On the sun's pole-equator flux differences

We study the possibility that large flux differences between the poles and the equator at the bottom of the solar convective zone are compatible with the small differences observed at the surface. The consequences of increasing the depth of the convective zone due to overshooting are explored.A Boussinesq model is used for the convective zone and we assume that the interaction of the global convection with rotation is modelled through a convective flux coefficient whose perturbed part is proportional to the local Taylor number. The numerical integration of the equations of motion and energy shows that coexistence between large pole-equator flux differences at the bottom and small ones at the surface is possible if the solar convective zone extends to a depth of 0.4R . The angular velocity distribution inside the convective zone is in agreement with the -dynamo theories of the solar cycle.     

On the Sun's differential rotation and pole-equator temperature difference

The Sun's differential rotation can be understood in terms of a preferential stabilization of convection (by rotation) in the polar regions of the lower part of the convection zone (where the Taylor number is large). A significant pole-equator difference in flux () can develop deep inside the convection zone which would be unobservable at the surface, because can be very efficiently reduced by large scale meridional motions rising at the poles and sinking at the equator. This is the sense of circulation needed to produce the observed equatorial acceleration of the Sun. Differential rotation is generated, therefore, in the upper part of the convection zone (where the interaction of rotation with convection is small) and results as the convection zone adjusts to a state of negligible Taylor number.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Observations of photospheric faculae at the center of the solar disk

Methods for the determination of the average optical depth of formation of weak Fraunhofer lines are compared, and their relative merits are discussed. Distinction should be made between the region of origin of the emergent radiation, and of the line depression. For weak or fairly weak lines the average optical depth of formation of the line depression is the relevant quantity; it should be determined by using a computational scheme based on the classical weighting functions of line formation; other methods give physically unsignificant or conflicting results.

     

On the solar oblateness: The combined effect of a pole-equator difference in effective temperature and mechanical heating

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.     

Modelling photospheric magnetoconvection

The increasing power of computers makes it possible to model the non-linear interaction between magnetic fields and convection at the surfaces of solar-type stars in ever greater detail. We present the results of idealized numerical experiments on two-dimensional magnetoconvection in a fully compressible perfect gas. We first vary the aspect ratio λ of the computational box and show that the system runs through a sequence of convective patterns, and that it is only for a sufficiently wide box (λ ≥ 6) that the flow becomes insensitive to further increases in λ. Next, setting λ = 6, we decrease the field strength from a value strong enough to halt convection and find transitions to small-scale steady convection, next to spatially modulated oscillations (first periodic, then chaotic) and then to a new regime of flux separation, with regions of strong field (where convection is almost completely suppressed) separated by broad convective plumes. We also explore the effects of altering the boundary conditions and show that this sequence of transitions is robust. Finally, we relate these model calculations to recent high-resolution observations of solar magnetoconvection, in plage regions as well as in light bridges and the umbrae of sunspots.     

The photospheric network

Spectroheliograms, obtained in certain Fraunhofer lines with the 82-cm solar image at the Kitt Peak National Observatory, show a bright photospheric network having the following properties:

1. It resembles, but does not coincide with, the chromospheric network, the structure of the photospheric network being finer and more delicate than the relatively coarse structure of the chromospheric network.
2. It is exactly cospatial with the network of non-sunspot photospheric magnetic fields.
3. Its visibility in a given photospheric Fraunhofer line is primarily dependent on the states of ionization and excitation from which the line is formed and secondarily dependent on the Zeemansensitivity of the line-being most visible in low-excitation lines of neutral atoms and least visible in high-excitation lines of singly ionized atoms.

We conclude that these magnetic regions of the solar atmosphere are a few hundred degrees hotter than their surroundings, and that they are visible in white light near the limb as photospheric faculae.     

The effect of photospheric heavy elements on the hot DA white dwarf temperature scale

Using the latest non-local thermodynamic equilibrium (non-LTE) synthetic spectra and stellar model calculations, we have evaluated the potential effect of the presence of heavy elements in the photospheres of hot H-rich DA white dwarfs. In particular, we have examined their influence on the effective temperature and surface gravity perceived from analysis of the Balmer line profiles. It is apparent that both the inclusion of non-LTE effects in the models and significant quantities of heavy elements act independently to lower the value of T _eff determined from a particular spectrum. Hence, the true effective temperatures of the heavy element-rich DA white dwarfs, currently estimated to be above 55 000 K, are apparently lower than previously reported from pure-H LTE analyses, by some 4000–7000 K. We do not see any similar influence on measurements of log g . This work concentrates on a group of relatively bright well-studied objects, for which heavy element abundances are known. As a consequence of this, establishment of correct temperatures for all other hot white dwarfs will require a programme of far-UV spectroscopy in order to obtain the essential compositional information. Since only stars with effective temperatures lying notionally in the range from ≈ 55 000 to 70 000 K (52 000–62 000 K when the non-LTE effects and heavy elements are taken into account) have been considered here, important questions remain regarding the magnitude of any similar effects in even hotter white dwarfs and pre-white dwarfs. The resulting implications for the plausibility of the evolutionary link between the main hot DA population and their proposed precursors, the H-rich central stars of planetary nebulae, need to be investigated.     

