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.     

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

The nature of the three-minute and five-minute oscillations observed in sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves from the photosphere to the solar corona. However, the real modes of these waves and the nature of the filters that result in rather narrow frequency bands of these modes are still far from being generally accepted, in spite of a large amount of observational material obtained in a wide range of wave bands. The significance of this field of research is based on the hope that local seismology can be used to find the structure of the solar atmosphere in magnetic tubes of sunspots. We expect that substantial progress can be achieved by simultaneous observations of the sunspot oscillations in different layers of the solar atmosphere in order to gain information on propagating waves. In this study we used a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere – corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to the optical ones. This implies an MHD wave traveling upward inside the umbral magnetic tube of the sunspot. For the five-minute oscillations the similarity in spectral details could be found only for optical oscillations at the chromospheric level in the umbral region or very close to it. The time delays seem to be similar. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records. Their nature still requires further observational and theoretical study for even a preliminary discussion.     

Dynamic phenomena in the chromospheric layer of a sunspot

We have studied running penumbral waves, umbral oscillations, umbral flashes and their interrelations from H observations of a large isolated sunspot. Using a subtraction image processing technique we removed the sharp intensity gradient between the umbra and the penumbra and enhanced the low contrast, fine features. We observed running penumbral waves which started in umbral elements with a size of a few arcseconds, covered the umbra and subsequently propagated through the penumbra. The period of the waves was 190 s and the mean propagation velocity was about 15 km s^–1. We detected intense brightenings, located between umbral elements from where waves started, which had the characteristics of umbral flashes. There are indications that umbral flashes are related to the propagation of the waves through the umbra and their coupling. The subtraction images also show considerable fine structure in the chromospheric umbra, with size between 0.3 and 0.8.     

On the sunspot transition region

The EUV line emission and relative line-of-sight velocity in the transition region between the chromosphere and corona of 36 sunspot regions are investigated, based on observations with the Coronal Diagnostic Spectrometer – CDS and the Solar Ultraviolet Measurements of Emitted Radiation – SUMER on the Solar and Heliospheric Observatory – SOHO. The most prominent features in the transition-region intensity maps are the sunspot plumes. In the temperature range between log T=5.2 and log T=5.6 we find that 29 of the 36 sunspots contain one or two sunspot plumes. The relative line-of-sight velocity in sunspot plumes is high and directed into the Sun in the transition region, for 19 of the sunspots the maximum velocity exceeds 25 km s^?1. The velocity increases with increasing temperature, reaches a maximum close to log T=5.5 and then decreases abruptly.

Attention is given to the properties of oscillations with a period of 3 min in the sunspot transition region, based on observations of six sunspots. Comparing loci with the same phase we find that the 3-min oscillations affect the entire umbral transition region and part of the penumbral transition region. Above the umbra the observed relation between the oscillations in peak line intensity and line-of-sight velocity is compatible with the hypothesis that the oscillations are caused by upward-propagating acoustic waves. Information about intensity oscillations in the low corona is obtained from observations of one sunspot in the 171 Å channel with the Transition Region And Coronal Explorer – TRACE. We conclude that we observe the 3-min sunspot oscillations in the chromosphere, the transition region and the low corona. The oscillations are observable over a wider temperature range than the sunspot plumes, and show a different spatial distribution than that of the plumes.

     

Evidence of Traveling Waves in Filament Threads

High-resolution Hα filtergrams (0.2″) obtained with the Swedish 1-m Solar Telescope resolve numerous very thin, thread-like structures in solar filaments. The threads are believed to represent thin magnetic flux tubes that must be longer than the observable threads. We report on evidence for small-amplitude (1 – 2 km s⁻¹) waves propagating along a number of threads with an average phase velocity of 12 km s⁻¹ and a wavelength of 4″. The oscillatory period of individual threads vary from 3 to 9 minutes. Temporal variation of the Doppler velocities averaged over a small area containing a number of individual threads shows a short-period (3.6 minutes) wave pattern. These short-period oscillations could possibly represent fast modes in accordance with numerical fibril models proposed by Díaz et al. (Astron. Astrophys. 379, 1083, 2001). In some cases, it is clear that the propagating waves are moving in the same direction as the mass flows.     

