The role of emerging bipoles in the formation of a sunspot penumbra

The generation of magnetic flux in the solar interior and its transport from the convection zone into the photosphere, the chromosphere, and the corona will be in the focus of solar physics research for the next decades. With 4 m class telescopes, one plans to measure essential processes of radiative magneto‐hydrodynamics that are needed to understand the nature of solar magnetic fields. One key‐ingredient to understand the behavior of solar magnetic field is the process of flux emergence into the solar photosphere, and how the magnetic flux reorganizes to form the magnetic phenomena of active regions like sunspots and pores. Here, we present a spectropolarimetric and imaging data set from a region of emerging magnetic flux, in which a proto‐spot without penumbra forms a penumbra. During the formation of the penumbra the area and the magnetic flux of the spot increases. First results of our data analysis demonstrate that the additional magnetic flux, which contributes to the increasing area of the penumbra, is supplied by the region of emerging magnetic flux. We observe emerging bipoles that are aligned such that the spot polarity is closer to the spot. As an emerging bipole separates, the pole of the spot polarity migrates towards the spot, and finally merges with it. We speculate that this is a fundamental process, which makes the sunspot accumulate magnetic flux. As more and more flux is accumulated a penumbra forms and transforms the proto‐spot into a full‐fledged sunspot (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Basic Principles of Solar Acoustic Holography – (Invited Review)

We summarize the basic principles of holographic seismic imaging of the solar interior, drawing on familiar principles in optics and parallels with standard optical holography. Computational seismic holography is accomplished by the phase-coherent wave-mechanical reconstruction of the p-mode acoustic field into the solar interior based on helioseismic observations at the solar surface. It treats the acoustic field at the solar surface in a way broadly analogous to how the eye treats electromagnetic radiation at the surface of the cornea, wave-mechanically refocusing radiation from submerged sources to render stigmatic images that can be sampled over focal surfaces at any desired depth. Holographic diagnostics offer a straight-forward assessment of the informational content of the observed p-mode spectrum independent of prospective physical models of the local interior anomalies that it represents. Computational holography was proposed as the optimum approach whereby to address the severe diffraction effects that confront standard tomography in the solar p-mode environment. It has given us a number of remarkable discoveries in the last two years and now promises a new insight into solar interior structure and dynamics in the local perspective. We compare the diagnostic roles of simple acoustic-power holography and phase-sensitive holography, and anticipate approaches to solar interior modeling based on holographic signatures. We identify simple computational principles that, applied to high-quality helioseismic observations, make it easy for prospective analysts to produce high-quality holographic images for practical applications in local helioseismology.     

Seismic Emission from A M9.5-Class Solar Flare

Following the discovery of a few significant seismic sources at 6.0 mHz from the large solar flares of October 28 and 29, 2003, we have extended SOHO/MDI helioseismic observations to moderate M-class flares. We report the detection of seismic waves emitted from the β γ δ active region NOAA 9608 on September 9, 2001. A quite impulsive solar flare of type M9.5 occurred from 20:40 to 20:48 UT. We used helioseismic holography to image seismic emission from this flare into the solar interior and computed time series of egression power maps in 2.0 mHz bands centered at 3.0 and 6.0 mHz. The 6.0 mHz images show an acoustic source associated with the flare some 30 Mm across in the East – West direction and 15 Mm in the North – South direction nestled in the southern penumbra of the main sunspot of AR 9608. This coincides closely with three white-light flare kernels that appear in the sunspot penumbra. The close spatial correspondence between white-light and acoustic emission adds considerable weight to the hypothesis that the acoustic emission is driven by heating of the lower photosphere. This is further supported by a rough hydromechanical model of an acoustic transient driven by sudden heating of the low photosphere. Where direct heating of the low photosphere by protons or high-energy electrons is unrealistic, the strong association between the acoustic source and co-spatial continuum emission can be regarded as evidence supporting the back-warming hypothesis, in which the low photosphere is heated by radiation from the overlying chromosphere. This is to say that a seismic source coincident with strong, sudden radiative emission in the visible continuum spectrum indicates a photosphere sufficiently heated so as to contribute significantly to the continuum emission observed.     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

prior to surface appearance of sunspot flux tubes and magneto-thermal pulsation of the Sun

