Three-minute oscillations in sunspots: Seismology of sunspot atmospheres

We show that no eigenmodes of sunspot oscillations with periods of ～ 3 min or shorter exist. A complex spectrum of the 3-min oscillations arises, because the sunspot atmosphere is a multiband filter for slow MHD waves. To ascertain why the filter transmission bands appear, we have investigated the propagation of waves through a sunspot atmosphere using both multilayered isothermal model atmospheres and various empirical model atmospheres. It turns out that there are several different mechanisms responsible for the appearance of transmission bands in the atmospheric filter for slow waves. The filter lowest-frequency transmission band arises from the effect of a Fabry-Perot interference filter at the resonance frequency of the temperature plateau. The frequency of this band is always lower than the cutoff frequency of the temperature minimum. The next (in frequency) transmission band appears at the cutoff frequency. The higher-frequency transmission bands result from the antireflection of the atmosphere, an effect well-known in optics and acoustics. The nonlinearity of the 3-min oscillations observed in the upper chromosphere and transition region has only an indirect effect on the properties of the filter, increasing its transmission in most bands due to a decrease in the amplitude of the wave reflected from the upper atmosphere caused by nonlinear wave absorption. Knowledge of the formation mechanisms for the 3-min oscillation spectrum has allowed us to suggest a technique for estimating the parameters of sunspot atmospheres from the 3-min oscillation spectrum, i.e., to lay the foundations for the seismology of sunspot atmospheres.     

Subphotospheric Resonator and Local Oscillations in Sunspots

The conditions under which the subphotospheric slow-wave resonator can be responsible for the local oscillations in a sunspot have been determined. A rich spectrum of local 3-min oscillations can be produced by the subphotospheric resonator only if the magnetic field in the resonator magnetic flux tube is much weaker than the surrounding sunspot magnetic field. Convective upflows of hot plasma in the sunspot magnetic field satisfy this condition. Consequently, there must be a correlation between the local oscillations and umbral dots, because the latter are produced by convective flows. Various modes of operation of the subphotospheric resonator give rise to wave packets of 3-min oscillations and umbral flashes. It is shown that giant local umbral flashes can emerge under certain conditions for the excitation of oscillations in the subphotospheric resonator.     

Investigation of Quasi-periodic Solar Oscillations in Sunspots Based on SOHO/MDI Magnetograms

In this work we study quasi-periodic solar oscillations in sunspots, based on the variation of the amplitude of the magnetic field strength and the variation of the sunspot area. We investigate long-period oscillations between three minutes and ten hours. The magnetic field synoptic maps were obtained from the SOHO/MDI. Wavelet (Morlet), global wavelet spectrum (GWS) and fast Fourier transform (FFT) methods are used in the periodicity analysis at the 95?% significance level. Additionally, the quiet Sun area (QSA) signal and an instrumental effect are discussed. We find several oscillation periods in the sunspots above the 95?% significance level: 3??C?5, 10??C?23, 220??C?240, 340 and 470 minutes, and we also find common oscillation periods (10??C?23 minutes) between the sunspot area variation and that of the magnetic field strength. We discuss possible mechanisms for the obtained results, based on the existing models for sunspot oscillations.     

The Role of Active Regions in the Generation of Torsional Oscillations

We present a model for torsional oscillations where the inhibiting effect of active region magnetic fields on turbulence locally reduces turbulent viscous torques, leading to a cycle- and latitude-dependent modulation of the differential rotation. The observed depth dependence of torsional oscillations as well as their phase relationship with the sunspot butterfly diagram are reproduced quite naturally in this model. The resulting oscillation amplitudes are significantly smaller than observed, though they depend rather sensitively on model details. Meridional circulation is found to have only a weak effect on the oscillation pattern.     

Oscillations Above Sunspots

The 3-min oscillations in the sunspot atmosphere are discussed, based on joint observing with the Transition Region and Coronal Explorer – TRACE and the Solar and Heliospheric Observatory – SOHO. We find that the oscillation amplitude above the umbra increases with increasing temperature, reaches a maximum for emission lines formed close to 1–2× 10⁵ K, and decreases for higher temperatures. Oscillations observed with a high signal-to-noise ratio show deviations from pure linear oscillations. The results do not support the sunspot filter theory, based on the idea of a chromospheric resonator. Whereas the filter theory predicts several resonant peaks in the power spectra, equally spaced 1 mHz in frequency, the observed power spectra show one dominating peak, close to 6 mHz. Spectral observations show that the transition region lines contribute less than 13 percent to the TRACE 171 Å channel intensity above the umbra. The 3-min oscillations fill the sunspot umbra in the transition region. In the corona the oscillations are concentrated to smaller regions that appear to coincide with the endpoints of sunspot coronal loops, suggesting that wave propagation along the magnetic field makes it possible for the oscillations to reach the corona.     

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.     

