Temperature fluctuations in the solar photosphere

The general problem of interpreting granulation data, in particular Edmonds' r.m.s. intensity fluctuation distribution against heliocentric angle , is discussed.A method is developed for investigating a variety of models of inhomogeneous departures from radiative equilibrium using two dimensional solutions of the equation of radiative transfer, and theoretical r.m.s. intensity fluctuation distributions are computed. It is found that only a very narrow range of models yields distributions which exhibit the essential features of Edmonds' distribution (a center-of-disk value of 14 % and a maximum value of 20.5 % at a heliocentric angle of 53°). The feature of these models is a maximum in the temperature fluctuations of about 660 K r.m.s., which represents a temperature difference between hot and cold regions of 2000 K, at a depth of about 250 km below ₅₀₀₀= 0.03. Below this the temperature fluctuations decrease rapidly in the next 70 km.These results are interpreted in terms of convective and radiative transport of energy. Velocities of the order of 8 km/sec are deduced in the essentially convective regime near 320 km, decreasing through 4 km/sec near the temperature fluctuation maximum to negligible values in the radiative region above 200 km.These features are shown to be consistent with modern theoretical and laboratory studies of convection in incompressible fluids. Further, these studies indicate that a second temperature fluctuation should occur at the bottom of a convective layer. For this reason, further photospheric models are studied in which, below the region of small temperature fluctuations near 320 km, the fluctuations increase sharply. For one of these models a theoretical intensity r.m.s. distribution is obtained which closely fits not only the maximum at = 53° in Edmonds' observed distribution but also the initial decrease and smaller minimum near 24°.Of the National Bureau of Standards and the University of Colorado.     

Five micron limb-darkening and the structure of the Jovian atmosphere

By observing the transit of various cloud features across the Jovian disk, Terrile and Westphal (1977) have constructed limb-darkening curves for three regions in the 4.6 to 5.1 μm band. Several models currently employed in describing the radiative or dynamical properties of planetary atmospheres are here examined to understand their implications for limb-darkening. The statistical problem of fitting these models to the observed data is reviewed and methods for applying multiple regression analysis are discussed. Analysis of variance techniques are introduced to test the viability of a given physical process as a cause of the observed limb-darkening. The intermediate flux region of the North Equatorial Belt appears to be in only modest departure from radiative equilibrium. The limb-darkening curve for the South Temperate Belt is rich in structure and cannot be satisfactorily ascribed to any single physical mechanism; a combination of several, as yet unidentified, processes is likely involved. The hottest areas of the North and South Equatorial Belts exhibit limb-darkening curves that are typical of atmospheres in convective equilibrium. In this case, we derive a measure of the departure of the lapse rate from the dry adiabatic value (η?1.68), which furnishes strong evidence for a phase transition at unit optical depth in the NEB and SEB. Although the system NH₃H₂S cannot be entirely ruled out, the freezing of an aqueous ammonia solution is shown to be consistent with the parameter fit and solar abundance data, while being in close agreement with Lewis' (1969a) cloud models.     

On the properties of umbral dots

On the basis of a three-dimensional radiative transfer analysis of several models it is shown that bright structures in sunspot umbrae which have horizontal diameters of 300 km or less cannot extend more than 300 km down into the umbra. Thus, such models are inconsistent with the hypothesis that the bright features are due to convection from the deep regions of the umbra. No such restrictions can be applied if the surface diameter is of order 500 km, but a model of this type is shown to be inconsistent with the available data. Thus a convective explanation of these bright features appears to be ruled out.A model having a diameter of 200 km is shown to be consistent with the available observations but these are not sufficiently precise to warrant any strong claim for the validity of this model. The features of this model are described and it is shown that near the limb the apparent brightness of these features compared to the umbral background should increase. However, order-of-magnitude calculations show that there is some doubt whether joule heating can account for the non-radiative energy requirements of this model.     

O-bearing Molecules in Carbon-rich Proto-Planetary Objects

We use high-precision multiband photometric data of the first-overtone RR Lyrae star U Comae to investigate the predictive capability of full-amplitude, nonlinear, convective hydrodynamical models. The main outcome of this investigation is that theoretical predictions properly account for the luminosity variations along a full pulsation cycle. Moreover, we find that this approach, because of the strong dependence of this observable and of the pulsation period on stellar parameters, supplies tight constraints on stellar mass, effective temperature, and distance modulus. Pulsational estimates of these parameters appear in good agreement with empirical ones. Finally, a well-defined bump just before the luminosity maximum gave the unique opportunity to calibrate the turbulent convection model adopted for handling the coupling between pulsation and convection.     

