Center-to-limb variations in the two-dimensional contrast of photospheric faculae

A semi-empirical model of a facular flux tube has been used to determine its center-to-limb appearance. The model is that of Osherovich et al. (1983). This model is in MHSE and includes tension forces. Results are presented in the form of contour maps, cross-sections of the contrast on axis, and integrated contrast as a function of viewing angle. Results are generally consistent with those of Caccin and Severino (1979), but not with observations of Chapman and Klabunde (1982).     

Reference models of sunspot chromospheres

Recent observational and theoretical studies of the structure of umbral chromosphres have led us to propose new models of the region. We combine space and ground based determinations of the densitytemperature structure of the transition region with existing Caii H, K, and IR triplet spectral data to establish relatively high density, gradient models of the sunspot chromosphere.Avrett in 1981 presented theSunspot Sunspot Model which can be characterized as a physically extended, low density, plateau model. However, in a similar study, the authors (Beebeet al., 1982) pointed out that the relatively high transition region pressures derived from space observations indeed are required to reproduce high resolution Caii spectral features. Studies of the umbral chromosphere as a resonant cavity for slow-mode magneto-acoustic waves producing umbral oscillations (Zhugzhdaet al., 1984) also lead to atmospheres of relatively small physical thickness, thus higher densities.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Constructing Semi-Empirical Sunspot Models for Helioseismology

One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun τ ₅₀₀₀=1 level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). The OPAL equation-of-state tables are used to derive the sound-speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1 Mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic-field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45° at the umbral – penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p ₁, and p ₂ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations.     

A comparison of synthetic and measured solar continuum intensities and limb darkening coefficients

Absolute continuum intensities and wavelength-dependent low-order polynomial fits to optical and infrared continuum limb darkening provide useful discriminants among single-component models of the solar photosphere. The thermal structure in best quantitative agreement with the recent center-limb measurements by Pierce and Slaughter (1977) and by Pierce et. al. (1977) is the semi-empirical model by Vernazza, Avrett and Loeser (VAL). However, the VAL model M temperatures must be scaled upward by a factor of 1.015 ±0.005 to be consistent with the Labs and Neckel absolute calibration of continuum high points in the optical region 0.40–0.65 m.     

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009a, 2009b). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.     

On the diagnostic of magnetic fields in sunspots through the interpretation of stokes parameters profiles

The inversion routine proposed by Aueret al. (1977), for the determination of vector magnetic fields from Stokes profiles, has been generalized to include magneto-optical and damping effects. Synthetic profiles have then been generated from a sunspot model atmosphere accounting for the depth variation of the relevant physical parameters such as the magnetic field amplitude, inclination angle, etc...., each variation being considered one at a time. Alfvén waves and magnetic inhomogeneities over the field of view have also been considered. These synthetic profiles have been presented to the inversion routine. The results of the fits show that the magnetic field amplitude and direction are always recovered with good accuracy when these quantities are constant in the model atmosphere, and, in those cases where te magnetic field vector is supposed to vary monotonically with optical depth, the values recovered are always intermediate between the values corresponding to the top and bottom of the atmosphere. Moreover, we found that the differences between synthetic and best-fit profiles are able to characterize, in many cases, the particular physical situation considered.     

A method for the determination of the lithium abundance in sunspots: Observations for 2011

Sunspot spectra for LiI 6708Å lines and for several FeI and CaI lines were obtained. Observations were performed in January and in August, 2011 using the TST-2 telescope with a charge-coupled camera at the Crimean Astrophysical Observatory. The sunspot models were calculated by using the observing profiles of FeI and CaI lines. Lithium abundance was determined by using the calculated sunspot models and LiI 6708Å observed profiles; this equals log(N _Li) = 0.98 and 0.95 (in the scale logA(H) = 12.0).     

On the electron density in sunspot plumes

Skylab observations of EUV line intensities in sunspot plumes, reported by Noyes et al. (1985), have been used to determine electron densities from theoretical curves of MgVI and MgVIII density-sensitive line ratios.     