We found an evidence that the luminosity of the Sun systematically decreased about 20 days before sunspot surface appearance by analysing time-lag correlation of time derivatives of running mean time profiles of the data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of Solar Maximum Mission (SMM) and of the data of the daily sunspot number. This indicates that sunspot flux tube cooling and heat transport blocking by the flux tubes start to take place in the interior of the solar convection zone well before the sunspot surface appearance. From this finding and our previous finding that the luminosity of the Sun systematically increased and the blocked heat appeared on the surface about 50 days after the sunspot surface appearance, a new view of sunspot formation and dynamics and a new view of the luminosity modulation emerged. (i) Sunspots of a solar cycle are formed from clusters of flux tubes which can be seen in the running mean time profile of the sunspot number as a peak with duration on the order of 100 to 200 days. (ii) Heat flow is blocked by the cluster of sunspot flux tubes inside the convection zone to decrease the luminosity about 20 days before the surface emergence of the sunspot cluster. (iii) The blocked heat appears on the surface about 50 days after the surface emergence of the cluster of sunspot flux tubes to heat up the surface. This appears as a thermal pulse in the running mean time profile of the ACRIM dat in between the peaks of the sunspot running mean time profile. This process of heating the surface makes the temperature gradient less steep and weakens the buoyancy of sunspot flux tubes below the surface. (vi) The radiative cooling of the surface layer by the excess heat release steepens the temperature gradient so that the buoyancy of the sub-surface magnetic flux tubes becomes stronger to cause the next surge of emergence of a cluster of sunspots and other magnetic activities, which creates a peak in the time profile of the sunspot number. We call this peak a magnetic pulse of the Sun and the coupled process of alternating pulsed appearance of heat and sunspots the magneto-thermal pulsation of the Sun.     

INTER-CYCLE VARIATIONS OF SOLAR IRRADIANCE: SUNSPOT AREAS AS A POINTER

Most of the present models and reconstructions of solar irradiance use the concept of Photometric Sunspot Index (PSI) to account for the influence of sunspots on solar brightness. Since PSI is based on measured sunspot areas a firm database of such areas is essential. We show, however, that a significant disagreement exists between the data provided by the Royal Greenwich Observatory (from 1874 to 1976) and newer measurements provided by the observatories of Rome, Yunnan, Catania, and the US Air Force. The overlap of the time intervals over which sunspot areas were measured at Greenwich and Rome allows us to quantify the difference between the Greenwich and other data sets. We find that the various data sets differ, at least in a statistical sense, mainly by a correction factor of between 1.15 and 1.25.The revised time series of sunspot areas correlates well with the Zürich sunspot relative numbers over the last 120 years, with the relationship between sunspot areas and sunspot numbers changing only slightly from one cycle to the next. In particular, no indication exists for any extraordinary magnetic behavior of the Sun during the last 2 decades, as might falsely be concluded if the various sunspot area data sets are uncritically combined. There are, however, some indications that cycles 15 and 16 deviate from the rest. We expect that our results should have a significant influence on the reconstruction of the historical solar irradiance.     

