The influence of faculae on sunspot heat blocking

We study the influence of faculae on sunspot heat blockage using a thermal model based on eddy heat diffusion through the convection zone. The facula is represented as a localized area of excess emission surrounding the sunspot, which is represented as a thermal plug. Our computations using a range of reasonable combinations of spot and facular depths show no significant influence of the facula on the long storage times of heat blocked by sunspots. However, the local cooling of surface layers produced by excess facular emission in this model propagates globally within the convection zone in a similar way to the heating produced by a spot. The net effect of spots and faculae on L over time scales longer than an active region lifetime should thus be determined by the global sum of sunspot flux deficits and facular excesses.     

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,     

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.     

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.     

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.     

Sunspot photometry and the total solar irradiance deficit measured in 1980 by ACRIM

Until now a simple Photometric Sunspot Index (PSI) model was used (e.g. Willsonet al., 1981) to describe the contribution of sunspots to the solar irradiance deficit measurement by ACRIM. In this work we replace this model by a photometry of sunspot pictures for the period of 19 August to 4 September, 1980 taking into account the individual features, like lightbridges or umbral dots, of each spot. The main results of this preliminary analysis are: (1) theA _u/A _p ratios and alsos the values vary in a wide range and are by no means constant as in the PSI model; (2) the general trend of the irradiance deficit from our analysis agrees well with the ACRIM measurements; (3) on some days there are differences of more than 50% between the deficits derived from our measurements and from the PSI model.Paper presented at the 11th Eurpean Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain     

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.     

Time profiles of solar irradiance dips

ACRIM data have been analyzed to study the time profiles of simple irradiance dips caused by single active regions. Comparison of the average characteristics of the dips appearing in the minimum and maximum of the solar cycle shows that there are no significant differences. In both periods we disclosed the facular irradiance excess in the profile wings having typical duration of two to three days and an amplitude of about 20% of the dip amplitude. The profiles were asymmetric, with a stronger and longer excess in the trailing wing. We determined an average profile which was attributed to an idealized active region, and we calculated the luminosity perturbation caused by it. Excess radiation in the wings of the profile compensates about 1/3 of the deficit in the dip. In the most simple case from our sample we compared the profile based on ACRIM measurements and the proxy profile estimated using sunspot and plage areas published in Solar Geophysical Data catalogues. The comparison indicates that the facular excess was compensating instantaneously about 2/3 of the luminosity deficit caused by sunspots.     

On the interpretation of the π-component splitting in sunspot spectra

It is shown that in order to explain the observed splitting of the -component in the sunspot umbra spectrum by the hypothesis of the coexistence in sunspots of weak- and strong-field regions with opposite polarities, one has to admit the additional assumption that in the weak-field regions the Doppler halfwidth ( _D) and the ratio between line opacity and continuum opacity ( ₀) are both less than those in the strong-field regions.     

A new type of a photoelectric magnetograph

The electro-optic deflector as an analyzer of circular polarization in the photoelectric magnetograph is described. The electro-optic deflector consists of an electro-optic crystal and a polarizing beamsplitter. The plane bifurcation of this beamsplitter coincides with the spectrograph dispersion direction. The beamsplitter bifurcates a spectral line in two components. The distance between them is ₀. The photometer slit is situated between these components. Both components of Zeeman splitting fall on the photometer slit but the distance between them varies from ₀ + 2 _H to ₀ – 2 _H (where _H is the Zeeman splitting) with the electric voltage frequency applied to the electro-optic crystal. The intensity variations at the photometer slit are proportional to 4 _H .     

Solar irradiance modulation by active regions during 1980

The solar irradiance modulation due to active regions during 1980 has been investigated in detail. Specifically, we estimate the uncertainties caused by ground-based data used as input in the modeling effort, and by our currently incomplete knowledge of the proper parameters that describe the angular variation of sunspot and facular contrasts. We conclude that the most significant uncertainties are due to errors in area measurements and, possibly, varying spot and facular brightness. A standard model for later use is derived by a best-fit technique of the currently available ACRIM irradiance data and the predictions of our models with appropriately varied parameters. Finally, we compute the expected irradiance for the entire year of 1980.NRC Senior Research Associate on leave from the Joint Institute for Laboratory Astrophysics and the Astro-Geophysics Department, University of Colorado at Boulder, Colo., U.S.A.     

On the Facular Area Surrounding Decaying Sunspots

The change in facular area around decaying sunspots is investigated. The data are from full-disk photometric images from CFDT1 (5 arc sec pixels) obtained at the Ca ii K-line = 393.4 nm. The 31 active regions are from a list previously used to study the decay rate of sunspots. We find a weak, marginally significant relation between spot decay rate and growth of the surrounding facular region (r² = 0.1255). We conclude that, for this group of decaying sunspots, the growth or decay of the surrounding facular region was not clearly related to the decay rate of an active regions sunspots.     