Oscillations and waves in a sunspot

Observations have been made in H of the vertical velocity distribution in a sunspot. Over the umbra the pattern consists of structures of scale-size 2–3. The velocity distribution undergoes oscillations with a period of about 165 s and typical amplitude ±3 km s^–1, but the pattern breaks down after one or two cycles because the period of oscillation varies typically by ±20 s from place to place. Transverse waves develop in the outer 0.1 of the umbral radius and propagate outwards with a velocity of about 20 km s^–1, becoming gradually invisible by or before the outer penumbral boundary; the amplitude is about ±1 km s^–1 at the umbra-penumbra border.The penumbral waves are believed to be basically of the Alfvén type, with 3 × 10^–8 g cm^–3. The umbral oscillations presumably represent gravity waves. In both cases the fluxes are inadequate by two orders of magnitude to account for the sunspot energy deficit.     

On the Possible Connection between Photospheric 5-Min Oscillation and Solar Flare Microwave Emission

Dynamic spectra of low-frequency modulation of microwave emission from solar flares are obtained. Data of 15 bursts observed in 1989–2000 with Metsähovi radio telescope at 37 GHz have been used. During 13 bursts a 5-min modulation of the microwave emission intensity was detected with the frequency of ν _I = 3.2± 0.24 (1σ) mHz. Five bursts revealed a 5-min wave superimposed on a ～1 Hz, linear frequency modulated signal generated, presumably, by coronal magnetic loop, this wave frequency is ν_fm = 3.38± 0.37 (1σ) mHz. Both intensity and frequency modulations detected are in good agreement with the data on 5-min global oscillations of photosphere and with the data on the umbral velocity oscillations observed in the vicinity of sunspots. Possible role of p-mode photospheric oscillations in modulation of microwave burst emission is discussed.     

Sunspot umbral oscillations in Mgii k

Time series observations of the profile of the Mgii k line 2795.52 have been obtained in five sunspots with the Ultraviolet Spectrometer and Polarimeter (UVSP) on the Solar Maximum Mission. The three sunspots with umbrae larger than the 3 × 3 pixel size show significant oscillations in integrated line intensity and line centroid, with frequencies in the range 5.29–7.55 mHz (periods of 132–190 s).The frequencies of significant peaks in average umbral power spectra agree well with the frequencies of the three lowest-frequency transmission peaks predicted by a model of resonant transmission of acoustic waves. If radiative delays are unimportant, and the line centroid can be interpreted straightforwardly as a Doppler shift, the measured velocity-intensity phase differences indicate the superposition of upward- and downward-propagating waves in the umbral chromosphere; this is further evidence for the resonant transmission model.A single, quiet Sun time series of k core profiles yields power spectra and a phase difference consistent with the existence of a chromospheric p-mode.The SMM data used in this work were available only because of the repair of the SMM spacecraft by the crew of Challenger on mission 41-C. The pilot for that mission and the commander of Challenger's last mission was Francis R. Scobee.This work is dedicated to his memory.     

The study of umbral flashes in the umbrae of two sunspots

The results of observations of the umbral flashes in two sunspots are reported. The sunspots differ in their morphological properties (evolution rates and activity levels) and in observation conditions (heliocentric distances). The oscillation parameters of the two sunspots do not coincide. The most significant differences are pronounced in the phase relations and amplitudes of observed oscillations.     

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.     

Seeing-Induced Errors in Solar Doppler Velocity Measurements

Imaging systems based on a narrow-band tunable filter are used to obtain Doppler velocity maps of solar features. These velocity maps are created by taking the difference between the blue- and red-wing intensity images of a chosen spectral line. This method has the inherent assumption that these two images are obtained under identical conditions. With the dynamical nature of the solar features as well as the Earth’s atmosphere, systematic errors can be introduced in such measurements. In this paper, a quantitative estimate of the errors introduced due to variable seeing conditions for ground-based observations is simulated and compared with real observational data for identifying their reliability. It is shown, under such conditions, that there is a strong cross-talk from the total intensity to the velocity estimates. These spurious velocities are larger in magnitude for the umbral regions compared to the penumbra or quiet-Sun regions surrounding the sunspots. The variable seeing can induce spurious velocities up to about 1 km s⁻¹. It is also shown that adaptive optics, in general, helps in minimising this effect.     

