An exact solution of the equation of transfer with three-term scattering indicatrix in an exponential atmosphere

The general equation for radiative transfer in the Milne-Eddington model is considered here. The scattering function is assumed to be quadratically anisotropic in the cosine of the scattering angle and Planck's intensity function is assumed for thermal emission. Here we have taken Planck's function as a nonlinear function of optical depth, viz.,B _v(T)=b _o+b ₁ e ^–. The exact solution for emergent intensity from the bounding face is obtained by the method of the Laplace transform in combination with the Wiener-Hopf technique.     

Behavior of the Line Profiles of the Sodium Doublet and the Calcium Triplet in the Spectrum of R CrB in the Shallow Minima of 1998-1999

The behavior of profiles of the Na I D line and of the infrared Ca II triplet for the star R Coronae Borealis (R CrB) during shallow light minima of 1998-1999 is traced using high-resolution spectra. During a light maximum, the sodium lines had an absorption profile with a shift of —(2-4) km/sec. During a light minimum, a narrow emission feature, which has an almost constant absolute intensity and a shift of —(8-10) km/sec, and an intense circumstellar absorption feature, which has a variable profile and a variable relative shift corresponding to an increase to 220 km/sec in the velocity of mass ejection, appeared in the cores of absorption lines. For several days before the onset of a light minimum, all three calcium lines exhibited a narrow emission feature in the line core with a shift of —(1-5) km/sec. All the subsequent changes in a line involved mainly the shape of the absorption line profile. The narrow emission feature's absolute intensity and relative position were maintained during all our observations. The behavior of the Na I D line profiles can be described qualitatively within the framework of the model of a spherical dust shell.     

Sources of error in the photoclinometric determination of planetary topography: A reappraisal

The technique of photoclinometry has frequently been used to determine planetary topography without proper consideration of possible sources of error. Previous studies of error sources have been limited in extent and have overlooked the importance of factors such as atmospheric scattering and the choice of a surface photometric function. This paper adopts a thorough and more direct approach to error analysis, whereby known topography is compared with photoclinometric profiles derived from synthetic quantised reflectance scans.Instrumental and geometric sources of error are found to exert a minimal influence on profiles in practice, provided that sufficient care is taken in the selection of images and the extraction of scans from those images. Environmental factors — relating to the scattering properties of the surface and, if present, atmosphere — are far more important. It is found that a simple Lommel-Seeliger law is unlikely to be appropriate to the majority of planetary terrains, given its inability to model the effects of multiple scattering or unresolved macroscopic roughness. It is further demonstrated that a Minnaert function or combination of Lommel-Seeliger and Lambert laws may empirically compensate for the first of these phenomena but not the second; in this respect, Hapke's equation is a far superior model of surface optical properties. In the case of an atmosphere, the need to correct for scattering by aerosols or suspended dust becomes more acute as atmospheric opacity increases and as particle scattering becomes more forward-biased. To perform this correction, a model for the combined reflectance of surface and atmosphere must be used when deriving profiles.Two case studies — of a small impact crater on Triton and a dust-mantled basaltic lava flow on Mars - are presented here. Regarding the latter, the implications that errors in photoclinometric flow thickness measurements have for inferred lava rheology are examined. Conservative estimates of errors in yield strength and apparent viscosity easily exceed 100% when one of the simplest photometric models possible — a Lommel-Seeliger law — is used to derive a profile.In the light of these findings, strategies are suggested for improving the results obtained from photoclinometry in the future.     