The solar UV continuum 1440–1680 Å and its center-to-limb variation

The solar UV continuum has been derived from intensity-calibrated observations with the High-Resolution Telescope and Spectrograph - HRTS - on its second rocket flight in 1978. A database has been constructed using the spatially-resolved solar spectrum 1180–1700 Å along a slit extending from near disk center to the solar limb and crossing a sunspot and two active regions. The angular resolution is approximately 1.8″. The data consist of 1772 spectral scans in the full center-to-limb range, including both quiet and active solar regions. The distribution of solar UV intensities has been derived and the center-to-limb variations of the continuum intensities in the quiet Sun are studied. Both quantities show spectral variations, particularly across the Sii continuum edge at 1521 Å. The spectra have been fitted to curves of constant color temperature above and below the Sii edge. The derived center-to-limb variations have been compared to the values of Samain (1979) which are frequently referred to in the literature. A relatively large discrepancy may be explained by the higher spectral and angular resolution of the HRTS as compared to the rocket instrument used by Samain. Comparisons with the VAL III model calculations by Vernazza, Avrett, and Loeser (1981) show discrepancies between the observations and the model predictions, particularly with regard to the sign and amount of the intensity change across the Sii continuum edge. It is noted that some of the results presented, i.e., absolute intensities and brightness temperatures may change, pending confirmation of the SUSIM Spacelab 2 irradiance results (VanHoosieret al., 1988).     

Intensity profiles of a sunspot near the solar limb

Photo-electric observations of the intensity profile of a sunspot at a heliocentric angle of 76° at four wavelengths are reported. An intensity peak at the centre-side penumbra-photosphere border predicted by Jensen et al. (1969) has been observed.     

The effects of sunspots on solar irradiance

Sunspots have an obvious direct effect upon the visible radiant energy falling upon the Earth. We show how to estimate this effect and compare it quantitatively with recent observations of the solar total irradiance (Willson et al., 1981). The sunspots explain about half of the total observed variance of one-day averages. Since the sunspot effect on irradiance produces an asymmetry of the solar radiation, rather than (necessarily) a variation of the total luminosity, we have also estimated the sunspot population on the invisible hemisphere. This extrapolation allows us to estimate the true luminosity deficit produced by sunspots, in a manner that tends toward the correct long-term average value. We find no evidence for instantaneous global re-emission to compensate for the sunspot flux deficit.     

Automation of Area Measurement of Sunspots

When drawing up a database for sunspots from a large collection of white-light films, a need for the automation of the process arises. The concepts used at the automation of the area measurements of sunspots are described. As an example, sunspot groups NOAA 5521 and 5528 are processed and the areas obtained are compared to the measurements published in the literature. Similar values are obtained, except umbral areas published by Steinegger et al. (1996) which are significantly larger than ours. We find that the differences may be attributed to the fact that the definition proposed by Steinegger et al. (1996) for the penumbra–umbra border of a sunspot is not equivalent to those used for the measurements of others of the umbral area.     

Interpretation of oscillations in UV lines observed above sunspot umbrae

Our theory of a resonator for slow magneto-atmospheric waves in the chromosphere of a sunspot umbra has been used to check different models of the structure of the chromosphere and transition region. Oscillations of velocity and intensity in Civ, Siiv, and Oiv lines observed by Gurman et al. (1982) on the SMM spacecraft have been compared with the calculated oscillations. The observed spectrum of resonant peaks could well be explained by a gradient model of the umbral chromosphere. Different assumptions concerning the structure of the transition region do not influence the calculated resonance periods, but the amplitudes and phases of oscillations are modified. There is strong evidence for a concentration of the observed oscillations in cold fine structure elements of the transition region, even if the filling factor of such elements is very small (some few percent). Isothermal rather than adiabatic oscillations in the cold elements should be assumed in order to explain the observed fluctuations of line intensity; the relative amplitudes of pressure oscillations in the hot main component with a steep gradient of temperature are too small to explain the observed intensity fluctuations.     