A Detailed Comparison of Cosmic Ray Gaps with solar Gnevyshev Gaps

After increasing almost monotonically from sunspot minimum, sunspot activity near maximum falters and remains in a narrow grove for several tens of months. During the 2–3 years of turmoil near sunspot maximum, sunspots depict several peaks (Gnevyshev peaks). The spaces between successive peaks are termed as Gnevyshev Gaps (GG). An examination showed that the depths of the troughs varied considerably from one GG to the next in the same cycle, with magnitudes varying in a wide range (<1% to ∼20%). In any cycle, the sunspot patterns were dissimilar to those of other solar parameters, qualitatively as well as quantitatively, indicating a general turbulence, affecting different solar parameters differently. The solar polar magnetic field reversal does not occur at the beginning of the general turmoil; it occurs much later. For cosmic ray (CR) modulation which occurs deep in the heliosphere, one would have thought that the solar open magnetic field flux would play a crucial role, but observations show that the sunspot GGs are not reflected well in the solar open magnetic flux, where sometimes only one peak occurred (hence no GG at all), not matching with any sunspot peak and with different peaks in the northern and southern hemispheres (north – south asymmetry). Gaps are seen in interplanetary parameters but these do not match exactly with sunspot GGs. For CR data available only for five cycles (19 – 23), there are CR gaps in some cycles, but the CR gaps do not match perfectly with gaps in the solar open magnetic field flux or in interplanetary parameters or with sunspot GGs. Durations are different and/or there are variable delays, and magnitudes of the sunspot GGs and CR gaps are not proportional. Solar polar magnetic field reversal intervals do not coincide with either sunspot GGs or CR gaps, and some CR gaps start before magnetic field reversals, which should not happen if the magnetic field reversals are the cause of the CR gaps.     

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ?ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ?ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ?ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.     

THE CORRELATION BETWEEN SUNSPOT AND CORONAL HOLE CYCLES AND A FORECAST OF THE MAXIMUM OF SUNSPOT CYCLE 23

We have shown in previous papers that a close relationship exists between the evolution of polar coronal hole area, estimated from K-coronameter observations, and the Wolf sunspot number, with a time lag of about half a solar cycle. In this paper we study the same relationship, but with the total coronal hole area at the base of the corona as obtained from a potential field model of the coronal magnetic field, which provides a more complete series of about three solar cycles. We confirm the relationship for the two last cycles and find that the forward time shift in the coronal hole area for the best correlation with sunspot number is almost the same for cycles 21 and 22, and this shift is also the time between peaks in both series. We use this result to make an early prediction of the time and size of the sunspot maximum for solar cycle 23, and find that this should occur early in 2001 and have a magnitude of about 190, similar to that of the two previous sunspot cycles.     

Simulating the generation of the solar toroidal magnetic field by differential rotation

Within the kinematic dynamo theory, we construct a mathematical model for the evolution of the solar toroidal magnetic field, excited by the differential rotation of the convective zone in the presence of a poloidal field of a relic origin. We use a velocity profile obtained by decoding the data of helioseismological experiments. For the model of ideal magnetic hydrodynamics, we calculate the latitudinal profiles of the increasing-with-time toroidal field at different depths in the solar convection zone. It is found that, in the region of differential rotation, the excited toroidal field shows substantial fluctuations in magnitude with depth. Based on the simulations results, we propose an explanation for the “incorrect polarity” of magnetic bipolar sunspot groups in solar cycles.     

The north–south asymmetry of solar activity at high latitudes

Solar long-term activity runs at high latitudes in three ways: (i) in phase with solar long-term activity at low latitudes; (ii) in antiphase with solar long-term activity at low latitudes and (iii) does not follow either (i) or (ii), and mainly occurs around the times of maxima of (i) and (ii). In the present study, we investigate the north–south asymmetry of solar activity at high latitudes and found the following. In Case (i), high-latitude filament activity, for example, is inferred to have the same dominant hemisphere as low-latitude activity in a cycle. In Case (ii), the north–south asymmetry of high-latitude activity, represented by both the polar faculae and the Sun's polar field strength, is usually different from that of low-latitude activity in a sunspot cycle, and even in a cycle of high-latitude activity (polar faculae and the Sun's polar field strength), suggesting that the north–south asymmetry of solar activity at high latitudes should have little or no connection with that of low latitudes. In Case (iii), the north–south asymmetry of solar activity at high latitudes (polar flares) should have little connection with that at low latitudes as well. The observed magnetic field at high latitudes is inferred to consist of two components: one comes from the emergence of the magnetic field from the Sun's interior and the other comes from the drift of the magnetic activity at low latitudes.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.     

