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1.
B. Schmieder 《Solar physics》1977,54(2):269-288
A method coupling the hydrodynamical equations and radiative transfer in a realistic solar model atmosphere is described. The influence of the temperature gradient of the model and the radiative dissipation is pointed out.The effect of the large temperature gradient is important in the layers where the optical depth 5000 is greater than 0.5; the ratio between the amplitude of the temperature and the velocity fluctuations decreases with the altitude by a factor 2 between = 1 and = 0.5 and in the case of the acoustic waves, the phase shift between these fluctuations is small.The radiative energy loss in the thick layers (
5000 = 1) leads to a decrease of the vertical phase velocity of the waves and to a damping of their amplitudes in the layers of intermediate optical depth (10-2 < 5000 < 0.5). The effect of the dissipation is negligible in the thin layers (5000 < 10-2). 相似文献
2.
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. 相似文献
3.
Masaya Saitou 《Astrophysics and Space Science》1989,162(1):47-56
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. 相似文献
4.
Observations of the intensity distribution near the solar limb at 2.43 and 22.5 , show the absence of limb brightening to within 1 or 2 arc sec of the limb. Observations at 1.2 mm indicate limb brightening at this wavelength. These results are compared with the Utrecht Reference Photosphere and with existing data on the solar flux in the millimeter range, and suggest that the temperature minimum is broad and extends above
5000 = 2 × 10–3. A sharp rise of temperature is required above
5000 = 10–5. 相似文献
5.
A critical analysis of the methods and results of estimating the optical thickness of the dust component in the Martian atmosphere 0, the particle size r
0, and the imaginary part of the refractive index n
ihas shown the following. (1) Observational data on the brightness distribution over the Martian disk as well as the phase dependences of diffusely reflected light and the azimuthal dependences of diffusely transmitted light are most appropriate to use only for verifying the reliability of the aerosol parameters determined by other methods. (2) If the morning and evening fogs in the atmosphere are disregarded, the Bouguer–Lambert–Beer method used to analyze the solar-brightness attenuation measured on the planetary surface yields overestimated extraatmospheric solar intensity I
0and atmospheric optical depth 0. At the Viking 1landing site, I
0and 0could be overestimated by a factor of 1.7 and by 0.35, respectively. (3) The aerosol size determined by analyzing measurements of the azimuthal dependences for the Martian sky brightness at low elevations of the Sun most likely corresponds to the fog particles. (4) If overestimated values of I
0were used to standardize the observations of the solar radiation transmitted by the Martian atmosphere, then n
iwere also overestimated; using overestimated 0also affected the reliability of the latter. (5) The problem of reliability of the available 0and r
0estimates for periods of high atmospheric transparency is yet to be solved. For the highest activity of the dust storm in 1971, it was found that 4.5 r
0 7.5 m for the lognormal particle size distribution with 2= 0.2 and the optical thickness of a dust cloud 0 15. (6) The spectral values of the apparent albedo of Mars measured in October 1971 at a phase angle of 42° in the spectral range 0.250 0.717 allowed the imaginary part of the refractive index to be estimated in terms of a model of a dust cloud composed of spherical particles with the lognormal size distribution with r
0= 4.5 m and 2= 0.2. 相似文献
6.
The results of daily monitoring of the Ca K flux variations of integrated sunlight during the period 1 July 1979–18 February 1980 are presented, and the data analyzed by both power spectrum and autocorrelation methods. The latter method is found to be superior; in it the autocorrelation function is fit to a model having three parameters, viz. the maximum long-term autocorrelation c
1, the rotational period 0 and an effective lifetime 1. Values of c
1 = 0.26, 0 = 25.9 days, and 1 = 500 days are obtained for the Ca K flux ratio; somewhat different values of c
1 = 0.77, 0 = 28.0 days, and 1 = 89 days are obtained for the sunspot number for the same period. Rotational modulation is clearly evident for the relatively weak chromosphere of the Sun and should be even more easily observed for more active stars. 相似文献
7.
