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.     

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.     

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.     

Long-term oscillations of sunspots and a special class of artifacts in SOHO/MDI and SDO/HMI data

A specific type of artifacts (named as “p2p”), that originate due to displacement of the image of a moving object along the digital (pixel) matrix of receiver are analyzed in detail. The criteria of appearance and the influence of these artifacts on the study of long-term oscillations of sunspots are deduced. The obtained criteria suggest us methods for reduction or even elimination of these artifacts. It is shown that the use of integral parameters can be very effective against the “p2p” artifact distortions. The simultaneous observations of sunspot magnetic field and ultraviolet intensity of the umbra have given the same periods for the long-term oscillations. In this way the real physical nature of the oscillatory process, which is independent of the artifacts have been confirmed again. A number of examples considered here confirm the dependence between the periods of main mode of the sunspot magnetic field long-term oscillations and its strength. The dependence was derived earlier from both the observations and the theoretical model of the shallow sunspot. The anti-phase behavior of time variations of sunspot umbra area and magnetic field of the sunspot demonstrates that the umbra of sunspot moves in long-term oscillations as a whole: all its points oscillate with the same phase.     

Turbulent effects of sunspot magnetic field reconstruction

We study the effects of two-dimensional turbulence generated in sunspot umbra due to strong magnetic fields and Alfven oscillations excited in sunspots due to relatively weak magnetic fields on the evolution of sunspots. Two phases of sunspot magnetic field decaying are shown to exist. The initial rapid phase of magnetic field dissipation is due to two-dimensional turbulence. The subsequent slow phase of magnetic field decaying is associated with Alfven oscillations. Our results correspond to observed data that provide evidence for two types of sunspot evolution. The effect of macroscopic diamagnetic expulsion of magnetic field from the convective zone or photosphere toward sunspots is essential in supporting the long-term stability and equilibrium of vertical magnetic flux tubes in sunspots.     

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.     

On the possibility of investigation of the magnetic field structure in subphotospheric layers of the Sun according to observations of sunspot torsional oscillations

A method of investigation of the magnetic field structure in subphotospheric layers of the Sun has been developed. The method is based on observations of the torisonal oscillations of single sunspots. Characteristics of the torsional oscillations have been obtained from observations of the longitudinal magnetic field and radial velocities of seven single sunspots in the photospheric line Fe I λ5253 Å. The parameters of the torsional oscillations and magnetic tubes in the deep layers have been determined. The radius of the cross section of a magnetic flux tube forming a sunspot is greatest near the Sun’s surface and is approximately equal to the radius of a sunspot umbra. Down to the deeper layers, it decreases quite quickly. The longitudinal electric current appearing in the magnetic tube changes direction. The typical time of the current changes is determined by the period of the torsional oscillations. The intensity of the longitudinal magnetic field in the tube increases with depth. The Alfven wave velocity averaged over the length of a magnetic tube is tens or hundreds of times less than this velocity in a sunspot umbra. It decreases with an increase in the period of oscillations. A decrease in the Alfven wave velocity leads to an increase in the twisting angle of magnetic field lines.     

Sunspot Rotations Derived from Magnetic and Velocity Fields Observations

The rotation of sunspot penumbrae has been investigated on the longitudinal magnetic and velocity fields, observed in the photospheric line Fe i λ5253 Å of five lone sunspots. We reconstructed the entire vectors of both fields from their line-of-sight components. All three components of both vectors revealed that the rotation of the sunspots was, in fact, a torsional oscillation. All components of each sunspot had the same rotational period. The penumbrae oscillation periods were distributed in the range from 3.4 days to 7.7 days. The phase of the velocity azimuthal component oscillation was ahead of the phases of all other components of both vectors. If the penumbra plasma density had been equal to the photospheric plasma density (10^?7 g cm^?3) then the oscillation magnetic energy of the components exceeded their kinetic energy approximately by a factor of 10–200. The obtained results led to the conclusion that these oscillations were constrained.     

