Temperature fluctuations in the solar photosphere

In paper I of this series it was shown that Edmonds' center-limb rms intensity fluctuation data provided strong evidence for the existence of a maximum in the horizontal temperature fluctuation near 250 km (optical depth 0.7). The data also gave a much less reliable indication of a second temperature fluctuation maximum approximately 100 km below this level. Two models, model 1 exhibiting a single temperature fluctuation maximum and model 2 which has two temperature fluctuation maxima, were put forward as worthy of further investigation. In this paper the theoretical mean limb-darkening for these models is compared with the observed limb-darkening. Neither is satisfactory and several modifications are discussed. Models of the first type can be made to fit these data only by making adjustments which appear to be inconsistent with convection as an explanation of the temperature fluctuations. Further, the agreement with the fluctuation data is now less satisfactory. However, a modified model of the second type is developed which is consistent with the convection hypothesis, which is in good agreement with the mean limb-darkening and is in qualitative agreement with the fluctuation data. This is interpreted as providing some evidence that the photospheric granulation arises from a shallow convection layer at the base of the photosphere.     

Anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R , the major axis scattering angle is 0.7 at =6 cm and it varies with heliocentric distance asR ^–1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to =20 cm, has a value 20±7 at 5R and varies with heliocentric distance asR ^–3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scales sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R and 4 km at 13R . These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

The decay phase of solar flare events

A study of the properties of the cosmic radiation of energy - 10 MeV generated by solar flares is reported. Data from four Pioneer spacecraft in interplanetary orbits, and separated by 180° in heliocentric longitude are employed. Attention is restricted to the properties evident at times in excess of 1 day after the occurrence of the parent flare. The anisotropic character of the radiation; the gradients in heliocentric longitude; the decay time constants; and the energy spectra of the radiation are all studied in detail.It is found that the equilibrium anisotropy assumes a direction - 45° E of the satellite-Sun line at very late times. It is suggested that the anisotropy at such times is parallel to E × B. This observation confirms that convection is the determining process in the escape of the solar cosmic rays from the solar system. It indicates that a positive radial gradient of solar cosmic radiation density has builtup at orbit of Earth some 4 days after a flare. This results in an effective convective velocity of approximately 1/2 the solar wind velocity. Direct measurements indicate the presence of strong gradients in heliocentric longitude even at very late times ( 4 days). These gradients are essentially invariant with respect to time, e-folding angles of n - 30° have been observed at - 10 MeV. The presence of these gradients has a major effect on the temporal variation of the cosmic ray flux during the decay phase of the flare effect. Thus, the observed decay time constant is either increased or decreased relative to the convective value depending on the position of the observer relative to the centroid of the cosmic ray population injected by the flare. The effect of the gradient becomes more pronounced at lower energies, and may even exceed the convective removal rate. The observed decay time constant, the characteristics of the anisotropy, and the gradient in longitude are shown to be inter-related as demanded by theory. It is shown that the exponent of the cosmic ray spectrum is dependent on the location of the observer relative to the centroid of the cosmic ray population injected by the parent flare. At a given point in the frame of reference of the cosmic ray population, the spectral exponent is invariant with time.Now at CSIRO, G.P.O. Box 124, Port Melbourne, Victoria 3207, Australia.On leave from Physical Research Laboratory, Ahmedabad, India.     

The Formation of MgI 4571 Å in the solar atmosphere

The two-dimensional equation of transfer is solved for the case of locally-controlled source function (LTE) and radiationally-controlled ionization. Horizontal fluctuations in electron temperature and macroscopic velocity fields are superposed on the basic one-dimensional model (cf. Altrock and Cannon, 1972). Output intensities are compared with observed rms intensity fluctuations and spatially-averaged intensities in Mg i 4571 Å. We find that at least one model (with a height-independent temperature fluctuation T/T=±0.02 in the range 0h450 km) can predict the magnitude of the intensity fluctuations in both the continuum and 4571 Å. The asymmetry of the line can be explained by adding a height-independent, temperature-correlated flow of amplitude 1 to 2 km s^–1. The relationship between these results and other multi-dimensional analyses is discussed.On leave from Department of Applied Mathematics, University of Sydney, Sydney, Australia.     

