The photospheric velocity field of Procyon

BUSS observations of the profiles of two well observed spectral lines in the ultraviolet spectrum of CMi (Procyon; F5 IV–V) are analysed with a Fourier transform method in order to determine values of various parameters of the velocity field of the upper photosphere. We find a microturbulent line-of-sight velocity componentL = 0.9 ± 0.4 km s^–1, a macroturbulent velocity componentL _M = 5.3 ± 0.2 km s^–1, and a rotational velocity componentv _R sini=10.0±1.2 km s^–1. In these calculations a single-moded sinusoidal isotropic macroturbulent velocity function was assumed. The result appears to be sensitive to the assumed shape of the macroturbulence function: for an assumed Gaussian shape the observations can be described withv _R sini=4 km s^–1 andL _M = 11.6 ± 2.7 km s^–1. A comparison is made with other results and theoretical predictions.     

Inhomogeneous convection and the equatorial acceleration of the sun

The interaction of rotation and turbulent convection is assumed to give rise to an inhomogeneous, but isotropic, latitude dependent turbulent energy transport, which is described by a convective conduction coefficient _c which varies with latitude. Energy balance in the convective zone is then possible only with a slow meridian circulation in the outer convective zone of the sun. The angular momentum transported by this circulation is balanced in a steady state by turbulent viscous transport down an angular velocity gradient. A detailed model is constructed allowing for the transition from convective transport to radiative transport at the boundaries of the convective zone, by using a perturbation analysis in which the latitude variation of _c is small. The solution for a thin compressible shell gives equatorial acceleration and a hotter equator than pole, assuming that the convection is preferentially stabilised at the equator. For agreement with the sun's equatorial acceleration the model predicts an equatorial temperature excess of 70 K and a surface meridional velocity of 350 cm/sec from pole to equator.     

Some comments on the photographic subtraction method of determining chromospheric velocities

The photographic subtraction formula expressing the Doppler signal in terms of line-of-sight velocity is rederived and the conditions governing its validity are carefully stated. By appealing to the observed profiles of individual bright and dark mottles it is shown that, in the case of H observations of the quiet chromosphere, two essential conditions are violated.An analysis based on Beckers' (1964) theoretical mottle profiles shows that, assuming the correctness of his model, the photographic subtraction method correctly maps regions of zero velocity and, provided the original photographs are taken sufficiently far from the centre of H, gives the correct signs of any line-of-sight velocities present. However, at H ± 0.25 Å the method gives inconsistent signs. Moreover, at all wavelengths in the line the magnitude of the Doppler signal depends not only on velocity but also on the source function S, optical thickness t ₀, and line broadening parameter ₀. Accordingly, there is no one-to-one correspondence between velocity and the Doppler signal since S, in particular, shows considerable variation from place to place over the quiet chromosphere.An alternative procedure which obviates these difficulties is suggested. It is also based on Beckers' model and yields a calibrated measure of the velocity in terms of ₀ (assumed constant) which is independent of spatial variations in S and t ₀.     

Analytical and graphical determination of the trajectory of a fireball using seismic data

In this paper we discuss two methods, one analytical and the other graphical, to determine the trajectory of a fireball using the arrival times of atmospheric shock waves recorded by a seismic network. In the analytical method the trajectory and the raypaths are assumed to be straight and we solve for the fireball velocity, the azimuth (?) and elevation angle (δ) of the trajectory, the coordinates of the intersection of the trajectory with the earth's surface, and the corresponding intersection time (t₀). Because the problem is nonlinear, we solve it iteratively. The fireball velocity cannot be determined uniquely, and trades off with t₀. The graphical method is based on the drawing of contours of arrival times, which should be elliptical for fireball shock waves. If the distribution of seismic stations is appropriate, the horizontal projection of the fireball is given by the axis of symmetry of the contours, which allows the estimation of ?, while δ can be estimated from the spacing between contours along the symmetry axis. Application of the two methods to data from four fireballs shows that the graphically derived parameters can be within a few degrees of the analytical parameters. In addition, a fireball recorded in the Czech Republic has reliable trajectory parameters derived from video recordings, which allows an independent assessment of the quality of the parameters determined analytically. In particular, ? and δ have errors of and , respectively, which are not particularly large considering that the station distribution was not favorable.     