Interpretation of oscillations in UV lines observed above sunspot umbrae

Our theory of a resonator for slow magneto-atmospheric waves in the chromosphere of a sunspot umbra has been used to check different models of the structure of the chromosphere and transition region. Oscillations of velocity and intensity in Civ, Siiv, and Oiv lines observed by Gurman et al. (1982) on the SMM spacecraft have been compared with the calculated oscillations. The observed spectrum of resonant peaks could well be explained by a gradient model of the umbral chromosphere. Different assumptions concerning the structure of the transition region do not influence the calculated resonance periods, but the amplitudes and phases of oscillations are modified. There is strong evidence for a concentration of the observed oscillations in cold fine structure elements of the transition region, even if the filling factor of such elements is very small (some few percent). Isothermal rather than adiabatic oscillations in the cold elements should be assumed in order to explain the observed fluctuations of line intensity; the relative amplitudes of pressure oscillations in the hot main component with a steep gradient of temperature are too small to explain the observed intensity fluctuations.     

Spatial distributions of sunspot oscillation modes at different temperatures

Three-and five-minute sunspot oscillations have different spatial distributions in the solar atmospheric layers. The spatial distributions are crucial for revealing the physical origin of sunspot oscillations and to investigate their propagation. In this study, six sunspots observed by Solar Dynamics Observatory/Atmospheric Imaging Assembly were used to obtain the spatial distributions of three-and five-minute oscillations. The fast Fourier transform method is applied to represent the power spectra of oscillation modes. We find that, from the temperature minimum to the lower corona, the powers of the fiveminute oscillation exhibit a circle-shape distribution around its umbra, and the shapes gradually expand with temperature increase. However, the circle-shape disappears and the powers of the oscillations appear to be very disordered in the higher corona. This indicates that the five-minute oscillation can be suppressed in the high-temperature region. For the three-minute oscillations, from the temperature minimum to the high corona, their powers mostly distribute within an umbra, and part of them are located at the coronal fan loop structures. Moreover, those relative higher powers are mostly concentrated in the position of coronal loop footpoints.     

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.     

The interpretation of oscillations in sunspot umbrae

We review possibilities for an interpretation of oscillations observed in several period bands (3 min., 5 min., 20 min.) and at different heights in sunspot umbrae. At subphotospheric depths two independent resonators are acting: A resonator for slow, quasi-transverse waves can explain the lifetimes of bright umbral dots (≥20 sec.), while a resonator for fast (acoustic), quasi-longitudinal waves could result in the 5-min. oscillations. The acoustic resonator strongly couples with the slow-mode longitudinal resonator at photospheric and chromospheric heights, the latter produces the resonance peaks in the 3-min. period band. The whole scheme of resonance levels generalizes and corroborates a chromospheric resonator model earlier proposed by the present authors. Comparisons with alternative models and recent measurements show that the present model most naturally explains the majority of observed data.     

Long-Period Oscillations of Sunspots Observed by SOHO/MDI

We processed magnetograms that were obtained with the Michaelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). The results confirm the basic properties of long-period oscillations of sunspots that have previously been established and also reveal new properties. We show that the limiting (lowest) eigenmode of low-frequency oscillations of a sunspot as a whole is the mode with a period of 10?–?12 up to 32?–?35 hours (depending on the sunspot’s magnetic-field strength). This mode is observed consistently throughout an observation period of 5?–?7 days, but its amplitude is subject to quasi-cyclic changes, which are separated by about 1.5?–?2 days. As a result, the lower mode with a period of about 35?–?48 hours appears in the power spectrum of sunspot oscillations. But this lowest mode is apparently not an eigenmode of a sunspot because its period does not depend on the magnetic field of the sunspot. Perhaps the mode reflects the quasi-periodic sunspot perturbations caused by supergranulation cells that surround it. We also analyzed SOHO/MDI artifacts, which may affect the low-frequency power spectra of sunspots.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.     

Chromospheric Sunspot Oscillations in Hα and Ca ii 8542 Å

We study chromospheric oscillations including umbral flashes and running penumbral waves in a sunspot of active region NOAA 11242 using scanning spectroscopy in Hα and Ca?ii 8542 Å with the Fast Imaging Solar Spectrograph (FISS) at the 1.6 meter New Solar Telescope at the Big Bear Solar Observatory. A bisector method is applied to spectral observations to construct chromospheric Doppler-velocity maps. Temporal-sequence analysis of these shows enhanced high-frequency oscillations inside the sunspot umbra in both lines. Their peak frequency gradually decreases outward from the umbra. The oscillation power is found to be associated with magnetic-field strength and inclination, with different relationships in different frequency bands.     

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.     

