Analysis of He I 1083 nm Imaging Spectroscopy Using a Spectral Standard

We develop a technique for the analysis of Hei 1083 nm spectra which addresses several difficulties through determination of a continuum background by comparison with a well-calibrated standard and through removal of nearby solar and telluric blends by differential comparison to an average spectrum. The method is compared with earlier analysis of imaging spectroscopy obtained at the National Solar Observatory/Kitt Peak Vacuum Telescope (NSO/KPVT) with the NASA/NSO Spectromagnetograph (SPM). We examine distributions of Doppler velocity and line width as a function of central intensity for an active region, filament, quiet Sun, and coronal hole. For our example, we find that line widths and central intensity are oppositely correlated in a coronal hole and quiet Sun. Line widths are comparable to the quiet Sun in the active region, are systematically lower in the filament, and extend to higher values in the coronal hole. Outward velocities of 2–4 km s^–1 are typically observed in the coronal hole. The sensitivity of these results to analysis technique is discussed.     

Identification of CrH and CrD Molecular Lines in the Sunspot Umbral Spectrum

High-resolution Fourier transform spectrometer sunspot umbral spectra obtained at the National Solar Observatory/Kitt Peak were used to identify molecular rotational lines arising from the infrared band systems of CrH and CrD molecules. Measurement of the equivalent width used the Gaussian-profile approximation method, which is suitable especially for faint lines. Equivalent widths are measured for an adequate number of best lines of the A – X (0,0) band of CrH and the A – X (0,0;1,0) bands of CrD and, thereby, the effective rotational temperatures are estimated.     

Digitization of Sunspot Drawings by Staudacher in 1749 – 1796

Original drawings by J.C. Staudacher made in the period of 1749 – 1796 were digitized. The drawings provide information about the size of the sunspots and are therefore useful for analyses sensitive to sunspot area rather than Wolf numbers. The total sunspot area as a function of time is shown for the observing period. The sunspot areas measured do not support the proposition of a weak, “lost” cycle between cycles 4 and 5. We also evaluate the usefulness of the drawings for the determination of sunspot positions for future studies.     

Prediction of the Maximum Amplitude and Timing of Sunspot Cycle 24

Precursor techniques, in particular those using geomagnetic indices, often are used in the prediction of the maximum amplitude for a sunspot cycle. Here, the year 2008 is taken as being the sunspot minimum year for cycle 24. Based on the average aa index value for the year of the sunspot minimum and the preceding four years, we estimate the expected annual maximum amplitude for cycle 24 to be about 92.8±19.6 (1-sigma accuracy), indicating a somewhat weaker cycle 24 as compared to cycles 21 – 23. Presuming a smoothed monthly mean sunspot number minimum in August 2008, a smoothed monthly mean sunspot number maximum is expected about October 2012±4 months (1-sigma accuracy).     

Infrared Spectroscopy from San Fernando Observatory: He I 1083 nm, O I 1316 nm, and Fe I 1565 nm

Imaging spectroscopy of the Sun was carried out at the California State University Northridge San Fernando Observatory using an InGaAs near-IR video camera. Using the Sii 1082.71 nm and Hei 1083.03 nm lines the Evershed effect is measured simultaneously in the photosphere and the chromosphere for three sunspots; the speed of the Evershed flow is measured to be between 3 to 8 times greater in the Hei line than in the Sii line, and the direction is radially inward in the chromosphere and outward in the photosphere. Telluric absorption lines prevented a meaningful measurement of Oi 1128.7 nm limb emission, but an upper limit of 20×10^–3 B is measured for chromospheric limb emission at Oi 1316.3 nm. Zeeman splitting in Fei 1564.9 nm was observed in six sunspot umbrae, and a linear relationship between magnetic field and umbral continuum intensity is confirmed.     