Silicon vidicon imaging of jupiter: 4100- to 8300-Å absolute reflectivities and limb darkening of spatially resolved regions

Jupiter was observed in six continuum wavelength channels in the region 4100–8300 Å, using a silicon vidicon imaging photometer. Spectral reflectivities and high spatial resolution limb-darkening curves for several belts and zones have been extracted from the data. Simple model fits to the data yield information regarding spectral and spatial variations in single-scattering albedos and shape of particle single-scattering phase functions. Belts appear to be more backscattering than zones, particularly in the blue. The data are in moderate agreement with limb-darkening predicted by models derived from the center-to-limb variation in equivalent width of the H₂ 4-0 S(1) quadrupole line (Cochran, 1976) in the South Tropical Zone, but strongly disagree with the results of such models for the North Equatorial Belt.     

Manganese and carbon lines as temperature indicators

Selected hyperfine structure broadened lines of various excitations and the carbon line at 5380 Å are tested as temperature diagnostics for photospheric heterogeneities. This is done by comparing the observed center-to-limb variation of the equivalent widths of these lines with predictions by several proposed models of homogeneous type. Model 10 (Elste, 1968), which also explains the limb-darkening of the continuum in the same spectral range, provides a better basis for the analysis of heterogeneities at different photospheric levels than other recent reference models.     

Photospheric limb-darkening signatures of global structure variations

Observations of short-term irradiance variations and consideration of mechanisms of the solar activity cycle suggest the possibility of long-term variation of the solar flux. Since the limb darkening is sensitive to effective temperature and convective efficiency, observations of the solar limb darkening may provide a useful means to detect and study long-term global variations. The limb-darkening responses to impulsive variation (in depth) of the source function, to effective temperature variation, and to convection variations are presented. For the variations considered, the limb-darkening variation is approximately linearly proportional to the associated parameters. The minimum detectable amplitude of those parametric variations is derived as a function of observational noise. Given our demonstrated errors of observation, single-parameter sensitivies are 3 K for effective temperature variation and 0.007 for local mixing-length variation for year to year changes at 99% confidence.     

Thermal-orbital evolution of Io and Europa

Coupled thermal-orbital evolution models of Europa and Io are presented. It is assumed that Io, Europa, and Ganymede evolve in the Laplace resonance and that tidal dissipation of orbital energy is an internal heat source for both Io and Europa. While dissipation in Io occurs in the mantle as in the mantle dissipation model of Segatz et al. (1988, Icarus 75, 187), two models for Europa are considered. In the first model dissipation occurs in the silicate mantle while in the second model dissipation occurs in the ice shell. In the latter model, ice shell melting and variations of the shell thickness above an ocean are explicitly included. The rheology of both the ice and the rock is cast in terms of a viscoelastic Maxwell rheology with viscosity and shear modulus depending on the average temperature of the dissipating layer. Heat transfer by convection is calculated using a parameterization for strongly temperature-dependent viscosity convection. Both models are consistent with the present orbital elements of Io, Europa, and Ganymede. It is shown that there may be phases of quasi-steady evolution with large or small dissipation rates (in comparison with radiogenic heating), phases with runaway heating or cooling and oscillatory phases during which the eccentricity and the tidal heating rate will oscillate. Europa's ice thickness varies between roughly 3 and 70 km (dissipation in the silicate layer) or 10 and 60 km (dissipation in the ice layer), suggesting that Europa's ocean existed for geological timescales. The variation in ice thickness, including both convective and purely conductive phases, may be reflected in the formation of different geological surface features on Europa. Both models suggest that at present Europa's ice thickness is several tens of km thick and is increasing, while the eccentricity decreases, implying that the satellites evolve out of resonance. Including lithospheric growth in the models makes it impossible to match the high heat flux constraint for Io. Other heat transfer processes than conduction through the lithosphere must be important for the present Io.     

The brightness temperatures of solar type III bursts

There is a characteristic maximum brightness temperature T _B 10¹⁵K for type III solar radio bursts in the solar wind. The suggestion is explored that the maximum observed values of T _Bmay be attributed to saturation of the processes involved in the plasma emission. The processes leading to fundamental and second harmonic emission saturate when T _Bis approximately equal to the effective temperature T _Lof the Langmuir waves. The expected maximum value of T _Bis estimated for this saturation model in two ways: from the growth rate for the beam instability, and from the maximum amplitude of the observed Langmuir turbulence. The agreement with the observed values is satisfactory in view of the uncertainties in the estimates (a) of the intrinsic brightness temperature from the observed brightness temperature, (b) of the actual growth rate of the beam instability, which must be driven by local, transient features (that are unobservable using available instruments) in the electron distribution, and (c) in the k-space volume filled by the Langmuir waves, and this is consistent with the observational data on two well-studied events at the orbit of the Earth and with statistical data for events over a range of radial distances from the Sun.     