Pulsars: Space kinematic characteristics and their connection with supernova remnants

The galactic distribution of pulsars and shell remnants of supernovae (SN) as investigated on the basis of newly-estimated parameters. Special attention was paid to taking into account all possible selection effects and an attempt was made to reveal a statistically-pure ensemble of objects. On the basis of this ensemble we studied the radial andz-distribution of pulsars and supernova remnants (SNR).It is shown that the radial distribution of both objects is considered to have an annular structure with the maximum surface density at a distance of 4.5–5.3 kpc (if the distance of the Sun from the galactic centre is assumed to be equal to 8.5 kpc). The scle-height of the progenitors of SNRs is not more than 110 pc and only 15% of the SNRs, whose progenitors may also be massive runaway stars, are situated at 300 pc. The mean application of the pulsars is not more than 300 pc which agrees with the hypothesis about the genetic connection with type-II SN outbursts at the kinematic aget _k5×10⁶ yr and thez-component of spatial velocity beingV _z=120 km s^–1.The possible precursors of type-I SNRs by the shape of their radial distribution in late spirals and the various model calculations given in the literature, are also discussed.     

Some results of the photospheric large-scale velocity research from Belgrade observations

On the basis of the possibility of sight-line velocity observations by a special equatorial solar spectrograph, a research programme for detection of photospheric large-scale velocities has been initiated. The first series of observations in the FeI 6302 Å absorption line has been limited to the central meridian.The combined limb effect assumed to incorporate an unresolved stationary photospheric motion, has been evaluated. The observed asymmetry of the obtained curve is mainly explained by dB ₀/dt.The remaining sight-line velocities along the central meridian, taken as random, gave an r.m.s. value of 32 m s^–1. In a few cases a certain kinematic situation in some areas along the central meridian lasted for 2 to 4 consecutive days. It is assumed that such velocity features belong to the kinematic picture of a large-scale photospheric motion which, as a whole, has not yet been clearly seen.     

Propagation of flare protons in the solar atmosphere

The velocity dispersion for a large number of solar proton events is analyzed in the energy regime of 10–60 MeV. It is found for all events that the time from the flare to particle maximum t _m is well represented by a sum of two components. The first component which is energy independent describes the propagation in the solar atmosphere, the second component describes the propagation in the interplanetary medium giving a velocity dispersion v × t _m = const. The additional study of time intensity profiles, onset times, and multispaceprobe observations reveals that the propagation in the solar atmosphere consists of three processes: (1) A rapid transport process in the initial ( 1 h) phase after the event fills up a fast propagation region (FPR), which may extend up to 60° from the flare site and which is tentatively identified with a large unipolar magnetic cell as seen on H synoptic charts, (2) a large-scale drift process which is energy independent with drift velocities v _D in the range 1° v _D 4°h^-1, and simultaneously (3) a diffusion process which yields the general broadening of the intensity time profiles for eastern hemisphere events, which is, however, of less importance than previously assumed.     

Type III radio bursts in the outer corona

Type III solar radio bursts observed from 3.0 to 0.45 MHz with the ATS-II satellite over the period April–October 1967 have been analyzed to derive two alternative models of active region streamers in the outer solar corona. Assuming that the bursts correspond to radiation near the electron plasma frequency, pressure equilibrium arguments lead to streamer Model I in which the streamer electron temperature derived from collision damping time falls off much more rapidly than in the average corona and the electron density is as much as 25 times the average coronal density at heights of 10 to 50 solar radii (R ). In Model II the streamer electron temperature is assumed to equal the average coronal temperature, giving a density enhancement which decreases from a factor of 10 close to the Sun to less than a factor of two at large distances (> 1/4 AU). When the burst frequency drift is interpreted as resulting from the outward motion of a disturbance that stimulates the radio emission, Model I gives a constant velocity of about 0.35c for the exciting disturbance as it moves to large distances, while with Model II, there is a decrease in the velocity to less than 0.2c beyond 10 R .     

A new estimate of the galactic halo mass based on the kinematics of globular clusters

We calculated the energy distribution function for globular clusters in our Galaxy, using the inversion procedure first suggested by Eddington. If the halo mass distribution is of the formM _H=r ^1.21, then the observed data on the velocity dispersion of F-clusters can be explained, resulting an enclosed mass of 4.3×10¹¹ M within a galactocentric radius of 33 kpc.     

On determining the electron density distribution of the solar corona from K-coronameter data

The electron density distribution of the inner solar corona (r 2 R ) as a function of latitude, longitude, and radial distance is determined from K-coronameter polarization-brightness (pB) data. A Legendre polynomial is assumed for the electron density distribution, and the coefficients of the polynomial are determined by a least-mean-square regression analysis of several days of pB-data. The calculated electron density distribution is then mapped as a function of latitude and longitude. The method is particularly useful in determining the longitudinal extent of coronal streamers and enhancements and in resolving coronal features whose projections on the plane of the sky overlap.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Region of anomalous compression under Bondi-Hoyle accretion

We investigate the properties of an axisymmetric gas flow without angular momentum onto a small compact object, in particular, on a Schwarzschild black hole in the supersonic region; the velocity of the object itself is assumed to be low compared to the speed of sound at infinity. First of all, we show that the streamlines intersect (i.e., a caustic is formed) on the symmetry axis at a certain distance r _x from the center on the front side if the pressure is ignored. The characteristic radial size of the region in which the streamlines emerging from the sonic surface at an angle no larger than θ₀ to the axis intersect is Δr = r _x θ ₀ ² /3. To refine the flow structure in this region, we have numerically computed the system without ignoring the pressure in the adiabatic approximation. We have estimated the parameters of the inferred region with anomalously high matter temperature and density accompanied by anomalously high energy release.     