The structure of a sunspot

Typical intensity profiles across a sunspot at several heliocentric angles are selected from recent observations of the Wilson Effect. In addition, the profile of the mean intensity at the surface of the spot is inferred from these observed profiles.With these data, the transfer equation is solved for the two-dimensional source function distribution within the sunspot for several models of the opacity distribution. For an opacity model in which unit optical depth in the umbra occurs at least 700 km below unit optical depth in the mean photosphere, it is possible to reproduce qualitatively all the features of the observed profiles.Although no assumption is made about the extent of the umbra below the surface, these solutions clearly show that, at a depth of 700 km below unit optical depth in the photosphere, the diameter of the umbral region, which is 10800 km at the surface, has increased to about 12000 km. Thus the shape of the umbral region below the surface is part of an inverted cone of semi-vertical angle approximately 45°. The run of gas pressure and density in the umbra is computed for the model and compared with the corresponding photospheric values.Of the National Bureau of Standards and University of Colorado.     

Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

The propagation of solar waves through the sunspot of AR?9787 is observed by using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magnetohydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere and less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.     

The 17-month periodicity of sunspot activity

A statistical study of sunspot activity during 1969 to 1986 was carried out by using the number of sunspot groups and their areas. We found a 17-month periodicity, which is consistent with the 500-day periodicity of flare occurrence (Ichimoto et al., 1985).Contributions from the Kwasan and Hida Observatories, University of Kyoto, No. 281.     

Detailed comparison between sunspot activity in ‘hot spots’ and galactic cosmic-ray intensity

The influence of sunspot activity on the condition of the solar-terrestrial environment during cycle 21 was examined using the data of sunspots and the modulation of the galactic cosmic-ray intensity. The hot spots discussed by Ichimoto et al. (1985) and Bai (1987a, 1988) were also found by analyzing the longitudinal distribution of sunspot groups.A detailed comparison between the time change of the sunspot activity in hot spots and that of the galactic cosmic rays observed by the neutron monitor reveals that several transient diminutions of the GCR intensity (with much longer duration than a Forbush decrease) occur at nearly the same time as the sporadic enhancement of sunspot area in the hot spots.Contributions from Kwasan and Hida Observatories, Kyoto University No. 303.     

Seismology of sunspot atmospheres

The present work deals with the theory of oscillations with periods of about 3 min observed in the chromosphere above sunspot umbrae. The model of these oscillations (slow mode magneto-acoustic waves trapped in a chromospheric resonant cavity) provides an independent method of checking empirical models of the chromosphere above sunspots. Making use of this method, we investigate sunspot models which have been derived from spectroscopic data; the calculated periods of the oscillations fit well the observed periods.     

The north–south asymmetry of filaments in solar cycles 16–21

In the present study, the north–south asymmetry of filaments in solar cycles 16–21 is investigated with the use of the solar filaments observed at the Observatoire de Paris, Section de Meudon from March 1919 to December 1989. Filament activity is found regularly dominated in each of cycles 16–21 in the same hemisphere as that inferred by sunspot activity, and it is found to run in a different asymmetrical behavior at different latitudinal bands, suggesting that the north–south asymmetry of filament activity should be a function of latitudes. The regularity on the north–south asymmetry of sunspot activity given by Li et al. (2002b) is demonstrated by filament activity. The periods in the north–south asymmetry of solar filament activity are 9.13, and 12.8 years without the solar cycle found.     

On the IAU 2000/2006 precession–nutation and comparison with other models and VLBI observations

In this paper, we discuss the fundamental aspects of the semi-analytical precession–nutation models that were adopted by IAU Resolutions in 2000 and 2006. We show that no significant discrepancies appear between those models (Mathews et al., J Geophys Res 107:B4, ETG 3-1–3-26, 2002, Capitaine et al., Astron Astrophys 412:567– 586, 2003) and other semi-analytical solutions or the INPOP06 numerical integration (Fienga et al., Astron Astrophys 477:315–327, 2008), especially for the quadratic terms. We also report on the most recent comparisons of the models with VLBI observations. We have employed different empirical models to fit the residuals, in attempting to characterize the nature of the observed curvature. The efficiencies of those empirical models are compared and their interpretations in terms of physical mechanisms are discussed. We show that a combination of linear and 18.6-year corrections is the most credible model for explaining the currently observed residuals, but that a longer span of observations is required before the true character of the effect can be determined. We note that the predictions from the ERA-2005 theory (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006) have diverged from recent VLBI results and suggest that the empirical nature of the ERA model is responsible.