Investigation of Long-Period Oscillations of Sunspots with Ground-Based (Pulkovo) and SOHO/MDI Data

We applied special data-processing algorithms to the study of long-period oscillations of the magnetic-field strength and the line-of-sight velocity in sunspots. The oscillations were investigated with two independent groups of data. First, we used an eight-hour-long series of solar spectrograms, obtained with the solar telescope at the Pulkovo Observatory. We simultaneously measured Doppler shifts of six spectral lines, formed at different heights in the atmosphere. Second, we had a long time series of full-disk magnetograms (10 – 34 hour) from SOHO/MDI for the line-of-sight magnetic-field component. Both ground- and space-based observations revealed long-period modes of oscillations (40 – 45, 60 – 80, and 160 – 180 minutes) in the power spectrum of the sunspots and surrounding magnetic structures. With the SOHO/MDI data, one can study the longer periodicities. We obtained two new significant periods (> 3σ) in the power spectra of sunspots: around 250 and 480 minutes. The power of the oscillations in the lower frequencies is always higher than in the higher ones. The amplitude of the long-period magnetic-field modes shows magnitudes of about 200 – 250 G. The amplitude of the line-of-sight velocity periodicities is about 60 – 110 m s⁻¹. The absence of low-frequency oscillations in the telluric line proves their solar nature. Moreover, the absence of low-frequency oscillations of the line-of-sight velocity in the quiet photosphere (free of magnetic elements) proves their direct connection to magnetic structures. Long-period modes of oscillation observed in magnetic elements surrounding the sunspot are spread over the meso-granulation scales (10″ – 12″), while the sunspot itself oscillates as a whole. The amplitude of the long-period mode of the line-of-sight velocity in a sunspot decreases rapidly with height: these oscillations are clearly visible in the spectral lines originating at heights of approximately 200 km and fade away in lines originating at 500 km. We found a new interesting property: the low-frequency oscillations of a sunspot are strongly reduced when there is a steady temporal trend (strengthening or weakening) of the sunspot’s magnetic field. Another important result is that the frequency of long-period oscillations evidently depends on the sunspot’s magnetic-field strength.     

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.     

Sunspot Time Series – Relations Inferred from the Location of the Longest Spotless Segments

Spotless days (i.e., days when no sunspots are observed on the Sun) occur during the interval between the declining phase of the old sunspot cycle and the rising phase of the new sunspot cycle, being greatest in number and of longest continuous length near a new cycle minimum. In this paper, we introduce the concept of the longest spotless segment (LSS) and examine its statistical relation to selected characteristic points in the sunspot time series (STS), such as the occurrences of first spotless day and sunspot maximum. The analysis has revealed statistically significant relations that appear to be of predictive value. For example, for Cycle 24 the last spotless day during its rising phase should be about August 2012 (± 9.1 months), the daily maximum sunspot number should be about 227 (± 50; occurring about January 2014±9.5 months), and the maximum Gaussian smoothed sunspot number should be about 87 (± 25; occurring about July 2014). Using the Gaussian-filtered values, slightly earlier dates of August 2011 and March 2013 are indicated for the last spotless day and sunspot maximum for Cycle 24, respectively.     

Sunspot Group Decay

We examine daily records of sunspot group areas (measured in millionths of a solar hemisphere or μHem) for the last 130 years to determine the rate of decay of sunspot group areas. We exclude observations of groups when they are more than 60° in longitude from the central meridian and only include data when at least three days of observations are available following the date of maximum area for a group’s disk passage. This leaves data for over 18 000 measurements of sunspot group decay. We find that the decay rate increases linearly from 28 μHem day⁻¹ to about 140 μHem day⁻¹ for groups with areas increasing from 35 μHem to 1000 μHem. The decay rate tends to level off for groups with areas larger than 1000 μHem. This behavior is very similar to the increase in the number of sunspots per group as the area of the group increases. Calculating the decay rate per individual sunspot gives a decay rate of about 3.65 μHem day⁻¹ with little dependence upon the area of the group. This suggests that sunspots decay by a Fickian diffusion process with a diffusion coefficient of about 10 km² s⁻¹. Although the 18 000 decay rate measurements are lognormally distributed, this can be attributed to the lognormal distribution of sunspot group areas and the linear relationship between area and decay rate for the vast majority of groups. We find weak evidence for variations in decay rates from one solar cycle to another and for different phases of each sunspot cycle. However, the strongest evidence for variations is with latitude and the variations with cycle and phase of each cycle can be attributed to this variation. High latitude spots tend to decay faster than low latitude spots.     

