Pulsar radio emission

A new version of the theory of pulsar radio emission is developed for the case of a coaxial rotator. It is based on the electric field that we established [G. S. Sahakian, Astrofizika, 37, 97 (1994)] for the radiation channel (the channel of open magnetic field lines) and on convenient approximations for the electron energy obtained in [G. S. Sahakian and É. S. Chubarian, Astrofizika, 37, 255 (1994)]. It is shown that, owing to the emission of photons of curvature radiation by particles, e e+_c', and photon annihilation, _c e⁺e^– in the lower part of the radiation channel, a special region (the magnetic funnel) is formed in which vigorous cascade multiplication of particles occurs. The height of the magnetic funnel is h 6R^0.2, where R is the radius of the neutron star and is its angular rotation rate. As a result of supersaturation of the plasma density in the magnetic funnel, a discharge occurs after each time intervalt5·10^–7–0.8B ₁₂ ^–1.4 R ₆ ^–0.2 , i.e., the longitudinal electric field disappears (B is the magnetic induction in the star). During the active radiative processes in the magnetic funnel, two main fluxes of particles with high ultrarelativistic energies are formed: an upward flux of electrons and a positron flux falling onto the star's magnetic cap. These fluxes are accompanied by narrow strips of positron and electron fluxes, respectively, of considerably lower energy, which are fairly powerful, coherent radio sources. The pulsar's radio luminosity is calculated to be L7.4·10^223.8 ₃₀ ³ R ₆ ^–2 erg/sec, where =BR 3/2 is the star's magnetic moment. Comparing this result with observations, we conclude that the magnetic moment and hence the mass of the neutron star evidently must be considerably smaller, on the average, for fast pulsars than for slow ones. It is shown that the magnetic moment of the neutron star can be determined from the intervals between micropulses in the pulse profiles. The problem of the origin of the macrostructure of the radio pulse is discussed.Translated from Astrofizika, Vol. 38, No. 1, pp. 141–185, January – March, 1995.     

Hα diagnostics of (post)-flare loops based on narrow-band filtergram observations

Using narrow-band H filtergrams, we develop a quantitative non-LTE approach to determine the physical conditions prevailing at the tops of (post)-flare loops observed against the solar disc. At temperatures 10000–15000 K, the tops of flare loops turn to emission at H line center when the gas pressure P _g reaches 1 dyn cm^–2 and should be clearly visible for P _g 3 dyn cm^–2, independently of the loop diameter. This situation corresponds to the electron density of the order 10¹² cm^–3. The contrast of flare-loops (in projection on the disc) at H line center is mainly the function of P _g , while in the line wings (H ± 1 Å) the loop can be visible in absorption or emission only when rather strong microturbulence is present or for unrealistically high gas pressures. Finally, we briefly discuss our diagnostical results in frame of the latest (post)-flare loop model.     

The radiative relaxation time in the chromosphere

The cooling effect of emission in the spectral lines, which dominates over continuous emission in the chromosphere and becomes important first around the temperature minimum, modifies greatly the radiative relaxation timet _r in the solar atmosphere. This rises from low photospheric values to a maximum of 8 min just aboveT _min, falls in the low chromosphere to 1.5 min because of line emission, but rises again to 6 min atT 7000–8400 K in the chromosphere where hydrogen ionization increases the specific heat.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Rapidly rotating polytropes in the post-Newtonian approximation to general relativity

The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order ⁴, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = ²/2G _c and a relativity parameter, =p _c / _c C ² , wherep _c and _c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order ². The critical rotation parameterv _c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974     

The interaction of matter and radiation in the hot model of the Universe,II

Heating of the primaeval plasma prior to the epoch of recombination results in distortions in the Rayleigh-Jeans region of the microwave relic radiation spectrum (1–60 cm, or more exactly =2.5_–7/8 cm). The present observational data allow limits to be set to such energy injection from which follow upper limits to (a) the amount of antimatter in the universe; (b) the parameters of primaeval turbulence; and (c) the adiabatic fluctuation spectrum for small masses (M<10¹¹ M ).If the heating takes place prior to the epocht=10_1012/5 sec (and in particular at the annihilation of electron-positron pairs atT10⁸–10¹⁰ K,t<300 sec), no observable distortions are expected in the relic radiation spectrum. Here =/_crit is the dimensionless average density of matter in the universe.Translated from the Russian by D. F. Smith.     