High-resolution photography of the solar chromosphere

Bright chromospheric mottles observed at the H line centre are found to have sizes ranging from 1450 to 4400 km and lifetimes of about 11 min. They occur in close juxtaposition to dark mottles which, at intermediate heliocentric angles ( 60°), are found to be displaced towards the limb relative to the associated bright mottles. The magnitude of the displacement indicates a height difference of 4300 km. In conjunction with height measurements of bright mottles beyond the limb (Loughhead, 1969), this implies that bright and dark mottles are phenomena of the lower ( 3300 km) and upper ( 5000–7600 km) chromosphere respectively.     

The angle of inclination of the sunspot symmetry axis to the solar surface

The Wilson effect, used before only as a method of determining the physical depression of sunspots, is used here to estimate a quite different parameter - the sunspot symmetry axis inclination angle to the solar surface, this explains the observed negative Wilson effect.On the basis of photoheliograms taken with three telescopes of the High-Altitude Solar observatory Peak Alma-Ata, the Wilson effect for the whole solar disk is investigated, the east and west parts of the disk being studied separately. 111 sunspots of regular shape at different heliocentric angles were measured, eight of them being under observations from one limb to the other. To study the dependence of the Wilson effect on the heliocentric angle, all observations within an angular interval of 10° were averaged. The dependence thus derived is described by two sinusoids having the zero point shifted along both axes. The shift of the zero Wilson effect to the west, i.e., a shift along the heliocentric angle axis, can be caused by the deviation of the sunspot axis to the east from the normal to the solar surface. On the line of sight-normal plane the angle corresponding to this deviation is =34°±14°.     

The photochemistry and dynamics of a dusty cometary atmosphere

A self-consistent solution of the dynamical and thermal structure of an H₂O-dominated, two-phase, dusty-gas cometary atmosphere has been obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum and energy together with the transfer of solar radiation in the streams responsible for the major photolytic processes and the heating of the nucleus. The validity of the model is restricted to the collision-dominated region where all the gas species are assumed to attain a common velocity and common temperature. Two models are considered for the transfer of solar radiation through the circum-nuclear dust halo. In the first only the direct extinction by the dust is considered. In the second, the finding of some recent models, that the diffuse radiation field due to multiple scattering by the dust halo more or less compensates for radiation removed by direct absorption when the optical depth is near unity, is approximated by neglecting the attenuation of the radiation by the dust altogether.As has been shown earlier, the presence of dust results in a transonic solution, and it is obtained by a two-step iterative procedure which makes use of the asymptotic behaviour of the radiation fields sufficiently far from the nucleus and a regularity condition at the sonic point.The calculations were performed for a medium sized comet (R _n =2.5 km) having a dust to gas production rate ratio of unity, at a heliocentric distance of 1 AU. The dust grains were assumed to be of the same radius (1), of low density (1g cm^–3) and be strongly absorbing (having the optical properties of magnetite).The main effect of the dust on the cometary atmosphere is dynamic. While the dust-gas coupling persists to about 20R _n , the strong throat effect of the dust friction on the gas causes the latter to go supersonic quite rapidly. Consequently the sub-sonic region around the nucleus is very thin, varying between 45 and 85m in the two models considered. On the other hand, while this highly absorbing dust has a temperature substantially above that of the gas in the inner coma, heat exchange between them does not significantly change the temperature profile of the gas. This is because of the predominance of the expansion cooling, and even more importantly, the IR-cooling by H₂O, in the inner coma. Consequently, the gas temperature goes through a strong inversion, as in the dust-free case, achieving a temperature as low as about 6K within about 50km of the nucleus, before increasing to about 700K atr=10⁴km, due to the high efficiency of photolytic heating over the cooling process in the outer coma. The Mach number achieves a maximum value of about 10 at the distance of the temperature minimum, thereafter steadily decreasing to a value of about 2.5 atr10⁴km.It is shown that while the dust attenuation has a strong effect on the production rate of H₂O, it also has an interesting effect on the electron density profile. It increases the electron density in the inner coma over the unattenuated case, while at the same time, decreasing it in the outer coma. In conclusion, the limitations of the present model and the necessity to extend it using a multi-fluid approach are discussed.     