The EUV spectrum of sunspot plumes observed by SUMER on SOHO

We present results from sunspot observations obtained by SUMER on SOHO. In sunspot plumes the EUV spectrum differs from the quiet Sun; continua are observed with different slopes and intensities; emission lines from molecular hydrogen and many unidentified species indicate unique plasma conditions above sunspots. Sunspot plumes are sites of systematic downflow. We also discuss the properties of sunspot oscillations     

Fluctuations of Solar Activity during the Declining Phase of the 11-Year Sunspot Cycle

The number of coronal mass ejections (CMEs) erupting from the Sun follows a trend similar to that of sunspot numbers during the rising and maximum phase of the solar cycle. In the declining phase, the CME number has large fluctuations, dissimilar to those of sunspot numbers. In several studies of solar – interplanetary and solar – terrestrial relationships, the sunspot numbers and the 2800-MHz flux (F10) are used as representative of solar activity. In the rising phase, this may be adequate, but in the declining phase, solar parameters such as CMEs may have a different behaviour. Cosmic-ray Forbush decreases may occur even when sunspot activity is low. Therefore, when studying the solar influence on the Earth, one has to consider that although geomagnetic conditions at solar maximum will be disturbed, conditions at solar minimum may not be necessarily quiet.     

Absorption of acoustic waves by sunspots

Observations of the scattering of acoustic waves by sunspots show a substantial deficit in scattered power relative to incident power. A number of calculations have attempted to model this process in terms of absorption at the magnetohydrodynamic Alfvén resonance. The results presented here extend these calculations to the case of a highly structured axisymmetric translationally invariant flux-tube embedded in a uniform atmosphere. The fractional energy absorbed is calculated for models corresponding to flux-tubes of varying radius, mean flux-density and location below the photosphere. The effects of twist are also included.It is found that absorption can be very efficient even in models with low mean magnetic flux density, provided the flux is concentrated into intense slender annuli. Twist is found to increase the range of wave numbers over which absorption is efficient, but it does not remove the low absorption at low azimuthal orders which is a feature of resonance absorption calculations in axisymmetric geometry, and which is in conflict with observation.These results suggest that resonance absorption could be an efficient mechanism in plage fields and fibril sunspots as well as in monolithic sunspots. At present it is too early to make any definite deductions about sunspot structure from the observations, but the possible future use of sunspot seismology to resolve open questions in the theory of sunspots is briefly discussed.     

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.     

Constructing Semi-Empirical Sunspot Models for Helioseismology

One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun τ ₅₀₀₀=1 level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). The OPAL equation-of-state tables are used to derive the sound-speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1 Mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic-field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45° at the umbral – penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p ₁, and p ₂ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations.     

Surface-Focused Seismic Holography of Sunspots: II. Expectations from Numerical Simulations Using Sound-Speed Perturbations

Helioseismic observations of sunspots show that wave travel times, at fixed horizontal phase speed, depend on the temporal frequency of the waves employed in the data analysis. This frequency variation has been suggested to be consistent with near-surface (vertical length scales of order one Mm or smaller) changes in wave propagation properties relative to the quiet Sun. We investigate this suggestion by employing numerical simulations of acoustic-wave propagation through models with horizontally and vertically inhomogeneous structure. Standard methods of surface-focused helioseismic holography are applied to the resulting simulated wave fields. We find that the travel-time shifts measured using holography from the simulations with deep sound-speed perturbations (relative to a plane-parallel quiet-Sun model) do not show a systematic frequency dependence at phase speeds above about 20 km s⁻¹. However, shallow sound-speed perturbations, similar to those proposed to model the acoustic scattering properties of sunspots observed with Hankel analysis, produce systematic frequency dependence at these phase speeds. In both cases, positive travel-time shifts can be caused by positive sound-speed perturbations. The details of the travel-time shifts are, however, model dependent.     

