Center-to-limb Variation Research Articles

Effects of magnetic fields on the center-to-limb variation in solar-type stars

Context. High-precision photometry of exoplanet transits obtained with the Kepler satellite allows one to derive information on the center-to-limb variation (CLV) of the host stars. Recent analyses indicate a small but systematic discrepancy between observations and theoretical expectations based on detailed multidimensional model atmospheres. It has been hypothesized that the discrepancy is related to the neglect of magnetic fields in the models. Aims. Our goal is to test the above hypothesis for solar-like stars. We further intend to quantify the consequences for interferometry, and the possibility of extracting information at the level of stellar magnetic activity from the CLV. Methods. We constructed a sequence of multidimensional models including magnetic fields of varying strengths. We derived theoretical predictions on the CLV, taking into account factors like the observational passband, stellar sphericity, the methodology of the light curve analysis, and interstellar extinction. Results. The models predict a relative brightening of the stellar limb with increasing magnetic field strength, which qualitatively goes in the direction of reducing the mismatch between observation and theory. Quantitatively, however, the mismatch is not fully eliminated. Interstellar extinction on a level AV ≲ 1 mag has little impact on the CLV and is largely degenerate with the influence of magnetic fields. Global magnetic activity at field strengths ≲300 G influences interferometric radius measurements to ≲1%. We emphasize that our results refer to measurements taken in the Kepler passband. Conclusions. The presence of magnetic activity appears to be a plausible explanation for the present discrepancy between observation and theory. The still-present partial mismatch needs to be understood. To this end, we point to improvements in modeling and wishes for more observational data of active stars, including spectral information.

Solar center-to-limb variation in Rossiter-McLaughlin and exoplanet transmission spectroscopy

Line profiles from spatially unresolved stellar observations consist of a superposition of local line profiles that result from observing the stellar atmosphere under specific viewing angles. Line profile variability caused by stellar magnetic activity or planetary transit selectively varies the weight and/or shape of profiles at individual surface positions. The effect is usually modeled with radiative transfer calculations because observations of spatially resolved stellar surfaces are not available. For the Sun, we recently obtained a broadband spectroscopic atlas of the solar center-to-limb variation (CLV). We use the atlas to study systematic differences between largely used radiative transfer calculations and solar observations. We concentrate on four strong lines useful for exoplanet transmission analysis, and we investigate the impact of CLV on transmission and Rossiter-McLaughlin (RM) curves. Solar models used to calculate synthetic spectra tend to underestimate line core depths but overestimate the effect of CLV. Our study shows that CLV can lead to significant systematic offsets in transmission curves and particularly in RM curves; transmission curves centered on individual lines are overestimated by up to a factor of two by the models, and simulations of RM curves yield amplitudes that are off by up to 5−10 m s−1 depending on the line. For the interpretation of transit observations, it is crucial for model spectra that accurately reproduce the solar CLV to become available which, for now, is the only calibration point available.

Center-to-limb Variation of Transition-region Doppler Shifts in Active Regions

Studying Doppler shifts provides deep insights into the flow of mass and energy in the solar atmosphere. We perform a comprehensive measurement of Doppler shifts in the transition region and its center-to-limb variation (CLV) in the strong-field regions (∣ B ∣ ≥ 50 G) of 50 active regions (ARs), using the Si iv 1394 Å line recorded by the Interface Region Imaging Spectrometer. To locate the ARs and identify strong-field regions, we have used the magnetograms obtained by the Helioseismic and Magnetic Imager (HMI). We find that in strong-field regions, on average, all the ARs show a mean redshift ranging between 4 and 11 km s−1, which varies with ARs. These flows show a mild CLV, with sizable magnitudes at the limb and substantial scatter in the mid-longitude range. Our observations do not support the idea that redshifts in the lower transition region (T ≲ 0.1 MK) are produced by field-aligned downflows as a result of impulsive heating and they warrant an alternative interpretation, such as a downflow of type-II spicules in the presence of a chromospheric wall created by cooler type-I spicules.