Center to limb variation of the intensity of the photospheric faculae

Center to limb variation of the excess brightness of photospheric facular granules was observed at 530 nm with a balloon-borne telescope of 10 cm aperture. Facular granules are found to be 9.2% and 16.2% brighter than the adjacent quiet region at cos = 0.65 and 0.50 respectively, being the angle between the Sun's normal and the line of sight. This observation, together with our earlier result (Hirayama, 1978), leads to facular models which are 600 K hotter than the photosphere if the diameter of facular granules is assumed to be 600 km, and 1000 K hotter if 150 km is assumed instead. It was also found that the soft X-ray bright points as observed with the Skylab do not correspond spatially to the photospheric facular granules near the polar region.     

Pre-Main-Sequence evolution of rotating low-mass stars

The evolutionary behaviour of rotating low-mass stars in the mass range 0.2 and 0.9M has been investigated during the pre-Main-Sequence phase. The angular momentum is conserved locally in radiative regions and totally in convective regions, according to a predetermined angular velocity distribution depending on the structure of the star. As the stars contract toward the zero-age Main Sequence, they spin up under the assumption that the angular momentum is conserved during the evolution of the stars. When the stars have differential rotations, their inner regions rotate faster than the outer regions. The effective temperatures and luminosities of rotating low-mass stars are obtained lower than those of non-rotating stars. They have lower central temperature and density values compared to those of non-rotating stars.     

Long-period observations of the solar wind plasma between 0.3 and 1.0 AU — Solar activity

Hourly interplanetary plasma data measured by Helios-1 satellite over the period 10 December 1974–31 December 1977 are analysed. This analysis showed that the slow solar wind first increases its speed with heliocentric distance and then becomes more or less constant; the mean speed in the range 0.3 to 1.0 AU is 350 km s^–1 for the slow solar plasma, while for the fast the mean value is between 650 and 700 km s^–1.It seems, particularly in the neighbourhood of the earth, that except for the two dominated types of solar wind (fast and slow) an additional (intermediate) appears at 450 km s^–1.During the phase of enhanced solar activity (11-yr solar cycle) the slow solar wind only is present, while at solar minimum all three types of the solar wind are equally represented.The dependence of the proton temperature on the solar wind speed, in the general solar wind, is the same irrespectively of the phase of solar activity. But, the same dependence is stronger during the compression at the leading edge than during the expansion at the trailing edge of a solar wind stream.     

Structure of sunspots

The sunspot models published so far do not reproduce the observed run of the umbral continuum intensities over the entire spectral range 0.5 < < 4 m. Moreover, in several previous models is the temperature gradient smaller than both the adiabatic and the radiative equilibrium gradient.Agreement between intensities computed from acceptable models and measured intensities can be obtained by introducing an additional opacity for 0.8 m, which is probably caused by the crowding of atomic and molecular lines. We present a new umbral model atmosphere with a wavelength dependent opacity enhancement factor which explains the continuum intensities and also reproduces plausible center-to-limb variations and line profiles. This model is in radiative equilibrium down to _0.5 = 1.5, with an effective temperature of 4000 ± 100K. For the deeper superadiabatic layers a small but probably significant departure from radiative equilibrium is indicated by the intensities in the range 1.5 < < 2.4 m.The uncertainties in the present model and the effect of the additional opacity on line profiles are briefly discussed.     

Observations of solar X-ray bursts in the energy range 5–15 keV

We simultaneously solve the equations of radiative transfer and statistical equilibrium for a model hydrogen atom including Lyman-, Lyman-, Balmer- and the Lyman, Balmer and Paschen continua. The model atmospheres we use are the results of Nakagawa et al. (1973) for a kinematic model of the chromospheric solar flare.We find that the models adequately predict the total intensity of B, its wing broadening, the presence of a red-shifted wing, the maximum electron density, the total line-of-sight second-level population and the narrowness in height of the B emitting region. The profile of B is strongly self-reversed, however, and agrees with observations only in the presence of 40–70 km s^–1 macroturbulent motion.We find that Nakagawa et al. (1973) seriously overestimate the radiative loss function, which will have a large effect on their models. Proper radiative loss calculations must be included in any physically realistic model.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Study of the X-ray selected BL Lac object 1727+502

In this paper, accretion disc and synchrotron emission models have been used to analyse simultaneous IR-optical-UV data of the BL Lac object 1727+502. In the following, some of its properties have been discussed. It is shown that the temperature of the disc is about 19, 000°k, the mass of the central black hole isM ₈ 5.4, and the accretion ratio is 10^–3 M /yr.     

