Helioseismic imaging of sunspots at their antipodes

Recent work by Braun, Duvall, and LaBonte has shown that sunspots absorb helioseismic waves. We propose that sunspot absorption causes a seismic deficit that should be imaged at the antipode of the sunspot. If these images are observable, it should be possible to produce seismic maps of magnetic regions on the far side of the Sun. This possibility opens a broad range of synoptic and diagnostic applications. Diagnostic applications would include lifetimes of higher-frequency modes, and possibly rotation of the solar interior and detection of subsurface magnetic structure. We outline elements of the theory of seismic imaging and consider some applications. We propose the extention of acoustic holography to solar interior diagnostics in the context of antipodal imaging.Now at the Institute for Astronomy, University of Hawaii, Honolulu, HI 96822, U.S.A.     

Detection of Periodic Oscillations in Sunspot-Associated Radio Sources

Using microwave observations made with the Nobeyama radioheliograph (=1.76 cm), we have studied temporal variations of sunspot-associated sources in the circularly polarized component. For all three cases of well-developed and rather stable sunspots we found nearly harmonic oscillations with periods in a range of 120–220 s. In one case of an unstable and quickly devolving active region, the fluctuations appear to be irregular with no dominant period. Sunspot-associated solar radio sources are known to be generated by cyclotron radiation of thermal electrons in magnetic tubes of sunspots at the level of the lower solar corona or chromosphere–corona transition region (CCTR). At the wavelength of 1.76 cm, the polarized emission arises in a layer where the magnetic field is B=2000 G (assuming the emission generated at the third harmonic of electron gyrofrequency). We suggest that the observed effect is a manifestation of the well-known 3-min oscillations observed in the chromosphere and photosphere above sunspots. The observed effects are believed to be a result of resonance oscillation of MHD waves inside a magnetic tube. Radio observations of this phenomenon open a new tool for studying regions of reflection of MHD waves near CCTR level. The method is very sensitive both to the height of the CCTR and magnetic fields above sunspots. Thus, detection of oscillations of the height of the transition region even with an amplitude of a few km are possible. The use of a spectrum of one of the observed sources obtained with the radio telescope RATAN-600 allows us to conclude that oscillations in magnetic field strength of about 4 G could be responsible for the effect and are reliably registered. The appearance of the famous 5-min oscillations in the solar atmosphere was also registered in some spectra of radio oscillations.     

Rotation of Plasma in Sunspots

In this paper we present the results of a sunspot rotation study using Abastumani Astrophysical Observatory photoheliogram data for 324 sunspots. The rotation amplitudes vary in theinebreak 2–64° range (with maximum at 12–14°), and the periods around 0–20 days (with maximum atinebreak 4–6 days). It could be concluded that sunspot rotations are rather inhomogeneous and asymmetric, but several types of sunspots are distinguished by their rotational parameters.During solar activity maximum, sunspot average rotation periods and amplitudes slightly increase. This can be affected by the increase of sunspot magnetic flux tube depth. So we can suppose that sunspot formation during solar activity is connected to a rise of magnetic tubes from deeper layers of the solar photosphere, strengthening the processes within the tube and causing variations in rotation.There is a linear relation between tilt-angle oscillation periods and amplitudes, showing higher amplitudes for large periods. The variations of those periods and especially amplitudes have a periodical shape for all types of sunspots and correlate well with the solar activity maxima with a phase delay of about 1–2 years.     

