Solar irradiance variations from photometry of active regions

The Extreme Limb Photometer (ELP) has been used to measure the irradiance fluctuation of the Sun due to selected active regions. Forty-five active regions that were completely scanned at various disk positions are included in the analysis. The contribution of these active regions to a global solar irradiance fluctuation has been correlated with photometric sunspot and facular indices (PSI and PFI) using published values of sunspot and calcium plage areas. The measured ELP fluctuations are converted to a global brightness fluctuation, B/B. The sunspot component of B/B correlates with PSI with r = 0.95. The facular component of B/B correlates with PFI with r - 0.72. The expression for PFI is important to the question of energy balance between sunspots and faculae and the results presented here are not incompatible with energy balance between the two phenomena; that is the energy deficit of sunspots may be balanced by the energy excess of faculae.     

The curious case of the greenwich faculae

We analyze the record of facular areas compiled by the Royal Greenwich Observatory (RGO) from daily white-light observations between 1874 and 1976. Curiously, the relative amplitudes of the three largest sunspot cycles 17, 18, and 19 in this record are reversed when they are ranked by facular area. We show that this negative correlation arises from a general decrease of the ratioA _F/A _S, of facular to sunspot area, with increasingA _S. Within a given cycle,A _F/A _Sdecreases in active regions of largeA _S, butA _F/A _Sis also lower at allA _S, in cycles of higher peak amplitude inA _S. This decrease ofA _F/A _Sin large spot groups is consistent with its decrease in younger, more active solar-mass stars, and it may explain why stars only slightly more magnetically active than the Sun tend to exhibit much greater variability in broad-band photometry. We suggest that the physical explanation is an increased spatial filling factor of magnetic flux, favoring formation of sunspots over faculae. We also explain why the decrease inA _F/A_Sis not seen in the disc-integrated Ca K plage areas, nor in theF10.7 microwave index, both of which exhibit remarkable linearity when plotted against smoothed sunspot area. This explanation suggests how complementary data on faculae and plages from RGO and Mt. Wilson could be used to improve empirical models of total irradiance variation, extending back to 1874.     

Magnetically non-split lines in faculae

Profile changes of five magnetically non-split lines going from the photosphere to faculae are investigated. The observations show that the profiles normalized to the continuum differ from those of the undisturbed photosphere only in the core. The outer parts of the profiles remain unchanged. Calculations using two recent facular models do not represent these observed profile changes. It is shown that a temperature increase in outer layers h 250 km does explain the observations. The problem of photospheric magnetograph calibration for facula magnetic field measurements is discussed.     

The dependence of facula-photosphere contrast in molecular lines on dissociation energy

Assuming local thermodynamic equilibrium and the same relative abundances to prevail both in photosphere and faculae, the concentration-optical depth curves for molecules CH, NH, OH, C₂, CN and CO have been obtained for the four combinations of two photospheric and two facular models and the relative excesses of these molecules in the photosphere over those in faculae have been calculated. The change of photospheric model significantly affects the relationship, for a given facular model, between and D ₀, the dissociation energy of the molecule concerned. Besides, the average depth of formation in the facular models and photospheric models shows a relationship with D ₀.     

On the possibility of constructing a radiative sunspot model in magnetohydrostatic equilibrium

It is currently believed that it is impossible to construct a radiative sunspot model in magnetohydrostatic equilibrium unless magnetic fields below the surface are excessively large (> 100 kG). This belief is based on results obtained using the mixing length theory of convection. We wish to point out that by using a different theory of convection, due to Öpik (1950), it is possible to compute a radiative sunspot model in which the field becomes no greater than 9000 G. By applying two boundary conditions, (i) depth of spot equals depth of convection zone, (ii) magnetic field has zero gradient at the base of the spot, we show that a radiative spot has a unique effective temperature for a given Wilson depression, . For = 650 km, we find T _e = 3800K ; for = 150 km, T _e = 3950K. According to our model, spots having T _e cooler than these values should not exist.     

Facular models and the sunspot energy deficit

The problem of the energy deficit in a sunspot is shown to be critically related to the depth of a given sunspot model. Recent facular models are discussed and a new model is derived from recent data using a two-dimensional radiative transfer analysis. The excess non-radiative energy required by this and other models is evaluated and it is shown that in some models this may account for a considerable fraction of the sunspot energy deficit. For these models the Alfvén energy travelling along the closed flux loops from the sunspot is insufficient to supply the requirements of the faculae and it is suggested that excess energy flux from below the faculae is also required. These results provide further support for deep as opposed to shallow sunspot models.     