Seismology of the solar convection zone

An attempt is made to infer the structure of the solar convection zone from observedp-mode frequencies of solar oscillations. The differential asymptotic inversion technique is used to find the sound speed in the solar envelope. It is found that envelope models which use the Canuto-Mazzitelli (CM) formulation for calculating the convective flux give significantly better agreement with observations than models constructed using the mixing length formalism. This inference can be drawn from both the scaled frequency differences and the sound speed difference. The sound speed in the CM envelope model is within 0.2% of that in the Sun except in the region withr > 0.99R _⊙. The envelope models are extended below the convection zone, to find some evidence for the gravitational settling of helium beneath the base of the convection zone. It turns out that for models with a steep composition gradient below the convection zone, the convection zone depth has to be increased by about 6 Mm in order to get agreement with helioseismic observations.     

On the global mean temperature of the thermosphere

The solar extreme ultraviolet (e.u.v.) flux and solar ultraviolet (u.v.) flux in the Schumann-Runge continuum region have been measured by spectrometers on board the Atmosphere Explorer satellites from about 1974 to 1981. The solar flux spectra measured on 23 April 1974 (a day the Atmosphere Explorer satellite reference spectrum was obtained), 13–28 July 1976 (a period of spotless conditions near solar cycle minimum), and 19 February 1979 (a day near solar cycle maximum) are used to examine the global mean temperature structure of the thermosphere above 120 km. The results show that for solar cycle minimum the calculated global mean exospheric temperature is in agreement with empirical model predictions, indicating that the energy absorbed by the thermosphere is balanced by downward molecular thermal conduction. For solar cycle maximum the energy absorbed by the thermosphere is not balanced by downward thermal conduction but agreement between the calculated and observed temperature is obtained with the inclusion of 5.3μm radiational cooling by nitric oxide. Model calculations of the minor neutral constituents in the thermosphere show that about three times more nitric oxide is produced during solar cycle maximum than solar cycle minimum conditions. The results suggest that nitric oxide cooling is small during solar cycle minimum, because of low nitric oxide densities and low thermospheric temperatures, but it becomes significantly larger during solar cycle maximum, when nitric oxide densities and thermospheric temperatures are larger.23 April 1974 was a moderately disturbed day and the results of the global mean temperature calculation indicate that it is necessary to consider a high latitude heat source associated with the geomagnetic activity to obtain agreement between the calculated and observed global mean temperature structure.     

Turbulence properties in the solar convection envelope： properties of the overshooting regions

We apply the turbulent convection model (TCM) to investigate properties of tur-bulence in the solar convective envelope, especially in overshooting regions. The results show TCM gives negative turbulent heat flux uγ′T′in overshooting regions, which is sim-ilar to other nonlocal turbulent convection theories. The turbulent temperature fluctuation T′T′shows peaks in overshooting regions. Most important, we find that the downward overshooting region below the base of the solar convection zone is a thin cellular layer filled with roll-shaped convective cells. The overshooting length for the temperature gradi-ent is much shorter than that for element mixing because turbulent heat flux of downward and upward moving convective cells counteract each other in this cellular overshooting region. Comparing the models' sound speed with observations, we find that raking the convective overshooting into account helps to improve the sound speed profile of our nonlocal solar models. Comparing the p-mode oscillation frequencies with observations,we validated that increasing the diffusion parameters and decreasing the dissipation pa-rameters of TCM make the p-mode oscillation frequencies of the solar model be in betteragreement with observations.     

The phase variations of the solar cycle

It has previously been shown that the statistics of the phase fluctuation of the sunspot cycle are compatible with the assumption that the solar magnetic field is generated deep in the Sun by a frequency stable oscillator and that the observed substantial phase fluctuation in the sunspot cycle is due to variation in the time required for the magnetic field to move to the solar surface (Dicke, 1978, 1979). It was shown that the observed phase shifts are strongly correlated with the amplitude of the solar cycle. It is shown here that of two empirical models for the transport of magnetic flux to the surface, the best fit to the data is obtained with a model for which the magnetic flux is carried to the surface by convection with the convection velocity proportional to a function of the solar cycle amplitude. The best fit of this model to the data is obtained for a 12-yr transit time. The period obtained for the solar cycle is T = 22.219 ± 0.032 yr. It is shown that the great solar anomaly of 1760–1800 is most likely real and not due to poor data.     