The influence of solar system oscillation on the variability of the total solar irradiance

Total solar irradiance (TSI) is the primary quantity of energy that is provided to the Earth. The properties of the TSI variability are critical for understanding the cause of the irradiation variability and its expected influence on climate variations. A deterministic property of TSI variability can provide information about future irradiation variability and expected long-term climate variation, whereas a non-deterministic variability can only explain the past.This study of solar variability is based on an analysis of two TSI data series, one since 1700 A.D. and one since 1000 A.D.; a sunspot data series since 1610 A.D.; and a solar orbit data series from 1000 A.D. The study is based on a wavelet spectrum analysis. First, the TSI data series are transformed into a wavelet spectrum. Then, the wavelet spectrum is transformed into an autocorrelation spectrum to identify stationary, subharmonic and coincidence periods in the TSI variability.The results indicate that the TSI and sunspot data series have periodic cycles that are correlated with the oscillations of the solar position relative to the barycenter of the solar system, which is controlled by gravity force variations from the large planets Jupiter, Saturn, Uranus and Neptune. A possible explanation for solar activity variations is forced oscillations between the large planets and the solar dynamo.We find that a stationary component of the solar variability is controlled by the 12-year Jupiter period and the 84-year Uranus period with subharmonics. For TSI and sunspot variations, we find stationary periods related to the 84-year Uranus period. Deterministic models based on the stationary periods confirm the results through a close relation to known long solar minima since 1000 A.D. and suggest a modern maximum period from 1940 to 2015. The model computes a new Dalton-type sunspot minimum from approximately 2025 to 2050 and a new Dalton-type period TSI minimum from approximately 2040 to 2065.     

Periodicities of Sunspot Number and Coronal Index Time Series During Solar Cycle 23

We investigate the presence and temporal evolution of short- and intermediate-term periodicities in the daily data of sunspot numbers and coronal index for the time span from May 1996 to December 2008, which covers the entire Solar Cycle 23. The daily sunspot number data have been analyzed for the full disk, and for northern and southern hemispheres of the Sun. Using the wavelet power spectrum technique, we find a number of quasi-periodic oscillations in all the data sets. We also find a prominent period of 22 to 35 days in the high-frequency range, and detect the Rieger period of 150 to 160 days in both data sets during different phases of Cycle 23. We also detect ∼1.3 year oscillation in both sunspot and coronal index time series. In addition, we find a number of other short and mid-term periods. We discuss possible explanations of the observed periodicities in the light of previous results and existing numerical models.     

Velocity oscillations in the solar atmosphere

From a series of long duration continuous Doppler records of selected spectral lines, characteristics of solar velocity oscillations have been studied. Statistical distribution of the durations of the bursts of oscillations has been estimated. From the nature of distortion of the waveforms of the oscillation, the presence of disturbing impulses has been speculated. Constancy and homogeneity of the oscillations have been examined from detailed spectral density plots. Duration indices for the oscillations at different heights in the solar atmosphere have been derived by estimating mean spectral densities of characteristic oscillation amplitudes during several individual bursts and comparing them with corresponding spectral densities from long records. The variation among experimental results has been explained as due to the limitations of the power spectral analysis method on short records.     

Spatial variations in parameters of quasi-hourly sunspot fragment oscillations and a singular penumbra oscillator

We obtained three-dimensional interpolated portraits for the radial and torsional oscillations of fragments of 12 sunspots in the form of deviations of their polar coordinates from drift as functions of the time and distance from the sunspot center. We performed a wavelet analysis of the two orthogonal components and determined the dominant oscillation modes; the period varies between 40 and 100 min for different sunspots. We revealed two types of dominant modes, one is associated with the sunspot and the other is associated with its surrounding pores: the central-mode frequency depends on the maximum field strength of the sunspot and decreases from its center toward the boundary, while the peripheral-mode frequency depends on the heliographic latitude and decreases toward the sunspot boundary from the far periphery. We revealed radial variations in frequency and amplitude with a spatial period of 0.8 sunspot radius. The types of dominant modes and the radial variations in oscillation parameters are linked with the subphotospheric structure of an active region—with two types of spiral waves and concentric magnetic-field waves. We estimated the mean pore oscillation energy to be ～10³⁰ erg and found a singular oscillator with a mean energy of ～10³¹ erg in the penumbra at a distance of 0.8 sunspot radius. We argue that the singular penumbra oscillator is the source of solar flares.     

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     

Oscillatory motions in sunspots

We observe vertical velocity oscillations in some sunspot umbrae with periods of about 180 s and peak to peak amplitudes up to 1 km s^–1. These oscillations are not visible in either the line depth, line width or the continuum intensity. No correlation seems to exist between the occurence of these oscillations and the presence of the chromospheric umbral flashes (Solar Phys. 7, 351, 1069). In the spot penumbra there is an indication of a long period oscillation, the period increasing from about 300 s in the inner penumbra to nearly 1000 s at the penumbra-photosphere boundary. An attempt has been made to interpret these oscillations in terms of gravity or acoustic waves, travelling along the magnetic field lines, taking into account the variation of scale height and magnetic field direction across the sunspot.