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.     

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).     

The Rotation Rates of Solar Magnetic Fields During Solar Cycles 21 – 23

Employing the synoptic maps of the photospheric magnetic fields from the beginning of solar cycle 21 to the end of 23, we first build up a time – longitude stackplot at each latitude between ±35°. On each stackplot there are many tilted magnetic structures clearly reflecting the rotation rates, and we adopt a cross-correlation technique to explore the rotation rates from these tilted structures. Our new method avoids artificially choosing magnetic tracers, and it is convenient for investigating the rotation rates of the positive and negative fields by omitting one kind of field on the stackplots. We have obtained the following results. i) The rotation rates of the positive and negative fields (or the leader and follower polarities, depending on the hemispheres and solar cycles) between latitudes ±35° during solar cycles 21–23 are derived. The reversal times of the leader and follower polarities are usually not consistent with the years of the solar minimum, nevertheless, at latitudes ±16°, the reversal times are almost simultaneous with them. ii) The rotation rates of the three solar cycles averaged over each cycle are calculated separately for the positive, negative and total fields. The latitude profiles of rotation of the positive and negative fields exhibit equatorial symmetries with each other, and those of the total fields lie between them. iii) The differences in rotation rates between the leader and follower polarities are obtained. They are very small near the equator, and increase as latitude increases. In the latitude range of 5° – 20°, these differences reach 0.05 deg day⁻¹, and the mean difference for solar cycle 22 is somewhat smaller than cycles 21 and 23 in these latitude regions. Then, the differences reduce again at latitudes higher than 20°.     

Widespread Occurrence of Trenching Patterns in the Granulation Field: Evidence for Roll Convection?

Time-averaged series of granulation images are analysed using COLIBRI, a purpose-adapted version of a code originally developed to detect straight or curvilinear features in aerospace images. The image-processing algorithm utilises a nonparametric statistical criterion that identifies a straight-line segment as a linear feature (lineament) if the photospheric brightness at a certain distance from this line on both sides is stochastically lower or higher than at the line itself. Curvilinear features can be detected as chains of lineaments, using a modified criterion. Once the input parameters used by the algorithm are properly adjusted, the algorithm highlights “ridges” and “trenches” in the relief of the brightness field, drawing white and dark lanes. The most remarkable property of the trenching patterns is a nearly universally present parallelism of ridges and trenches. Since the material upflows are brighter than the downflows, the alternating, parallel light and dark lanes should reflect the presence of roll convection in the subphotospheric layers. If the numerous images processed by us are representative, the patterns revealed suggest a widespread occurrence of roll convection in the outer solar convection zone. In particular, the roll systems could form the fine structure of larger scale, supergranular and/or mesogranular convection flows. Granules appear to be overheated blobs of material that could develop into convection rolls owing to instabilities of roll motion.     

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.     

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.     

A Comparison of Solar Cycle Variations in the Equatorial Rotation Rates of the Sun’s Subsurface, Surface, Corona, and Sunspot Groups

Using the Solar Optical Observing Network (SOON) sunspot-group data for the period 1985?–?2010, the variations in the annual mean equatorial-rotation rates of the sunspot groups are determined and compared with the known variations in the solar equatorial-rotation rates determined from the following data: i) the plasma rotation rates at 0.94R_⊙,0.95R_⊙,…,1.0R_⊙ measured by the Global Oscillation Network Group (GONG) during the period 1995?–?2010, ii) the data on the soft-X-ray corona determined from Yohkoh/SXT full-disk images for the years 1992?–?2001, iii) the data on small bright coronal structures (SBCS) that were traced in Solar and Heliospheric Observatory (SOHO)/EIT images during the period 1998?–?2006, and iv) the Mount Wilson Doppler-velocity measurements during the period 1986?–?2007. A large portion (up to ≈?30^° latitude) of the mean differential-rotation profile of the sunspot groups lies between those of the internal differential-rotation rates at 0.94R_⊙ and 0.98R_⊙. The variation in the yearly mean equatorial-rotation rate of the sunspot groups seems to be lagging behind that of the equatorial-rotation rate determined from the GONG measurements by one to two years. The amplitude of the GONG measurements is very small. The solar-cycle variation in the equatorial-rotation rate of the solar corona closely matches that determined from the sunspot-group data. The variation in the equatorial-rotation rate determined from the Mount Wilson Doppler-velocity data closely resembles the corresponding variation in the equatorial-rotation rate determined from the sunspot-group data that included the values of the abnormal angular motions (>?|3^°|?day^?1) of the sunspot groups. Implications of these results are pointed out.     