Radio emission of fast cosmic ions

It is usually assumed that the ions of cosmic rays contribute nothing to the observable electromagnetic radiation. However, this is true only when these ions are moving in a vacuum or a quiet (nonturbulent) plasma. In the case of fast ions in a turbulent plasma, there is an effective nonlinear mechanism of radiation which is discussed in this paper. The fast ion (relativistic or nonrelativistic) moving in the plasma creates a polarization cloud around itself which also moves with the particles. The turbulent plasma waves may scatter on the moving electric field of this polarization cloud. In the process of this scattering an electromagnetic wave with frequency (2.7) is generated. Let ₁ and k₁ be the frequency and wave vector of turbulent plasma waves,V is the velocity of the ion, and is the angle between the wave vector of electromagnetic radiation and the direction of the ion velocity. The method of calculating the probability of the conversion of plasma waves (k₁) into electromagnetic waves (k) by scattering on an ion with velocityV is described in detal in Section 2 (Equation (2.14)).The spectral coefficients of spontaneous radiation in the case of scattering of plasma waves on polarization clouds created by fast nonrelativistic ions are given in (3.6) for an ion energy distribution function (3.4) and in (3.8) for more general evaluations. The Equations (3.9)–(3.13) describe the spectral coefficients of spontaneous emission for different modes of plasma turbulence (Langmuir (3.9), electron cyclotron in a weak (3.10) or strong (3.11) magnetic field and ion acoustic (3.12)–(3.13) waves). The coefficients of reabsorption or induced emission are given by Equations (3.14) and (3.16)–(3.19). There is a maser effect in the case of scattering of plasma waves on a stream of ions. The effective temperature of the spontaneous emission is given by Equation (3.15). The spectral coefficients of radiation due to scattering of plasma waves on relativistic ions are calculated in the same manner (Equations (4.14)–(4.15)). The total energy loss due to this radiation is given in Equations (4.23)–(4.25). The coefficients of induced emission are given in (4.26)–(4.28).The results are discussed in Section 5. It is shown that the loss of energy by nonlinear plasma radiation is much smaller than the ionization loss. However, the coefficients of synchrotron radiation of electrons and nonlinear radiation of ions under cosmic conditions may be comparable in the case of a weak magnetic field and fairly low frequencies (5.5)–(5.6). Usually the spectrum of nonlinear plasma radiation is steeper than in the case of synchroton radiation. Equation (5.10) gives the condition for nonlinear radiation to prevail over thermal radiation.Translated by D. F. Smith.     

Quasi-linear model for the plasma mechanism of narrow-band microwave burst generation

Characteristic features of the plasma model for radio emission from the extending fronts of solar flare energy release are studied. It is shown that the electron distribution is formed near the thermal fronts as stationary beam injection through the boundary into the cold plasma semi-space. A principal new result is a conclusion about the localization of a plasma turbulence region — the source of emission in a narrow layer before the thermal front, that makes it possible to explain the burst narrow-band feature in a natural way. Wide capabilities of the flare loop structure analysis using the narrow-band emission parameters are demonstrated.     

Stochastic scattering and other contributions to the Sun's wake in the local hydrogen cloud

Gas streaming through the solar system experiences both destructive and scattering processes, the latter primarily in collisional interactions with the solar wind protons. The scattering interactions can be important in filling the downstream wake. They may effectively increase the velocity dispersion and also cause discrete orbit changes.The downstream intensity moment is here evaluated analytically for particles suffering a single, discrete collision, and compared with the moment from a thermal velocity dispersion (both in the absence of a central force field). The elastic scattering collisions of protons in H-gas lead to a contribution to theL backscatter from the wake equivalent to an initial thermal velocity of about 1 km s^–1, giving an intensity for cool gas of the order of 10R. This exceeds the contribution due to focussing in the solar gravitational field if the radiation pressure is not less than 0.8 of the gravitational attraction.     

A carbon star outflow envelope about IC 418

We present the results of near-infrared mapping, optical spectroscopy, and millimetric COJ+2-1 observations of the halo about IC 418. As a result, we confirm that NIR emission extends outside of the principal emission shell, and into a zone characterized by weak optical grain scattering and (in all probability) strong FIR emission. An analysis of the optical and FIR data suggests an overall shell mass 0.026M (for an assumed distance 0.412 kpc) — although the absence of associated CO emission suggests that the shell, if neutral, must possess a relatively low molecular abundance.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Continuum radiation from active galactic nuclei

