The rise of flux-tubes with intense magnetic fields from the base of the convection zone to the solar surface has been substantiated as a probable mechanism for sunspot formation. The origin of flux-tubes of sufficient strength (~10^5 G) is however uncertain. This paper considers the instability of a large-scale toroidal magnetic field caused by the magnetic suppression of convective heat transport as a candidate for the flux tube forming mechanism. The consideration employs the analytical dependence of the eddy diffusion on the magnetic field supplied by mean-field magnetohydrodynamics. The instability tends to produce regions of increased field strength with spatial scales of an order of 100 Mm at the base of the convection zone. Characteristic growth times of the instability are short compared to the 11-year cycle. The threshold field strength for the onset of the instability increases from several hundred Gauss in the vicinity of the equator to some kilo-Gauss at middle latitudes. Growth rates of unstable disturbances decrease with latitude. These latitudinal trends can be the reason for the observed confinement of sunspot activity to a near-equatorial belt.
We study and compare characteristics of sunspot group latitude distribution in two catalogs: the extended Greenwich (1874--2014) and Schwabe ones (1825--1867). We demonstrate that both datasets reveal similar links between latitude and amplitude characteristics of the 11-year cycle: the latitude dispersion correlates with the current activity and the mean latitude of sunspots in the cycle's maximum is proportional to its amplitude, It agrees with conclusions that we made in previous papers for the Greenwich catalog. We show that the latitude properties of sunspot distribution are much more sta…
The Maunder Minimum (1645-1715 approximately) was a period of very low solar activity and a strong hemispheric asymmetry, with most of sunspots in the southern hemisphere. In this paper, two data sets of sunspot latitudes during the Maunder minimum have been recovered for the international scientific community. The first data set is constituted by latitudes of sunspots appearing in the catalogue published by Gustav Spörer nearly 130 years ago. The second data set is based on the sunspot latitudes displayed in the butterfly diagram for the Maunder Minimum which was published by Ribes and Nesme-…
In this paper, we explore the evolution of sunspot latitude distribution and explore its relations with the cycle strength. With the progress of the solar cycle, the distributions in two hemispheres from mid-latitudes propagate toward the equator and then (before the usual solar minimum) these two distributions touch each other. By visualizing the evolution of the distributions in two hemispheres, we separate the solar cycles by excluding this hemispheric overlap. From these isolated solar cycles in two hemispheres, we generate latitude distributions for each cycle, starting from cycle 8 to cy…
Digitized images of full disk CaK spectroheliograms from two solar observatories were used to study cycle variation of ephemeral regions (ERs) over ten solar cycles 14-23. We calculate monthly averaged unsigned latitude of ERs and compare it with annual sunspot number. We find that average latitude of ERs can be used as a predictor for strength of solar cycle. For a short-term prediction (dT about 1-2 years), maximum latitude of ephemeral regions (in current cycle) defines the amplitude of that cycle (higher is the latitude of ERs, larger are the amplitudes of sunspot cycle). For a long-term p…
We analyse a sunspot simulation in an effort to understand the origin of the convective instabilities giving rise to the penumbral and umbral distinct regimes. We applied the criterion from Gough \& Tayler (1966), accounting for the stabilising effect of the vertical magnetic field to investigate the convective instabilities in a MURaM sunspot simulation. We find: (1) a highly unstable shallow layer right beneath the surface extending all over the simulation box in which convection is triggered by radiative cooling in the photosphere; (2) a deep umbral core (beneath -5 Mm) stabilised against o…
Two important sources of information about sunspots in the Maunder minimum are the Spörer catalog and observations of the Paris observatory, which cover in total the last quarter of the 17th and the first two decades of the 18th century. These data, in particular, contain information about sunspot latitudes. As we showed in previous papers, dispersions of sunspot latitude distributions are tightly related to sunspot indices, so we can estimate the level of solar activity in this epoch by a method which is not based on direct calculation of sunspots and is weakly affected by loss of observation…
Tilt angles of close to 30,600 sunspots are determined using Mount Wilson daily averaged magnetograms taken from 1974 to 2012, and MDI/SoHO magnetograms taken from 1996 to 2010. Within a cycle, more than 90% of sunspots have a normal polarity alignment along the east-west direction following Hale's law. The median tilts increase with increasing latitude (Joy's law) at a rate of ~0.5 degree per degree of latitude. Tilt angles of spots appear largely invariant with respect to time at a given latitude, but they decrease by ~0.9degree per year on average, a trend which largely reflects Joy's law f…
We study the latitudinal distribution of sunspots observed from 1874 to 2009 using the center-of-latitude (COL). We calculate COL by taking the area-weighted mean latitude of sunspots for each calendar month. We then form the latitudinal distribution of COL for the sunspots appearing in the northern and southern hemispheres separately, and in both hemispheres with unsigned and signed latitudes, respectively. We repeat the analysis with subsets which are divided based on the criterion of which hemisphere is dominant for a given solar cycle. Our primary findings are as follows: (1) COL is not mo…
Based on the rotating turbulent thermal convection model and using the rotating equivalent temperature assumption and new convection criterion, this paper analyzed the repression of the vorticity gradient on the heat transport and explained that the formation of sunspots originated from the variation of the vorticity gradient in the solar troposphere.