Measurement of Kodaikanal White-Light Images – III. Rotation Rates and Activity Cycle Variations

The Kodaikanal sunspot data set covering the interval 1906–1987 is analyzed for differential rotation of sunspots of different sizes. As is known, smaller sunspots rotate faster than larger sunspots, and this result is verified in the analysis of this data set. These results agree well with the Mount Wilson sunspot results published earlier. The activity cycle dependence of sunspot rotation is studied. An increase in this rate at the minimum phase is seen, which has been reported earlier. It is demonstrated that this cycle variation is seen for sunspots in all size categories, which suggests that it is not a relative increase in the number of the faster-rotating small sunspots that causes the cycle dependence. These results are discussed as they may relate to subsurface dynamic properties of the Sun.     

Erratum to: Width of Sunspot Generating Zone and Reconstruction of Butterfly Diagram

Based on the extended Greenwich – NOAA/USAF catalogue of sunspot groups, it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of the SGZ. The ratio of the sunspot number to the width of the SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of the SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (Solar Phys. 179, 189, 1998), the latitude distribution of sunspot groups (“the Maunder butterfly diagram”) for the eighteenth and the first half of the nineteenth centuries is reconstructed and compared with historical sunspot observations.     

Investigation of the Solar Differential Rotation of Compact Magnetic Elements for 1966 – 1986

The differential rotation of compact magnetic elements during activity cycles 20 and 21 (1966 – 1986) is studied by using solar synoptic charts. For each hemisphere the compact magnetic elements with the polarity of the circumpolar magnetic field have larger rotation rates than the elements with the opposite polarity. This difference in rotation rates is present during the whole cycle except during the polarity reversal of the circumpolar field.     

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.     

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.     

Evidence of Magnetic Helicity in Emerging Flux and Associated Flare

The aim of this paper is to look at the magnetic helicity structure of an emerging active region and show that both emergence and flaring signatures are consistent with a same sign for magnetic helicity. We present a multiwavelength analysis of an M1.6 flare occurring in the NOAA active region 10365 on 27 May 2003, in which a large new bipole emerges in a decaying active region. The diverging flow pattern and the “tongue” shape of the magnetic field in the photosphere with elongated polarities are highly suggestive of the emergence of a twisted flux tube. The orientation of these tongues indicates the emergence of a flux tube with a right-hand twist (i.e., positive magnetic helicity). The flare signatures in the chromosphere are ribbons observed in Hα by the MSDP spectrograph in the Meudon solar tower and in 1600 Å by TRACE. These ribbons have a J shape and are shifted along the inversion line. The pattern of these ribbons suggests that the flare was triggered by magnetic reconnection at coronal heights below a twisted flux tube of positive helicity, corresponding to that of the observed emergence. It is the first time that such a consistency between the signatures of the emerging flux through the photosphere and flare ribbons has been clearly identified in observations. Another type of ribbons observed during the flare at the periphery of the active region by the MSDP and SOHO/EIT is related to the existence of a null point, which is found high in the corona in a potential field extrapolation. We discuss the interpretation of these secondary brightenings in terms of the “breakout” model and in terms of plasma compression/heating within large-scale separatrices.     

