Specifics of the solar photospheric convection at granulation,mesogranulation, and supergranulation scales

The power spectra of temperature and vertical velocity variations in the solar photosphere are calculated using the data obtained through observations of a nonperturbed region near the solar disk center in the neutral iron line λ ≈ 639.3 nm conducted at the 70 cm German Vacuum Tower Telescope (VTT) located in the Canary Islands (Spain). The variations of these spectra with altitude are analyzed. It is found that the primary power in the lower photosphere is localized in the range of frequencies that correspond to granulation with a peak at the λ ≈ 1.5–2.0 Mm scale and is reduced with altitude, the power spectrum maximum in the upper photospheric layers is shifted towards larger scales (Δλ ≤ 1 Mm), and the power of variations of the vertical supergranulation velocity (λ ≈ 20–30 Mm) virtually does not change with altitude. An isolated mesogranulation regime (λ ≈ 5–12 Mm) is not found at any of the studied altitudes. The obtained results suggest that the convective structure of the solar photosphere at mesogranulation scales behaves like granulation: the mesostructures are a part of an extended distribution of granulation scales. It is shown that the supergranulation flows are stable throughout the entire photosphere and reach much higher altitudes than the granulation flows.     

Discrete cellular scales of solar convection

The theoretical power spectrum of velocity fields and flux fluctuations at the solar photosphere is calculated using a quasi-nonlinear framework of superposition of unstable convective eigenmodes excited in the solar convection zone. It is demonstrated that this power spectrum exhibits at least three distinct peaks corresponding to granulation, mesogranulation and supergranulation. The vertical velocity and the brightness fluctuation at the solar surface are found to be correlated. The theoretical framework can be adopted for application to other types of stars in order to predict the dominant length scales in the power spectrum of convection in these stars.     

Magnetic flux separation in photospheric convection

Three-dimensional non-linear magnetoconvection in a strongly stratified compressible layer exhibits different patterns as the strength of the imposed magnetic field is reduced. There is a transition from a magnetically dominated regime, with small-scale convection in slender hexagonal cells, to a convectively dominated regime, with clusters of broad rising plumes that confine the magnetic flux to narrow lanes where fields are locally intense. Both patterns can coexist for intermediate field strengths, giving rise to flux separation: clumps of vigorously convecting plumes, from which magnetic flux has been excluded, are segregated from regions with strong fields and small-scale convection. A systematic numerical investigation of these different states shows that flux separation can occur over a significant parameter range and that there is also hysteresis. The results are related to the fine structure of magnetic fields in sunspots and in the quiet Sun.     

Testing turbulent convection theory in solar models – I. Structure of the solar convection zone

Turbulent convection models (TCMs) based on hydrodynamic moment equations are compared with the classical mixing-length theory (MLT) in solar models. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion and anisotropy of turbulence that have been ignored in the MLT. Free parameters introduced by the TCMs are also tested in order to find appropriate values for astrophysical applications. It is found that the TCMs usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the TCMs. As a result of calibrating to the present solar values, our solar models usually have rather smaller values of the mixing length to local pressure scaleheight ratio than the standard solar model. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the superadiabatic convection region but a smaller one near the boundaries of the convection zone. It is interesting to note that, due to a careful treatment of turbulence developing towards isotropic state, our non-local TCM results in radially dominated motion in the central part and horizontally dominated motion near the boundaries of the convection zone, just as what has been observed in many 3D numerical simulations. Our solar models with the TCMs give small but meaningful differences in the temperature and sound speed profiles compared with the standard solar model using the MLT.     

Spectral analyses of solar photospheric fluctuations

The application of the fast-Fourier-transform (FFT) algorithm to calculating one-dimensional and bi-dimensional (temporal and spatial), power and cross-power (coherence and phase) spectra is examined for solar photospheric fluctuations. Alternative methods for smoothing raw spectra, direct averaging (employing various weights) and indirect truncation of the correlation function, are compared, and indirect smoothing is compared with spectra calculated by mean-lagged-product (MLP) methods. Besides providing the raw spectrum, FFT techniques easily allow computing a series of spectra with varying amounts of smoothing. From these spectra a range of satisfactory compromise between resolution and stability can be determined which helps in the interpretation of spectral trends, and in identifying more clearly the existence and significance of spectral features. For bi-dimensional spectra presented as contour plots, this range of satisfactory smoothing can be restricted, particularly when spectral trends must be represented by small-scale contours. Equivalent spectra (i.e. comparable equivalent degrees of freedom) computed or smoothed by different methods have minor, but not negligible, differences. Examination of these differences favors computing of FFT spectra smoothed by averaging for photospheric fluctuations.     

The solar photospheric abundance of iron

A new value of the solar photospheric abundance of iron, independent of line-shape parameters, is derived. Our analysis is based on a study of 40 weak infrared lines (0.85<λ<2.5 μ) for which theoretical oscillator strengths (calculated with configuration interactions taken into account) have recently been computed by Kurucz (1974). The abundance obtained, A _Fe = 7.57±0.11 (in the usual scale where log N _H = 12.00) is in agreement with the ‘high’ solar values recently reported in the literature and with the meteoritic abundance.     

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.     

Spectral analyses of solar photospheric fluctuations

Synthetic one-dimensional scans of brightness fluctuations are generated from intergranulegranule profiles (IGP), which approximate observed scans of granulation fluctuations except that the local (i.e. IGP) mean intensity is kept constant. Comparing the power spectrum of such scans with the power spectrum of observed scans shows that nearly two thirds of the low-wavenumber (k < 0.0025 km^-1) granulation power is due to this variable mean effect. This result favors the interpretation of granulation as turbulent thermal convection but cannot rule out the laminar convection interpretation.     