Summary Active galactic nuclei (AGN) can be divided into two broad classes, where the emitted continuum power is dominated either by thermal emission (radio-quiet AGN), or by nonthermal emission (blazars). Emission in the 0.01–1 m range is the primary contributor to the bolometric luminosity and is probably produced through thermal emission from an accretion disk, modified by electron scattering and general relativistic effects. The 1–1000 m continuum, the second most important contributor to the power, is generally dominated by thermal emission from dust with a range of temperatures from 40 K to 1000–2000 K. The dust is probably reemitting 0.01–0.3 m continuum emission, previously absorbed in an obscuring cone (or torus) or an extended disk. The 1–10 keV X-ray emission is rapidly variable and originates in a small region. This emission may be produced through Compton scattering by hot thermal electrons surrounding an accretion disk, although the observations are far from being definitive. The weak radio emission, which is due to the nonthermal synchrotron process, is usually elongated in the shape of jets and lobes (a core may be present too), and is morphologically distinct from the radio emission of starburst galaxies.In the blazar class, the radio through ultraviolet emission is decidedly non-thermal, and apparently is produced through the synchrotron process in an inhomogeneous plasma. The plasma probably is moving outward at relativistic velocities within a jet in which the Lorentz factor of bulk motion (typically 2–6) increases outward. This is inferred from observations indicating that the opening angle becomes progressively larger from the radio to the optical to the X-ray emitting regions. Shocks propagating along the jet may be responsible for much of the flux variability. In sources where the X-ray continuum is not a continuation of the optical-ultraviolet synchrotron emission, some objects show variability consistent with Compton scattering by relativistic electron in a large region (in BL Lacertae), while other objects produce their X-ray emission in a compact region, possibly suggesting pair production.When orientation effects are included, all AGN may be decomposed into a radio-quiet AGN, a blazar, or a combination of the two. Radio-quiet AGN appear to have an obscuring cone or torus containing the broad emission line clouds and an ionizing source. Most likely, the (non-relativistic) directional effects of this obscuring region give rise to the difference between Seyfert 1 and 2 galaxies or narrow and broad line radio galaxies. For different orientations of the nonthermal jet, relativistic Doppler boosting can produce BL Lacertae objects or FR I radio galaxies, or at higher jet luminosities, flat-spectrum high-polarization quasars or FR II radio galaxies.     

The charge state in a highly dense molecular cloud

We have calculated the desorption rates of both physisorbed and chemisorbed ions from grain surfaces, due to the temperature increase at densities higher than 10^–13 g cm^–3. It has been found that physisorbed ions desorb from grain surfaces at neutral densities ofn>1.3×10¹¹ cm^–3, assuming that the desorption energyD is equal to 0.1 eV, while the desorption of chemisorbed ions from grain surface can only occur at neutral densities ofn>10¹⁵ cm^–3, at which point thermal ionization becomes more dominant.The electrons are assumed to be emitted from grain surfaces in a manner similar to the thermonic emission from heated solid surfaces. It was found that the temperature at which electrons are emitted from negatively charged grains depends on the value of the work function of the material of the grain.The charge state has been calculated for two limiting cases. Neglecting the grain surface reactions in case 1, the resulting relative charge density represents an upper limit, such that the electrical conductivity remains high. In this situation the magnetic flux dissipation is mainly contributed by ambipolar diffusion. In the second case, it has been assumed that the charged particles are chemically adsorbed on grain surfaces such that their desorption is negligible. In this case the charge density decreases sharply with increase of neutral density. Therefore, the electrical conductivity decreases sufficiently and Ohmic dissipation becomes effective.     

Dynamics of a cloud of fast electrons travelling through the plasma

A simulation of normal type III radio bursts has been made in a whole frequency range of about 200 MHz to 30 kHz by the usage of the semi-analytical method as developed in previous papers for the plasma waves excited by a cloud of fast electrons. Three-dimensional plasma waves are computed, though the velocities of fast electrons are assumed to be one-dimensional. Many basic problems about type III radio bursts and associated solar electrons have been solved showing the following striking or unexpected results.Induced scattering of plasma waves, by thermal ions, into the plasma waves with opposite wave vectors is efficient even for a solar electron cloud of rather low number density. Therefore, the second harmonic radio emission as attributed to the coalescence of two plasma waves predominates in a whole range from meter waves to km waves. Fundamental radio emission as ascribed to the scattering of plasma waves by thermal ions is negligibly small almost in the whole range. On the other hand, third harmonic radio emission can be strong enough to be observed in a limited frequency range.If, however, the time integral of electron flux is, for example, 2 × 10¹³ cm^–2 (>5 keV) or more at the height of 4.3 × 10¹⁰ cm ( _p = 40 MHz) above the photosphere, the fundamental may be comparable with or greater than the second harmonic, but an effective area of cross-section of the electron beam is required to be very small, 10¹⁷ cm² or less, and hence much larger sizes of the observed radio sources must be attributed to the scattering alone of radio waves.The radio flux density expected at the Earth for the second harmonic can increase with decreasing frequencies giving high flux densities at low frequencies as observed, if x-dependence of the cross-sectional area of the electron beam is x ^1.5 or less instead of x ², at least at x 2 × 10¹² cm.The second harmonic radio waves are emitted predominantly into forward direction at first, but the direction of emission may reverse a few times in a course of a single burst showing a greater backward emission at the low frequencies.In a standard low frequency model, a total number of solar electrons above 18 keV arriving at the Earth orbit reduces to 12% of the initial value due mainly to the collisional decay of plasma waves before the waves are reabsorbed by the beam electrons arriving later. However, no deceleration of the apparent velocity of exciter appears. A change in the apparent velocity, if any, results from a change in growth rate of the plasma waves instead of the deceleration of individual electrons.Near the Earth, the peak of second harmonic radio flux as emitted from the local plasma appears well after the passage of a whole solar electron cloud through this layer. This is ascribed to the secondary and the third plasma waves as caused in non-resonant regions by the induced scattering of primary plasma waves in a resonant region.     

