On the dependence of sunspot minimum intensity on area

Highly resolved photographs of 25 sunspots and pores of different areas in 2 continuous wavelengths, obtained in summer 1966 at the Sacramento Peak Observatory, have been used to reinvestigate the dependence of sunspot minimum intensity on area. Special care was taken to correct for parasitic light caused by blurring or image motion and by light scattering in the instrument and atmosphere. We find a very small, if any, dependence ofI _min on sunspot area in contradiction to older measurements but in agreement with Sitnik's and Zwaan's statements.     

Flares and changing magnetic fields

An observational study of maps of the longitudinal component of the photospheric fields in flaring active regions leads to the following conclusions:

1. The broad-wing Hα kernels characteristic of the impulsive phase of flares occur within 10″ of neutral lines encircling features of isolated magnetic polarity (‘satellite sunspots’).
2. Photospheric field changes intimately associated with several importance 1 flares and one importance 2B flare are confined to satellite sunspots, which are small (10″ diam). They often correspond to spot pores in white-light photographs.
3. The field at these features appears to strengthen in the half hour just before the flares. During the flares the growth is reversed, the field drops and then recovers to its previous level.
4. The magnetic flux through flare-associated features changes by about 4 × 10¹⁹ Mx in a day. The features are the same as the ‘Structures Magnétiques Evolutives’ of Martres et al. (1968a).
5. An upper limit of 10²¹ Mx is set for the total flux change through McMath Regions 10381 and 10385 as the result of the 2B flare of 24 October, 1969.
6. Large spots in the regions investigated did not evince flux changes or large proper motions at flare time.
7. The results are taken to imply that the initial instability of a flare occurs at a neutral point, but the magnetic energy lost cannot yet be related to the total energy of the subsequent flare.
8. No unusual velocities are observed in the photosphere at flare time.

     

Investigation of the linear polarization in infrared absorption bands

We consider the effects of the grain size, shape, structure, and chemical composition as well as the angle between the grain rotation axis and the incident ray on the full widths at half maximum (FWHM) of the polarization bands in the two deepest infrared absorption bands observed in the spectra of protostars, the water-ice band centered at 3.1 μm and the silicate band centered at 9.7 μm, using a core—mantle confocal spheroid model with various axial ratios a/b and relative volumes of the core material. We have found that the observed polarization bands with FWHM_p < 0.3 μm in the water-ice absorption band can be explained only by oblate and prolate particles with r _v ≤ 0.35 μm and the polarization bands with FWHM_p ≈ 0.3 μm can be explained only by particles with r _v ≈ 0.35 μm. Broad silicate absorption bands (FWHM ≈ 3 μm) with broad polarization bands (FWHM_p ≈ 2.7 μm) can be explained by particles with r _v ≈ 0.35 μm. Narrow silicate absorption bands (FWHM ≤ 3 μm) with any FWHM of the polarization bands can be explained by a mixture of particles of two types of olivine. Narrow polarization bands (FWHM_p ≈ 2 μm) with broad absorption bands can be explained only by very small particles, r _v ≤ 0.1 μm. We have found the relationships between the effective polarization and extinction cross sections and estimated the ranges of observed polarizabilities that can be explained by particles of given shape and orientation in each of the bands independently. Independent studies of the observational data for each of the bands are shown to give a wider choice of particle model parameters.     

Higgs field topology of a pair of sunspots and its observed manifestations

Fundamental properties of both the phase and amplitude distributions of the Higgs field characterizing a pair of equally-quantized, Abelian Higgs sunspots are examined. Guided by symmetry principles one shows that in case of equal (opposite) orientation of the spots' magnetic field the lines of a constantphase represent a family of hyperbolae (circles) passing through the centers of sunspots, F₁ and F₂, whereas the curves of a fixedamplitude are in both cases the Cassini curves with the foci F₁ and F₂. Following the hypothesis that both spots' penumbral and spot-connected filaments are stretched out along the lines of constant phase these theoretical findings are shown to mimic remarkably well the data inferred from observations.     

Relation of the coronal green line intensity to magnetic fields and sunspot areas in the solar cycle

The intensity of the green coronal Fe XIV λ530.3-nm line is correlated with sunspot areas and the magnetic field strength calculated for a distance of 1.1R _⊙. The relation of the green line emission to large-scale and local magnetic fields is shown to change differently with cycle phase. Large-scale coronal magnetic fields play a decisive role at the ascending phase, while a slightly higher correlation of the green line intensity with the local magnetic fields of sunspots is observed at the descending phase. Our results can be used to construct and test various solar coronal heating models.     