Nature of Quiet Sun Oscillations Using Data from the Hinode, TRACE, and SOHO Spacecraft

We study the nature of quiet-Sun oscillations using multi-wavelength observations from TRACE, Hinode, and SOHO. The aim is to investigate the existence of propagating waves in the solar chromosphere and the transition region by analyzing the statistical distribution of power in different locations, e.g. in bright magnetic (network), bright non-magnetic and dark non-magnetic (inter-network) regions, separately. We use Fourier power and phase-difference techniques combined with a wavelet analysis. Two-dimensional Fourier power maps were constructed in the period bands 2??C?4?minutes, 4??C?6?minutes, 6??C?15?minutes, and beyond 15?minutes. We detect the presence of long-period oscillations with periods between?15 and 30?minutes in bright magnetic regions. These oscillations were detected from the chromosphere to the transition region. The Fourier power maps show that short-period powers are mainly concentrated in dark regions whereas long-period powers are concentrated in bright magnetic regions. This is the first report of long-period waves in quiet-Sun network regions. We suggest that the observed propagating oscillations are due to magnetoacoustic waves, which can be important for the heating of the solar atmosphere.     

Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

The propagation of solar waves through the sunspot of AR?9787 is observed by using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magnetohydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere and less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.     

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.     

Search for magnetic field oscillations in a sunspot umbra

In order to search for oscillations in velocity and magnetic field strength within a sunspot umbra, a time series of spectra has been obtained through a circular analyzer and the Gregory-Coudé telescope at the Observatorio del Teide, Tenerife. The velocity oscillations clearly show peaks of power at periods between 2 and 7 minutes, with a maximum at 5 minutes. The apparent variations of the magnetic field strength, however, don't exhibit significant oscillations; these fluctuations are rather produced by the influence of parasitic stray light from the surrouding quiet sun which are also visible in the measured time variations of the umbral contrast of continuum intensity.     

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.     

OBSERVATIONS OF SUNSPOT UMBRAL OSCILLATIONS

The solar vacuum telescopes VTT and GCT at Tenerife have been used to obtain high-resolution two-dimensional spectro-polarimetric observations of oscillations in the photospheric layers of sunspots. At the GCT the area of the sunspot has been scanned by shifting the spectrograph slit; at the VTT a Fabry–Pérot interferometer has been applied to get narrow-band filtergrams directly and to scan through the line profile.The spectra of velocity oscillations show the known features of closely packed power peaks in bands of periods around 3 min (strengthened) and 5 min (weakened with respect to the quiet Sun). In the same frequency bands the more reliable VTT data show significant oscillations of the magnetic field strength as well, which could not be attributed to disturbing influences. Maximum power of both velocity and magnetic oscillations and a strong correlation between them, in the 3-min band in particular, is found to occur in those parts of the umbra where the magnetic lines of force are parallel to the line of sight. The oscillations are characterized by a marked spatial fine structure and a non-stationary behaviour.     

Differential rotation of the sun determined tracing sunspots and oscillations of sunspot tilt angle

The time and spatial characteristics of 324 large sunspots (S50 millionths of the solar hemisphere) selected from the Abastumani Astrophysical Observatory photoheliogram collection (1950–1990) have been studied. The variations of sunspot angular rotation velocity residuals and oscillations of sunspot tilt angle were analyzed. It has been shown that the differential rotation rate of selected sunspots correlates on average with the solar cycle. The deceleration of differential rotation of large sunspots begins on the ascending arm of the activity curve and ends on the descending arm reaching minimum near the epochs of solar activity maxima. This behavior disappears during the 21st cycle. The amplitudes and periods of sunspot tilt-angle oscillations correlate well with the solar activity cycle. Near the epochs of activity maximum there appear sunspots with large amplitudes and periods showing a significant scatter while the scatter near the minimum is rather low. We also found evidence of phase difference between the sunspot angular rotation velocity and the amplitudes and periods of tilt-angle oscillations.     

