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1.
We have considered the transport equation for radiative transfer to a problem in semi-infinite non-conservative atmosphere with no incident radiation and scattering albedo 0 < 1. Usint the Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. We have obtained theH-function of Dasgupta (1977) by equating the emergent intensity with the intensity at zero optical depth.  相似文献   

2.
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.  相似文献   

3.
By performing the one-sided Laplace transform on the scalar integro-differential equation for a semi-infinite plane-parallel isotropic scattering atmosphere with a scattering albedo 0 1, an integral equation for the emergent intensity has been derived. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity. The intensity at any optical depth for a positive scattering angle is also derived by inversion. The intensity at any optical depth for a negative scattering angle is also derived in terms of Cauchy's principal value using Plemelj's formulae.  相似文献   

4.
We have calculated the changes that would occur in mean intensity due to the presence of aberration and advection terms in radiative transfer equation. We have considered an absorbing medium with velocities 1000, 2000, 3000, 4000, and 5000 km s–1 (-0.0033, 0.017, where =V/C,V is the velocity of the medium andC is the velocity of the light). Calculations have been done in a comoving frame with monochromatic radiation field. We have calculated the deviation in mean intensity defined as 0)]/J(V = 0)]$$ " align="middle" border="0"> , whereJ is the mean intensity. We have taken two types of absorbing media (1) with a source of constant emission and (2) with emission source. As the emission decreases as 1/n 2 wheren is the number of layer, wheren=1 corresponds to max and n=N corresponds to =0We find that for a total optical depth of one, the maximum change is about 2% whenB(r)=1 and about 6%, whenB(r)1/n 2 whereB(r) is the Planck function. When the optical depth increases to 5 the maximum change in the case of the constant source function falls to 1.5%, where as in the other case in which the Planck function changes as 1/r 2 the maximum changes remains at 6%. Further increase of the optical depth will reduce the changes to less than 2%. The amplification factor in the case of the Planck function varying as 1/r 2 is more than when the emission sources are constant.  相似文献   

5.
The numerical solution of radiative transfer equation including curvature with both absorption and scattering has been developed in the frame work of Discrete Space Theory. Two cases have been considered: (A) irradiation of the atmosphere at =T and (B) no irradiation on either side of the atmosphere. Isotropic scattering has been assumed. It is found that the emergent luminosities (defined by r 2 I(r, ) ) from scattering dominated atmospheres are smaller than those from absorption dominated atmospheres.  相似文献   

6.
To extend Shapiro's (1973a, b) calculations of black hole accretion to the regimes of interstellar gas densities and of black hole masses for which emergent luminosities are expected to be high, the radiation hydrodynamics of spherically symmetric gas flows in static isotropic metrics is discussed. Since for the more luminous objects the optical depth of the accretion volume becomes large, particular attention has to be paid to radiative transfer through non-Euclidean spaces, and a method for solving the full transfer problem is presented. The method is applied to accretion into black holes of mass between 10M and 105 M , under the conservative assumption that all other heat sources, like dissipation of magnetic or turbulent energy, can be neglected in comparison to the compressional work term,p dV. In the interstellar gas parameter range of interest, the radiation field is then dominated by emission and absorption of synchrotron radiation from inner zones of the flow. Temperature stratifications, luminosities and emergent spectra resulting from these processes are calculated.  相似文献   

7.
The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein'sA, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the rate equations to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.  相似文献   

8.
An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z and if (z) and p(z) are not too rapidly varying, then (t) m (z , t)+N p(z , t) where m and N depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

9.
R. Muller 《Solar physics》1975,45(1):105-114
High resolution pictures (about 0.3) of photospheric faculae near the solar limb have been obtained with the Pic du Midi 50 cm refractor; their granular structure then clearly appears. The microphotometric study of these facular granules shows that the ratio of their intensity to the photospheric intensity, I f/I ph (cos) reaches a maximum near cos = 0.3 and then decreases towards the limb. The values of this ratio have been corrected with a most likely spread function. Then a temperature model of a facular granule is obtained: with respect to the neighbouring photosphere, this granule appears as a photospheric hot cloud which does not extend high in the solar atmosphere (thickness 100 km above 5000 = 1). The temperature excess is 750K at maximum. This hot region is located over a layer which is cooler than the normal photosphere at the same level. Another hot region might extend above the photospheric hot cloud, possibly up to the chromosphere. This photospheric facula model which is confined to the lower photosphere seems to indicate that this phenomenon is different from the photospheric network which is visible up to the lower chromosphere.  相似文献   