Structure of Saturn's Mesosphere from the 28 Sgr Occultations

We analyze an extensive data set of immersion and emersion lightcurves of the occultation of 28 Sgr by Saturn's atmosphere on 3 July 1989. The data give profiles of number density as a function of altitude at a variety of latitudes, at pressures ranging from about 0.5 to about 20 μbar. The atmosphere is essentially isothermal in this range, with a temperature close to 140 K for an assumed mean molecular weight of 2.135. Owing to favorable ring geometry, an accurate radial scale is available for all observations, and we confirm the substantial equatorial bulge produced by zonal winds of ∼450 m/s first observed in the Voyager radio-occultation experiments. The fact that the bulge is still present at microbar pressures suggests that the equatorial winds persist to high altitudes. According to our radial scale, the 2.4-μbar level, which corresponds to half-flux in the stellar occultations, is at an equatorial radius of 60,960 km. This radial scale is in good agreement with the Voyager radio-occultation data at mbar pressures and allows smooth interpolation of the isothermal structure between the stellar-occultation and radio-occultation regions. We do not have such a smooth interpolation between our data and Voyager ultraviolet occultation data, unless we discard the lowest 200 km of Voyager ultraviolet data. When this is done, we obtain a complete atmospheric model from an equatorial radius of 61,500 km down to an equatorial radius of 60,500 km. This model gives excellent agreement between all 28 Sgr, Voyager, and Pioneer 11 data.     

Convection in the Presence of an Inclined Axis of Rotation with Applications to the Sun

Thermal convection in a horizontal fluid layer heated from below and rotating about an arbitrary axis is studied analytically with the attention focused on mean flows and drifts generated by the convection velocity field. Mean flows occur in both horizontal directions when the angle between the rotation vector and the vertical is finite but less than 90°. In the case of a hexagonal convection pattern, a wavelike drift is found in the presence of a horizontal component of rotation. Applications to solar convection are discussed. Considering the simplicity of the model the agreement with observations is surprisingly good.     

Umbral boundaries,convection, and the depth of sunspots

The boundary between the umbra and penumbra of a sunspot is consistently observed to be very sharp, on the order of 500 km. Approximating the sunspot as a static region in a homogeneous medium with a radiative surface, temperature distributions resulting from a variety of convective motions exterior to the sunspot are calculated. The calculations suggest that, for the exterior convection to produce the observed boundary, the maximum depth of the region of inhibited convection below a sunspot umbra is on the order of 10³ km.     

Semi-empirical solar line blanketing

The line blanketing procedure described in an earlier paper has been tested by a series of blanketed solar model atmosphere calculations incorporating methodological and data variations. The results of those tests show the method to be reasonably insensitive to data uncertainties and to certain assumptions employed. The method was also checked by calculating several blanketed stellar atmospheres for comparison with blanketed atmospheres computed by other investigators. Except at the highest atmospheric levels the comparisons of the model structures were good and the blanketing method appears to be validated.Central solar intensities were computed for two semi-empirical solar models and for a theoretical model using the present blanketing method. The results are compared with the observations of Labs and Neckel (1968) in the region 3300 Å to 6500 Å. It is found the blanketing improves agreement of the model predictions with observations in a substantial way, particularly at short wavelengths. Limb-darkening predictions with blanketing were also made for these models at four wavelengths and compared with observations. The blanketing generally produces an important improvement in the comparisons; however, the amount of blanketing to be included for limb-darkening is uncertain.The temperature distribution of the blanketed theoretical model was compared with semi-empirical solar models and a blanketed model by Athay (1970) including non-LTE effects. Over a large range in optical depth the agreement is reasonably good; at small optical depths (₀ 0.01) large divergences are seen which may be due to the effects of non-LTE and to the neglect of strong lines in the present blanketing method. In addition to the good structural comparisons, the quality of the blanketed theoretical model in terms of comparison with central intensity and limb darkening is nearly as good as the semi-empirical models. We conclude that theoretical model atmospheres of solar type or nearly solar type computed with current constant-flux programs and with blanketing included are of high quality.Possible improvements in the blanketing method of importance in some instances are suggested; these include the use of a picket-fence procedure, the inclusion of strong lines, and the consideration of non-LTE effects. Further applications to the solar UV region and to stellar atmospheres are suggested.Publications of the Goethe Link Observatory, Indiana University, No. 131.     

On the effects of higher convection modes on the thermal evolution of small planetary bodies

The effects of higher modes of convection on the thermal evolution of a small planetary body is investigated. Three sets of models are designed to specify an initially cold and differentiated, an initially hot and differentiated, and an initially cold and undifferentiated Moon-type body. The strong temperature dependence of viscosity enhances the thickening of lithosphere so that a lithosphere of about 400 km thickness is developed within the first billion years of the evolution of a Moon-type body. The thermally isolating effect of such a lithosphere hampers the heat flux out of the body and increases the temperature of the interior, causing the solid-state convection to occur with high velocity so that even the lower modes of convection can maintain an adiabatic temperature gradient there. It is demonstrated that the effect of solid-state convection on the thermal evolution of the models may be adequately determined by a combination of convection modes up to the third or the fourth order harmonic. The inclusion of higher modes does not affect the results significantly.