Polar faculae and sunspot cycles

The monthly number of polar faculae of the Sun were determined from white-light images at spectral band (eff) = (4100 ± 200) Å obtained at the Kislovodsk Solar Station during 1960–1994. Corrected monthly numbers were obtained with the help of the visibility function. The level of polar activity larger than 1 above the monthly running mean was calculated, and the relation between the polar faculae and sunspot cycle was studied. We confirmed earlier results (Makarov and Makarova, 1987) that the monthly number of polar faculae, NPF _m (t) correlates with the monthly sunspot area A _m (Sp)(t + T) with a time shift T 6 yr. The new polar faculae cycle began in the middle of 1991. Peculiarities of the first part of sunspot cycle 23 are discussed.Guest scientist with the University of Arizona and Zetetic Institute. Tucson, Arizona 85719, U.S.A.     

Facular excess radiation and the energy balance of solar active regions

Plage areas and intensities derived from CaII K spectroheliograms are used as a proxy for the facular irradiance excess of solar active regions for the period 19 August to 4 September 1980. Using a calibration method proposed by Vrnak et al. (1991), the photospheric facular index (PFI) with constant facular contrastC _p = 0.018 is replaced by a variableC _p , depending on the plage brightness. A sgnificant increase ofC _p from 0.015 to 0.025 is found for plage areas varying from a few to approx. 6 · 10³ millionths hemispheres.Combining the facular irradiance excess with sunspot deficits (as determined for the same period by Steinegger et al. 1990) yields good aggrement with the irradiance variations measured by ACRIM I, using a center-to-limb variation ofC _p according to Chapman and Meyer (1986). The ratio of facular excess to sunspot deficit (integrated over solid angle 2) decreases from values of 1.5 to 2 for regions with sunspot areas below 100 millionths hemispheres to 0.2 for sunspots of areas > 1000 millionths hemispheres,     

Heat flow near obstacles in the solar convection zone

Disturbances in the heat flow in the solar convection zone are calculated with a turbulent thermal diffusion coefficient based on a mixing length approximation. As a consequence of the radiative boundary condition at the surface and the strong increase of the diffusion coefficient with depth, the convection zone resembles a thermally superconducting shell enclosed between a thin surface layer and an interior core of low thermal conductivity. Thermal disturbances originating in the convection zone do not penetrate into the interior, and penetrate only weakly through the solar surface. A thermally isolating obstacle buried entirely in the convection zone casts a shadow of reduced temperature at the solar surface; the brightening surrounding this shadow is undetectable. The shadow is weak unless the object is located close to the surface (less than 2000 km). Assuming a sunspot to be an area of reduced thermal conductivity which extends a finite depth into the convection zone, the heat flow around this obstacle is calculated. The heat flux blocked below the spot (missing flux) spreads over a very extended area surrounding the spot. The brightening corresponding to this missing flux is undetectable if the reduction of the thermal conductivity extends to a depth greater than 1000 km. It is concluded that no effect other than a decrease of the convective efficiency is needed to explain the temperature change observed at the solar surface in and around a sunspot. The energy balance is calculated between magnetic flux tubes, oriented vertically in the solar surface, (magnetic elements in active regions and the quiet network) and their surroundings. Near the visible surface radiation enters the tube laterally from the surrounding convection zone. The heating effect of this influx is important for small tubes (less than a few arcseconds). Due to this influx tubes less than about 1 in diameter can appear as bright structures irrespective of the amount of heat conveyed along the tube itself. Through the lateral influx, small tubes such as are found in the quiet network act as little leaks in the solar surface through which an excess heat flux escapes from the convection zone.     

A New Look at Solar Irradiance Variation

We compare total solar irradiance (TSI) and ultraviolet (F _uv) irradiance variation reconstructed using Ca?K facular areas since 1915, with previous values based on less direct proxies. Our annual means for 1925??C?1945 reach values 30??C?50?% higher than those presently used in IPCC climate studies. A high facula/sunspot area ratio in spot cycles 16 and 17 seems to be responsible. New evidence from solar photometry increases the likelihood of greater seventeenth century solar dimming than expected from the disappearance of magnetic active regions alone. But the large additional brightening in the early twentieth century claimed from some recent models requires complete disappearance of the magnetic network. The network is clearly visible in Ca K spectroheliograms obtained since the 1890s, so these models cannot be correct. Changes in photospheric effective temperature invoked in other models would be powerfully damped by the thermal inertia of the convection zone. Thus, there is presently no support for twentieth century irradiance variation besides that arising from active regions. The mid-twentieth century irradiance peak arising from these active regions extends 20 years beyond the early 1940s peak in global temperature. This failure of correlation, together with the low amplitude of TSI variation and the relatively weak effect of Fuv driving on tropospheric temperature, limits the role of solar irradiance variation in twentieth century global warming.     