10.
A simplified representation of the temperature distribution in the solar photosphere is proposed: ( 0) = 0 - 1 log 0. An expression is derived for the emergent continuous spectrum from the simple model. The limitations and applications of the simple model are discussed.  相似文献   

11.
The exotic quantum process of photon splitting has great potential to explain the softness of emission in soft gamma repeaters (SGRs) if they originate in neutron stars with surface fields above the quantum critical fieldB cr = 4.413×1013 Gauss. Splitting becomes prolific at such field strengths: its principal effect is to degrade photon energies, initiating a cascade that softens gamma-ray spectra. Uniform field cascade calculations have demonstrated that emission could be softened to the observed SGR energies for fields exceeding about 1014 Gauss. Recently, we have determined splitting attenuation lengths and maximum energies for photon escape in neutron star environments including the effects of magnetospheric dipole field geometry. Such escape energies esc suitably approximate the peak energy of the emergent spectrum, and in this paper we present results for esc as a function of photon emission angles for polar cap and equatorial emission regions. The escape energy is extremely insensitive to viewing perspective for equatorial emission, arguing in favour of such a site for the origin of SGR activity.  相似文献   

12.
An exact solution of the transport equation in radiative transfer for an axially symmetric Rayleigh scattering problem in semi-infinite planetary atmosphere both for emergent intensity and intensity at any optical depth has been derived with the help of the Laplace transform and the Wiener-Hopf technique, and by use of the constancy of net flux. Chandrasekhar's results for emergent intensity have been verified. New expressions for theH l andH r functions have been obtained.  相似文献   

13.
Yu D. Zhugzhda 《Solar physics》1991,132(2):205-213
We have established a statistical relation between the facular contribution to the solar irradiance and the intensity of the associated calcium plage. For the solar irradiance data the ACRIM measurements were used. The quiet-Sun level of the irradiance was determined as a function of the time for the period studied. A sample of plages in the period of the solar activity minimum was selected, during the periods when no spots were present on the solar disc. We have expressed the dependence studied through the parameter C p in the proxy PFI concept. The parameter C p could be related to the plage intensity (I) as C p = 0.006I + 0.003. The mean value of the parameter C p ranged between 0.015 and 0.017 depending on the choice of samples.  相似文献   

14.
Spectroheliograms have been obtained in the line cores of two infrared multiplets of neutral oxygen. Those made in the lines of the 7770 Å multiplet show a very smooth intensity distribution, with faculae and sunspot penumbrae at a very low contrast with respect to the undisturbed photosphere. Spectroheliograms made in the core of 8446.37 Å show evidence of coupling with chromospheric features and of blending with a line of neutral iron.An analysis of a 7772 Å spectroheliogram indicates that a magnetic field of approximately 1500 G is required to produce the disappearing penumbra phenomenon. This value is consistent with the recent observations of Beckers and Schröter (1969).  相似文献   

15.
Steiner  Oskar 《Solar physics》2000,196(2):245-268
A magnetopause that separates two regimes of different flow, additional to the separation of a magnetic field from a field-free plasma, gives rise to the formation of asymmetric Stokes profiles. Using a simple two-layer model atmosphere, where one layer comprises a magnetic field, the other being field-free, it is shown by analytical derivation that a wide variety of Stokes V profiles can be produced, having amplitude asymmetries a in the range –a. These include two-humped V profiles, which have two lobes of equal sign. For the most simple models, the asymmetry depends on the ratio of continuum intensity to the Planck radiation intensity of the magnetic layer at the wavelength of the spectral line under consideration, and on the line depth. Two-humped profiles (|a|>1) require the temperature of the magnetic layer to surpass the temperature of the line-core forming region, implying a temperature inversion, so that the V profile is partially in emission. The confrontation of this formation scenario with properties of observed one-lobe profiles of quiet-Sun network regions is inconclusive due to insufficient spatial resolution and lack of a sufficient sample of simultaneously recorded Stokes spectral lines of varying line depths. It seems, however, to be in good agreement with the observed frequent occurrence of abnormal V profiles of the very strong Nai D 2 and D 2 spectral line. A possible observational verification for the present formation scenario of abnormal Stokes V profiles and a novel method of Stokes inversion are discussed.  相似文献   

16.
The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor –1 for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B r| and MMF intensity |H| (in gauss)|B r|(H 0)min×(1+C|H|)where =1.5×10–5 normalizes the photospheric field strength to 1 AU distance from the Sun, (H 0)min=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor –1.  相似文献   