We use the historic record of sunspot groups compiled by the Royal Greenwich Observatory together with the sunspot number to derive the statistical properties of sunspot group emergence in dependence of cycle phase and strength. In particular we discuss the latitude, longitude, area and tilt angle of sunspot groups as functions of the cycle strength and of time during the solar cycle. Using these empirical characteristics the time-latitude diagram of sunspot group emergence (butterfly diagram) is reconstructed from 1700 onward on the basis of the Wolf and group sunspot numbers. This reconstruc…
We study the latitudinal distribution and evolution of sunspot areas from Solar Cycle 12 to Solar Cycle 23 (SC12-SC23) and sunspot-groups of from Solar Cycle 8 to Solar Cycle 23 (SC8-SC23) for even and odd cycles. The Rician distribution is the best-fit function for both even and odd sunspots group latitudinal occurrence. The mean and variance for even northern/southern butterfly wing sunspots are 14.94/14.76 and 58.62/56.08, respectively, and the mean and variance for odd northern/southern wing sunspots are 15.52/15.58 and 61.77/58.00, respectively. Sunspot groups of even cycle wings are thus…
The subsurface structure of a solar sunspot is important in the stability of the sunspots and the energy transport therein. Two subsurface structure models have been proposed, the monolithic and cluster models, but no clear observational evidence supporting a particular model has been found so far. To obtain clues about the subsurface structure of sunspots, we analyzed umbral flashes in merging sunspots registered by IRIS Mg II 2796 Angstrom slit-jaw images (SJIs). Umbral flashes are regarded as an observational manifestation of magnetohydrodynamic (MHD) shock waves originating from convection…
We investigate the rising flux tube and the formation of sunspots in an unprecedentedly deep computational domain that covers the whole convection zone with a radiative magnetohydrodynamics simulation. Previous calculations had shallow computational boxes (< 30 Mm) and convection zones at a depth of 200 Mm. By using our new numerical code R2D2, we succeed in covering the whole convection zone and reproduce the formation of the sunspot from a simple horizontal flux tube because of the turbulent thermal convection. The main findings are (1) The rising speed of the flux tube is larger than the up…
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 SGZ. The ratio of the sunspot number to the width of 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 SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes o…
Light bridges are the most prominent manifestation of convection in sunspots. The brightest representatives are granular light bridges composed of features that appear to be similar to granules. An in-depth study of the convective motions, temperature stratification, and magnetic field vector in and around light bridge granules is presented with the aim of identifying similarities and differences to typical quiet-Sun granules. Spectropolarimetric data from the Hinode Solar Optical Telescope were analyzed using a spatially coupled inversion technique to retrieve the stratified atmospheric param…
Sunspot groups and bipolar magnetic regions (BMRs) serve as an observational diagnostic of the solar cycle. We use Debrecen Photohelographic Data (DPD) from 1974-2014 that determined sunspot tilt angles from daily white light observations, and data provided by Li & Ulrich that determined sunspot magnetic tilt angle using Mount Wilson magnetograms from 1974-2012. The magnetograms allowed for BMR tilt angles that were anti-Hale in configuration, so tilt values ranged from 0 to 360° rather than the more common $\pm$ 90°. We explore the visual representation of magnetic tilt angles on a traditiona…
Strong solar flares occur in $δ$-spots characterized by the opposite-polarity magnetic fluxes in a single penumbra. Sunspot formation via flux emergence from the convection zone to the photosphere can be strongly affected by convective turbulent flows. It has not yet been shown how crucial convective flows are for the formation of $δ$-spots. The aim of this study is to reveal the impact of convective flows in the convection zone on the formation and evolution of sunspot magnetic fields. We simulated the emergence and transport of magnetic flux tubes in the convection zone using radiative magne…
The goal of this paper is to investigate Reynolds stresses and to check if it is plausible that they are responsible for angular momentum transfer toward the solar equator. We also analysed meridional velocity, rotation velocity residuals and correlation between the velocities. We used sunspot groups position measurements from GPR (Greenwich Photographic Result) and SOON/USAF/NOAA (Solar Observing Optical Network/United States Air Force/National Oceanic and Atmospheric Administration) databases covering the period from 1878 until 2011. In order to calculate velocities we used daily motion of s…
We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and contain information about polarity and strength of magnetic field in sunspots. We identify clusters of sunspots of same polarity, and used these clusters to form ``bipole pairs''. The orientation of these bipole pairs was used to measure their tilts. We find that the latitudinal profile of tilts does not monotonically increase with latitude as most previous stud…