Basic properties of sunspots: equilibrium,stability and long-term eigen oscillations

A number of fundamental questions as regards the physical nature of sunspots are formulated. In order to answer these questions, we apply the model of a round-shaped unipolar sunspot with a lower boundary consisting of cool plasma and with strong magnetic field at the depth of about 4 Mm beneath the photosphere, in accordance with the data of local helioseismology and with certain physically sound arguments (the shallow sunspot model). The magnetic configuration of a sunspot is assumed to be close to the observed one and similar to the magnetic field of a round solenoid of the appropriate size. The transverse (horizontal) and longitudinal (vertical) equilibria of a sunspot were calculated based on the thermodynamic approach and taking into account the magnetic, gravitational, and thermal energy of the spot and the pressure of the environment. The dependence of the magnetic field strength in the sunspot center, B ₀, on the radius of the sunspot umbra a is derived theoretically for the first time in the history of sunspot studies. It shows that the magnetic field strength in small spots is about 700 Gauss (G) and then increases monotonically with a, tending asymptotically to a limit value of about 4000 G. This dependence, B ₀(a) includes, as parameters, the gravity acceleration on the solar surface, the density of gas in the photosphere, and the ratio of the radius of the spot (including penumbra), a _p, to the radius of its umbra a. It is shown that large-scale subsurface flows of gas in the sunspot vicinity, being the consequence but not the cause of sunspot formation, are too weak to contribute significantly to the pressure balance of the sunspot. Stability of the sunspot is provided by cooling of the sunspot plasma and decreasing of its gravitational energy due to the vertical redistribution of the gas density when the geometric Wilson depression of the sunspot is formed. The depth of a depression grows linearly with B ₀, in contrast to the quadratic law for the magnetic energy. Therefore, the range of stable equilibria turns out to be limited: large spots, with radius a larger than some limit value (about 12–18 Mm, depending on the magnetic field configuration), are unstable. It explains the absence of very large spots on the Sun and the appearance of light bridges in big spots that divide the spot into a few parts. The sunspots with B ₀≈2.6÷2.7 kilogauss (kG) and a≈5 Mm are most stable. For these spots, taken as a single magnetic structure, the period of their vertical eigen oscillations is minimal and amounts, according to the model, to 10–12 hours. It corresponds well to the period derived from the study of long-term oscillations of sunspots using SOHO/MDI data.     

Two-micron spectrophotometry of Uranus and its rings

Multiaperture K photometry and 2.0- to 2.5-μm spectrophotometry of Uranus and its ring system are presented. The photometric results are used, together with a previously published measurement, to set limits on the geometric albedos of Uranus and the rings at ～2.2 μm: (0.74 ± 0.02) × 10(su?4) ≤ p_K (Uranus) ≤ (1.5 ± 0.3) × 10^?4, and (2.7 ± 0.6) × 10^?2 ≤ p_K (rings) ≤ (3.4 ± 0.1) × 10^?2. Reflectance spectra of Uranus and Uranus plus rings show features in the planet's spectrum which are attributed to gaseous CH₄ absorption, and a 2.20-μm feature in the combined spectrum which may be due to the rings. This feature is tentatively identified with either the 2.26-μm absorption feature of NH₃ frost, or the 2.2-μm OH band exhibited by certain silicate minerals. The results of JHK photometry of Uranus' satellite, Ariel (U1), indicate that the infrared colors of this object are very similar to those of the satellites U2, U3, and U4.     

On the Possible Connection between Photospheric 5-Min Oscillation and Solar Flare Microwave Emission

Dynamic spectra of low-frequency modulation of microwave emission from solar flares are obtained. Data of 15 bursts observed in 1989–2000 with Metsähovi radio telescope at 37 GHz have been used. During 13 bursts a 5-min modulation of the microwave emission intensity was detected with the frequency of ν _I = 3.2± 0.24 (1σ) mHz. Five bursts revealed a 5-min wave superimposed on a ～1 Hz, linear frequency modulated signal generated, presumably, by coronal magnetic loop, this wave frequency is ν_fm = 3.38± 0.37 (1σ) mHz. Both intensity and frequency modulations detected are in good agreement with the data on 5-min global oscillations of photosphere and with the data on the umbral velocity oscillations observed in the vicinity of sunspots. Possible role of p-mode photospheric oscillations in modulation of microwave burst emission is discussed.     