The solar photospheric abundance of zirconium

Zirconium (Zr), together with strontium and yttrium, is an important element in the understanding of the Galactic nucleosynthesis. In fact, the triad Sr‐Y‐Zr constitutes the first peak of s‐process elements. Despite its general relevance not many studies of the solar abundance of Zr were conducted. We derive the zirconium abundance in the solar photosphere with the same CO⁵BOLD hydrodynamical model of the solar atmosphere that we previously used to investigate the abundances of C‐N‐O. We review the zirconium lines available in the observed solar spectra and select a sample of lines to determine the zirconium abundance, considering lines of neutral and singly ionised zirconium. We apply different line profile fitting strategies for a reliable analysis of Zr lines that are blended by lines of other elements. The abundance obtained from lines of neutral zirconium is very uncertain because these lines are commonly blended and weak in the solar spectrum. However, we believe that some lines of ionised zirconium are reliable abundance indicators. Restricting the set to Zr II lines, from the CO⁵BOLD 3D model atmosphere we derive A (Zr) = 2.62 ± 0.06, where the quoted error is the RMS line‐to‐line scatter (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

24MgH+ in the solar photospheric spectrum

The²⁴MgH⁺ (A ¹⁺ –X ¹⁺) molecular lines have been identified in the photospheric spectrum. The rotational excitation temperature determined from the analysis of molecular line intensities of²⁴MgH⁺ is found to be of the order of 4850 K which corresponds to the photospheric temperature of the Sun. The CNDO/2 dipole moments of²⁴MgH⁺ for internuclear distance range: (1.3–2.1) Å in theX ¹⁺ state can be approximated byM(R)=4.92+1.33R. Estimations for the spontaneous emission Einstein coefficients (A _{v v} ) and the absorption oscillator strengths (f _{v v} ) for the (1, 0), (2, 0), and (2, 1) transitions in theX ¹⁺ state of the²⁴MgH⁺ ion are also made.Work partially supported by the CNPq, Brasilia under contract number 30.4076/77.     

Dynamical effects in solar photospheric flux tubes

The interaction of an intense flux tube, extending vertically through the photosphere, with p-modes in the ambient medium is modelled by solving the time dependent MHD equations in the thin flux tube approximation. It is found that a resonant interaction can occur, which leads to the excitation of flux tube oscillations with large amplitudes. The resonance is not as sharp as in the case of an unstratified atmosphere, but is broadened by a factor proportional toH ^–2, whereH is the local pressure scale height. In addition, the inclusion of radiative transport leads to a decrease in the amplitude of the oscillations, but does not qualitatively change the nature of the interaction.     

Formation of solar prominences by photospheric shearing motions

A numerical simulation is performed to investigate the prominence formation in a magnetic arcade by photospheric shearing motions. A two-and-a-half-dimensional magnetohydrodynamic (MHD) code is used, in which the gravitational force, radiative cooling, thermal conduction and a simplified form of coronal heating are included. It is found that a footpoint shear induces an expansion of the magnetic arcade and cooling of the plasma in it. Simultaneously the denser material from the lower part of the arcade is pulled up by the expanding field lines. A local enhancement of radiative cooling is thus effected, which leads to the onset of thermal instability and the condensation of coronal plasma. The condensed material grows vertically to form a sheet-like structure making dips on field lines, leading to the formation of the Kippenhahn- Schlüter type prominence. The mass of the prominence is found to be supplied not only by the condensation of the material in the vicinity but also by the siphon-type upflows. The upward growth of the vertical sheet-structure of the prominence is saturated at a certain stage and the newly condensed material is found to slide down from above the prominence along magnetic field lines. This drainage of material leads to the formation of an arc-shaped cavity of low density and low pressure around the prominence. The problem of force and heat balance is addressed and the prominence is found to be not in a static equilibrium but in a dynamic interaction with its environment.     

Computation of solar magnetic fields from photospheric observations

The observational difficulties of obtaining the magnetic field distribution in the chromosphere and corona of the Sun has led to methods of extending photospheric magnetic measurements into the solar atmosphere by mathematical procedures. A new approach to this problem presented here is that a constant alpha force-free field can be uniquely determined from the tangential components of the measured photospheric flux alone. The vector magnetographs now provide measurements of both the solar photospheric tangential and the longitudinal magnetic field. This paper presents derivations for the computation of the solar magnetic field from these type of measurements. The fields considered are assumed to be a constant alpha force-free fields or equivalent, producing vanishing Lorentz forces. Consequently, magnetic field lines and currents are related by a constant and hence show an identical distribution. The magnetic field above simple solar regions are described from the solution of the field equations.     

Remarks on the convergency of photospheric model conceptions and the solar quasi continuum

A comparison is made of the observed intensity in the solar continuous spectrum with those predicted by some models. Arguments are given that the bend-off observed for < 0.6 is a real phenomenon, and due to a veiled line haze.     

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.

     

A new method for the analysis of the solar photospheric spectrum

A new numerical method for the analysis of the high dispersion photospheric spectrum is described. In particular the method is applied to study the C₂(0, 0) d ³ Πg-a ^a Πu molecular band. From measurements of the equivalent widths of C₂ lines, a rotational temperature of 4450 ± 305 K is obtained, and the band intensity log W ₀ /S ₀ = ?0.051 ± 0.101 is found.     

Probing solar convection

In the solar convection zone, acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov's technique. Particular care is taken to include diffraction effects, which are important, especially for high-degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p-mode eigenfrequencies. The contribution of scattering to the linewidths is estimated and the sensitivity of the results to the assumed spectrum of the turbulence is studied. Finally, the theoretical predictions are compared with recently measured linewidths of high-degree modes.