Equilibrium and decay of sunspots

We suggest a quantitative sunspot model developed in terms of mean-field magnetohydrodynamics (MHD). The model consistently describes the distributions of magnetic field, fluid velocity, and thermodynamic parameters in a sunspot and the surrounding matter. Two versions of the model allow the MHD equilibrium in sunspots and their slow decay to be analyzed. The baroclinic flow converging to the sunspot plays an important role in the equilibrium. Several calculated characteristics—almost uniform distributions of brightness and magnetic field inside sunspots, their abrupt changes at the boundary, and nearly linear decreases in the area and magnetic flux of decaying sunspots with time—qualitatively agree with the observations.     

Cyclic and Long-Term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) were used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that presented in Pevtsov et al. (Astrophys. J. Lett. 742, L36, 2011), we selected the sunspot with the strongest measured field strength for each observing week and computed monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500?–?700 gauss (G), but no statistically significant long-term trends. Next, we used the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for cycles 15?–?19. This relationship was used to create a proxy of the peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500?–?700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300?–?350 G, and, following a broad maximum in 1920?–?1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scaled the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (the linear fit to the data yields a slope of ??0.2±0.8 G?year^?1). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21?–?23) with a mean downward trend of ≈?15 G?year^?1.     

太阳黑子本影振荡的周期测量

本影振荡是出现在太阳黑子内的一种常见现象,精确测定它们的振荡周期对于理解黑子的结构和演化有着重要意义。应用快速傅里叶变换方法对空间望远镜HINODE在2007年5月1日观测的活动区AR10953内的黑子本影数据进行了细致的分析,结果发现在该活动区本影内存在一种典型的3 min振荡,其振荡周期约为154 s。     

Local Modulation of Solar Oscillations by Magnetic Fields

The amplitudes of solar oscillations measured in Doppler velocity are modulated by the presence of a strong photospheric magnetic field. Here we show that the amount of modulation cannot be predicted solely on the local photospheric magnetic field strength. Qualitatively, magnetic fields of similar strength have similar effects on the oscillations. Quantitatively, however, we find a neighborhood effect, so that the presence of a nearby sunspot affects oscillations in the area in its vicinity that has normal quiet-Sun magnetic field strength. Thus, different types of magnetic regions alter the oscillatory power to a varying degree, and the p-mode power within regions of similar magnetic field strength is more reduced if there is a sunspot present. The neighborhood effect falls off with distance from the sunspot. We also show that our measurements of the power modulation, in which we look at the effects on oscillations pixel by pixel, can be made consistent with results of amplitude modulation of modes as obtained from ring-diagram analysis of active regions, but only if the neighborhood effect on quiet-Sun regions is taken into account.     

Sunspots and large-scale magnetic fields at various heights

Height variation of the magnetic field structure over groups of sunspots for heights ranging from the photosphere to the source surface (R = 2.5 Ro, where Ro is the radius of the Sun) is examined. For all heights, starting from the photospheric level, groups of sunspot are shown as being independent of long-lived boundaries of large-scale structures rotating with a period shorter than the Carrington period. At heights of 1–1.5 Ro, there is a clear relation between sunspot groups and boundaries separating the head and tail sunspots in the groups (the Hale boundaries). The rotation periods of these structures are close to the Carrington period, their lifespan being less than three to five rotations. The maximal intensity of the solar magnetic field drops by two orders when height increases from H = 1 to H = 1.1 Ro. Further decrease in intensity proceeds gradually (dropping by one order from H = 1.1 to 2.5 Ro). The results obtained can be considered as evidence that large-scale magnetic field structures and long-lived boundries between them (the lines dividing polarities of the magnetic field or zero lines) all exist irrespective of sunspot fields being generated by other sources than sunspots. At the photospheric level, active regions fields are superimposed on these structures.