Do the fundamental constants vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio μ = m _p/m _e was estimated by measuring the H₂ wavelengths in the spectra of distant quasars. We analyze high-resolution (FWHM≈7 km s^?1) spectra of the two damped Lyman-α systems at redshifts z _abs=2.3377 and 3.0249 observed in the spectra of the quasars Q 1232+082 and Q 0347?382, respectively. Our analysis yielded the most conservative estimate for the possible variation of μ in the past ～ 10 Gyr, Δμ/μ = (5.7 ± 3.8) × 10^?5. Since the significance of this result does not exceed 1.5σ, further observations are needed to increase the statistical significance. This is the most stringent limit on the possible cosmological variation of μ to date.     

High abnormal rotation rates of sunspots and flare productivity

Solar activity, such as flares and CMEs, affect the interplanetary medium, and Earth’s atmosphere. Therefore, to understand the Space Weather, we need to understand the mechanisms of solar activity. Towards this end, we use 1135 events of solar H_α flares and the positional data of sunspots from the archive of Solar Geophysical Data (SGD) for the period January–April, 2000 and compute the abnormal rotation rates that lead to high flare productivity. We report that the occurrence of 5 or more flares in a day in association with a given sunspot group can be defined as high flare productivity and the sunspots that have an abnormal rotation rates of ～4–10 deg day^?1 trigger high flare productivity. Further, in order to compare the flare productivity expressed as the strength of the flux emitted, especially the soft X-ray (SXR) flares in the frequency range of 1–8 Å, we compute the flare index of SXR flares and find that 8 out of 28 active regions used in this study satisfy the requirement for being flare productive. This enables us to conclude that the high rotation rates of sunspots are an important mechanism to understand the flare productivity, especially numerical flare productivity that includes flares of all class.     

Compressive and rarefactive dust-acoustic Gardner solitons beyond the K-dV limit with two-temperature ions dusty plasma

The Gardner equation is derived and numerically solved. This equation shows the existence of compressive and rarefactive dust-acoustic (DA) solitons with two-temperature ions beyond the K-dV (Korteweg–de Vries) limit. These may be referred to as DA Gardner solitons (DA-GSs). Here we deal with a dusty plasma, composed of negatively charged cold mobile dust fluids, inertialess Boltzmann electrons and ions with two distinctive temperatures. The basic features of the compressive and rarefactive DA solitons are identified. These solitons are found to exist beyond the K-dV limit, i.e. they exist for μ _i1～μ _c. Here μ _i1=n _i10/Z _d n _d0, Z _d is the number of electrons residing upon the dust grain surface, and n _i0 (n _d0) is the lower temperature ion (dust) number density at equilibrium. These DA-GSs are completely different from the K-dV solitons, because μ _c (the critical value) corresponds to vanishing of the nonlinear coefficient of the K-dV equation, and μ _i1～μ _c corresponds to K-dV solitons, with extremely large amplitude, for which the validity of the reductive perturbation method breaks down. It has been found that, depending on whether the parameter μ _i1 is less than or greater than the critical value, the DA-GSs exhibit compression for μ _i1>μ _c and rarefaction for μ _i1<μ _c. The basic features of double layers with arbitrary amplitude are also briefly discussed, employing the pseudo-potential approach. The present investigation might be relevant to the electrostatic solitary structures observed in various cosmic dust-laden plasmas, such as supernova shells, Saturn’s F-ring, the ionopause of Halley’s comet, etc.     

On the surface composition of Io

The wavelength dependence of the reflectivity of Io indicates the presence of two materials on the surface of this satellite of Jupiter. These materials are sulfur and an unspecified material (R₁) which shows a wavelength dependence of its reflectivity for 0.3 μm < λ < 1.0 μm similar to the non-H₂O frost spectrum of the rings of Saturn. A 60/40 admixture of these two spectra matches the observed reflection spectrum of Io from 0.3μm–3 μm, if the spectrum of R₁ is featureless for λ > 1 μm. Sulfur will give rise to a posteclipse brightening. The variation with wavelength of the temperature dependence of the reflectivity of sulfur will allow an observational confirmation of the presence of sulfur on Io. The material R₁ should show a large geometrical albedo. The translucency of sulfur is consistent with the polarization-phase curve to Io. The material R₁ is also required to be translucent. The thermal conductivity of a cooled sulfur powder under vacuum was measured and found to agree with the value determined for the upper layer of Io from observations at 10 μm. It is shown that this agreement is not necessarily meaningful.     