Detection of Na, K, and Hαabsorption in the atmosphere of WASP-52b using ESPRESSO

WASP-52b is a low-density hot Jupiter orbiting a moderately active K2V star. Previous low-resolution studies have revealed a cloudy atmosphere and found atomic Na above the cloud deck. Here we report on the detection of excess absorption at the Na doublet, the Hαline, and the K D1line. We derived a high-resolution transmission spectrum based on three transits of WASP-52b, observed with the ultra-stable, high-resolution spectrograph ESPRESSO at the Very Large Telescope array. We measured a line contrast of 1.09 ± 0.16% for Na D1, 1.31 ± 0.13% for Na D2, 0.86 ± 0.13% for Hα, and 0.46 ± 0.13% for K D1, with a line FWHM range of 11–22 km s−1. We also found that the velocity shift of these detected lines during the transit is consistent with the planet’s orbital motion, thus confirming their planetary origin. We did not observe any significant net blueshift or redshift that could be attributed to planetary winds. We used activity indicator lines as control but found no excess absorption. However, we did notice signatures arising from the Center-to-Limb variation (CLV) and the Rossiter-McLaughlin (RM) effect at these control lines. This highlights the importance of the CLV + RM correction in correctly deriving the transmission spectrum, which, if not corrected, could resemble or cancel out planetary absorption in certain cases. WASP-52b is the second non-ultra-hot Jupiter to show excess Hαabsorption after HD 189733b. Future observations targeting non-ultra-hot Jupiters that show Hαcould help reveal the relation between stellar activity and the heating processes in the planetary upper atmosphere.

CLASP Constraints on the Magnetization and Geometrical Complexity of the Chromosphere-Corona Transition Region

Abstract The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a suborbital rocket experiment that on 2015 September 3 measured the linear polarization produced by scattering processes in the hydrogen Lyα line of the solar disk radiation. The line-center photons of this spectral line radiation mostly stem from the chromosphere-corona transition region (TR). These unprecedented spectropolarimetric observations revealed an interesting surprise, namely that there is practically no center-to-limb variation (CLV) in the Q/I line-center signals. Using an analytical model, we first show that the geometric complexity of the corrugated surface that delineates the TR has a crucial impact on the CLV of the Q/I and U/I line-center signals. Second, we introduce a statistical description of the solar atmosphere based on a 3D model derived from a state-of-the-art radiation magnetohydrodynamic simulation. Each realization of the statistical ensemble is a 3D model characterized by a given degree of magnetization and corrugation of the TR, and for each such realization we solve the full 3D radiative transfer problem taking into account the impact of the CLASP instrument degradation on the calculated polarization signals. Finally, we apply the statistical inference method presented in a previous paper to show that the TR of the 3D model that produces the best agreement with the CLASP observations has a relatively weak magnetic field and a relatively high degree of corrugation. We emphasize that a suitable way to validate or refute numerical models of the upper solar chromosphere is by confronting calculations and observations of the scattering polarization in ultraviolet lines sensitive to the Hanle effect.

A Novel Investigation of the Small-scale Magnetic Activity of the Quiet Sun via the Hanle Effect in the Sr i 4607 Å Line

Abstract One of the key research problems in stellar physics is to decipher the small-scale magnetic activity of the quiet solar atmosphere. Recent magneto-convection simulations that account for small-scale dynamo action have provided three-dimensional (3D) models of the solar photosphere characterized by a high degree of small-scale magnetic activity, similar to that found through theoretical interpretation of the scattering polarization observed in the Sr i 4607 Å line. Here we present the results of a novel investigation of the Hanle effect in this resonance line based on 3D radiative transfer calculations in a high-resolution magneto-convection model having most of the convection zone magnetized close to the equipartition and a surface mean field strength G. The Hanle effect produced by the model’s magnetic field depolarizes the zero-field scattering polarization signals significantly, to the extent that the center-to-limb variation (CLV) of the calculated spatially averaged polarization amplitudes is compatible with the observations. The standard deviation of the horizontal fluctuations of the calculated scattering polarization signals is very sensitive to the model’s magnetic field, and we find that the predicted spatial variations are sufficiently sizable so as to be able to detect them, especially with the next generation of solar telescopes. We find that at all on-disk positions, the theoretical scattering polarization signals are anticorrelated with the continuum intensity. To facilitate reaching new observational breakthroughs, we show how the theoretically predicted polarization signals and spatial variations are modified when deteriorating the signal-to-noise ratio and the spectral and spatial resolutions of the simulated observations.