Pulsar radio emission. I. Oblique rotator

The problem of pulsar radio emission for the case of a coaxial rotator was investigated in our preceding paper [G. S. Sahakian, Astrofizika,38, 143 (1995)]. In this paper it is solved for the realistic case in which the star's magnetic axis does not coincide with its rotational axis (an inclined rotator). It is shown that above the star's magnetic cap a special region, called a magnetic funnel, is formed in which vigorous processes of particle multiplication occur. The height of this region is h 8·10^60.2 ₃₀ ^1/3 R ₆ ^1.3 cm and its radius r(r/c)^0.5 depends little on the inclination angle a ( is the angular rotation rate, is the magnetic moment, R is the star's radius, and r is distance from the center of the star). It is shown that the pulsar radio emission is produced in the magnetic funnel. Here, in the course of active radiative processes, two main particle fluxes with a high ultrarelativistic energy are formed: an upward electron flux and a positron flux falling onto the star's magnetic cap. These main fluxes are accompanied by individual narrow strips of positron and electron fluxes with a relatively low energy, which are fairly powerful, coherent radio sources. Such secondary fluxes are formed immediately after the annihilation of photons of curvature radiation emitted by particles of the main fluxes. The pulsar's radio luminosity is estimated to be L7.4·10^233.52 ₃₀ ^8/3 (a), where (a) is a known function (1 for a<50°). Equating the theoretical and observed radio luminosities L and L₀, we obtain the formula ₃₀P^1.32R ₆ ^0.4 (2.1·10^–27L₀/)^3/8 for the magnetic moment of the pulsar's neutron star, where P is the pulsar's period. The magnetic moments of slow pulsars calculated from this formula turn out to be considerably larger than those of fast pulsars. This means that the masses of slow pulsars are larger, on the average, than those of fast pulsars. The magnetic funnel operates with interruptions, periodically undergoing a discharge, so that the production of pulsar radio emission operates with interruptions. The durations of the production of radio emission and of the interruptions between those processes are on the order of h/c2.7·10^–40.2 ₃₀ ^1/3 sec, i.e., pulsar radio emission has a microstructure. Consequently, a study of the microstructure of the profiles of observed radio pulses enables one to obtain additional information about the magnetic moments of the neutron stars.Translated from Astrofizika, Vol. 39, No. 2, pp. 313–335, April–June, 1996.     

Radial pulsation of less-massive yellow supergiants

The conclusions of the present paper broadly are: (a) The galactic concentration of doubles by comparing the distributions in galactic latitudes 0°<20° and >40° is nearly twice as large as the galactic concentration of stars in general. (b) The astrographic catalogues are not complete in the fainter magnitudes. (c) The large value of the ratioT:O _k (observed to optical number of pairs) from Kreiken's formula shows that almost all stars in the group 0<d5 and quite a few in the other two groups, viz., 5<d10 and 10<d15 might be shown true binaries. Consequently, Aitken's working definition of a true binary should be extended if it were to include all true binaries. (d) The doubles are probably stars of Population I. (e) The logarithm to the base 10 of the cumulative counts can be represented by an empirical relationA+B(m–1.5)+C(m–1.5)².Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846)     

The clustering of Lα absorption lines in the QSO spectra

For nine published high-resolution QSO spectra a correlation analysis of their L forest lines has been performed. The two-point correlation functions show some quasi-periodic structure of magnitude ||0.3. Their characteristic separation along the line-of-sight amounts to s ₀=3×10^–3 or to s ₀=5×10^–3 for =1 and 0.2, respectively. Especially the distribution of nearest neighbouring line positions in two close QSO pairs allows for the interpretation that the absorption clouds lie in sheet-like structures as predicted by the pancake theory. The correlation data contain some hints on metal absorbers within the forest of unidentified lines.     