On the Sudden Depression of Radio Emission From Plasma Above a Fast-Moving Sunspot

We present a very rare case of unexpected depression of radio emission above a sunspot using solar observations from RATAN-600. The sunspot had a very high proper motion on the solar surface. The depression lasted for 5 days without significant changes in area or magnitude of magnetic field of the associated sunspot. The observations show that the depression cannot be explained by the absorption of the emission during its propagation through the overlying magnetosphere of the AR or through the cold and opaque matter of a prominence. The theoretical interpretation of the phenomenon is based on the hypothesis that the motion of the sunspot on the photosphere leads to the significant expanding of the magnetic loop originated at this sunspot. The extension of the twisted magnetic rope results in the loss of equilibrium of the system: the closed magnetic structure (the twisted magnetic loop) seems destined to transform into an open one. The only mechanism of plasma heating which would be `switched off' in such a non-equilibrium configuration is that based on the quasi-static topological relaxation of a force-free magnetic field towards a configuration of minimum energy. Relaxation of magnetic fields does not occur in a non-equilibrium state. As a consequence, the energy release in the twisted magnetic rope and the temperature of the plasma of the local radio source have to fall down abruptly. Thus, the discussed phenomenon argues in favor of the relaxation model of plasma heating.     

On the Possibility for Action Conservation in the Solar Cycle

The sunspot series are investigated in detail by use of a wavelet transform. By simple arguments, we present a reduced sunspot time-series, which can be argued to be approximately proportional to the magnetic flux density at the coronal surface. This reduced sunspot index correctly reproduces the (average) 22 year solar cycle. Closer scrutiny of the sunspot variation shows that the frequency of the solar cycle and the energy in the magnetic field vary consistently with conservation of action, i.e., energy divided by frequency. The analysis is based on the available data beginning with the year 1700, and analyzed by a wavelet transform. The present results relate to observations reported previously in the literature.     

The time-delayed solar cycle luminosity modulation by sub-surface magnetic flux tubes

In order to explore the mechanism of the solar cycle luminosity change observed by the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of the spacecraft Solar Maximum Mission, we examined running mean time profiles of the daily ACRIM data from the declining phase of solar cycle 21 to the rising phase of solar cycle 22. By comparing them with those of the daily sunspot number, integrated surface magnetic field flux, integrated He I 10830 Å line equivalent width data, and two kinds of data sets of the daily integrated Ca II K line index as indices of the surface magnetic activities, we found (i) that the running mean time profiles of the six independent data sets have several peaks and valleys in common in one solar cycle with time intervals on the order of a few hundreds of days, and (ii) that the peaks and valleys of the ACRIM data profiles followed the peaks and valleys of all the other five indices of the surface activities by 40 to 60 days. This time delay phenomenon suggests (i) that the luminosity modulation was not directly caused by dark and bright features of the surface magnetic activities that the other five indices represent, and (ii) that the missing sunspot radiative flux which was blocked by sub-surface magnetic flux tubes of sunspots and sunspot groups should be re-radiated 40 to 60 days after the surface emergence of the magnetic flux tubes. The concept of the time delay resolves the enigma of the missing sunspot radiative flux and the enigma of the ACRIM experiment that the luminosity dropped when a sunspot or a sunspot group appeared on the surface while the yearly mean of the luminosity decreased and increased along with the decrease and increase of the yearly sunspot number of the 11-year solar cycle. A model of the mechanism to understand these phenomena is presented and its application to other stars is suggested.     

Measurement of Kodaikanal white-light images – VI. Variation of Rotation Rate with Age of Sunspot Groups

We find from an analysis of the Kodaikanal sunspot group data that the rotation rates of spot groups increase with their age when the rotation rates are computed after sorting the spot groups life-span-wise. We confirm these findings from an analysis of the Mt. Wilson sunspot data set too. We show that this trend is in good agreement with the internal rotation profiles from helioseismology (GONG) observations and is also consistent with the concept that the footpoints of the magnetic loops of spot groups are initially anchored in the deeper layers in the solar interior and rise to shallower layers as the spots age, and that the spots reflect the rotation rates at the respective depths at which their footpoints are temporally located. We project the `first-day rotation rates' and the `daily rotation rates' of spot groups on the rotation profiles from the GONG observations and derive the initial anchoring depths of the footpoints of the magnetic loops of the spot groups and their rates of rise as the spot groups age. Our results of the rotation rates are in antithesis to the results reported by investigators from the Greenwich spot group data that show a deceleration in rotation rates as the spot groups age which are also inconsistent with the rotation profiles from helioseismology observations.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solar Flare Occurrence Rate and Probability in Terms of the Sunspot Classification Supplemented with Sunspot Area and Its Changes