Center-to-limb variation of intensity and polarization in continuum spectra of FGK stars for spherical atmospheres

One of the necessary parameters needed for the interpretation of the light curves of transiting exoplanets or eclipsing binaries, as well as interferometric measurements of a star or microlensing events is how the intensity and polarization of a light change from the center to the limb. Scattering and absorption processes in stellar atmosphere affect both the center-to limb variation of intensity (CLVI) and polarization (CLVP). In this paper, we present a study of the CLVI and CLVP in continuum spectra considering different contributions of scattering and absorption opacity for different spectral type stars with spherical atmospheres. We solve the polarized radiative transfer equation in the presence of continuum scattering, considering spherical stellar model atmospheres. We developed two independent codes based on Feautrier and short characteristics methods to cross-check our results. We calculate the CLVI and CLVP in continuum for the Phoenix grid of spherical stellar model atmospheres for a range of $T_{eff} = 4000 - 7000 \rm K$, $\log g = 1.0 - 5.5$ and $\lambda = 4000 - 7000 \rm \AA$, which are tabulated and available at the CDS. For sub-giant and dwarf stars ($\log g = 3.0 - 4.5$), lower $\log g$ and lower $T_{eff}$ of a star lead to higher limb polarization of the star. For giant and supergiant stars ($\log g = 1.0 - 2.5$), the highest effective temperature yields the largest polarization. By decreasing of the $T_{eff}$ of a star down to $4500 - 5500 \rm K$ (depending on $\log g$) the limb polarization decreases and reaches a local minimum. It increases again down to $T_{eff}$ of $4000 \rm K$. For the most compact dwarf stars ($\log g = 5.0 - 5.5$) the limb polarization degree shows a maximum for models with $T_{eff}$ in the range $4200 - 4600 \rm K$ (depending on $\log g$) and decreases toward higher and lower temperatures.

The center-to-limb variation across the Fraunhofer lines of HD 189733

The center-to-limb variation (CLV) describes the brightness of the stellar disk as a function of the limb angle. Across strong absorption lines, the CLV can vary quite significantly. We obtained a densely sampled time series of high-resolution transit spectra of the active planet host star HD 189733 with UVES. Using the passing planetary disk of the hot Jupiter HD 189733 b as a probe, we study the CLV in the wings of the Ca ii H and K and Na i D1 and D2 Fraunhofer lines, which are not strongly affected by activity-induced variability. In agreement with model predictions, our analysis shows that the wings of the studied Fraunhofer lines are limb brightened with respect to the (quasi-)continuum. The strength of the CLV-induced effect can be on the same order as signals found for hot Jupiter atmospheres. Therefore, a careful treatment of the wavelength dependence of the stellar CLV in strong absorption lines is highly relevant in the interpretation of planetary transit spectroscopy.

FTS atlas of the Sun’s spectrally resolved center-to-limb variation

The Sun's spectrum varies with center-to-limb distance. This variation is governed by the underlying temperature-density structure of the solar atmosphere. To explore the spectrally resolved center-to-limb variation (CLV) we make use of two spectral atlases recorded with the Fourier transform spectrometer (FTS) at the McMath-Pierce facility at Kitt Peak. One spectral atlas obtained 10 arcsec inside the solar limb was recorded in 1978-79 as part of the first survey of the Second Solar Spectrum, while the other atlas is the well used reference NSO/Kitt Peak FTS atlas for the disk center. Both atlases represent fully resolved spectra without any spectral stray light. We then construct an atlas of the limb/disk-center ratio between the two spectra over the wavelength range 4084-9950 \AA. This ratio spectrum, which expresses the CLV amplitude relative to the continuum, is as richly structured as the intensity spectrum itself, but the line profiles differ greatly in both shape and amplitude. It is as if we are dealing with a new, unfamiliar spectrum of the Sun, distinctly different from both the intensity spectrum (which we here refer to with the acronym SS1) and the linear polarization of the Second Solar Spectrum (for which we use acronym SS2). In analogy we refer to the new ratio spectrum as SS3. While there is hardly any resemblance between SS3 and SS2, we are able to identify a non-linear mapping that can translate SS1 to SS3 in the case of weak to medium-strong spectral lines that are mainly formed in LTE (being directly coupled to the local temperature-density structure). This non-linear mapping is successfully modeled in terms of two free parameters that are found to vary approximately linearly over the entire wavelength range covered. These parameters and the various SS3 line profiles provide a novel, rich set of observational constraints on model atmospheres.