Analytical solutions of cylindrical shock waves in magnetogasdynamics,I

The C.C.W. method has been used to investigate the propagation of converging and diverging cylindrical shock waves in a non-uniform medium under the influence of a magnetic field of constant strength. A comparison has also been made between the two types of cylindrical shock waves, simultaneously for both weak and strong cases of the magnetic field. Density distribution is assumed to be _o = r ^–, where is the density at the axis of symmetry and a constant. The analytical expressions for shock velocity and shock strength as well as the pressure, the density, and the particle velocity just behind the shock front have been derived for both the cases.     

The formation of spicules in the course of the chromospheric network magnetic field reconnection

We investigate the physical processes occurring in the supergranule boundary cylinder layer (SBCL). Taking into account the Coriolis force, we obtain an expression for the component of the magnetic field and velocity in the SBCL. Within the framework of linear MHD, we consider the formation and coalescence of magnetic tubes, i.e. spicules, in the course of the reconnection of the SBCL magnetic field. The estimated number of spicules appearing on each supergranule cell is in agreement with observations. This number depends on the solar latitude : (1) if the normal component of the magnetic fieldB _z is assumed to be independent of , then the maximum number of spicules should be at = 71°; (2) ifB _z is assumed to be the component of the dipolar fieldB _z sin , then the maximum number should be at the pole: = 90°. The timescale of the formation and the coalescence of the magnetic tubes is 10–20 min, which is of the order of the observed lifetime of the spicules.     

Micro- and macroturbulent motions and the velocity spectrum of the solar photosphere

A given motion field in a stellar atmosphere is usually observed through filters defined by line shifts and -broadenings and conventionally called macroturbulence and microturbulence.These filters can be defined and computed exactly, as a function of the wave number of the velocity field (Figure 1).We apply the results to several cases of an assumed motion field spectrum, and to observations of broadenings and displacements of solar Fraunhofer lines formed at a depth ₅ = 0.1 (Figure 2).The results show that virtually all energy of the photospheric motions at that level is contained in a small range of wavenumbers, corresponding to the observed distribution of granular cell diameters. In other words: a well-developed spectrum of hydrodynamical turbulence extending over a large range of wavelengths does not exist at that level of the photosphere.     

Generalized Expanding and Shearing Anisotropic Bianchi Type I Magnetofluid Cosmological Model in General Relativity

The behaviour of magnetic field in anisotropic Bianchi type I cosmological model for perfect fluid distribution in General Relativity, is investigated. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. It is assumed that the component ¹ ₁ of shear tensor ^j _i is proportional to the expansion () which leads to A = (BC)ⁿ. The other physical and geometrical aspects of the model are also discussed, Bali (1986) obtained the cosmological model for n = 1 in presence of magnetic field. We have investigated the model for general values of n and discussed the particular case and general behaviour of the model.     

Unseen matter and angular momentum in the Milky Way and other galaxies: Simple two-component models

Simple two-component (dark+bright) models are built up for the Milky Way, where both the density distribution and the rotation curve are deduced from known observations. The derived dark to bright mass ratio turns out to be in the range 10, in close agreement with the results of more refined approaches, with a weak dependence on the geometry of the model. The related angular momentum appears to be well in agreement with theoretical predictions, if proto-galaxies gain angular momentum via either gravitational interactions or peculiar velocities of their own sub-units, according to a logarithmic distribution of the squared fractional angular momenta close to a Maxwellian one. The rougher assumption that the whole system is represented by a rigidly rotating polytrope leads to dark components rounder than _D 0.7 if proto-galaxies gain angular momentum via gravitational interactions, and to much more flattened dark components if proto-galaxies gain angular momentum via peculiar velocities of their own sub-units and few (4) sub-units are present at the beginning. To fit the observed positions of several galaxies on the (Oê _B q _B ) plane-ê _B representing the ellipticity andq _B close to the ratio of maximum rotational to central peculiar velocity, averaged for all the inclinations to the line of sight — galaxies are modelled by two-component (dark+bright) rigidly rotating, concentric, co-polar, homogeneous spheroids and the Galaxy is assumed to be a typical system. An acceptable fit is produced only under the assumption that protogalaxies gain their angular momentum in late stages of evolution, i.e., after having decoupled from the Hubble flow.     