Short-Term Periodicities in Sunspot Activities During the Descending Phase of Solar Cycle 23

In the present study, the short-term periodicities in the daily data of the sunspot numbers and areas are investigated separately for the full disk, northern, and southern hemispheres during Solar Cycle 23 for a time interval from 1 January 2003 to 30 November 2007 corresponding to the descending and minimum phase of the cycle. The wavelet power spectrum technique exhibited a number of quasi-periodic oscillations in all the datasets. In the high frequency range, we find a prominent period of 22 – 35 days in both sunspot indicators. Other quasi-periods in the range of 40 – 60, 70 – 90, 110 – 130, 140 – 160, and 220 – 240 days are detected in the sunspot number time series in different hemispheres at different time intervals. In the sunspot area data, quasi-periods in the range of 50 – 80, 90 – 110, 115 – 130, 140 – 155, 160 – 190, and about 230 days were noted in different hemispheres within the time period of analysis. The present investigation shows that the well-known “Rieger periodicity” of 150 – 160 days reappears during the descending phase of Solar Cycle 23, but this is prominent mainly in the southern part of the Sun. Possible explanations of these observed periodicities are delivered on the basis of earlier results detected in photospheric magnetic field time series (Knaack, Stenflo, and Berdyugina in Astron. Astrophys. 438, 1067, 2005) and solar r-mode oscillations.     

Forecasting the Time Series of Sunspot Numbers

Forecasting the solar cycle is of great importance for weather prediction and environmental monitoring, and also constitutes a difficult scientific benchmark in nonlinear dynamical modeling. This paper describes the identification of a model and its use in the forecasting the time series comprised of Wolf’s sunspot numbers. A key feature of this procedure is that the original time series is first transformed into a symmetrical space where the dynamics of the solar dynamo are unfolded in a better way, thus improving the model. The nonlinear model obtained is parsimonious and has both deterministic and stochastic parts. Monte Carlo simulation of the whole model produces very consistent results with the deterministic part of the model but allows for the determination of confidence bands. The obtained model was used to predict cycles 24 and 25, although the forecast of the latter is seen as a crude approximation, given the long prediction horizon required. As for the 24th cycle, two estimates were obtained with peaks of 65±16 and of 87±13 units of sunspot numbers. The simulated results suggest that the 24th cycle will be shorter and less active than the preceding one.     

Temperature Dependence of Molecular Line Strengths and Fe i 1565 nm Zeeman Splitting in a Sunspot

Spectroscopic observations at 1565 nm were made in the eastern half of the main umbra of NOAA 9885 on 1 April 2002 using the National Solar Observatory McMath-Pierce Telescope at Kitt Peak with a tip-tilt image stabilization system and the California State University Northridge–National Solar Observatory infrared camera. The line depth of the OH blend at 1565.1 nm varies with the observed continuum temperature; the variation fits previous observations except that the continuum temperature is lower by 600 K. The equivalent width of the OH absorption line at 1565.2 nm shows a temperature dependence similar to previously published umbral molecular observations at 640 nm. A simple model of expected OH abundance based upon an ionization analogy to molecular dissociation is produced and agrees well with the temperature variation of the line equivalent width. A CN absorption line at 1564.6 nm shows a very different temperature dependence, likely due to complicated formation and destruction processes. Nonetheless a numerical fit of the temperature variation of the CN equivalent width is presented. Finally a comparison of the Zeeman splitting of the Fei 1564.8 nm line with the sunspot temperature derived from the continuum intensity shows an umbra somewhat cooler for a given magnetic field strength than previous comparisons using this infrared 1564.8 nm line, but consistent with these previous infrared measurements the umbra is hotter for a given magnetic field strength than magnetic and temperature measurements at 630.2 nm would suggest. Differences between the 630.2 nm and 1564.8 nm umbral temperature and magnetic field relations are explained with the different heights of formation of the lines and continua at these wavelengths.     

An Analysis of the Sunspot Groups and Flares of Solar Cycle 23

Designing a statistical solar flare forecasting technique can benefit greatly from knowledge of the flare frequency of occurrence with respect to sunspot groups. This study analyzed sunspot groups and Hα and X-ray flares reported for the period 1997 – 2007. Annual catalogs were constructed, listing the days that numbered sunspot groups were observed (designated sunspot group-days, SSG-Ds) and for each day a record for each associated Hα flare of importance category one or greater and normal or bright brightness and for each X-ray flare of intensity C 5 or higher. The catalogs were then analyzed to produce frequency distributions of SSG-Ds by year, sunspot group class, likelihood of producing at least one flare overall and by sunspot group class, and frequency of occurrence of numbers of flares per day and flare intensity category. Only 3% of SSG-Ds produced a substantial Hα flare and 7% had a significant X-ray flare. We found that mature, complex sunspot groups were more likely than simple sunspot groups to produce a flare, but the latter were more prevalent than the former. More than half of the SSG-Ds with flares had a maximum intensity flare greater than the lowest category (C-class of intensity five and higher). The fact that certain sunspot group classes had flaring probabilities significantly higher than the combined probabilities of the intensity categories when all SSG-Ds were considered suggest that it might be best to first predict the flaring probability. For sunspot groups found likely to flare, a separate diagnosis of maximum flare intensity category appears feasible.     