CENTER-TO-LIMB OBSERVATIONS AND MODELING OF THE Ca I 4227 Å LINE

The observed center-to-limb variation (CLV) of the scattering polarization in different lines of the Second Solar Spectrum can be used to constrain the height variation of various atmospheric parameters, in particular the magnetic fields via the Hanle effect. Here we attempt to model non-magnetic CLV observations of the $Q/I$ profiles of the Ca I 4227 A line recorded with the ZIMPOL-3 at IRSOL. For modeling, we use the polarized radiative transfer with partial frequency redistribution with a number of realistic 1-D model atmospheres. We find that all the standard FAL model atmospheres, used by us, fail to simultaneously fit the observed ($I$, $Q/I$) at all the limb distances ($\mu$). However, an attempt is made to find a single model which can provide a fit at least to the CLV of the observed $Q/I$ instead of a simultaneous fit to the ($I$, $Q/I$) at all $\mu$. To this end we construct a new 1-D model by combining two of the standard models after modifying their temperature structures in the appropriate height ranges. This new combined model closely reproduces the observed $Q/I$ at all the $\mu$, but fails to reproduce the observed rest intensity at different $\mu$. Hence we find that no single 1-D model atmosphere succeeds in providing a good representation of the real Sun. This failure of 1-D models does not however cause an impediment to the magnetic field diagnostic potential of the Ca I 4227 A line. To demonstrate this we deduce the field strength at various $\mu$ positions without invoking the use of radiative transfer.

Center-to-limb variation of the area covered by magnetic bright points in the quiet Sun

CONTEXT: The quiet Sun magnetic fields produce ubiquitous bright points (BPs) that cover a significant fraction of the solar surface. Their contribution to the total solar irradiance (TSI) is so-far unknown. AIMS: To measure the center-to-limb variation (CLV) of the fraction of solar surface covered by quiet Sun magnetic bright points. The fraction is referred to as 'fraction of covered surface', or FCS. METHODS: Counting of the area covered by BPs in G-band images obtained at various heliocentric angles with the 1-m Swedish Solar Telescope on La Palma. Through restoration, the images are close to the diffraction limit of the instrument (~0.1 arcsec). RESULTS: The FCS is largest at disk center (~1 %), and then drops down to become 0.2 % at 'mu'= 0.3 (with 'mu' the cosine of the heliocentric angle. The relationship has large scatter, which we evaluate comparing different subfields within our FOVs. We work out a toy-model to describe the observed CLV, which considers the BPs to be depressions in the mean solar photosphere characterized by a depth, a width, and a spread of inclinations. Although the model is poorly constrained by observations, it shows the BPs to be shallow structures (depth < width) with a large range of inclinations. We also estimate how different parts of the solar disk may contribute to TSI variations, finding that 90 % is contributed by BPs having 'mu' > 0.5, and half of it is due to BPs with 'mu' > 0.8.

Spectro-Polarimetric Observations of Solar Magnetic Fields and the SOHO/MDI Calibration Issue

Comparisons of solar magnetic-field measurements made in different spectral lines are very important, especially in those lines in which observations have a long history or (and) specific diagnostic significance. The spectral lines Fe i 523.3 nm and Fe i 525.0 nm belong to this class. Therefore, this study is devoted to a comprehensive analysis using new high-precision Stokes-meter full-disk observations. The disk-averaged magnetic-field strength ratio R=B(523.3)/B(525.0) equals 1.97±0.02. The center-to-limb variation (CLV) is R=1.74−2.43μ+3.43μ 2, where μ is the cosine of the center-to-limb angle. For the disk center, we find R=2.74, and for near-limb areas with μ=0.3, R equals 1.32. There is only a small dependence of R on the spatial resolution. Our results are rather close to those published three decades ago, but differ significantly from recent magnetographic observations. An application of our results to the important SOHO/MDI magnetic data calibration issue is discussed. We conclude that the revision of the SOHO/MDI data, based only on the comparison of magnetic-field measurements in the line pair Fe i 523.3 nm and Fe i 525.0 nm (increasing by a factor of 1.7 or 1.6 on average according to recent publications) is not obvious and new investigations are urgently needed.