Long-Term Changes in Sunspot Activity,Occurrence of Grand Minima,and Their Future Tendencies

Long-term changes in the magnetic activity of the Sun were studied in terms of the empirical mode decomposition that revealed their essential modes. The occurrence of grand minima was also studied in their relation to long-term changes in sunspot activity throughout the past 11 000 yr. Characteristic timescales of long-term changes in solar activity manifest themselves in the occurrence of grand minima. A quantitative criterion has been defined to identify epochs of grand minima. This criterion reveals the important role of secular and bicentennial activity variations in the occurrence of grand minima and relates their amplitudes with the current activity level, which is variable on a millennial timescale. We have revealed specific patterns in the magnetic activity between successive grand minima which tend to recur approximately every 2300 yr but occasionally alternate with irregular changes. Such intermittent activity behavior indicates low dimensional chaos in the solar dynamo due to the interplay of its dominant modes. The analysis showed that in order to forecast activity level in forthcoming cycles, one should take into account long-term changes in sunspot activity on a ≈2300-yr timescale. The regularities revealed suggest solar activity to decrease in the foreseeable future.     

Combined Analysis of Solar Neutrino and Solar Irradiance Data: Further Evidence for Variability of the Solar Neutrino Flux and Its Implications Concerning the Solar Core

A search for any particular feature in any single solar neutrino dataset is unlikely to establish variability of the solar neutrino flux since the count rates are very low. It helps to combine datasets, and in this article we examine data from both the Homestake and GALLEX experiments. These show evidence of modulation with a frequency of 11.85 year⁻¹, which could be indicative of rotational modulation originating in the solar core. We find that precisely the same frequency is prominent in power spectrum analyses of the ACRIM irradiance data for both the Homestake and GALLEX time intervals. These results suggest that the solar core is inhomogeneous and rotates with a sidereal frequency of 12.85 year⁻¹. From Monte Carlo calculations, it is found that the probability that the neutrino data would by chance match the irradiance data in this way is only 2 parts in 10 000. This rotation rate is significantly lower than that of the inner radiative zone (13.97 year⁻¹) as recently inferred from analysis of Super-Kamiokande data, suggesting that there may be a second, inner tachocline separating the core from the radiative zone. This opens up the possibility that there may be an inner dynamo that could produce a strong internal magnetic field and a second solar cycle.     

Latitude Dependence of the Variations of Sunspot Group Numbers (SGN) and Coronal Mass Ejections (CMEs) in Cycle 23

The 12-month running means of the conventional sunspot number Rz, the sunspot group numbers (SGN) and the frequency of occurrence of Coronal Mass Ejections (CMEs) were examined for cycle 23 (1996 – 2006). For the whole disc, the SGN and Rz plots were almost identical. Hence, SGN could be used as a proxy for Rz, for which latitude data are not available. SGN values were used for 5° latitude belts 0° – 5°, 5° – 10°, 10° – 15°, 15° – 20°, 20° – 25°, 25° – 30° and > 30°, separately in each hemisphere north and south. Roughly, from latitudes 25° – 30° N to 20° – 25° N, the peaks seem to have occurred later for lower latitudes, from latitudes 20° – 25° N to 15° – 20° N, the peaks are stagnant or occur slightly earlier, and then from latitudes 15° – 20° N to 0° – 5° N, the peaks seem to have occurred again later for lower latitudes. Thus, some latitudinal migration is suggested, clearly in the northern hemisphere, not very clearly in the southern hemisphere, first to the equator in 1998, stagnant or slightly poleward in 1999, and then to the equator again from 2000 onwards, the latter reminiscent of the Maunder butterfly diagrams. Similar plots for CME occurrence frequency also showed multiple peaks (two or three) in almost all latitude belts, but the peaks were almost simultaneous at all latitudes, indicating no latitudinal migration. For similar latitude belts, SGN and CME plots were dissimilar in almost all latitude belts except 10° – 20° S. The CME plots had in general more peaks than the SGN plots, and the peaks of SGN often did not match with those of CME. In the CME data, it was noticed that whereas the values declined from 2002 to 2003, there was no further decline during 2003 – 2006 as one would have expected to occur during the declining phase of sunspots, where 2007 is almost a year of sunspot minimum. An inquiry at GSFC-NASA revealed that the person who creates the preliminary list was changed in 2004 and the new person picks out more weak CMEs. Thus a subjectivity (overestimates after 2002) seems to be involved and hence, values obtained before and during 2002 are not directly comparable to values recorded after 2002, except for CMEs with widths exceeding 60°.     