Analysis of the Helioseismic Power-Spectrum Diagram of a Sunspot

The continuous high spatial resolution Doppler observation of the Sun by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager allows us to compute a helioseismic k–ω power-spectrum diagram using only oscillations inside a sunspot. Individual modal ridges can be clearly seen with reduced power in the k–ω diagram that is constructed from a 40-hour observation of a stable and round sunspot. Comparing this with the k–ω diagram obtained from a quiet-Sun region, one sees that inside the sunspot the f-mode ridge is more reduced in power than the p-mode ridges, especially at high wavenumbers. The p-mode ridges all shift toward lower wavenumber (or higher frequency) for a given frequency (or wavenumber), implying an increase of phase velocity beneath the sunspot. This is probably because the acoustic waves travel across the inclined magnetic field of the sunspot penumbra. Line-profile asymmetries exhibited in the p-mode ridges are more significant in the sunspot than in the quiet Sun. Convection inside the sunspot is also highly suppressed, and its characteristic spatial scale is substantially larger than the typical convection scale of the quiet Sun. These observational facts demand a better understanding of magnetoconvection and interactions of helioseismic waves with magnetic field.     

Automatic Sunspots Detection on Full-Disk Solar Images using Mathematical Morphology

Sunspots are solar features located in active regions of the Sun, whose number is an indicator of the Sun’s magnetic activity. Therefore accurate detection and classification of sunspots are fundamental for the elaboration of solar activity indices such as the Wolf number. However, irregularities in the shape of the sunspots and their variable intensity and contrast with the surroundings, make their automated detection from digital images difficult. Here, we present a morphological tool that has allowed us to construct a simple and automatic procedure to treat digital photographs obtained from a solar telescope, and to extract the main features of sunspots. Comparing the solar indices computed with our algorithm against those obtained with the previous method exhibit an obvious improvement. A favorable comparison of the Wolf sunspot number time series obtained with our methodology and from other reference observatories is also presented. Finally, we compare our sunspot and group detection to that of other observatories.     

The Effect of Abnormal Granulation on Acoustic Wave Travel Times and Mode Frequencies

Observations indicate that in plage areas (i.e. in active regions outside sunspots) acoustic waves travel faster than in the quiet Sun, leading to shortened travel times and higher p-mode frequencies. Coupled with the 11-year variation of solar activity, this may also explain the solar cycle variation of oscillation frequencies. While it is clear that the ultimate cause of any difference between the quiet Sun and plage is the presence of magnetic fields of order 100 G in the latter, the mechanism by which the magnetic field exerts its influence has not yet been conclusively identified. One possible such mechanism is suggested by the observation that granular motions in plage areas tend to be slightly “abnormal”, dampened compared to the quiet Sun. In this paper we consider the effect that abnormal granulation observed in active regions should have on the propagation of acoustic waves. Any such effect is found to be limited to a shallow surface layer where sound waves propagate nearly vertically. The magnetically suppressed turbulence implies higher sound speeds, leading to shorter travel times. This time shift Δ τ is independent of the travel distance, while it shows a characteristic dependence on the assumed plage field strength. As a consequence of the variation of the acoustic cutoff with height, Δ τ is expected to be significantly higher for higher frequency waves within the observed regime of 3 – 5 mHz. The lower group velocity near the upper reflection point further leads to an increased envelope time shift, as compared to the phase shift. p-mode frequencies in plage areas are increased by a corresponding amount, Δ ν/ν=ν Δ τ. These characteristics of the time and frequency shifts are in accordance with observations. The calculated overall amplitudes of the time and frequency shifts are comparable to, but still significantly less than (by a factor of 2 to 5), those suggested by measurements.     