Interferometric properties of pulsating C-rich AGB stars

We present the first theoretical study on center-to-limb variation (CLV) properties and relative radius interpretation for narrow and broad-band filters, on the basis of a set of dynamic model atmospheres of C-rich AGB stars. We computed visibility profiles and the equivalent uniform disc radii (UD-radii) in order to investigate the dependence of these quantities upon the wavelength and pulsation phase. After an accurate morphological analysis of the visibility and intensity profiles determined in narrow and broad-band filter, we fitted our visibility profiles with a UD function simulating the observational approach. UD-radii have been computed using three different fitting-methods to investigate the influence of the sampling of the visibility profile: single point, two points and least square method. The intensity and visibility profiles of models characterized by mass loss show a behaviour very different from a UD. We found that UD-radii are wavelength dependent and this dependence is stronger if mass loss is present. Strong opacity contributions from C2H2 affect all radius measurements at 3 micron and in the N-band, resulting in higher values for the UD-radii. The predicted behaviour of UD-radii versus phase is complicated in the case of models with mass loss, while the radial changes are almost sinusoidal for the models without mass loss. Compared to the M-type stars, for the C-stars no windows for measuring the pure continuum are available.

Discriminant analysis of solar bright points and faculae

While photospheric magnetic elements appear mainly as Bright Points (BPs) at the disk center and as faculae near the limb, high-resolution images reveal the coexistence of BPs and faculae over a range of heliocentric angles. This is not explained by a "hot wall" effect through vertical flux tubes, and suggests that the transition from BPs to faculae needs to be quantitatively investigated. To achieve this, we made the first recorded attempt to discriminate BPs and faculae, using a statistical classification approach based on Linear Discriminant Analysis(LDA). This paper gives a detailed description of our method, and shows its application on high-resolution images of active regions to retrieve a center-to-limb distribution of BPs and faculae. Bright "magnetic" features were detected at various disk positions by a segmentation algorithm using simultaneous G-band and continuum information. By using a selected sample of those features to represent BPs and faculae, suitable photometric parameters were identified in order to carry out LDA. We thus obtained a Center-to-Limb Variation (CLV) of the relative number of BPs and faculae, revealing the predominance of faculae at all disk positions except close to disk center (mu > 0.9). Although the present dataset suffers from limited statistics, our results are consistent with other observations of BPs and faculae at various disk positions. The retrieved CLV indicates that at high resolution, faculae are an essential constituent of active regions all across the solar disk. We speculate that the faculae near disk center as well as the BPs away from disk center are associated with inclined fields.

On the intensity contrast of solar photospheric faculae and network elements

Sunspots, faculae and the magnetic network contribute to solar irradiance variations. The contribution due to faculae and the network is of basic importance, but suers from considerable uncertainty. We determine the contrasts of active region faculae and the network, both as a function of heliocentric angle and magnetogram signal. To achieve this, we analyze near-simultaneous full disk images of photospheric continuum intensity and line- of-sight magnetic eld provided by the Michelson Doppler Interferometer (MDI) on board the SOHO spacecraft. Starting from the surface distribution of the solar magnetic eld we rst construct a mask, which is then used to determine the brightness of magnetic features, and the relatively eld-free part of the photosphere separately. By sorting the magnetogram signal into dierent bins we are able to distinguish between the contrasts of dierent concentrations of magnetic eld. We nd that the center-to-limb variation (CLV) of the contrast changes strongly with magnetogram signal. Thus, the contrasts of active region faculae (large magnetogram signal) and the network (small signal) exhibit a very dierent CLV, showing that the populations of magnetic flux tubes that underly the two kinds of features are dierent. The results are compatible with, on average, larger flux tubes in faculae than in the network. This implies that these elements need to be treated separately when reconstructing variations of the total solar irradiance with high precision. We have obtained an analytical expression for the contrast of photospheric magnetic features as a function of both position on the disk and spatially averaged magnetic eld strength, by performing a 2-dimensional t to the observations. We also provide a linear relationship between magnetogram signal and the =c os(), where is the heliocentric angle, at which the contrast is maximal. Finally, we show that the maximum contrast per unit magnetic flux decreases rapidly with increasing magnetogram signal, supporting earlier evidence that the intrinsic contrast of magnetic flux tubes in the network is higher.