A polytropic model for a two-component galaxy

A model is presented consisting of two different axially deformed polytropic spheroids, homocentric and coaxial — with arbitrary values for the two masses, the two equatorial radii and the two polytropic indices — interacting with each other only gravitationally. The model represents the two main components, halo and bulge plus disk, of a galaxy. The flattening of the two spheroids is assumed to be due to rigid-body rotation and tidal interaction, and the treatment follows closely the method of Chandrasekhar and Lebovitz for single polytropic structures. All useful quantities are evaluated up to first order in the two rotation frequencies. The main properties of sequences of models intended to mimic evolution at constant masses and constant angular momenta are presented.     

Observations of a surge prominence as a continuum event

Observations of a surge prominence event on 31 May 1971 are discussed. The continuum emission observed during the upward acceleration of the surge is attributed to the scattering of photospheric radiation by free electrons. The observed scattered light intensity amounts to a few times 10^–5 that of the central disk intensity leading to a column density of n _e L10²⁰ cm^–2. The actual electron density when taking into account the presence of inhomogeneities is n _e 10¹² cm^–3. The dynamic and morphological behaviour of the surge is considered.     

Diffuse Component Spectra of Solar Active Regions at Submillimeter Wavelengths

Solar maps at 212 and 405 GHz obtained by the Solar Submillimetric Telescope (SST) show regions of enhanced brightness temperature, which coincide with the location of active regions. A statistical study of the radio emission from these active regions was performed for the first time at such high frequencies during 23 days on June and July 2002, when the atmospheric opacity was low. The brightest regions on the maps were chosen for this study, where the brightness excess observed varies from 3 to 20% above quiet Sun levels (i.e., 200–1000 K) at both wavelengths. Sizes of the regions of enhanced emission calculated at half the maximum value were estimated to be between 2′ and 7′. These sizes agree with observed sizes of active regions at other wavelengths such as Hα and ultraviolet. An important result is that the flux density spectra of all sources increase toward submillimeter frequencies, yielding flux density spectral index with an average value of 2.0. The flux density of the active region sources were complemented with that from maps at 17 and 34 GHz from the Nobeyama Radio Heliograph. The resulting spectra at all four frequencies were fit considering the flux density to be due to thermal bremsstrahlung from the active region. In the calculations, the source radius was assumed to be the mean of the measured values at 212 and 405 K. The effective temperatures of the radio emitting source, assumed homogeneous, obtained from this fit were 0.6–2.9 × 10⁴ K, for source diameters of 2′–7′.     

Reflection and transmission by a vertically inhomogeneous planetary atmosphere

By appealing to the reciprocity principle simple expressions are derived for the plane albedo and the transmissivity of a vertically inhomogeneous, plane parallel atmosphere. The plane albedo is shown to equal the angular distribution of the reflected intensity for isotropie Illumination of unit intensity incident at the top of the atmosphere, while the transmissivity equals the angular distribution of the transmitted intensity for isotropie illumination of unit Intensity incident at the bottom of the atmosphere. Chandrasekhar's solution of the planetary problem (including a Lambert reflecting lower boundary) in terms of the solution to the standard problem (no reflecting ground) is extended to apply to an inhomogeneous atmosphere resting on a surface that reflects radiation anisotropically but with no dependence on the direction of incidence (anisotropic Lambert reflector). The computational aspects are discussed and a procedure for computing the planetary albedo and transmissivity Is outlined for a vertically inhomogeneous, anisotropically scattering atmosphere overlying a partially reflecting surface. Numerical verification and illustration are also provided and it is shown that the assumed vertical variation of the single scattering albedo strongly affects the plane albedo but only weakly the transmissivity.     