HCN fluorescence on Titan

The HCN emission features near 3 μm recently detected by Geballe et al. (2003, Astrophys. J. 583, L39) are analyzed with a model for fluorescence of sunlight in the ν₃ band of HCN. The emission spectrum is consistent with current knowledge of the atmospheric temperature profile and the HCN distribution inferred from millimeter-wave observations. The spectrum is insensitive to the abundance of HCN in the thermosphere and the thousand-fold enhancement relative to photochemical models suggested by Geballe et al. (2003, Astrophys. J. 583, L39) is not required to explain the observations. We find that the spectrum can be matched with temperatures from 130 to 200 K, with slightly better fits at high temperature, contrary to the temperature determination of 130±10 K of Geballe et al. (2003, Astrophys. J. 583, L39). The HCN emission spectrum is sensitive to the collisional de-excitation probability, P₁₀, for the ν₃ state and we determine a value of 10⁻⁵ with an accuracy of about a factor of two. Analysis of absorption lines in the C₂H₂ν₃ band near 3 μm, detected in the same spectrum, indicate a C₂H₂ mole fraction near 0.01 μbar of 10⁻⁵ for P₁₀=10⁻⁴. The derived mole fraction, however, is dependent upon the value adopted for P₁₀ and lower values are required if P₁₀ at Titan temperatures is less than its room temperature value.     

An auroral enhancement of O2λ1.27-μm emission

The ground-level zenith radiance of the atmospheric emission at λ1.27 μm was radiometrically observed to increase by a factor of approximately two with the onset of an IBC III⁺ auroral breakup above Chatanika, Alaska, on 10 March 1975. Time-resolved optical spectra clearly show that the slow component of the enhancement is associated with the (0,0) band of the infrared atmospheric system of O₂. Photometric and incoherent scatter radar data are used to define the energy-deposition profile and the absolute energy flux for the event. The magnitude of the O₂λ1.27-μm enhancement compares favourably with the predictions of an auroral excitation model which includes only secondary-electron excitation of molecular oxygen in the O₂(a¹Δ_g) source term.     

Applying an Automatic Image-Processing Method to Synoptic Observations

We used an automatic image-processing method to detect solar-activity features observed in white light at the Kislovodsk Solar Station. This technique was applied to automatically or semi-automatically detect sunspots and active regions. The results of this automated recognition were verified with statistical data available from other observatories and revealed a high detection accuracy. We also provide parameters of sunspot areas, of the umbra, and of faculae as observed in Solar Cycle 23 as well as the magnetic flux of these active elements, calculated at the Kislovodsk Solar Station, together with white-light images and magnetograms from the Michaelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). The ratio of umbral and total sunspot areas during Solar Cycle 23 is ≈?0.19. The area of sunspots of the leading polarity was approximately 2.5 times the area of sunspots of the trailing polarity.     

Correlation of parameters characterizing the latitudinal distribution of sunspots

We attempt to establish a correlation between the solar activity level and some characteristics of the latitude distribution of sunspots by means of center-of-latitude (COL) of observed sunspots. We calculate the COL by taking the area weighted mean latitude of sunspots for each calendar month during a cycle, and adopt the cycle-integrated sunspot area as a measure of the strength of a cycle. We first determine the latitudinal distribution of COL of sunspots. We then compute three different statistical correlations between the cycle-integrated sunspot areas and the fitting parameters of all sunspot cycles from 1878 to 2009. Our main findings are as follows: (1) The distribution of COL is bimodal well represented by a double Gaussian function. (2) Ignoring cycle 19, the characteristic width of the distribution of COL shows a significant correlation with the cycle amplitude. (3) A correlation between the location of the maxima of the COL distribution (either centroid₁ or centroid₂) and the sum of sunspot area can be found, when the data point corresponding to the solar cycle 19 is omitted.     

Io: Are vapor explosions responsible for the 5-μm outbursts?