Time-Distance Inversion Methods and Results – (Invited Review)

The current interpretations of the travel-time measurements in quiet and active regions on the Sun are discussed. These interpretations are based on various approximations to the 3-D wave equation such as the Fermat principle for acoustic rays and the Born approximation. The ray approximation and its modifications have provided the first view of the 3-D structures and flows in the solar interior. However, more accurate and computationally efficient approximations describing the relation between the wave travel times and the internal properties are required to study the structures and flows in detail. Inversion of the large three-dimensional datasets is efficiently carried out by regularized iterative methods. Some results of time-distance inversions for emerging active regions, sunspots, meridional flows and supergranulation are presented. An active region which emerged on the solar disk in January 1998, was studied from SOHO/MDI for eight days, both before and after its emergence at the surface. The results show a complicated structure of the emerging region in the interior, and suggest that the emerging flux ropes travel very quickly through the depth range of our observations. The estimated speed of emergence is about 1.3 km s^–1. Tomographic images of a large sunspot reveal sunspot `fingers' - long narrow structures at a depth of about 4 Mm, which connect the sunspot with surrounding pores of the same polarity.     

A Comparison of Feature Classification Methods for Modeling Solar Irradiance Variation

Physical understanding of total and spectral solar irradiance variation depends upon establishing a connection between the temporal variability of spatially resolved solar structures and spacecraft observations of irradiance. One difficulty in comparing models derived from different data sets is that the many ways for identifying solar features such as faculae, sunspots, quiet Sun, and various types of “network” are not necessarily consistent. To learn more about classification differences and how they affect irradiance models, feature “masks” are compared as derived from five current methods: multidimensional histogram analysis of NASA/National Solar Observatory/Kitt Peak spectromagnetograph data, statistical pattern recognition applied to SOHO/Michelson Doppler Imager photograms and magnetograms, threshold masks allowing for influence of spatial surroundings applied to NSO magnetograms, and “one-trigger” and “three-trigger” algorithms applied to California State University at Northridge Cartesian Full Disk Telescope intensity observations. In general all of the methods point to the same areas of the Sun for labeling sunspots and active-region faculae, and available time series of area measurements from the methods correlate well with each other and with solar irradiance. However, some methods include larger label sets, and there are important differences in detail, with measurements of sunspot area differing by as much as a factor of two. The methods differ substantially regarding inclusion of fine spatial scale in the feature definitions. The implications of these differences for modeling solar irradiance variation are discussed. K.L. Harvey and S.R. Walton are deseased, to whom this paper is dedicated.     

Phase-sensitive Holography of Solar Activity

Phase-correlation statistics comparing acoustic radiation coming out of a particular point on the solar photosphere with acoustic radiation going into it show considerably reduced sound travel times through the subphotospheres of active regions. We have now applied techniques in phase-sensitive seismic holography to data from the Solar Oscillations Investigation – Michelson Doppler Imager (SOI-MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft to obtain high resolution phase-correlation maps of a large, complex active region and the `acoustic moat' which surrounds it. We report the following new results: First, the reduced sound travel-time perturbations in sunspots, acoustic moats, and isolated plages increase approximately in proportion to the logarithm of the surface magnetic flux density, for flux densities above 10 G. This is consistent with an interpretation of the travel-time anomalies, observed with holographic and other local-helioseismic procedures, as caused by acoustic Wilson-like depressions in photospheres of magnetic regions. Second, we find that, compared with isolated plages, the acoustic moats have an additional sound travel-time reduction on the order of 3–5 s which may be explained by a thermal excess due to the blockage of convective transport by the sunspot photosphere. Third, the combined effect of the Wilson depression in plages, acoustic moats, and sunspots may explain the observed variation of global p-mode frequencies with the solar cycle. Fourth, we find that active regions, including sunspots, acoustic moats, and plages, significantly reflect p modes above the acoustic cut-off frequency, where the surface of the quiet Sun acts as a nearly perfect absorber of incident acoustic radiation.     

Statistical Properties Of Sunspots In 1996–2004: I. Detection, North–South Asymmetry And Area Distribution