Velocity fields in the solar atmosphere

Observations of velocity fields in the solar atmosphere made with the Mount Wilson solar magnetograph are analyzed. These observations, which were made with very high velocity sensitivity, cover nearly 250 hours and were made with apertures of several sizes and at various parts of the solar disk, and in strong and weak magnetic fields. The amplitudes of the 300-sec oscillations are about 25% weaker in regions where the magnetic field is greater than 80 gauss than where the field is less than 10 gauss. No difference in the frequencies of the oscillations could be found between strong-field and field-free regions. It is suggested that the oscillations occur only where the field is absent and the lower amplitude in a strong field represents the fraction of the magnetograph aperture occupied by a magnetic field. The element sizes for the 300-sec oscillations are probably at least 5–10 arc seconds.Observations made simultaneously with two lines formed at different depths in the solar atmosphere showed small phase differences in the 5-min oscillations. The upper level showed shorter period oscillations when the lower level oscillations underwent phase changes.A short period oscillation is found superposed on the 300-sec oscillation. These SPOs come in bursts that last for a minute or two and have average amplitudes that fall in the range 0.05–0.10 km/sec peak to peak. All attempts to explain them as instrumental or seeing effects have failed. Their periods fall in the range 1–5 seconds. The horizontal scale of these oscillations is smaller than that of the 300-sec oscillations, and the SPOs are more nearly isotropic oscillations than are these around 300 seconds. They do not represent a high-frequency tail of the latter. These observations did not have a digitizing interval short enough to analyze the SPOs for power spectra, but it is clear from the tracings that they are not a nearly monochromatic oscillation as are the longer waves. The amplitudes of the SPOs in the solar atmosphere must be very large and they contribute greatly to the non-radiative energy flux. It is suggested that they represent a large microturbulence line-broadening effect.     

Observations of sunspot transition region oscillations

Oscillations with a period of 3 minutes are observed in the transition region of six sunspots with the Solar and Heliospheric Observatory - SOHO joint observing programme for velocity fields in sunspot regions. Observations of the transition region lines Ov 629 and Nv 1238, 1242 with the SUMER instrument show significant differences in the amplitude of the 3-minute oscillations from one sunspot to another, both in intensity and line-of-sight velocity. In four sunspots the central part of the umbra is observed. Two of these sunspots show coincidence between the maxima in peak line intensity and velocity directed towards the observer, as is expected for an upward-propagating acoustic wave. The two other sunspots show large oscillation amplitudes and a difference of 25° between maxima in intensity and blue shift. The possible effect of partial wave reflection on the observed phase relation is discussed. For one sunspot only a part of the umbra, close to the penumbra, was observed and the observations show a difference of 50° between maxima in intensity and blueshift. For the smallest sunspot the observations are found to be contaminated by contributions from an area without oscillations. Observed oscillations in line width are small, but probably significant in two sunspots. The observations of NOAA 8378 allow us to compare simultaneous recordings of the oscillations in the chromospheric Siii 1260 line with the oscillations in the transition region lines. We question the suggestion by Fludra (1999) that the sunspot transition region oscillations are a typical feature of the sunspot plumes.     

Flare-Induced Excitation of Solar p modes

Solar flares release large amounts of energy at different layers of the solar atmosphere, including at the photosphere in the case of exceptionally major events. Therefore, it is expected that large flares would be able to excite acoustic waves on the solar surface, thereby affecting the p-mode oscillation characteristics. We have applied the ring-diagram analysis technique to 3-D power spectra obtained for different flare regions in order to study how flares affect the amplitude, frequency and width of the acoustic modes. Data from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) has been used. We have used data obtained for several active regions of the current solar cycle that have produced flares. In most cases, during the period of high flare activity, power in p modes appears to be larger when compared to that in non-flaring regions of similar magnetic field strength.     

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.     

Time profiles of solar irradiance dips

ACRIM data have been analyzed to study the time profiles of simple irradiance dips caused by single active regions. Comparison of the average characteristics of the dips appearing in the minimum and maximum of the solar cycle shows that there are no significant differences. In both periods we disclosed the facular irradiance excess in the profile wings having typical duration of two to three days and an amplitude of about 20% of the dip amplitude. The profiles were asymmetric, with a stronger and longer excess in the trailing wing. We determined an average profile which was attributed to an idealized active region, and we calculated the luminosity perturbation caused by it. Excess radiation in the wings of the profile compensates about 1/3 of the deficit in the dip. In the most simple case from our sample we compared the profile based on ACRIM measurements and the proxy profile estimated using sunspot and plage areas published in Solar Geophysical Data catalogues. The comparison indicates that the facular excess was compensating instantaneously about 2/3 of the luminosity deficit caused by sunspots.     