On gravitational orbits and the virial theorem

We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E _kin/E _pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits.     

Stellar structure with a Boltzmann factor: An extension to chemically heterogeneous H−He-stars

We present an attempt for an extension of the modified Boltzmann model, which was introduced by Callebautet al. (1982) as an improvement of the polytropic models, to the case of chemically-heterogeneous stars in equilibrium, containing H and He, by proposing a density profile of the formp=C ₁ T ^N exp (–_H m(–_*)/kT) +C ₂ T ^N exp (–_He m(–_*)/kT. Analytical properties are derived and numerical as well as analytical arguments are presented for the conclusion that this hypothesis for a density profile imposes an almost constant chemical profile to the model as a whole, thereby making it in this form unsuited for the study of heterogeneous stars. A comparison is made with the former Boltzmann model in the homogeneous limit.     

The Bilderberg model of the photosphere and low chromosphere

From 17 through 21 April 1967, an international study week was held in the Bilderberg near Arnhem, Netherlands, with the aim of obtaining an internationally acceptable model of the solar photosphere and low chromosphere. It was found that such a model, based on observed intensities and center-to-limb observations of the solar continuous spectrum, could indeed be established. This model, henceforth called the Bilderberg Continuum Atmosphere (BCA), is shown in Table I, which gives the temperature, gas and electron pressures, and other data as functions of the continuous optical depth at 5000 Å between 5000 = 10^–7 and 25. The model is characterized by a flat temperature minimum of 4600 °K between 5000 10^–2 to 10^–4. The model is homogeneous, and in hydrostatic equilibrium. A hydrogen-helium ratio of 10 has been assumed.Much divergence remains in the interpretation of line-profile observations with regard to the establishment of a photospheric model (Section 4). It proved to be as yet impossible to obtain reliable information on the variation with depth of the following functions: temperature fluctuations, turbulence velocities, convective velocities, and vibrational velocity amplitudes (Section 5). Provisionally, it is assumed that _macro = 2 km/sec and _micro = 1 km/sec, isotropic and independent of depth.     

The innermost corona observed at the 1973 June 30 eclipse

Slitless flash spectrograms in heights below 8000 km above the solar limb were obtained by the University of Kyoto Expedition at Atar, Mauritania. The integrated intensities of Fexiv 5303, Fex 6374, Fexi 7892, and the continuum are measured as a function of height above the solar limb at eleven points (P.A. = 284–300°) around the third contact point. It is found that a significant amount of the emission in Fex 6374 originates in chromospheric levels well below 8000 km. This implies that the interspicular region of the chromosphere is occupied by coronal material. The average values of the electron temperature and the electron density in the interspicular region are derived from the Fex 6374 and the Fexi 7892 intensities on the assumption of spherical symmetry: T _e = 0.9–1.1 × 10⁶ K and N _e = 9–10 × 10⁸ cm^–3. The intensity variations of the coronal lines and the continuum with position angle are also studied. Strong correlations between Fexiv 5303 and the continuum and between Fex 6374 and Fexi 7892 are found. From the Fex 6374 intensities it is inferred that there is a density fluctuation in the innermost corona by at least a factor of two.Contributions from the Kwasan and Hida Observatories, University of Kyoto, No. 271.     

On the acceleration of interstellar grains

Dust grains of radiir _g 3×10^–6 cm, injected into the intercloud medium at speeds in the range 10⁷–10⁸ cm s^–1, may be stochastically accelerated to speeds 0.1c due to scattering by irregularities in the galactic magnetic field.     