The vector approach to the problem of physical libration of the Moon: the linearized problem

A flexible and informative vector approach to the problem of physical libration of the rigid Moon has been developed in which three Euler differential equations are supplemented by 12 kinematic ones. A linearized system of equations can be split into an even and odd systems with respect to the reflection in the plane of the lunar equator, and rotational oscillations of the Moon are presented by superposition of librations in longitude and latitude. The former is described by three equations and consists of unrestricted oscillations with a period of T ₁ = 2.878 Julian years (amplitude of 1.855″) and forced oscillations with periods of T ₂ = 27.201 days (15.304″), one stellar year (0.008″), half a year (0.115″), and the third of a year (0.0003″) (five harmonics altogether). A zero frequency solution has also been obtained. The effect of the Sun on these oscillations is two orders of magnitude less than that of the Earth. The libration in latitude is presented by five equations and, at pertrubations from the Earth, is described by two harmonics of unrestricted oscillations (T ₅ ≈ 74.180 Julian years, T ₆ ≈ 27.347 days) and one harmonic of forced oscillations (T ₃ = 27.212 days). The motion of the true pole is presented by the same harmonics, with the maximum deviation from the Cassini pole being 45.3″. The fifth (zero) frequency yields a stationary solution with a conic precession of the rotation axis (previously unknown). The third Cassini law has been proved. The amplitudes of unrestricted oscillations have been determined from comparison with observations. For the ratio $ \frac{{\sin I}} {{\sin \left( {I + i} \right)}} \approx 0.2311 $ \frac{{\sin I}} {{\sin \left( {I + i} \right)}} \approx 0.2311 , the theory gives 0.2319, which confirms the adequacy of the approach. Some statements of the previous theory are revised. Poinsot’s method is shown to be irrelevant in describing librations of the Moon. The Moon does not have free (Euler) oscillations; it has oscillations with a period of T ₅ ≈ 74.180 Julian years rather than T ≈ 148.167 Julian years.     

The Growth of Facular Area Surrounding Large, Decaying Sunspots

In a previous paper, we investigated the facular area around 31 decaying sunspots of varied size. The growth of facular area as a function of spot decay was marginally significant (r ² = 0.1255, p = 0.05). Using new data, this paper examines the change in facular area surrounding large decaying sunspots some of which grew very rapidly. The data are from full-disk photometric images taken with CFDT2 (2.5″ pixels). For 10 sunspots, we find a statistically significant increase in facular area as a function of the spot decay rate with a regression coefficient, squared, of r ² = 0.611 (p < 0.02).     

Observations of Rotating Sunspots from TRACE

Recent observations from TRACE in the photospheric white-light channel have shown sunspots that rotate up to 200° about their umbral centre over a period of 3–5 days. The corresponding loops in the coronal fan are often seen to twist and can erupt as flares. In an ongoing study, seven cases of rotating sunspots have been identified, two of which can be associated with sigmoid structures appearing in Yohkoh/SXT and six with events seen by GOES. This paper analyzes the rotation rates of the sunspots using TRACE white-light data. Observations from AR 9114 are presented in detail in the main text and a summary of the results for the remaining six sunspots is presented in Appendixes A–F. Discussion of the key results, particularly common features, are presented, as well as possible mechanisms for sunspot rotation. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1026138413791     

Oscillations in Sunspots observed in the Near Infrared

Spectropolarimetric time series of two sunspots are investigated to search for magnetic field oscillations. While the existence of velocity oscillations in the five-minute band is clearly confirmed, periodic variations of the magnetic field strength or the magnetic angles inclination and azimuth are small and restricted to very narrow areas. They occur in single frequency bins, but different for magnetic field strength and angles. Small dark structures embedded in one penumbra or in the near surroundings of the other spot exhibit enhanced power for the magnetic variations at all frequencies. Phase differences are rather unsure. The obtained values are in agreement with intrinsic magnetic field variations produced by slow magnetoacoustic modes as well as with an opacity mechanism connected with fast modes.     