We present an analysis of twisting motions in penumbral filaments in sunspots located at heliocentric angles from $30^\circ$ to $48^\circ$ using three time series of blue continuum images obtained by the Broadband Filter Imager (BFI) onboard {\it Hinode}. The relations of the twisting motions to the filament brightness and the position within the filament and within the penumbra, respectively, are investigated. Only certain portions of the filaments show twisting motions. In a statistical sense, the part of the twisting portion of a filament located closest to the umbra is brightest and posses…
We propose that the flux-rope $Ω$ loop that emerges to become any bipolar magnetic region (BMR) is made by a convection cell of the $Ω$-loop's size from initially-horizontal magnetic field ingested through the cell's bottom. This idea is based on (1) observed characteristics of BMRs of all spans ($\sim$ 1000 km to $\sim$ 200,000 km), (2) a well-known simulation of the production of a BMR by a supergranule-size convection cell from horizontal field placed at cell bottom, and (3) a well-known convection-zone simulation. From the observations and simulations, we (1) infer that the strength of the…
We amend Babcock's original scenario for the global dynamo process that sustains the Sun's 22-year magnetic cycle. The amended scenario fits post-Babcock observed features of the magnetic activity cycle and convection zone, and is based on ideas of Spruit and Roberts (1983) about magnetic flux tubes in the convection zone. A sequence of four schematic cartoons lays out the proposed evolution of the global configuration of the magnetic field above, in, and at the bottom of the convection zone through sunspot Cycle 23 and into Cycle 24. Three key elements of the amended scenario are: (1) as the …
It is generally believed that sunspots are the emergent part of magnetic flux tubes in the solar interior. These tubes are created at the base of the convection zone and rise to the surface due to their magnetic buoyancy. The motion of plasma in the convection zone being highly turbulent, the surface manifestation of sunspots may retain the signature of this turbulence, including its intermittency. From direct observations of sunspots, and indirect observations of the concentration of cosmogenic isotopes $^{14}$C in tree rings or $^{10}$Be in polar ice, power spectral densities in frequency ar…
The striking similarity between the cyclic equatorward migration of the torsional oscillation belts and the sunspot activity latitudes inspired several attempts to seek an explanation of the torsional phenomenon in terms of interactions between flux ropes and plasma motions. The aim of the present work is to examine the spatial and temporal coincidences of the torsional waves and the emergence of sunspot magnetic fields. The locations of the shearing latitudes have been compared with the distributions of certain sunspot parameters by using sunspot data of more than two cycles. The bulges of th…
The continuous high spatial-resolution Doppler observation of the Sun by Solar Dynamics Observatory / Helioseismic and Magnetic Imager allows us to compute helioseismic k-omega power-spectrum diagram using only oscillations inside a sunspot. Individual modal ridges can be clearly seen with reduced power in the k-omega diagram constructed by use of 40-hour observation of a stable and round sunspot. Comparing with the k-omega diagram obtained from a quiet-Sun region, inside the sunspot the f-mode ridge gets more power reduction than p-mode ridges, especially at high wavenumber. The p-mode ridges…
Jurcak et al (2018) have reported that, in a sample of more than 100 umbral cores in sunspots, the umbral-penumbral boundary (UPB) is characterized by a remarkably narrowly-defined numerical value (1867 G) of the vertical component of the magnetic field. Gough and Tayler (1966), in their study of magneto-convection, showed that the onset of convection in the presence of a magnetic field is controlled by a parameter δ which also depends on the vertical component of the field. Combining the Jurcak et al result with various empirical models of sunspots leads us to propose the following hypothesis…
Observations reveal that strong solar flares and coronal mass ejections tend to occur in complex active regions characterized by delta-sunspots, spot rotation, sheared polarity inversion lines (PILs), and magnetic flux ropes. Here we report on the first modeling of spontaneous delta-spot generation as a result of flux emergence from the turbulent convection zone. Utilizing state-of-the-art radiative magnetohydrodynamics code R2D2, we simulate the emergence of a force-free flux tube in the convection zone that stretches down to -140 Mm. Elevated by large-scale convective upflows, the tube appea…
We present a systematic study of sunspot physical parameters using full disk magnetograms from MDI/SoHO and HMI/SDO. Our aim is to use uniform datasets and analysis procedures to characterize the sunspots, paying particular attention to the differences and similarities between "Hale" and "anti-Hale" spots. Included are measurements of the magnetic tilt angles, areas, fluxes and polarity pole separations for 4385 sunspot groups in Cycles 23 and 24 each measured, on average, at $\sim$66 epochs centered on meridian-crossing. The sunspots are classified as either "Hale" or "anti-Hale", depending o…