Infrared emission of dust grains in the clusters of galaxies

The observations of the reddening of the distant galaxies and the weak diffuse radiation in the clusters of galaxies can be interpreted as a consequence of the presence of dust grains in the intergalactic medium. When allowance is made for the destruction of the grains in collision with particles of the hot gas, its lifetime is about 10⁷–10⁸ yr at a gas concentrationn _g 10^–3 cm^–3. The detection of the infrared (IR) emission from the galaxy clusters might be the test for the proof of the presence of dust grains in the intergalactic medium. In this paper the estimates of the expected intensities and fluxes of IR emission for the spectral region 50–300 are presented for two galaxy clusters in Coma and Perseus. The parameters of the hot gas spatial distribution are chosen from X-ray observations. Having assumed that intergalactic dust can be ejected only from the galaxies, we used such a model for intergalactic dust grains which explains very well the interstellar dust effects. It is shown that the dust temperature, which is determined from the general energetic balance of the dust grains, can achieve some scores of degrees of Kelvin. Two models of the dust spatial distribution are considered. It is found that the maximum of IR flux for the Coma cluster lies near =100 and the same for the Perseus cluster near 50–70. The total fluxes of IR emission from these clusters are about 10⁵–10⁶ Jy and can be detected by modern observational methods.     

The structure of the spiral arm S4 in andromeda galaxy

TheUBV photometry of 690 stars in the spiral arm S4 and the U magnitudes of 120 stars in the spiral arm S6 with the help of the 2 m RCC telescope of the Rozhen Observatory at the Bulgarian Academy of Sciences, has been used to obtain the colour-magnitude and colour-colour diagrams across the arms. Our age estimations are compared with van den Bergh's (1964). The age gradient across the S4 arm has been found. The colour excessE _B-V is highest at the inner edge of the arm S4. From the age we have evaluated the velocity of star formation propagation across the arm S4 60 km s^–1 , pattern frequency _p 14 km s^–1 kpc^–1 and corotation radiusR _c20 kpc. The structure of S4 along the arm is complicated. In the OB 82 region an age gradient is absent. The young associationOB 79b is located near the outer edge of S4 and it has a large absorptionA _v2^m.5 contrary to the density wave prediction. This association bears no relation to the spiral density wave and it is probably, supernova events that stimulated the star formation in it. The colour excessE _R-V is randomly distributed and the youngest stars are concentrated in the middle of the S6 arm. A value of pattern frequency _p = 12km s^–1 kpc^–1 andR _c=12 kpc of our Galaxy has been obtained from the age distribution of the open clusters and cepheids across the Carina-Sagittarius arm. The spiral structure of M31 is compared with that of the galaxy. There is a similarity between S4 in M31 and Carina-Sagittarius in the Galaxy, and also between the S6 and Perseus arms. The Orion arm in the Galaxy bears no relation to the wave density.     

Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

The Energy Equation in the Lower Solar Convection Zone

As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U _r(r,)=P ₂(cos)₂(r)/r ²+P ₄(cos)₄(r)/r ² +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P ₂(cos), P ₄(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting ₄(r)=–H₂(r) with H–1.6, a constant. The value of ₂(r) is negative, i.e., the P ₂ flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.     

Emission cores in H and K lines

Profiles of the H and K lines of Mgii and the K line of Ca ii are computed using a two-level atom for five model atmospheres distinguished from each other mainly by the location of the temperature minimum. In the five models the temperature minimum and the chromospheric temperature are adjusted to give best agreement between computed and observed profiles. The parameters and r ₀ are prescribed as functions of from a density model of the atmosphere. By comparing computed and observed profiles of the K₃, K₂ and inner K₁ components of the lines we determine both the approximate depth variation of _D and the best of the temperature models. We find that the Doppler width increases rapidly with height in the chromosphere beginning from a value of 1.6 km/sec at ₀ 10^–2. This latter value corresponds closely to the thermal velocity of Mg atoms in the upper photosphere. The preferred temperature model is one for which the temperature minimum occurs near ₀( 2800) 10^–4–10^–5 with a value T _min 4200 ° and which has a temperatu near 7000 ° at ₀ = 10^–6 where K₂ is formed. The intensity in K₃ is determined largely by d _D/d in the K₂ and K₃ regions.