We investigate the solar flare occurrence rate and daily flare probability in terms of the sunspot classification supplemented with sunspot area and its changes. For this we use the NOAA active region data and GOES solar flare data for 15 years (from January 1996 to December 2010). We consider the most flare-productive 11 sunspot classes in the McIntosh sunspot group classification. Sunspot area and its changes can be a proxy of magnetic flux and its emergence/cancellation, respectively. We classify each sunspot group into two sub-groups by its area: ??Large?? and ??Small??. In addition, for each group, we classify it into three sub-groups according to sunspot area changes: ??Decrease??, ??Steady??, and ??Increase??. As a result, in the case of compact groups, their flare occurrence rates and daily flare probabilities noticeably increase with sunspot group area. We also find that the flare occurrence rates and daily flare probabilities for the ??Increase?? sub-groups are noticeably higher than those for the other sub-groups. In case of the (M+X)-class flares in the ??Dkc?? group, the flare occurrence rate of the ??Increase?? sub-group is three times higher than that of the ??Steady?? sub-group. The mean flare occurrence rates and flare probabilities for all sunspot groups increase with the following order: ??Decrease??, ??Steady??, and ??Increase??. Our results statistically demonstrate that magnetic flux and its emergence enhance the occurrence of major solar flares.     

Statistical behavior of sunspot groups on the solar disk

In the present study we have produced a diagram of the latitude distribution of sunspot groups from the year 1874 through 1999 and examined statistical characteristics of the mean latitude of sunspot groups. The reliability of the observed data set prior to solar cycle 19 is found quite low as compared with that of the data set observed after cycle 19. A correlation is found between maximum latitude at which first sunspot groups of a new cycle appear and the maximum solar activity of the cycle. It is inferred that solar magnetic activity during the early part of an extended solar cycle may contain some information about the strength of forthcoming solar cycle. A formula is given to describe latitude change of sunspot groups with time during an extended solar cycle. The latitude-migration velocity is found to be largest at the beginning of solar cycle and decreases with time as the cycle progresses with a mean migration velocity of about 1.61° per year.     

Global Forces in Eruptive Solar Flares: The Lorentz Force Acting on the Solar Atmosphere and the Solar Interior

We compute the change in the Lorentz force integrated over the outer solar atmosphere implied by observed changes in vector magnetograms that occur during large, eruptive solar flares. This force perturbation should be balanced by an equal and opposite force perturbation acting on the solar photosphere and solar interior. The resulting expression for the estimated force change in the solar interior generalizes the earlier expression presented by Hudson, Fisher, and Welsch (Astron. Soc. Pac. CS-383, 221, 2008), providing horizontal as well as vertical force components, and provides a more accurate result for the vertical component of the perturbed force. We show that magnetic eruptions should result in the magnetic field at the photosphere becoming more horizontal, and hence should result in a downward (toward the solar interior) force change acting on the photosphere and solar interior, as recently argued from an analysis of magnetogram data by Wang and Liu (Astrophys. J. Lett. 716, L195, 2010). We suggest the existence of an observational relationship between the force change computed from changes in the vector magnetograms, the outward momentum carried by the ejecta from the flare, and the properties of the helioseismic disturbance driven by the downward force change. We use the impulse driven by the Lorentz-force change in the outer solar atmosphere to derive an upper limit to the mass of erupting plasma that can escape from the Sun. Finally, we compare the expected Lorentz-force change at the photosphere with simple estimates from flare-driven gasdynamic disturbances and from an estimate of the perturbed pressure from radiative backwarming of the photosphere in flaring conditions.