The first statistical results in sunspot distributions in 1996–2004 obtained from the Solar Feature Catalogues (SFC) are presented. A novel robust technique is developed for automated identification of sunspots on SOHO/MDI white-light (WL) full-disk solar images. The technique applies image standardization procedures for elimination of the limb darkening and non-circular image shape, uses edge-detection methods to find the sunspot candidates and their edges and morphological operations to smooth the features and fill in gaps. The detected sunspots are verified with the SOHO/MDI magnetograms by strong magnetic fields being present in sunspots. A number of physical and geometrical parameters of the detected sunspot features are extracted and stored in the relational SFC database including umbra/penumbra masks in the form of run-length data encoding of sunspot bounding rectangles. The detection results are verified by comparison with the manual daily detection results in Meudon and Locarno Observatories in 2002 and by correlation (about 96%) with the 4 year sunspot areas produced manually at NOAA. Using the SFC data, sunspot area distributions are presented in different phases of the solar cycle and hemispheres which reveals a periodicity of the north–south asymmetry with a period of about 7–8 years. The number of sunspots increases exponentially with the area decrease with the index slightly increasing from −1.15 (1997) to −1.34 (2001).     

Lifetimes of High-Degree <Emphasis Type="Italic">p</Emphasis> Modes in the Quiet and Active Sun

We study variations of the lifetimes of high-ℓ solar p modes in the quiet and active Sun with the solar activity cycle. The lifetimes in the degree range ℓ=300 – 600 and ν=2.5 – 4.5 mHz were computed from SOHO/MDI data in an area including active regions and quiet Sun using the time – distance technique. We applied our analysis to the data in four different phases of solar activity: 1996 (at minimum), 1998 (rising phase), 2000 (at maximum), and 2003 (declining phase). The results from the area with active regions show that the lifetime decreases as activity increases. The maximal lifetime variations are between solar minimum in 1996 and maximum in 2000; the relative variation averaged over all ℓ values and frequencies is a decrease of about 13%. The lifetime reductions relative to 1996 are about 7% in 1998 and about 10% in 2003. The lifetime computed in the quiet region still decreases with solar activity, although the decrease is smaller. On average, relative to 1996, the lifetime decrease is about 4% in 1998, 10% in 2000, and 8% in 2003. Thus, measured lifetime increases when regions of high magnetic activity are avoided. Moreover, the lifetime computed in quiet regions also shows variations with the activity cycle.     

Photospheric Magnetic Field of the Sun: Two Patterns of the Longitudinal Distribution

Longitudinal distributions of the photospheric magnetic field studied on the basis of National Solar Observatory (Kitt Peak) data (1976 – 2003) displayed two opposite patterns during different parts of the 11-year solar cycle. Helio-longitudinal distributions differed for the ascending phase and the maximum of the solar cycle on the one hand and for the descending phase and the minimum on the other, depicting maxima around two diametrically opposite Carrington longitudes (180° and 0°/360°). Thus the maximum of the distribution shifted its position by 180° with the transition from one characteristic period to the other. Two characteristic periods correspond to different situations occurring in the 22-year magnetic cycle of the Sun, in the course of which both global magnetic field and the magnetic field of the leading sunspot in a group change their sign. During the ascending phase and the maximum (active longitude 180°) polarities of the global magnetic field and those of the leading sunspots coincide, whereas for the descending phase and the minimum (active longitude 0°/360°) the polarities are opposite. Thus the observed change of active longitudes may be connected with the polarity changes of Sun’s magnetic field in the course of 22-year magnetic cycle.     

A search for acoustic amplitude deficit at the antipodes of sunspots

We present a search for the acoustic oscillation deficit which may exist at the antipodes of sunspots. Dopplergrams from Big Bear Solar Observatory 1988 helioseismology data were selected for five days on which large sunspots were known to be on the unseen hemisphere of the Sun. Acoustic oscillation amplitudes in the antipodal regions of these sunspots were compared with amplitudes in surrounding quiet-Sun regions. We did not detect a statistically significant acoustic amplitude deficit in our data. Our results indicate that the amplitude deficit at the sunspot antipodal points is limited to no more than 3% of the acoustic amplitude in the region, for solar oscillation modes of spherical harmonic degree l 200. We conclude that no strong acoustic deficit exists at the antipodes of sunspots. A more sensitive search, requiring more elaborate observations than we have performed, would be desirable in order to determine if a weak acoustic amplitude deficit exists at some level at the antipodes of sunspots, perhaps at higher spatial frequencies of oscillation. The noise level in any signals detected by such observations would probably limit their usefulness as seismic probes. However, information on the lifetimes of solar oscillation modes can be deduced even if no acoustic amplitude deficit is detected.