Taking into account the effect of roughness (or local departures from sphericity) of the emitting layers in the chromosphere-corona transition zone (CCT) allows one to determine the optical depths of layers responsible for resolved structures in Cii, Ciii, Oiv, and Ovi lines. The result, at the top of the irregularities, is of the order of respectively 1 3.5,2.0, 1.6,0.5, and for the bottom of these irregularities, 2 = 0.7, 0.4, 0.3, 0.25. The characteristic angle of these irregularities is, respectively, of the order of 35 °, 33 °, 35 °, and 41 °. For unresolved structures of Civ and Ovi (already analyzed in the spherical symmetry hypothesis in Paper III), one finds 1 0.6; 0.9 and 2 0.12; 0.2 in the case of quiet areas; in the case of active areas, the range is broader for Civ and Ovi, from 1.0 to 1.7 for 1 and from 0.2 to 0.9 for 2. The values obtained from Ovi are in reasonable agreement with each other for resolved and unresolved structures. And the obtained values of 1 and 2 correspond not too badly with the determinations made in Paper III, by methods not exceedingly influenced by the spherical symmetry hypothesis. 相似文献
8.
A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(p + 22), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(p +42). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn. 相似文献
9.
Dimensional analysis is used to derive the distribution of solar flare energies,p() = A-3/2, in accordance with recent observational and numerical results. Several other scalings, notably
fl
2
, where fl is the flare duration, are obtained as well. 相似文献
10.
A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions (=optical depth, 0=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionb
m(,,0) with Sobolev's function
m(,0) playing the role of a source-function. Because the incident direction does not intervene,
m is simply expressed as a single integral term involvingb
m. For bottom illumination, an analogous equation holds for the other new functionh
m(,,0). However, simple reciprocity relations link the two functions so that it is only necessary to considerb
m; (ii) a transfer equation for the other new functiona
m(,,,0) with a source-function provided by Sobolev's functionD
m(,,0). For bottom illumination, another functionf
m(,,,0) is introduced; by a similar argument using reciprocity relations,f
m is reduced toa
m rendering necessary only the consideration ofa
m. However, a fundamental decomposition formula is obtained which shows thata
m is expressible algebraically in terms of functions of a single angular variable. The functions
m andD
m are shown to be the values in the horizontal plane ofb
m anda
m, respectively. The other auxiliary functionsX
m andY
m are also expressed algebraically in terms ofb
m. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionb
m appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration. 相似文献
11.
Empirical solar models contain the effect of heating due to radiative energy loss from acoustic waves. We estimate here the temperature difference between the radiative equilibrium model and the empirical model. At optical depth 5000 = 0.1 this difference is small, but near the temperature minimum (5000 = 10–4) it reaches between 53 and 83 K. The temperature difference between the equator and the poles caused by a hypothetical difference in the heating is estimated. 相似文献
12.
An empirical method for determining line source functions, previously applied by us to the cores of infrared lines has now been extended to the whole line profile and was applied to centre-limb observations of sixteen lines of five infrared multiplets, mainly of high excitation potential (Table I). The present investigation was performed in two steps. In the first part of the paper approximate values are derived for the depth dependence of the four functions named in the title of this paper, where
L
is the ratio between the actual and the LTE population of the lower level of the transitions involved. In the second part of the paper we use these empirically derived functions to compute the line profiles. From the remaining differences between observed and computed profiles, corrections are derived to the four functions. The main results are: (a) Convective velocities: see Table IV.(b)(Micro-)turbulent velocities: see Figure 8. Between
5 = 10-4 and 10-1:
1.4 km s-1, which is an upper limit since an unknown contribution of macroscopic motions could not be separated, (c) Line source functions: see Figures 9, 15 and 16. The source functions are close to the black-body function for
5 10-3, slight deviations occur in higher levels. The interesting behaviour of the Caii source function near
5 = 10-5 should be noted. (d) Non LTE-functions: first approximations for the functions log
L
(
5) were derived empirically in the first part, and are shown in Figure 10; the second approximation shows them to be too large and the real values seem to be closer to one-half or one-third of these functions. 相似文献
13.