The solar continuum from 900 to 130 000 Å and the photospheric temperature model

In order to obtain a better agreement between observed and computed values of the solar intensity, an improved temperature distribution is deduced for the range 0.02<0< 10. The intensity observations here considered refer to the wavelength region between 1980 and 129 500, and the center-limb variations generally go down to cos = 0.1. The improved model, given in Figure 4 and Table II, differs rather little from the Utrecht 1964 model, used here as a reference.It appears necessary to introduce an empirical correction function to be applied to the continuous absorption coefficient. This function was derived for the spectral region between 2000 and 130000 Å; it is shown in Figure 5.Furthermore, an extension of the model (1.10^–7<0< 2.10^–2) is deduced (see Table III and Figure 8), which reasonably well represents the observations of the ultraviolet solar flux ( 900–1700 Å).     

On depth-dependence of photospheric oscillations

We report on results from photographic observations of photospheric oscillations as a function of depth. Using rms-values and power-spectra from shifts of entire line-profiles, we find qualitatively an increase of the velocity-amplitude with increasing height. We get more quantitative informations by comparing measured asymmetries of line-profiles with calculated ones derived from Voigt-functions containing a depth dependent velocity-field.We find the scale-height H ₀ of photospheric velocity oscillations to be 930±100 km. This result is to be compared with H ₀ = 1100±200 km obtained by Canfield (1976), who used velocity weighting functions of the line centres.Further, we show that a general observed line asymmetry of medium strong lines (c-shape) does not depend on the phase of oscillations.Mitt. aus dem Kiepenheuer-Institut Nr. 178.     

The photospheric abundance of iron

The center-to-limb variation of equivalent widths of 198 Fei lines in the spectral region 5500 to 7000 Å was studied with five photospheric models. The gf-values of Corliss and Warner (1964) were used in the analysis. The photospheric iron abundance was found to vary with excitation potential. This can be explained by a systematic error in the gf-values of high excitation lines and an error of 250 to 500K in the temperature of the arcs used for measuring the gf-values. Departures from LTE in the solar Fei lines are also a possibility. The adopted photospheric abundance of iron, log(N _Fe/N _H) is - 5.2.     

The equatorial photospheric rotation rate

The equatorial photospheric rotation rate has been observed on 14 days in 1978–1980. The resulting rotation rate, = 14.14±0.04°/day, is 2% slower than the rate as observed for long-lived sunspots.Stationed at Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Simulating photospheric Doppler velocity fields

A method is described for constructing artificial data that realistically simulate photospheric velocity fields. The velocity fields include rotation, differential rotation, meridional circulation, giant cell convection, supergranulation, convective limb shift, p-mode oscillations, and observer motion. Data constructed by this method can be used for testing algorithms designed to extract and analyze these velocity fields in real Doppler velocity data.     

The photospheric magnetic flux budget

The ensemble of bipolar regions and the magnetic network both contain a substantial and strongly variable part of the photospheric magnetic flux at any phase in the solar cycle. The time-dependent distribution of the magnetic flux over and within these components reflects the action of the dynamo operating in the solar interior. We perform a quantitative comparison of the flux emerging in the ensemble of magnetic bipoles with the observed flux content of the solar photosphere. We discuss the photospheric flux budget in terms of flux appearance and disappearance, and argue that a nonlinear dependence exists between the flux present in the photosphere and the rate of flux appearance and disappearance. In this context, we discuss the problem of making quantitative statements about dynamos in cool stars other than the Sun. This paper evolved out of a more comprehensive version which appeared in Harvey (1993).     

Spectral analyses of solar photospheric fluctuations

Successful subtraction of instrumental background variations has permitted spectral analyses of two-dimensional measurement arrays of granulation brightness fluctuations at the center of the disk, arrays obtained from Stratoscope I, 1959B-flight, high-resolution frames B1551 and B3241.

1. RMS's, uncorrected for instrumental blurring, are 0.0850 of mean intensity for B1551 and 0.0736 for B3241, somewhat higher than other determinations. These between-frame and between-investigation differences probably result from a combination of calibration errors, frame resolution differences, and, most likely, granulation pattern differences.
2. Significant variations over each array of mean intensities and RMS's, determined for sub-arrays with dimensions in the 2500–10000 km range, indicate spatial brightness and RMS variations larger than the ‘scale’ of the granulation pattern, supporting a turbulent interpretation of photospheric convection.
3. One-dimensional power-spectra shapes provide objective and discriminating criteria for determining granulation pattern differences and, possibly, frame resolution.
4. Two-dimensional power spectra show small, essentially random deviations from axial symmetry which lie almost entirely within the 50% confidence limits.
5. Spectral densities and fluctuation power spectra, computed from the two-dimensional power spectra and corrected for instrumental blurring, noise, and blemishes, have a useable radial wavenumber range nearly double that of earlier Stratoscope I analyses.
6. Corrected RMS's obtained from the corrected fluctuation power spectra, 0.145 ± 0.046 for B1551 and 0.136 ± 0.048 for B3241, depend critically on the accuracy of the correction.
7. The spectra's wavenumber range includes the granulation-fluctuation-producing domain but not the Kolmogoroff domain of turbulence spectra.