It is proposed that a vapor explosion of a submerged pool of liquid sulfur will remove the crust overlying an area of ～50-km diameter. Thermal radiation from the exposed liquid sulfur pool with a surface temperature of 600 K is then presumed to be responsible for the 5-μm outbursts that have been observed. The explosive volcanoes are expected to leave black sulfur calderas, which are, indeed, found on the surface. The 5-μm outburst observed by W. M. Sinton (1980), Astrophys. J.235, L49-L51) on June 11, 1979 (UT), is identified with a new caldera found on Voyager 2 photographs but which had not been present on Voyager 1 pictures.     

Stability and regions of motion in the restricted three-body problem when both the primaries are finite straight segments

In this paper we have studied the locations and stability of the Lagrangian equilibrium points in the restricted three-body problem under the assumption that both the primaries are finite straight segments. We have found that the triangular equilibrium points are conditional stable for 0<μ<μ _c , and unstable in the range μ _c <μ≤1/2, where μ is the mass ratio. The critical mass ratio μ _c depends on the lengths of the segments and it is observed that the range of μ _c increases when compared with the classical case. The collinear equilibrium points are unstable for all values of μ. We have also studied the regions of motion of the infinitesimal mass. It has been observed that the Jacobian constant decreases when compared with the classical restricted three-body problem for a fixed value of μ and lengths l ₁ and l ₂ of the segments. Beside this we have found the numerical values for the position of the collinear and triangular equilibrium points in the case of some asteroids systems: (i) 216 Kleopatra-951 Gaspara, (ii) 9 Metis-433 Eros, (iii) 22 Kalliope-243 Ida and checked the linear stability of stationary solutions of these asteroids systems.     

The near-IR spectrum of Titan modeled with an improved methane line list

We have obtained spatially resolved spectra of Titan in the near-infrared J, H and K bands at a resolving power of ∼5000 using the near-infrared integral field spectrometer (NIFS) on the Gemini North 8 m telescope. Using recent data from the Cassini/Huygens mission on the atmospheric composition and surface and aerosol properties, we develop a multiple-scattering radiative transfer model for the Titan atmosphere. The Titan spectrum at these wavelengths is dominated by absorption due to methane with a series of strong absorption band systems separated by window regions where the surface of Titan can be seen. We use a line-by-line approach to derive the methane absorption coefficients. The methane spectrum is only accurately represented in standard line lists down to ∼2.1 μm. However, by making use of recent laboratory data and modeling of the methane spectrum we are able to construct a new line list that can be used down to 1.3 μm. The new line list allows us to generate spectra that are a good match to the observations at all wavelengths longer than 1.3 μm and allow us to model regions, such as the 1.55 μm window that could not be studied usefully with previous line lists such as HITRAN 2008. We point out the importance of the far-wing line shape of strong methane lines in determining the shape of the methane windows. Line shapes with Lorentzian, and sub-Lorentzian regions are needed to match the shape of the windows, but different shape parameters are needed for the 1.55 μm and 2 μm windows. After the methane lines are modeled our observations are sensitive to additional absorptions, and we use the data in the 1.55 μm region to determine a D/H ratio of 1.77 ± 0.20 × 10⁻⁴, and a CO mixing ratio of 50 ± 11 ppmv. In the 2 μm window we detect absorption features that can be identified with the ν₅ + 3ν₆ and 2ν₃ + 2ν₆ bands of CH₃D.     

Bimodal Distribution of Magnetic Fields and Areas of Sunspots

We applied automatic identification of sunspot umbrae and penumbrae to daily observations from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to study their magnetic flux density (B) and area (A). The results confirm an already known logarithmic relationship between the area of sunspots and their maximum flux density. In addition, we find that the relation between average magnetic flux density ( $B_{\rm avg}$ ) and sunspot area shows a bimodal distribution: for small sunspots and pores (A≤20 millionth of solar hemisphere, MSH), $B_{\rm avg} \approx 800~\mbox{G}$ (gauss), and for large sunspots (A≥100 MSH), $B_{\rm avg}$ is about 600 G. For intermediate sunspots, average flux density linearly decreases from about 800 G to 600 G. A similar bimodal distribution was found in several other integral parameters of sunspots. We show that this bimodality can be related to different stages of sunspot penumbra formation and can be explained by the difference in average inclination of magnetic fields at the periphery of small and large sunspots.