Brightness of the Coronal Green Line and Prediction for Activity Cycles 23 and 24

Cyclic variations of the mean semi-annual intensities I of the coronal green line 530.3 nm are compared with the mean semi-annual variations of the Wolf numbers W during the period of 1943–1999 (activity cycles 18–23). The values of I in the equatorial zone proved to correlate much better with the Wolf numbers in a following cycle than in a given one (the correlation coefficient r is 0.86 and 0.755, respectively). Such increase of the correlation coefficient with a shift by one cycle differs in different phases of the cycle, being the largest at the ascending branch. The regularities revealed make it possible to predict the behaviour of W in the following cycle on the basis of intensities of the coronal green line in the preceding cycle. We predict the maximum semi-annual W in cycle 23 to be 110–122 and the epoch of minimum between cycles 23 and 24 to take place at 2006–2007. A slow increase of I in the current cycle 23 permits us to forecast a low-Wolf-number cycle 24 with the maximum W50 at 2010–2011. A scheme is proposed on the permanent transformation of the coronal magnetic fields of different scales explaining the found phenomenon.     

Inclusion of sdBs in evolutionary population synthesis for binary stellar populations and the application: the determination of photo-z and galaxy morphology

Subdwarf B stars (sdBs) can significantly change the ultraviolet spectra of populations at age t～1 Gyr, and have been even included in the evolutionary population synthesis (EPS) models by Han et al. (Mon. Not. R. Astron. Soc. 380:1098, 2007). In this study we present the spectral energy distributions (SEDs) of binary stellar populations (BSPs) by combining the EPS models of Han et al. (Mon. Not. R. Astron. Soc. 380:1098, 2007) and those of the Yunnan group (Zhang et al. in Astron. Astrophys. 415:117, 2004; Mon. Not. R. Astron. Soc. 357:1088, 2005), which have included various binary interactions (except sdBs) in EPS models. This set of SEDs is available upon request from the authors. Using this set of SEDs of BSPs we build the spectra of Burst, E, S0–Sd and Irr types of galaxies by using the package of Bruzual and Charlot (Mon. Not. R. Astron. Soc. 344:1000, 2003). Combined with the photometric data (filters and magnitudes), we obtain the photometric redshifts and morphologies of 1502 galaxies by using the Hyperz code of Bolzonella et al. (Astron. Astrophys. 363:476, 2000). This sample of galaxies is obtained by removing those objects, mismatched with the SDSS/DR7 and GALEX/DR4, from the catalogue of Fukugita et al. (Astron. J. 134:579, 2007). By comparison the results with the SDSS spectroscopic redshifts and the morphological index of Fukugita et al. (Astron. J. 134:579, 2007), we find that the photo-z fluctuate with the SDSS spectroscopic redshifts, while the Sa–Sc galaxies in the catalogue of Fukugita et al. (Astron. J. 134:579, 2007) are classified earlier as Burst-E galaxies.     

A phenomenological model for the precession of planets and bending of light

We presented a phenomenological mode that attributes the precession of perihelion of planets to the relativistic correction. This modifies Newton’s equation by adding an inversely cube term with distance. The total energy of the new system is found to be the same as the Newtonian one. Moreover, we have deduced the deflection of light formula from Rutherford scattering. The relativistic term can be accounted for quantum correction of the gravitational potential and/or self energy of objects.     

Asteroseismology and the degeneracy of model solutions for subgiant stars

Stellar evolutionary models are essential for the determination of stellar masses and ages. Several parameters can be used to characterize the structure of subgiant stars. Amongst others we can find: the helium and metal abundances, mixing length and core overshooting. In many cases, these parameters are scaled taking into account the solar values. Yet, the universality of such scalings has been put to question. As shown here, by allowing some freedom to these parameters we end up with a degeneracy of model solutions. This puts serious limitations on the determination of mass and age. Asteroseismology may provide a valuable help to break such a degeneracy. This is illustrated with an application to the subgiant star μ Her.