On the HCN and CO2 abundance and distribution in Jupiter's stratosphere

Observations of Jupiter by Cassini/CIRS, acquired during the December 2000 flyby, provide the latitudinal distribution of HCN and CO₂ in Jupiter's stratosphere with unprecedented spatial resolution and coverage. Following up on a preliminary study by Kunde et al. [Kunde, V.G., and 41 colleagues, 2004. Science 305, 1582-1587], the analysis of these observations leads to two unexpected results (i) the total HCN mass in Jupiter's stratosphere in 2000 was (6.0±1.5)×¹⁰¹³ g, i.e., at least three times larger than measured immediately after the Shoemaker-Levy 9 (SL9) impacts in July 1994 and (ii) the latitudinal distributions of HCN and CO₂ are strikingly different: while HCN exhibits a maximum at 45° S and a sharp decrease towards high Southern latitudes, the CO₂ column densities peak over the South Pole. The total CO₂ mass is (2.9±1.2)×¹⁰¹³ g. A possible cause for the HCN mass increase is its production from the photolysis of NH₃, although a problem remains because, while millimeter-wave observations clearly indicate that HCN is currently restricted to submillibar (∼0.3 mbar) levels, immediate post-impact infrared observations have suggested that most of the ammonia was present in the lower stratosphere near 20 mbar. HCN appears to be a good atmospheric tracer, with negligible chemical losses. Based on 1-dimensional (latitude) transport models, the HCN distribution is best interpreted as resulting from the combination of a sharp decrease (over an order of magnitude in Kyy) of wave-induced eddy mixing poleward of 40° and an equatorward transport with velocity. The CO₂ distribution was investigated by coupling the transport model with an elementary chemical model, in which CO₂ is produced from the conversion of water originating either from SL9 or from auroral input. The auroral source does not appear adequate to reproduce the CO₂ peak over the South Pole, as required fluxes are unrealistically high and the shape of the CO₂ bulge is not properly matched. In contrast, the CO₂ distribution can be fit by invoking poleward transport with a velocity and vigorous eddy mixing (). While the vertical distribution of CO₂ is not measured, the combined HCN and CO₂ results imply that the two species reside at different stratospheric levels. Comparing with the circulation regimes predicted by earlier radiative-dynamical models of Jupiter's stratosphere, and with inferences from the ethane and acetylene stratospheric latitudinal distribution, we suggest that CO₂ lies in the middle stratosphere near or below the 5-mbar level.     

Collisionless deceleration of fast electron streams in the solar coronal plasma

The collisionless deceleration of electron streams responsible for type IIIb bursts has been investigated. For this the difference between the mean velocities of electron streams at plasma levels corresponding to 25 and 12.5 MHz, on one hand, at 12.5 and 6.25 MHz, on the other hand, is estimated. The mean velocity of electron streams between these levels is determined by the time delay in the moments of arrival of radio bursts from these levels. The distance between plasma levels is determined under the assumption that the (statistical) mean velocity of sources of the diffusive type III bursts is constant and equal toc/3 at all considered levels of the solar corona.It is shown that under this assumption the electron streams with the initial velocities of the order of 0.4–0.8c undergo a sufficient deceleration which is characterized by a decrease in their mean velocity by 15–17% between plasma levels at 25 to 6.25 MHz. The stream deceleration becomes more essential with the growth of the initial velocity of the stream. On the other hand, the deceleration disappears when the initial velocity of the stream is of the order of 0.35c. This critical velocityV _s ^* - 0.35c is assumed to define a boundary between two different expansion regimes of fast electrons moving in the solar corona. In the first regime (V _s >V _s ^* ) the induced scattering of plasma waves produces energy losses of the streams. A decrease in the velocities of streams up to the value of the order of 0.35c is due to these losses. In the second regime (V _s -V _s ^* ) a quasilinear expansion of streams is realized. In this case the energy losses of the streams are almost absent.     

Free convection effects on the flow past a moving vertical infinite porous plate

An analysis of the effects of free convection currents on the flow field of an incompressible viscous fluid past an infinite porous plate, which is uniformly accelerated upwards in its own plane, is presented, when the fluid is subjected to a variable suction (or injection) velocity. It is assumed that this normal velocity at the porous plate varies att^–1/2, wheret denotes time. The equations governing the flow are solved numerically, using two-point boundary value shooting techniques.     

Time-dependent Green's functions of the cosmic ray equation of transport

Two spherically symmetric time-dependent Green's functions of the equation of transport for cosmic rays in the interplanetary region are derived by transform techniques. The solar wind velocity is assumed radial and of constant speedV. In the first model the radial diffusion coefficient =₀ r (₀ constant), and in the second solution =₀= constant. The solutions are for monoenergetic, impulsive release of particles from a fixed heliocentric radius. Integration of the solutions over timet, fromt=0 tot=, gives the steady-state Green's functions obtained previously.