Role of a tachyonic field in accelerating the Universe in the presence of a perfect fluid

Recently, a tachyonic field was presented as a dark energy model to represent the present acceleration of the Universe. In this paper, we consider a mixture of tachyonic fluid with a perfect fluid. For this purpose we consider barotropic fluid and Generalized Chaplygin gas (GCG). We present a particular form of the scale factor. We solve the equations of motion to get exact solutions of the density, tachyonic potential and the tachyonic field. We introduce a coupling term to show that the interaction decays with time. We also show that the nature of the potentials vary, so the interaction term reduces the potential in both cases.     

Acoustic Power Absorption and its Relation to Vector Magnetic Field of a Sunspot

The distribution of acoustic power over sunspots shows an enhanced absorption near the umbra – penumbra boundary. Previous studies revealed that the region of enhanced absorption coincides with the region of strongest transverse potential field. The aim of this paper is to i) utilize the high-resolution vector magnetograms derived using Hinode SOT/SP observations and study the relationship between the vector magnetic field and power absorption and ii) study the variation of power absorption in sunspot penumbrae due to the presence of spine-like radial structures.     

Evolution of the Level of Sunspot Activity in Solar Cycles I. Evolution in the Descending Phase

Taking the 13-point smoothed monthly sunspot number, Ri, and the deviation of the 13 associated monthly sunspot numbers from the smoothed one, D_i, as a number-pair describing the global level of sunspot activity, the evolution of the level is statistically studied for the period from the month which is just 48 months before the minimum to the minimum in the descending phase, using the observed data of Solar Cycles 10 to 22. Our results show (1) for 46 months (94%) of the studied 49 months it is found that for a given month, the distribution of the 13 pairs which come from the 13 solar cycles on a log Ri-D_i plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level α= 5%, and for 36 months (73%) the fitting is even better, for α= 1%;(2) time variations of these two parameters and their correlations in the studied period can be described respectively by functions of time, whose main trends may be expressed by a linear or simple curvilinear function; (3) the evolutionary path of the level of sunspot activity may be represented by a logarithmic function as log R_i=0.704 In D_i-0.291.     

Application of Fuzzy Sets to the Determination of Sunspot Areas

The computation of sunspot areas is important for many applications in solar physics. Some uncertainty is, however, inherent to this determination, since there is uncertainty in defining the limits of sunspots, as well as their umbrae and penumbrae, particularly in high-resolution images where large variations in intensity are observed, mainly in the penumbrae and photosphere regions. In this paper a methodology based on the classical histogram method is presented that enables the generation of fuzzy sets that correspond to the umbrae and penumbrae of sunspots, as well as to the complete sunspots, which enable the representation of the uncertainty in their locations. The areas of the sunspots and of their umbrae and penumbrae are then obtained by computing the areas of the fuzzy sets used to represent them. Two operators are used: the Rosenfeld Area operator, which generates a real number for the area, and the Fuzzy Area operator, which generates a fuzzy number, providing more information about the uncertainty of the area. A comparison of the obtained results with the area values given by the classical cumulative histogram method is made and the differences analyzed.     

Return Meridional Flow in the Convection Zone from Latitudinal Motions of Umbrae of Sunspot Groups

We have derived the velocities of meridional flows by measuring the latitudinal motions (or drifts) of umbrae of spot groups classified into three categories of area: 0 – 5 μ, 5 – 10 μ, and >10 μ (μ area in millionths of the solar hemisphere). The latitudinal drifts (or the meridional flows) in all three categories are directed equatorward in both the northern and southern hemispheres. By sorting the spot groups into three area classes, we are able to relate the respective latitudinal drifts with the three depths in the convection zone where the footpoints of the flux loops of the spot groups of each area class are anchored. We obtain estimates of the anchor depths through a comparison of the rotation rates of the spot groups of each area class with the rotation-rate profiles from helioseismic inversions. The equatorward drifts obtained provide estimates of the meridional flows at the three depths in the convection zone and thereby suggest the presence of return meridional flows as envisaged in the flux-transport dynamo models, which have remained undetected so far. The data sources for this study are measurements of positions and areas of umbrae of sunspots from the photographic white-light images of the Sun of the Kodaikanal Observatory archives for the period 1906 – 1987 and a very similar, but independent, data set from the Mt. Wilson Observatory archives for the period 1917 – 1985.     