     

High-resolution analysis of solar photospheric oscillations

The coherent 5-min photospheric pressure oscillations with spherical harmonic degrees in the range 100 <l< 1000 were directly imaged over the photosphere with the monochromatic solar telescope FPSS at Meudon Observatory. Movie films were obtained with images spatially filtered to select sizes of increasing wave numbers (or l). Areas with ephemeral concentrations of coherent waves evolve in shape and may move horizontally with velocities of several tenths of km s^–1. When a large number of waves are interacting, the maximum vertical velocity V _max of the pulsation reaches around 1000 m s^–1, irrespective of the size. Extrapolation to the ideal case of a single isolated wave gives V _max proportional to size. For the areas of the smallest scale measured (l = 1000), when about 100 waves are interacting, V _max is found to be 260 + 25 m s^–1 at an altitude of 210 km above the reference level ₅₀₀₀ = 1 and increases vertically with a scale height of 750 ± 400 km.     

Amplitude distributions of solar photospheric fluctuations

Amplitude distributions, which are nearly Gaussian, have been calculated for radial velocity, continuum brightness, spectral line equivalent width and spectral line central residual intensity fluctuations measured from high-dispersion high-resolution spectrograms taken at the center of the solar disk. The RMS and skewness S for each distribution have been calculated in a manner which allows testing of the homogeneity of the granulation pattern (i.e. variations in its statistics across the solar disk and with time). Pattern inhomogeneity across the disk is strongly indicated, and further evidence suggesting appreciable pattern persistence over time intervals 15 minutes is presented. The possibilities for investigations of S and its associated bi-spectrum are discussed. The qualitative values of S obtained are shown not to be due to unusually bright, rising granules (though a statistical tendency towards such granules is possible). An attempt to explain S for continuum brightness fluctuations in terms of the nonlinear effects of Planckian emission and opacity fluctuations in a stratified photosphere, leads to contradiction with the measured amplitude distributions, a contradiction which is probably due to an oversimplified treatment of radiative transfer in an inhomogeneous photosphere.     

The total photospheric motion field

Brief consideration is given to the conception of the total photospheric motion field. A synthesis of the most thorough investigations is made and the radial (V ^rad) and tangential (V ^tg) components of the velocity amplitude of the total photospheric motion field are deduced. At depth logτ₅ = ?3.0 V ^rad and V ^tg have average values of 1.2 and 1.7 km s^?1 respectively. They increase smoothly with depth and reach their maximum values of V ^rad=3.0, V ^tg=3.4 km s^?1 at depths logτ₅= ?0.2 and logτ₅ = +0.4 respectively. In the deep photospheric layers both components seem to decrease with depth.     

Spectral analyses of solar photospheric fluctuations

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.     

Magnetic-field structure of the photospheric network

A method is developed to determine the physical parameters of the spatially unresolved photospheric network. The apparent magnetic fluxes are recorded simultaneously in the two FeI lines 5250 and 5247 Å, which belong to the same multiplet and have practically the same oscillator strength and excitation potential of the lower level, but differ in the effective Lande factor. By analysing magnetograph recordings in this pair of lines together with simultaneous recordings in the two FeI lines 5250 and 5233 Å, it is possible to separate the effects on the line profiles due to Zeeman splitting and temperature enhancement in the network.From an analysis of the observations the following properties of the photospheric network are obtained: Field strengths of about 2000 G are present in the network in quiet regions. The characteristic size of the magnetic-field structures in the network appears to be in the range 100–300 km. The 5250 Å line is weakened by roughly 50% in the network. If the line had been non-magnetic, the weakening would have been about 20%. The rest of the weakening is caused by the strong Zeeman splitting. The downward velocity at the supergranular cell boundaries is estimated to be of the order of 0.5 km s^-1.     

The photospheric velocity field of Procyon

BUSS observations of the profiles of two well observed spectral lines in the ultraviolet spectrum of CMi (Procyon; F5 IV–V) are analysed with a Fourier transform method in order to determine values of various parameters of the velocity field of the upper photosphere. We find a microturbulent line-of-sight velocity componentL = 0.9 ± 0.4 km s^–1, a macroturbulent velocity componentL _M = 5.3 ± 0.2 km s^–1, and a rotational velocity componentv _R sini=10.0±1.2 km s^–1. In these calculations a single-moded sinusoidal isotropic macroturbulent velocity function was assumed. The result appears to be sensitive to the assumed shape of the macroturbulence function: for an assumed Gaussian shape the observations can be described withv _R sini=4 km s^–1 andL _M = 11.6 ± 2.7 km s^–1. A comparison is made with other results and theoretical predictions.