A two-dimensional solar model

We present a two-dimensional, nearly flux constant solar atmosphere which includes a physical model of granulation. If the inhomogeneous character of the solar photosphere is neglected in the construction of empirical models, the result is an underestimate of the temperature gradient in the layers below 0.5 and an overestimate of the convective flux penetration into the observable layers. The two-dimensional model adequately reproduces the mean limb darkening, the magnitude and center-to-limb variation of the intensity fluctuations, and the rms vertical and horizontal convective velocities.     

Three-dimensional structure of the solar wind: Variation of density with the solar cycle

Interplanetary Scintillation (IPS) measurements obtained from a large number of compact radio sources (nearly 150 sources) distributed over the heliocentric distance range 15–175 solar radii (R() and heliographic latitude 75° N-75° S have been used to study the global three-dimensional density distribution of the solar wind plasma. Contours of constant electron-density fluctuations (N _e) in the heliospheric plasma obtained for both the solar minimum and maximum show a strong solar latitude dependence. During low solar activity, the equatorial density-fluctuation value decreases away from the equator towards higher latitudes and is reduced by 2.5 times at the poles; the level of turbulence is reduced by a factor of 7; the solar-wind mass flux density at the poles is 25% lower than the equatorial value. However, during high solar activity, the average distribution of density fluctuations becomes spherically symmetric. In the ecliptic, the variation of N _e with the heliocentric distance follows a power law of the formR ^–2.2 and it does not show any change with solar activity.     

Solar rotation in the subphotospheric layers

The solar rotation rate at latitudes 0°, 15° and 30° has been inferred by averaging the results of 120 regions of 15°×15°, which have been studied over a total area of about 75° in latitude and 360° in longitude. A local helioseismology technique, the ring diagram analysis method, has been used to analyse the horizontal velocity vectors from about 0.95 R up to the surface. Our results are in very good agreement with those of other authors over most of the depth range. However, near the surface we find sharp local features which are not reported in other studies. The independent measurements of the rotation rate in the north and south hemispheres show asymmetries below 0.975 R . The data used are full-disc dopplergrams taken by Solar Oscillation Investigation/Michelson Doppler Imager (SOI/MDI) on board of the SOlar and Heliospheric Observatory (SOHO) during its first Dynamic Program, between 1996 May and June.     

A prominence model based on spectral observations

Intensities and profiles of the H, H, H, K, and D₃ lines are measured in a solar prominence. From the profiles of these lines we estimate T = 6400 K and _t = 5.7 km s^–1. We construct a simple isothermal model which explains the H intensity and profile for an assumed total particle density n _T = 3 × 10¹¹ cm^–3, and a filling factor, = 1/6.From this model we find that the source function in the H line is nearly constant through the prominence. We estimate from the model that the radiative energy loss at the center of the prominence is of the order of 10⁷ erg s^–1 g^–1.     

A new microwave/X-ray diagnostic for the thermal phase of solar flares

We have observed 10 solar bursts during the thermal phase using the Haystack radio telescope at 22 GHz. We show that these high frequency flux observations, when compared with soft X-ray band fluxes, give useful information about the temperature profile in the flare loops. The microwave and X-ray band fluxes provide determinations of the maximum loop temperature, the total emission measure, and the index of the differential emission measure (q(T)/T = cT^–1). The special case of an isothermal loop ( = ) has been considered previously by Thomas et al. (1985), and we confirm their diagnostic calculations for the GOES X-ray bands, but find that the flare loops we observed departed significantly from the isothermal regime. Our results ( = 1–3.5) imply that, during the late phases of flares, condensation cooling ( 3.5) competes with radiative cooling ( 1.5). Further, our results appear to be in good agreement with previous deductions from XUV rocket spectra ( 2–3).