The kinematics of 512 stars in the system of FK5

The proper motions of 512 stars reduced to the system of FK5 were used for the determination of the velocity components X,Y,Z of the solar motion, Dort's constants A,B, and corrections n, k to Newcomb's precession values. It was found that the transition from FK4 to FK5 gives negligible and unsignificant changes to all the determined quantities.     

Absolute and relative amplitudes of variations in radius of classical cepheids

On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R for SPC and 10R <R60R for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R (only Y Oph has R8R ).     

The ellipsoidal variables IV: Light variations

The V variations of ellipsoidal variables are investigated as a function of the spectral type of the primary. A model is developed on the assumption that the primary has near Main-Sequence characteristics. It is argued that the observed minimum in the V variations around spectral type F is real and is due to variations in the gravity-darkening exponent . The absolute upper limit to V variations is found to be 0.2 mag.     

An analysis of 1983 observations of facular contrast with an extreme limb photometer

Analysis of facular contrast I/I _qs from Extreme Limb Photometer (ELP) data of the summer of 1983 yield a mean contrast of 0.91 ± 0.19% and 1.57 ± 0.16% for apertures 1 and 2 located at = 0.198 and at = 0.111, respectively. The ratio of the mean contrast in the outer aperture (closer to the limb) to that of the inner one is 1.71 ± 0.40, indicating an increase in the mean facular contrast toward the limb. This result is in agreement with observations made in 1975, 1979, and 1982. The errors are dominated by the random presence of solar active regions. The combined results from all seasons follow an approximately ^–1 curve. Facular excess solar oblateness signals for 1983 are 33.8 ± 6.6 arc ms and 16.5 ± 2.1 arc ms for ELP apertures 1 and 2, respectively, in reasonable agreement with the 1983 excess solar oblateness results of Dicke, Kuhn, and Libbrecht (1985).     

On the difference in darkness between sunspots

The effects of the magnetic field as well as the velocity field on sunspot equilibrium are discussed. The gas pressure difference, P, between a spot and the environments in the same horizontal layer is primarily determined by the magnetic field. Using recent model atmospheres we find that P shows a maximum value, P _max, at a depth of 650 ± 150 km below the photosphere. The value of P _max suggests that the curvature of the field lines is important for the equilibrium.It appears that, at an optical depth of unity in the umbra, the density has a value close to that of the environment at the same geometric depth (see Figure 4). If such is the case the expression for the umbra temperature (Equation (15)) may be considerably simplified (Equations (17) and (18)) and compared with observations.     

Facular structures derived from precise two-color contrast observations

A precise solar surface photometric observing system was developed and intensity observations of the whole Sun were carried out at a fairly quiet period from December 1987 to April 1988, attaining the photometric accuracy of 10^–3. Using 28 days observation of 4 hours duration each and 0.3 s time interval, we obtained the center-to-limb variation of the ratio of the facular intensity contrast (I _f÷I_o) between two colors of 545 nm (G) and 770 nm (R): (I _f÷I₀)_G÷(I_f÷I₀)_R = 2.20 – 1.16, where is the direction cosine between the line of sight and the surface normal. While this relationship was obtained mostly for active regions from the whole Sun data, we also found an almost identical relation for the quiet Sun network by excluding active regions. This suggests the similarity of faculae at both places.Using the above relation and the difference of optical depth, , in two colors, we found that the facular temperature gradient, dT/d _G, is smaller than that of the quiet photosphere if the gradient is measured more or less vertically (i.e., seen at > 0.7) in accord with Foukal and Duvall (1985), while it is larger than that of the quiet photosphere if the temperature gradient is measured more obliquely (i.e., seen at > 0.7). These findings are free from the low spatial resolution of the present observations because the contrast ratio was used, and also independent of a specific model of hot-wall or hillock. In particular, if the true contrast of facular bright points of 0'2 size is taken as 40% in the green from high-resolution observations, the facular point temperature may even be increasing towards higher geometrical levels ar _G 1. We found also that the area filling factor in active regions is on the order of a few percent or so in accordance with the previous studies.     

A constant-α force-free-field analysis of the active region AR 4711 of February, 1986

The theory of Yang, Chang, and Harvey (1983) is used to perform this analysis of the big active region AR 4711 of February, 1986, which produced many big and strong flares with proton events, SIDs and other significant geophysical effects. The various physical quantities are calculated, yielding for M a value up to 5.36 × 10³² erg, sufficient to supply the energies of the observed flare activities in this active region. Observations of the twisting of the entire quadrupolar sunspot group and the variations of the magnetic energies with dates all agree with our theoretical expectations.It is found that the maximum of the f number of flare activity occurred about one day later than the maximum of M, i.e., the release of free magnetic energy to produce flare activity requires a time interval of about one day. This, together with the formula of M can be useful in solar prediction work.Similar to the famous active region of August 1972 (McMath 11976), the separation of both footpoints of the new emerging magnetic flux along the neutral line of the old bipolar group led to the formation of a compact quadrupolar sunspot group, with strong twisting of penumbral filaments.Visiting Professor from the Astrophysics Division, Geophysics Department, Peking University, Beijing, China.