Center‐to‐Limb Variation of Solar Granulation from Partial Eclipse Observations

We have measured the center-to-limb variation (CLV) of parameters describing geometric and photometric statistical properties of the solar granulation at 6708 A. This work is based on an excellent series of white-light images obtained with the Swedish Vacuum Solar Telescope at Roque de los Muchachos Observatory, La Palma, during the partial solar eclipse of 1994 May 10. The lunar limb profile, which is visible in each frame, was used as a calibration tool for estimating the point-spread function of the combined optical system formed by the atmosphere and the telescope. Before restoration, noise was removed from the images by a novel application of the so-called optimum filter for two-dimensional objects. The latter was optimized in terms of rms error and was constructed from very precise smoothed models of the specific power spectrum of the granulation at each position on the solar disk. The determination of the positions on the solar disk was achieved with high accuracy by matching the position of the Moon's limb in our images to a numerical simulation of the eclipse geometry. The CLV curve of the ΔIrms granular contrast shows one of the steepest gradients among those reported in the literature and quite a high value (9.6%) at the disk center considering that our working wavelength is in the far-red range of the solar spectrum. The elliptical shape of the restored power spectra with ellipticities equal to those expected just from foreshortening proves that radiative transfer effects do not alter the isotropy of the horizontal intensity pattern of the solar granulation, at least up to μ = 0.4. The mean wavenumber, , derived from the two-dimensional power spectra azimuthally integrated along the ellipses amounts to a value of 6.15 Mm-1 at the center of the solar disk and then shows a decrease toward the limb. Apart from the power spectra analysis, a direct statistical study of the granulation size and brightness, based on the image segmentation for defining granular contours, has also been performed. A general increase in both granular and intergranular areas is found as we move toward the solar limb. The mean granular cell area varies from 1.36 Mm2 at μ = 1 up to 2.06 Mm2 at μ = 0.6, and in parallel, the granular filling factor (the percentage of area of the image covered by granules) decreases from 44.2% to 42.8%. In the small area range, the granular brightness increases linearly with the granular cell size and is preserved constant, on average, for granular cells larger than ~20. No slope variation is found for the intergranular intensities versus granular cell areas. Observations close to the solar limb detect granular structures as small as 053 or even smaller up to a distance of at least ≈05 from the limb, showing that the ΔT associated with the granulation persist at least until z ≈ 200 km. However, this penetration could be different for small and large granules because we find several hints indicating the progressive disappearance of small structures toward the limb.

On the Determination of the Quiet-Sun Center-to-Limb Variation in Ca II K Spectroheliograms

We present a method for the determination of the center-to-limb variation (CLV) for Caii K spectroheliograms. It is based on the calculation of intensity histograms for rings of constant area. Using a simple cutoff criterion in the cumulative histograms, we are able to derive CLVs of the quiet Sun regardless of the solar activity level. Using an example from the literature, we show in which way different methods of normalization of the quiet-Sun CLV may affect the results.