Latitudinal Distribution of Polar Faculae

The distribution of polar faculae with respect to latitude is investigated, using data obtained at the Ussuriysk Observatory during the years 1963–1994. To correct the data for the effect of visibility, a visibility function of polar faculae is derived. Corrected surface density of polar faculae is calculated as a function of latitude and time. During most part of each solar cycle, polar faculae exhibit pronounced concentrations at high latitudes with maxima of the surface density located near the poles. Such concentrations of polar faculae (below referred to as `polar condensations') are formed after a lapse of 1–2 years from the polar magnetic field reversals, and then they persist for 7–9 years, until the high-latitude magnetic fields again start to reverse. During several years after the sunspot minima, the polar condensations co-exist with the new latitudinal belts of polar faculae which appear at middle latitudes and then migrate toward the poles. To describe the evolution of the polar condensations quantitatively, the polar faculae density n at latitudes above 60° has been approximated by means of the power law nn ₀ cos^m where is polar angle. The parameters n ₀ and m both are found to vary during the course of the solar cycle, reaching maximum values near or shortly after the minimum of sunspot activity. At the minimum phase of the solar cycle, on average, the surface density of polar faculae varies as cos¹⁴. In addition to the 11-yr variation, the latitude–time distribution of polar faculae exhibits short-term variations occurring on the time scale of 2–3 years.     

A photometric study of faculae and sunspots between 1.2 and 1.6 μm

We investigate further the interpretation of dark magnetic faculae observed in previous imaging of the solar photosphere at 1.63 m. We show that their contrast at 1.63 m increases with magnetic flux beyond a threshold value of 2 × 10¹⁸ Mx and blends smoothly with the contrast vs flux relation measured at this wavelength for larger structures of sunspot size. Not all facular structures that are bright in Ca K are dark at 1.63 m, apparently because their magnetic flux is not large enough. After correction for blurring, the contrast of the dark faculae observed near the disc center at 1.63 m is approximately 4%. But our observations at 1.23 m, which probe slightly higher photospheric levels, do not show these dark faculae. These results indicate that magnetic flux tubes of diameter as small as 500 km significantly inhibit convective heat flow to the photosphere, much as do sunspot flux tubes of much larger diameter. They also suggest that, in even smaller flux tubes, the inhibition becomes rapidly less significant. Finally, we show that the sunspot-size dependence of umbral infrared contrast versus wavelength that we observe can probably be explained in terms of instrumental blurring. Observations with lower scattered light will be required to determine whether a real decrease of contrast with diameter also plays a role.     

Magnetic theories of solar flares

We have used the 512 channel diode array and vacuum telescope at KPNO to study the photospheric intensity distribution around sunspots, for comparison with isotherms predicted by convective blocking models of heat flow. Raster scan observations of 10 spots on 18 days were carried out in 1980 and 1981. Continuum passbands of 0.25 Å width were selected to avoid contamination by weak Fraunhofer lines, whose strength is sensitive to the presence of magnetic faculae often found near spots. Our observations show no evidence of extended bright rings around the spots at the level of 1–2%, as reported in one recent study using photographic photometry and much wider passbands. But 6 of the 10 spots we measured show marginally significant (2–3σ) bright rings of peak amplitude 0.1–0.3%. We are not able to explain these rings as a result of either residual facular signal, or instrumental effects. The excess radiative flux in these rings is small compared to the missing flux in the spot umbra and penumbra. We compare the brightness of the observed rings with peak brightnesses calculated from models of heat flow around spots of various depths and radii. Even if the spot is assumed to be unrealistically shallow, a detectable bright ring requires that the effective thermal conductivity (and/or its depth gradient) in layers surrounding the spot be significantly lower than the values indicated by mixing length models of the solar convection zone.     

Faculae and east-west asymmetry of sunspot area

Asymmetry of sunspot area with respect to the central meridian is found to depend strongly on the location of the spot group in its chromospheric facula or plage. The usual area excess for spots in the eastern half of the disk is reversed for the relatively rare spot groups situated in the following part of the plage. Qualitatively, the observed asymmetries can be explained by supposing that the apparent area of the spot is decreased by overlying bright facula, especially west of central meridian where the spot (in the usual preceding position) is viewed through the relatively bright and extensive follower part of the plage. However, the variation with central meridian distance of the mean area of spots and of faculae demands a more complex model, in which the spatial distribution of facula and plage also depends on the location of the spot group. Since both facula and spot effects are seen along the same line of sight, optical depth must change slowly with geometric depth, that is, in the active region the atmosphere is relatively transparent.     

