ap star α ²CVn was measured to be −363 ± 17 G, in very good agreement with measurements in the literature. The estimated longitudinal magnetic field for Bal 09 is 34 ± 63G—appreciably lower than values established earlier for six subdwarfs, ≈1.5 kG. The results of the regression analysis for both individual spectral subranges and for intervals containing characteristic spectral features did not indicate reliable detections of a magnetic field exceeding the uncertainties in 〈B _z 〉. The uncertainty in 〈B _z 〉, which was 60–80 G for the entire spectral range and 140–200 G for selected spectral intervals, leads to an estimated upper limit on the longitudinal magnetic field 〈B _z 〉 for Bal 09. This estimate for 〈B _z 〉 can place observational constraints on theoretical explanations for the amplitude variations of the pulsations, rotational splitting of multiplets, and possible variations of the internal structure of the star.