The recent discovery of localised intense magnetic fields in the solar photosphere is one of the major surprises of the past few years. Here we consider the theoretical nature of small amplitude motions in such an intense magnetic flux tube, within which the field strength may reach 2 kG. We give a systematic derivation of the governing expansion equations for a vertical, slender tube, taking into account the dependence upon height of the buoyancy, compressibility and magnetic forces. Several special cases (e.g., the isothermal atmosphere) are considered as well as a more realistic, non-isothermal, solar atmosphere. The expansion procedure is shown to give good results in the special case of a uniform basic-state (in which gravity is negligible) and for which a more exact treatment is possible.The form of both pressure and velocity perturbations within the tube is discussed. The nature of pressure perturbations depends upon a critical transition frequency,
p
, which in turn is dependent upon depth, field strength, pressure and density in the basic (unperturbed) state of the tube. At a given depth in the tube pressure oscillations are possible only for frequencies greater than
p
for frequencies below
p
exponentially decaying (evanescent) pressure modes occur. In a similar fashion the nature of motions within the flux tube depends upon a transition frequency,
v
. At a given depth within the tube vertically propagating waves are possible only for frequencies greater than
v
; for frequencies below
v
exponentially decaying (evanscent) motions occur.The dependence of both
v
and
p
on depth is determined for each of the special cases, and for a realistic solar atmosphere. It is found that the use of an isothermal atmosphere, instead of a more realistic temperature profile, may well give misleading results.For the solar atmosphere it is found that
v
is zero at about 12 km above optical depth 5000= 1, thereafter rising to a maximum of 0.04 s–1 at some 600 km above 5000 = 1. Below 5000 = 1, in the convection zone,
v
has a maximum of 0.013 s–1. The transition frequency,
p
, for the pressure perturbations, is peaked at 0.1 s–1 just below 5000 = 1, falling to a minimum of 0.02 s–1 at about one scale-height deeper in the tube 相似文献
14.
With the help of a model atmosphere of the Sun we evaluate the pole-equator difference in flux (as measured by Dicke and Goldenberg) assuming the following type of pole-equator temperature difference (T=T
e
–T
p
): (a) T 2K for > 0 (0 0.05); (b) T 10K for < 0.The small T at all optical depths given by (a) could, for example, be due to a pole-equator difference in effective temperatures. At small optical depths a difference in mechanical heating could give rise to the larger temperature difference given by (b). We compare the results of our calculations with Dicke and Goldenberg's observations.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
15.
Shuichi Tamazawa Kiyotaka Toyama Noboru Kaneko Yôrô Ôno 《Astrophysics and Space Science》1975,32(2):403-421
Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of
is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn
0=108 cm–3 andT
0=104 K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×1033 erg s–1, which primarily arises from the optical surface (1) ofT104 K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10. 相似文献
16.
Dlugach Zh. M. Korablev O. I. Morozhenko A. V. Moroz V. I. Petrova E. V. Rodin A. V. 《Solar System Research》2003,37(1):1-19
Atmospheric aerosols play an important role in forming the Martian climate. However, the basic physical properties of the Martian aerosols are still poorly known; there are many contradictions in their estimates. We present an analytical overview of the published results and potentialities of various methods. We consider mineral dust. Zonally averaged data obtained from mapping IR instruments (TES and IRTM) give the optical thickness of mineral aerosols 9 = 0.05–0.1 in the 9-m band for quite atmospheric conditions. There is a problem of comparing these estimates with those obtained in the visible spectral range. We suggest that the commonly used ratio vis/9 >2 depends on the interpretation and it may actually be smaller. The ratio vis/9 1 is in better agreement with the IRIS data (materials like montmorillonite). If we assume that vis/9 = 1 and take into account the nonspherical particle shape, then the interpretation of ground-based integrated polarimetric observations ( < 0.04) can be reconciled with IR measurements from the orbit. However, for thin layers, the sensitivity of both methods to the optical thickness is poorly understood: on the one hand, polarimetry depends on the cloud cover and, on the other hand, the interpretation of IR measurements requires that the atmospheric temperature profile and the surface temperature and emissivity be precisely known. For quite atmospheric conditions, the local optical-thickness estimates obtained by the Bouguer–Lambert–Beer method and from the sky brightness measured from Viking 1 and 2 and Mars Pathfinder landers are much larger: = 0.3–0.6. Estimates of the contrasts in images from theVikingorbiters yield the same values. Thus, there is still a factor of 3 to 10 difference between different groups of optical-thickness estimates for the quiet atmosphere. This difference is probably explained by the contribution of condensation clouds and/or by local/time variations. 相似文献
17.
An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension
ik
. The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor
ik
is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved.The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor
ik
is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/,b=p
/ (,p, p
are the density of the vacuum energy and of its pressures in the radial and transverse directions) and determining the vacuum elastic properties. Generally speaking, they depend on the valueP/c2 in the stellar centre where is the mass density. From general physical considerations it is shown that 0 1 + lim
P (l/q). The field equations are solved for the simple version of the theoryb=–a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun. 相似文献
18.
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
19.
D. L. Lambert 《Solar physics》1968,3(1):118-124
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
20.
Mohamed Adelsharaf 《Astrophysics and Space Science》1979,60(1):199-212
In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE
n which is denoted as
n
(). The main result of this analysis enables us to establish a two-term recurrence formula for
n
(0) and a three-term recurrence formula for
n
(); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy. 相似文献