Fluctuations in the Intensity of Radiation Emerging from a Multicomponent Stochastic Atmosphere. II

This part of a series of papers examines the more general problem in which it is assumed that the fluctuations in the intensity of radiation emerging from a medium are caused by random variations in both the optical thickness of the structural elements and the power of the energy sources contained in them. The frequency dependence of the relative mean square deviation (RelMSD) is investigated for different possible relationships among the parameters of the fine structure components. It is shown that the level of fluctuations at the central frequencies of a line can be greater than or smaller than in the far wings. The dependence of the RelMSD on the number of components and the number of possible realizations of their optical properties is discussed. The influence of random variations in the scattering coefficient on the observed integral intensity of a spectrum line is also examined. Observations of several relatively strong EUV lines from the SOHO/ SUMER space program are presented for comparison. These data indicate that there is a correlation between the frequency dependence of the RelMSD and the characteristic temperature for formation of these lines.__________Translated from Astrofizika, Vol. 48, No. 2, pp. 303–313 (May 2005).     

Analysis of the spectral features of a recent supernova 1987n

We present an attempt to analyse the spectra of SN 1987n in NGC 7606, covering a period of 10 days from the time of maximum brightness. The velocities in the rest frame of NGC 7606 and the depths of the spectral lines at maximum light are very close to those of SN 1981b in NGC 4536, slight differences being nevertheless present. A distance to NGC 7606 of 46±11 Mpc for anH ₀ value of 50 km s^–1 Mpc^–1 is inferred from Pskovskii's relation.The analysis carried out within a standard simple model of spectral synthesis involves a high uncertainty in the abundance determinations for the intermediate-mass elements quoted. This uncertainty arises on the one hand from the free choice of the excitation temperature and from the sensitivity to changes in the excitation temperature of the depths of the strongest lines of those elements and, on the other hand, from the impossibility of obtaining within this model an estimate of other abundances — He, O, Na, S — which have NLTE populations.The analysis developed in a new model based (as is the standard one) on Sobolev's approximation but allowing for a more realistic continuum treatment points to an important attenuation effect on the radiation in the lines, due to the continuum scattering, which can also affect abundance determinations.     

A river erosion estimate on the Loess Plateau: a case study from Luohe River, a second-order tributary of the Yellow River

Based on fieldwork and terrace ages, which were determined using ¹⁴C, TL and paleosol stratigraphy, a general model was established for the development of the Yellow River terrace system. The ages for the terraces and valley flats of the Yellow River system are T₆—1.67–0.85 Ma BP, T₅—0.85–0.47 Ma BP, T₄—0.47–0.10 Ma BP, T₃—0.10–0.007 Ma BP, T₂—7.0–0.7 ka BP, T₁—0.7–0.3 ka BP, the higher valley flat—0.3–0.15 ka BP and the lower valley flat 0.15–0 ka BP, respectively. Each terrace or valley flat and corresponding paleo-valley represents a river erosion/deposition cycle. Using this model and selected geomorphic parameters of terraces and paleo-valleys from 10 typical cross sections of Luohe River, a tributary of the Yellow River, an attempt is made here to estimate paleo-river erosion since the Pleistocene on the Loess Plateau.     

Photon path-length distribution function (I)

The determination of the photon path-length distribution function (PLDF) for the case of linearly anisotropic (Rocard) scattering in a semi-infinite plane-parallel homogeneous atmosphere using the Piessens-Huysmans method is described in detail. It has been shown that in this case the PLDF may have a minimum at small path-lengths — a feature which is never encountered in isotropic scattering. The respective regions with minima in the (µ, )-plane have been sorted out. As a rule, the average path-length in the case of the forward/backward Rocard scattering is larger/smaller than that in the isotropic case. The precise average path-lengths for a number of parameters are shown in Table I.     

Surface properties and effective resolution from ground-based observations of Mercury

A detailed study to evaluate ground-based photographs of Mercury has been carried out. Models of the surface scattering properties have been assumed and smeared with a Gaussian function for direct comparison with center-to-limb scans along Mercury's intensity equator. Data from a range of phase angles from 31° to 92° have been compared with smeared models assuming a Lambert surface, a surface which obeys the Lommel-Seeliger law and one which is Minnaertian, having a variable coefficient. Within the limits of the observations a lunar Minnaert surface yields the most consistent interpretation. An objective evaluation of the resolution of the photographs is obtained in terms of Gaussian half-widths.     

Hydromagnetic emission of the interplanetary plasma

A new type of geomagnetic pulsation — the serpentine emission — has been discovered in the 0–2 Hz range. The particular feature which characterizes the serpentine emission is the wide modulation of the carrier frequency. A theory to account for this type of disturbance involves radiation from the solar wind. The frequency modulation is explained in terms of Doppler shifts and variation of the direction of the interplanetary magnetic field.