Cloud Models for Solar Faculae

Assuming the clouds as plane parallel structures above the photosphere, center-to-limb contrast variations of various cloud models for solar faculae with approximations such as optically thin or thick, hot or cold, and with or without surface reflections, have been investigated. It has been found that the observed facular contrast data from Frazier (1971) and Taylor et al. (1998) at the 525 nm continuum is best represented by a cloud which is 230 K hotter than the undisturbed photosphere, with an optical depth =0.4283, and with isotropic surface reflections causing 11% of the background photons to be lost before penetrating into the cloud. This model and some other cloud models are shown to provide a fit better than the other physical and non-physical facular models presented previously.     

The sector structure of the active longitudes in solar cycles

The longitudinal distributions of the polar faculae, bright K Ca⁺ points, and sunspot areas have been investigated in three-year intervals at the minima and maxima of the last five solar cycles in the rotation system which corresponds to the background magnetic field:T = 27.23 days (Mikhailutsa, 1994b). It has been shown that there were three specific features of the polar faculae and bright K Ca⁺ point longitudinal distributions: (1) The longitudes of maxima and minima of the distributions were approximately the same in the last five solar cycles. (2) There were predominantly two opposite longitudinal maxima and two opposite longitudinal minima in the distributions of each hemisphere. (3) The distributions of the northern and southern hemispheres were in opposite phase. The extremes of the sunspot area longitudinal distributions were preferentially between the longitudes of the polar facular extremes. The period of the sector structure rotation was defined more precisely:T = 27.227 ± 0.003 days. The results found can serve as an indication that there is a global foursector structure seated in the solar interior which plays a visible role in the polar facular and sunspot distributions.     

An Observed Decline in the Amplitude of Recent Solar-Cycle Peaks

There has been much speculation about the extended minimum between Solar Cycles 23 and 24. Cycle 24 itself has been unusually weak compared with recent cycles. We present quantitative evidence for the weakness of both Cycles 23 and, particularly, 24. The data are objective indices derived from precision photometric images obtained on a daily basis at the San Fernando Observatory. These data form the longest running, homogeneous photometric record known to us. We show sunspot areas from red images and facular/network areas from Ca ii K-line images. Spot and facular area are a simple and direct measurement of the strength of solar activity. The data clearly show the decline in the amplitude of sunspot maxima for Cycles 23 and 24 compared with Cycle 22. The relative amplitudes of mean spot area for Cycles 22 through 24 are 1.0, 0.74, and 0.37, respectively. There is also an indication that the facular-to-spot area ratio has increased in Cycle 24.     

Statistical Characteristics of CMEs and Flares Associated with Solar Type II Radio Bursts

We present results from a study of sunspots and faculae on continuum and Caii K images taken at the San Fernando Observatory (SFO) during 1989–1992; a total of approximately 800 images in each bandpass were used. About 18000 red sunspots, 147000 red faculae, and 800000 Caii K faculae were identified based on their contrasts. In addition, we computed the contrasts of pixels on the red images cospatial with Caii K faculae. Sunspot contrasts show a strong dependence on size but no dependence on heliocentric angle. There are continuous but systematic differences among facular regions. We find that the contrast of Caii K faculae is relatively insensitive to heliocentric angle, but is a strong function of facular size, in the sense that larger Caii K faculae are always brighter. The contrast of red faculae is a function of both heliocentric angle and size: the contrast functions show that larger regions contain larger flux tubes, contain deeper flux tubes, and have larger filling factors than small facular regions. Comparisons of cospatial pixels on red and Caii K images show a tight correlation between the average contrast of a region in the continuum and its size and heliocentric angle in the Caii K images. The average contrast of all facular regions is positive everywhere on the disk, even though the largest regions contain flux tubes which appear dark at disk center.     

Multi-channel magnetograph observations

Simultaneous observations of photospheric magnetic fields, Caii K emission, the photospheric network and continuum faculae show that these four quantities are correlated in a complicated manner. The photospheric and calcium networks show increasing contrast with increasing magnetic field strength up to field strengths of about 500 G. Higher values of the magnetic field are found only in pores and sunspots. Continuum faculae also show increasing contrast with increasing magnetic field strength (even at the disk center), but this contrast reaches a maximum at field strengths of about 200 G. At higher field strengths, continuum faculae become monotonically darker until pore or spunspot conditions are reached.Measurements of the photospheric network and the continuum faculae over a wide range of result in families of limb contrast curves. These curves indicate that the dependence on H is as important as the dependence on . They also indicate that the magnetic field has a preferred inclination of about 50°. The facular contrast shows little dependence on resolution. This is interpreted in terms of a geometric model in which faculae are clumps of many individual flux tubes. These tubes are closely packed and unresolvable in the photosphere, but are more widely spaced, and therefore resolvable, in the low chromosphere.Visiting Astronomer, Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.