Umbral oscillations as resonant modes of magneto-atmospheric waves

Umbral oscillations in sunspots are identified as a resonant response of the umbral atmosphere to forcing by oscillatory convection in the subphotosphere. The full, linearized equations for magneto-atmospheric waves are solved numerically for a detailed model of the umbral atmosphere, for both forced and free oscillations. Resonant fast modes are found, the lowest mode having a period of 153 s, typical of umbral oscillations. A comparison is made with a similar analysis by Uchida and Sakurai (1975), who calculated resonant modes using an approximate (quasi-Alfvén) form of the wave equations. Whereas both analyses give an appropriate value for the period of oscillation, several new features of the motion follow from the full equations. The resonant modes are due to upward reflection in the subphotosphere (due to increasing sound speed) and downward reflection in the photosphere and low chromosphere (due to increasing Alfvén speed); downward reflection at the chromosphere-corona transition is unimportant for these modes.     

Temporal variations of the magnetic field in sunspots

We obtained simultaneous spectra with a spatial resolution of 1/2 and a temporal resolution of 15 s in H, Ca ii-K, Caii 8542 Å, and three Fei lines of the sunspot group responsible for the large flares of August, 1972 (McMath No. 11976). A time series taken 1972, August 3 in the Fei 6173 Å Zeeman sensitive line was analyzed for oscillations of field strength and the angle between the field and the line of sight, and for changes of the field associated with the Ca ii-K umbral flashes discovered by Beckers and Tallant (1969). The power spectra show no significant peaks, conflicting with the results of Mogilevskii et al. (1972) who reported oscillations in the longitudinal component of the field strength with periods of 56, 90, and 150 s. Changes in the field were not observed to be correlated with the occurrence of umbral flashes. These results place restrictions on magnetic modes of energy transport between the photospheric layers and the chromospheric layers where the umbral flashes are observed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The Behavior of Sunspot Contrast during Cycle 23

Results are presented from a study of various sunspot contrast parameters in broadband red (672.3 nm) Cartesian full-disk digital images taken at the San Fernando Observatory (SFO) over eight years, 1997 – 2004, of the twenty-third sunspot cycle. A subset of over 2700 red sunspots was analyzed and values of average and maximum sunspot contrast as well as maximum umbral contrast were compared to various sunspot parameters. Average and maximum sunspot contrasts were found to be significantly correlated with sunspot area (r _s=− 0.623 and r _s=− 0.714, respectively). Maximum umbral contrast was found to be significantly correlated with umbral area (r _s=− 0.535). These results are in agreement with the works of numerous other authors. No significant dependence was detected between average contrast, maximum contrast, or maximum umbral contrast during the rising phase of the solar cycle (r _s=0.024, r _s=0.033, and r _s=0.064, respectively). During the decay phase, no significant correlation was found between average contrast or maximum contrast and time (r _s=− 0.057 and r _s=0.009, respectively), with a weak dependence seen between maximum umbral contrast and cycle (r _s=0.102).     

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.     

Quasi-periodic Oscillations of Solar Active Regions in Connection with Their Flare Activity – NoRH Observations

The sunspot-associated sources at the frequency of 17 GHz give information on plasma parameters in the regions of magnetic field about B=2000 G at the level of the chromosphere-corona transition region. The observations of short period (from one to ten minutes) oscillations in sunspots reflect propagation of magnetohydrodynamic (MHD) waves in the magnetic flux tubes of the sunspots. We investigate the oscillation parameters in active regions in connection with their flare activity. We confirm the existence of a link between the oscillation spectrum and flare activity. We find differences in the oscillations between pre-flare and post-flare phases. In particular, we demonstrate a case of powerful three-minute oscillations that start just before the burst. This event is similar to the cases of the precursors investigated by Sych et al. (Astron. Astrophys. 505, 791, 2009). We also found well-defined eight-minute oscillations of microwave emission from sunspot. We interpret our observations in terms of a relationship between MHD waves propagating from sunspots and flare processes.