Variations of microwave emission from solar active regions

Based on observational data obtained with the RT-22 Crimean Astrophysical Observatory radio telescope at frequencies of 8.6 and 15.4 GHz, we investigate the quasi-periodic variations of microwave emission from solar active regions with periods T_p<10 min. As follows from our wavelet analysis, the oscillations with periods of 3–5 min and 10–40 s have the largest amplitudes in the dynamic power spectra, while there are virtually no oscillations with T_p<10 s. Our analysis shows that acoustic modes with T_p?1 min strongly dissipate in the lower solar corona due to thermal conduction losses. The oscillations with T_p=10–40 s are associated with Alfvén disturbances. We analyze the influence of acoustic and Alfvén oscillations on the thermal mechanisms of microwave emission in terms of the homogeneous model. We discuss the probable coronal heating sources.     

STRUCTURE AND ROTATION OF THE SOLAR INTERIOR: INITIAL RESULTS FROM THE MDI MEDIUM-L PROGRAM

The medium-l program of the Michelson Doppler Imager instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to 300. The data for the program are partly processed on board because only about 3% of MDI observations can be transmitted continuously to the ground. The on-board data processing, the main component of which is Gaussian-weighted binning, has been optimized to reduce the negative influence of spatial aliasing of the high-degree oscillation modes. The data processing is completed in a data analysis pipeline at the SOI Stanford Support Center to determine the mean multiplet frequencies and splitting coefficients. The initial results show that the noise in the medium-l oscillation power spectrum is substantially lower than in ground-based measurements. This enables us to detect lower amplitude modes and, thus, to extend the range of measured mode frequencies. This is important for inferring the Sun's internal structure and rotation. The MDI observations also reveal the asymmetry of oscillation spectral lines. The line asymmetries agree with the theory of mode excitation by acoustic sources localized in the upper convective boundary layer. The sound-speed profile inferred from the mean frequencies gives evidence for a sharp variation at the edge of the energy-generating core. The results also confirm the previous finding by the GONG (Gough et al., 1996) that, in a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. Inverting the multiplet frequency splittings from MDI, we detect significant rotational shear in this thin layer. This layer is likely to be the place where the solar dynamo operates. In order to understand how the Sun works, it is extremely important to observe the evolution of this transition layer throughout the 11-year activity cycle.     

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.     

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.     

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 velocity field associated with the birth of sunspots

A velocity field is found to occur prior to the birth of sunspots or during the rapidly developing phase of new spots. Fraunhofer lines are always shifted redwards in the observed active regions which are situated at various distances from the disk center. The velocity amplitude derived from Na i D1-line, 5895.940, amounts to, at maximum, 1.5 km s^–1 which is always a little larger than that derived from the weaker line, NI i 5892.883. The velocity field disappears when the spot ceases to grow. The lifetime of the velocity is, at least, 1 hr. The velocity field is interpreted in terms of the continuous downward flow in the process of formation of sunspots.Bray and Loughhead (1964) regard the disturbance in the granulation pattern accompanying the birth and growth of sunspot pores as an evidence of the existence of rising loops of magnetic flux. In view of the similarity of the phase of development of active regions and the lifetime in the observations by Bray and Loughhead and by us, we suggest that the velocity field may be a spectroscopic feature accompanying the rising magnetic loops in the photosphere and the chromosphere. We briefly discuss the observed mode of penetration of the magnetic flux to the solar surface before and after the appearance of AFS's.     

The effects of sunspots on solar irradiance

Sunspots have an obvious direct effect upon the visible radiant energy falling upon the Earth. We show how to estimate this effect and compare it quantitatively with recent observations of the solar total irradiance (Willson et al., 1981). The sunspots explain about half of the total observed variance of one-day averages. Since the sunspot effect on irradiance produces an asymmetry of the solar radiation, rather than (necessarily) a variation of the total luminosity, we have also estimated the sunspot population on the invisible hemisphere. This extrapolation allows us to estimate the true luminosity deficit produced by sunspots, in a manner that tends toward the correct long-term average value. We find no evidence for instantaneous global re-emission to compensate for the sunspot flux deficit.     