Solar activity is studied using a cluster analysis of the time-fluctuations of sunspot number. In the historic period (1850-1932) the cluster exponent was approximately equal to 0.37 (strong clustering) for the high activity components of the solar cycles. In the modern period (last seven solar cycles: 1933-2007) the cluster exponent was approximately equal to 0.50 (random, white noise-like). Comparing these results with the corresponding data from laboratory experiments on convection it is shown, that in the historic period emergence of sunspots in the solar photosphere was dominated by turbu…
After reviewing potential early indicators of an upcoming solar cycle at high latitudes, we focus attention on the rush-to-the-poles (RTTP) phenomenon in coronal green line emission. Considering various correlations between properties of the RTTP with the upcoming solar cycle we find a correlation between the rate of the RTTP and the time delay until the maximum of the next solar cycle. On the basis of this correlation and the known internal regularities of the sunspot number series we predict that, following a minimum in 2019, cycle 25 will peak in late 2024 at an amplitude of about 130 (in t…
The sunspot cycle is the magnetic cycle of the Sun produced by the dynamo process. A central idea of the solar dynamo is that the toroidal and the poloidal magnetic fields of the Sun sustain each other. We discuss the relevant observational data both for sunspots (which are manifestations of the toroidal field) and for the poloidal field of the Sun. We point out how the differential rotation of the Sun stretches out the poloidal field to produce the toroidal field primarily at the bottom of the convection zone, from where parts of this toroidal field may rise due to magnetic buoyancy to produc…
The maximum of a solar cycle contain two or more peaks, known as Gnevyshev peaks. Studies of this property of solar cycles may help for better understanding the solar dynamo mechanism. We analysed the 13-month smoothed monthly mean Version-2 international sunspot number (SN) during the period 1874-2017 and found that there exists a good correlation between the amplitude (value of the main and highest peak) and the value of the second maximum (value of the second highest peak) during the maximum of a solar cycle.Using this relationship and the earlier predicted value 86 (~92) of the amplitude o…
We present a high-resolution, highly stratified numerical simulation of rotating thermal convection in a spherical shell. Our aim is to study in detail the processes that can maintain a near surface shear layer (NSSL) as inferred from helioseismology. Using the reduced speed of sound technique we can extend our global convection simulation to $0.99\,R_{\odot}$ and include near the top of our domain small-scale convection with short time scales that is only weakly influenced by rotation. We find the formation of a NSSL preferentially in high latitudes in the depth range $r=0.95-0.975R_\odot$. T…
The combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during 1874-2013 are analyzed and studied the relatively long-term variations in the annual sums of the areas of sunspot groups in 0-10 deg, 10-20 deg, and 20-30 deg latitude intervals of the Sun's northern and southern hemispheres. The variations in the corresponding north-south differences are also studied. Long periodicities in these parameters are determined from the fast Fourier transform (FFT), maximum entropy method (MEM), and Morlet wavelet analysis. It is found that in the difference between the sums …
Coronal mass ejections (CMEs) originate from closed magnetic field regions on the Sun, which are active regions and quiescent filament regions. The energetic populations such as halo CMEs, CMEs associated with magnetic clouds, geoeffective CMEs, CMEs associated with solar energetic particles and interplanetary type II radio bursts, and shock-driving CMEs have been found to originate from sunspot regions. The CME and flare occurrence rates are found to be correlated with the sunspot number, but the correlations are significantly weaker during the maximum phase compared to the rise and declining…
We study the temporal evolution of downflows observed at the lateral edges of penumbral filaments in a sunspot located very close to the disk center. Our analysis is based on a sequence of nearly diffraction-limited scans of the Fe I 617.3 nm line taken with the CRisp Imaging Spectro-Polarimeter at the Swedish 1 m Solar Telescope. We compute Dopplergrams from the observed intensity profiles using line bisectors and filter the resulting velocity maps for subsonic oscillations. Lateral downflows appear everywhere in the center-side penumbra as small, weak patches of redshifts next to or along th…
We measure the starspot radii and latitude distribution on the K4 dwarf HAT-P-11 from Kepler short-cadence photometry. We take advantage of starspot occultations by its highly-misaligned planet to compare the spot size and latitude distributions to those of sunspots. We find that the spots of HAT-P-11 are distributed in latitude much like sunspots near solar activity maximum, with mean spot latitude of $16 \pm 1$ degrees. The majority of starspots of HAT-P-11 have physical sizes that closely resemble the sizes of sunspots at solar maximum. We estimate the mean spotted area coverage on HAT-P-11…