Presence of LaO, ScO and VO Molecular Lines in Sunspot Umbral Spectra

High-resolution Fourier Transform Spectrometer sunspot umbral spectra of the National Solar Observatory/National Optical Astronomy Observatory at Kitt Peak were used to detect rotational lines from 19 electronic transition bands of the molecules LaO, ScO and VO, in the wavenumber range of 11 775 to 20 600 cm⁻¹. The presence of lines from the following transitions is confirmed: A ² Π _r1/2 – X ² Σ ⁺(0, 0; 0, 1), A ² Π _r3/2 – X ² Σ ⁺(1, 0), B ² Σ ⁺ – X ² Σ ⁺(0, 0; 0, 1; 1, 0) and C ² Π _r1/2 – A′²Δ _r3/2(0, 0; 1, 1) of LaO; A ² Π _r3/2 – X ² Σ ⁺(0, 0), A ² Π _r1/2 – X ² Σ ⁺(0, 0) and B ² Σ ⁺ – X ² Σ ⁺(0, 0) of ScO; and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 1; 1, 0; 0, 2) and (2, 0) of VO. However, the presence of A ² Π _r3/2 – X ² Σ ⁺(0, 0) and C ² Π _r3/2 – A′²Δ _r5/2(0, 0; 1, 1) of LaO and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 0) of VO are found to be doubtful because the lines are very weak, and detections are difficult owing to heavy blending by strong rotational lines of other molecules. Equivalent widths are measured for well-resolved lines and, thereby, the effective rotational temperatures are estimated for the systems for which the presence is confirmed.     

Time – Distance Modelling in a Simulated Sunspot Atmosphere

In time?–?distance helioseismology, wave travel times are measured from the cross-correlation between Doppler velocities recorded at any two locations on the solar surface. However, one of the main uncertainties associated with such measurements is how to interpret observations made in regions of strong magnetic field. Isolating the effects of the magnetic field from thermal or sound-speed perturbations has proved to be quite complex and has yet to yield reliable results when extracting travel times from the cross-correlation function. One possible way to decouple these effects is by using a 3D sunspot model based on observed surface magnetic-field profiles, with a surrounding stratified, quiet-Sun atmosphere to model the magneto-acoustic ray propagation, and analyse the resulting ray travel-time perturbations that will directly account for wave-speed variations produced by the magnetic field. These artificial travel-time perturbation profiles provide us with several related but distinct observations: i) that strong surface magnetic fields have a dual effect on helioseismic rays?–?increasing their skip distance while at the same time speeding them up considerably compared to their quiet-Sun counterparts, ii) there is a clear and significant frequency dependence of both skip-distance and travel-time perturbations across the simulated sunspot radius, iii) the negative sign and magnitude of these perturbations appears to be directly related to the sunspot magnetic-field strength and inclination, iv) by “switching off” the magnetic field inside the sunspot, we are able to completely isolate the thermal component of the travel-time perturbations observed, which is seen to be both opposite in sign and much smaller in magnitude than those measured when the magnetic field is present. These results tend to suggest that purely thermal perturbations are unlikely to be the main effect seen in travel times through sunspots, and that strong, near-surface magnetic fields may be directly and significantly altering the magnitude and lateral extent of sound-speed inversions of sunspots made by time?–?distance helioseismology.     

Periodic motions of a small body in the Newtonian field of a regular polygonal configuration of ν+1 bodies

We study the simple periodic orbits of a particle that is subject to the gravitational action of the much bigger primary bodies which form a regular polygonal configuration of (ν+1) bodies when ν=8. We investigate the distribution of the characteristic curves of the families and their evolution in the phase space of the initial conditions, we describe various types of simple periodic orbits and we study their linear stability. Plots and tables illustrate the obtained material and reveal many interesting aspects regarding particle dynamics in such a multi-body system.