Active Region Magnetic Fields. I. Plage Fields

We present observations taken with the Advanced Stokes Polarimeter (ASP) in active-region plages and study the frequency distribution of the magnetic field strength (B), inclination with respect to vertical (γ), azimuthal orientation (χ), and filling factor (f). The most common values at disk center are B = 1400 G, γ < 10°, no preferred east-west orientation, and f = 15%. At disk center, there is a component of weak (<1000 G), more horizontal fields that corresponds to arching field lines connecting footpoints of different polarities. The center-to-limb variation (CLV) of the field strength shows that, close to the limb (μ = 0.3), the field strength is reduced to 800 G from its disk-center value. This can be interpreted as a gradient of B with height in solar plages of around -3 G km-1. From this CLV study, we also deduce that magnetic field lines remain vertical for the entire range of heights involved. A similar analysis is performed for structures found in active regions that show a continuous distribution of azimuths (resembling sunspots) but that do not have a darkening in continuum. These azimuth centers show slightly larger values of B than normal plages, in particular at their magnetic center. Filling factors are also larger on average for these structures. The velocities in the magnetic component of active regions have been studied for both averaged Stokes profiles over the entire active region and for the spatially resolved data. The averaged profiles (more representative of high filling factor regions) do not show any significant mean velocities. However, the spatial average of Doppler velocities derived from the spatially resolved profiles (i.e., unweighted by filling factor) show a net redshift at disk center of 200 m s-1. The spatially resolved velocities show a strong dependence on filling factor. Both mean velocities and standard deviations are reduced when the filling factor increases. This is interpreted as a reduction of the p-mode amplitude within the magnetic component. Strong evidence for velocities transverse to the magnetic field lines has been found. Typical rms values are between 200 and 300 m s-1, depending on the filling factor. The possible importance of these transverse motions for the dynamics of the upper atmospheric layers is discussed. The asymmetries of the Stokes profiles and their CLV have been studied. The averaged Stokes V profiles show amplitude and area asymmetries that are positive at disk center and become negative at the limb. Both asymmetries, and for the two Fe I lines, are maximized away from disk center. The spatially resolved amplitude asymmetries show a clear dependence on filling factor: the larger the filling factor, the smaller the amplitude asymmetry. On the other hand, the area asymmetry is almost independent of the filling factor. The only observed dependence is the existence of negative area-asymmetry profiles at disk center for filling factors smaller than 0.2. Around 20% of the observed points in a given plage have negative area asymmetry. The amplitude asymmetry of Stokes V is, on the other hand, always positive. The amplitude asymmetries of the linear polarization profiles are observed to have the same sign as the Stokes V profiles. Similarly, the same CLV variation of the linear polarization amplitude asymmetries as for Stokes V has been found. The scenarios in which this similarity can exist are studied in some detail.

Precision IR and visible solar photometry

A precision Solar Photometric Telescope (SPT) was constructed to study the large-scale thermal structure of the solar photosphere. This instrument does full-disk, broad-band (10 nm FWHM), two-color (500 and 650 nm) imaging of the solar photosphere. Data obtained by the SPT reveals network structures correlated with the supergranulation velocity field, and the CaK network of the chromosphere. Infrared array photometry extends these measurements to 1.6 and 2.2 micron. The observed correlation of the network brightness signal with the CaK network is positive at visible wavelengths. The correlation between the network at the opacity minimum (1.6 micron) and in the higher photosphere (2.2 micron) is positive also. The root-mean-square (r.m.s.) amplitude of the contrast at disk center is (2.34 ± 0.38) × 10-3, (1.83 ± 0.51) × 10-3, (1.02 ± 0.21) × 10-3, and (1.11 ± 0.21) × 10-3 for the green, red, H, and K band, respectively. It is consistent with a brightness temperature modulation of 2.9 K. The r.m.s. amplitude of the contrast of active region network shows a large increase toward the limb, and the quiet region network shows little center-to-limb variation (CLV). Power-spectrum analysis shows that the bright facular points in the active regions appear in the form of enhanced network.

Red shift of spectral lines in the Sun's chromosphere

An unexplained center-to-limb variation (CLV) of solar wavelengths has been known for 75 years. A theory is described which not only explains this variation but also predicts its amplitude without the use of any adjustable parameter. The model considered is based on the fact that the momentum transfer of the solar photons to the electrons of the atoms of the solar atmosphere produces secondary radiation due to bremsstrahlung. The energy of this bremsstrahlung radiation is taken away from the energy of the initial photons and leads to a red shift. No ad hoc parameters are used, and all constants are either fundamental physical constants or well-known solar parameters. The model can explain the variation of the CLV as a function of its position on the disk and near the limb, and even the change in the lineshapes especially near the limb. >