Observations of cool stars reveal dark spot-like features on their surfaces. Compared to sunspots, starspots can be bigger or cover a larger fraction of the stellar surface. While sunspots appear only at low latitudes, starspots are also found in polar regions, in particular on rapidly rotating stars. Sunspots are believed to result from the eruption of magnetic flux-tubes rising from the deep interior of the Sun. The strong magnetic field locally reduces convective heat transport to the solar surface. Such flux-tube models have also been invoked to explain starspot properties. However, these …
In sunspot umbrae, convection is largely suppressed by the strong magnetic field. Previous measurements reported on negligible convective flows in umbral cores. Based on this, numerous studies have taken the umbra as zero reference to calculate Doppler velocities of the ambient active region. To clarify the amount of convective motion in the darkest part of umbrae, we directly measured Doppler velocities with an unprecedented accuracy and precision. We performed spectroscopic observations of sunspot umbrae with the Laser Absolute Reference Spectrograph (LARS) at the German Vacuum Tower Telesco…
A striking feature of the solar cycle is that at the beginning, sunspots appear around mid-latitudes, and over time the latitudes of emergences migrate towards the equator.The maximum level of activity (e.g., sunspot number) varies from cycle to cycle.For strong cycles, the activity begins early and at higher latitudes with wider sunspot distributions than for weak cycles. The activity and the width of sunspot belts increase rapidly and begin to decline when the belts are still at high latitudes. Surprisingly, it has been reported that in the late stages of the cycle the level of activity (sun…
The correlation between geomagnetic activity and the sunspot number in the 11-year solar cycle exhibits long-term variations due to the varying time lag between the sunspot-related and non-sunspot related geomagnetic activity, and the varying relative amplitude of the respective geomagnetic activity peaks. As the sunspot-related and non-sunspot related geomagnetic activity are caused by different solar agents, related to the solar toroidal and poloidal fields, respectively, we use their variations to derive the parameters of the solar dynamo transforming the poloidal field into toroidal field …
A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the…
MHD simulations of sunspots have successfully reproduced many aspects of sunspot fine structure as consequence of magneto convection in inclined magnetic field. We study how global sunspot properties and penumbral fine structure depend on the magnetic top boundary condition as well as on grid spacing. The overall radial extent of the penumbra is subject to the magnetic top boundary condition. All other aspects of sunspot structure and penumbral fine structure are resolved at an acceptable level starting from a grid resolution of 48 [24] km (horizontal [vertical]). We find that the amount of in…
We investigate how the splitting of the leading sunspot and associated flux emergence and cancellation in active region NOAA 11515 caused an eruptive M5.6 flare on 2012 July 2. Our study employs multi-wavelength observations from HMI, AIA and ChroTel. Emerging flux formed a neutral line ahead of the leading sunspot and new satellite spots. The sunspot splitting caused a long-lasting flow toward this neutral line, where a filament formed. Further flux emergence, partly of mixed-polarity, as well as episodes of flux cancellation occurred repeatedly at the neutral line. Following a nearby C-class…
Galactic cosmic rays (GCRs), the highly energetic particles that may raise critical health issues for astronauts in space, are modulated by solar activity with their intensity lagging behind the sunspot number (SSN) variation by about one year. Previously, this lag has been attributed to a combined effect of outward convecting solar wind and inward propagating GCRs. However, the lag's amplitude and its solar-cycle dependence are still not fully understood (Ross & Chaplin, 2019). By investigating the solar surface magnetic field, we find that the source of heliospheric magnetic field -- the ope…
Polar Filaments Capture High Latitude Solar Poloidal Field Interactions and can Foretell the Future Sunspot Cycle Amplitude before Polar Field Precursors
We study the effect of turbulent drift of a large-scale magnetic field that results from the interaction of helical convective motions and differential rotation in the solar convection zone. The principal direction of the drift corresponds to the direction of the large-scale vorticity vector. Thus, the effect produces a latitudinal transport of the large-scale magnetic field in the convective zone wherever the angular velocity has a strong radial gradient. The direction of the drift depends on the sign of helicity and it is defined by the Parker-Yoshimura rule. The analytic calculations are do…
We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 degrees latitude, we find for the fir…