Acoustic power mapping for active regions from MDI, HLH, and TON data

Based on the HLH and TON ground-based helioseismological projects and the SOHO/MDI spaceborne project, we obtained acoustic power maps of active regions averaged over 1 mHz intervals. These maps allowed the spatial and frequency distributions of acoustic power in an active region and its surroundings to be studied. The time step of the HLH data is 42 s, which makes it possible to investigate the acoustic power up to 11.9 mHz. Data in the Ca II K and Ni I lines, which originate in the middle chromosphere and the photosphere, respectively, give an idea of the height distribution of acoustic oscillation energy in the solar atmosphere. The acoustic halo produced by excess acoustic power around sunspots clearly shows up on acoustic maps in the Ca II K line and, to a lesser degree, in the Doppler Ni I line shifts. Ground-based observations also reveal a large enhancement of acoustic power inside sunspots. Our tests show that this effect results from the combination of a high intensity gradient in the data and atmospheric seeing. The latter was reduced by referencing each image to the sunspot. The spatial distribution of power inside the sunspot due to atmospheric seeing was found to depend on the exposure time of the data used. Excluding the nonsolar effects, a common property of all acoustic maps is the suppression of the solar-oscillation acoustic power in active regions.     

Photospheric and Chromospheric Oscillations in Solar Faculae

The differences between physical conditions in solar faculae and those in sunspots and quiet photosphere (increased temperature and different magnetic field topology) suggest that oscillation characteristics in facula areas may also have different properties. The analysis of 28 time series of simultaneous spectropolarimetric observations in facula photosphere (Fe?i 6569 Å, 8538 Å) and chromosphere (Hα, Ca?ii 8542 Å) yields the following results. The amplitude of five-minute oscillations of line-of-sight (LOS) velocity decreases by 20?–?40% in facula photosphere. There are only some cases revealing the inverse effect. The amplitude of four- to five-minute LOS velocity oscillations increases significantly in the chromosphere above faculae, and power spectra fairly often show pronounced peaks in a frequency range of 1.3?–?2.5 mHz. Evidence of propagating oscillations can be seen from space?–?time diagrams. We have found oscillations of the longitudinal magnetic field (1.5?–?2 mHz and 5.2 mHz) inside faculae.     

The quest for the solar g modes

Solar gravity modes (or g modes)—oscillations of the solar interior on which buoyancy acts as the restoring force—have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well-observed acoustic modes (or p modes). The relative high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this article, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made—from both data and data-analysis perspectives—to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.     

Determining Absorption,Emissivity Reduction,and Local Suppression Coefficients inside Sunspots

The power of solar acoustic waves is reduced inside sunspots mainly due to absorption, emissivity reduction, and local suppression. The coefficients of these power-reduction mechanisms can be determined by comparing time – distance cross-covariances obtained from sunspots and from the quiet Sun. By analyzing 47 active regions observed by SOHO/MDI without using signal filters, we have determined the coefficients of surface absorption, deep absorption, emissivity reduction, and local suppression. The dissipation in the quiet Sun is derived as well. All of the cross-covariances are width corrected to offset the effect of dispersion. We find that absorption is the dominant mechanism of the power deficit in sunspots for short travel distances, but gradually drops to zero at travel distances longer than about 6°. The absorption in sunspot interiors is also significant. The emissivity-reduction coefficient ranges from about 0.44 to 1.00 within the umbra and 0.29 to 0.72 in the sunspot, and accounts for only about 21.5% of the umbra’s and 16.5% of the sunspot’s total power reduction. Local suppression is nearly constant as a function of travel distance with values of 0.80 and 0.665 for umbrae and whole sunspots respectively, and is the major cause of the power deficit at large travel distances.     

OSCILLATIONS IN PROMINENCE FINE-STRUCTURES

Oscillatory spectra of solar quiescent prominences highlight the importance of incorporating the effect of prominence fine-structure in the theory of prominence oscillations. We determine the magnetohydrodynamic modes of oscillation of an elementary, zero- model of a prominence fibril, arguing that the fast body kink modes, namely, the string and the internal magnetic Love modes, produce the observed short periodicities in prominence fine-structures. Estimates for the periods of these modes are presented: the modes are subject to testing in future high-resolution observations.