17.
The study of supernova (SN) models with slow energy pumping is continued. At maximum luminosity the main characteristics of a SN are shown to be independent of the initial structure of the model (Table I, Figure 1). However, they depend on the massM e of the envelope, and on the intensity of energy pumpingL , with an increase ofM e leading qualitatively to the same changes in the SN parameters as a decrease inL (Table I, Figures 2 and 3). A simple relationship connecting the important SN parameters is obtained (Equation (6)). From the inflection of the color indexB-V curve, the possibility of deriving the characteristic time of energy pumping with intensityL 1044 erg s–1 is pointed out. The comparison of the extragalactic type I SN observations with the results of calculations leads to the estimate ofM e 0.3–0.7M.An investigation of the galactic type I SN remnants is carried out (Table III). The estimate ofM e 0.2–0.3M is obtained for the remnants of supernovae SN 1006, SN 1572, and SN 1604. It completely fits the results for the extragalactic type I SNs. The total initial mass of SN 1604 presupernova was shown to be at least about 7M .It was established that the Crab nebula resulted from the outburst of a peculiar SN. The unique properties of such SNs, including SN 1054, are due to the low intensity of energy pumping (L 1042 erg s–1). The mass of the envelope of the Crab nebula is evaluated to beM e 0.7M . SN 1054 was shown to have m max v =–4 m . 0 at maximum luminosity.  相似文献   

18.
Residual intensity fluctuation measurements within the wings of the 5183.6 Mgi b1 line, obtained from two, high-resolution, high-dispersion, Sacramento Peak Observatory spectrograms, have been subtracted from intensity fluctuations in the adjacent continuum in order to isolate fluctuations associated exclusively with line formation. The useable spectral range for studying these lineformation fluctuations is restricted to wavelengths between 1040 and 7170 km because the subtraction increases the relative importance of noise and large-scale photographic variations across the spectrograms could not be completely removed. Power and cross-power (coherence and phase) spectra proved to be valuable diagnostic tools in isolating line-formation fluctuations.Over this spectral range, the line-formation fluctuations are characterized by flat power spectra as compared to those for continuum fluctuations, appreciable fluctuation rms relative to that for continuum fluctuations, and the necessity to multiply the wing fluctuations by a factor 0.95 min 1.00 to most effectively isolate these fluctuations (Figures 3 and 4). That continuum fluctuations are modified in shape but otherwise not drastically changed in the line wings explains the flat spectrum. The relative rms's vary from 0.34 in the inner wing to 0.22 in the outer. The range of possible values for min results from uncertainties in the photographic density-residual intensity calibration.  相似文献   

19.
Some properties of the photospheric granulation near the centre of the quiet sun have been investigated on the basis of two high-definition Stratoscope photographs. We obtain (1) a number density of 54 granules per 10 × 10, (2) a total number of granules on the whole surface of 6.3 × 106, (3) a mean cell diameter of 1.5 or 1100 km and a mean granule diameter of 1.2 or 850 km, the difference of 250 km being ascribed to the mean width of the dark intergranular lanes, (4) frequency distributions of cell diameters and granule diameters (Figures 1 and 2), and (5) an isophotal map in relative intensity (Figure 3). In general, larger granules are brighter than smaller granules (Figure 4). Cross-section profiles are shown for some granules and intergranular lanes (Figures 5 and 6). These quantities have not yet been corrected for the finite resolution of the telescope.  相似文献   

20.
Four different models for a K-giant atmosphere (T e=4500K, logg=2) have been computed. Each model is characterized by the inclusion of different opacity sources (H, H–, (H), metals, blanketing effect, He–) in order to obtain an evaluation of the model sensitivity concerning the atmospheric structure and the emergent flux. The results show that hydrogen, metals and blanketing effect must be taken into account to achieve self-consistent and reliable models.A picture of the influence of the frequency distribution of the absorption coefficient on the model features is also shown.
Sommario Sono stati calcolati quattro differenti modelli di una stella gigante K(T e=4500K, logg=2). Ogni modello è caratterizzato dalla inclusione di differenti sorgenti di opacità (H, H–, (H), metalli, effetto blanketing, He–) per ottenere una valutazione della sensibilità del modello per quel che riguarda la struttura atmosferica ed il flusso emergente. I risultati ottenuti mostrano che per costruire modelli auto-consistenti e con un buon grado di affidabilità occorre tener conto almeno delle seguenti sorgenti di opacità: H, metalli, effetto blanketing.Si mostra inoltre come sia possibile una descrizione schematica dell'influenza del coefficiente di assorbimento sulle varie caratteristiche del modello.
  相似文献   

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