Model of local oscillations in sunspots

We have analyzed the properties of oscillations in a sunspot based on SDO observations with a duration of 6 h. The 3-min oscillation spectrum has turned out to consist of dozens of spectral lines. The line widths are at the spectral resolution limit. The oscillations in a sunspot have been broken down into individual areas with a size of a few arcseconds, each having its own oscillation spectrum. These oscillation properties cannot be explained in terms of the existing models based on the assumption that the sunspot oscillates as a whole. We propose a model of local oscillations that explains the complex spectrum of the oscillations and their locality. We show that in addition to the chromospheric resonator, there exists a subphotospheric resonator for slow MHD waves. The existence of this resonance layer allows the locality of the oscillations and their complex spectrum to be explained in terms of Parker’s model.     

On the linear transformation and resonant absorption of Alfvén p-modes in sunspots

We analyse the linear transformation of Alfvén p-modes into quasisurface waves and the resonant absorption of Alfvén p-waves in a slowly varying medium with a density gradient, parallel to the ambient homogeneous magnetic field. It is pointed out, that the energy transfer from Alfvén p-waves to quasisurface waves appear to take place in sunspots. The results obtained also suggest that Alfvén p-waves generated by overstability in sunspots may be absorbed in deep layers under sunspots. Moreover, it is very likely that part of the downward wave flux is reflected and hence it is possibble that essentially the energy from sunspots is transported outward by magnetogravitational waves, to which Alfvén p-waves are transformed.     

Absorption of acoustic waves by sunspots

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

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.     

Torsional oscillations of umbra and penumbra of sunspots

Torsional oscillations of seven single spots are studied based on the observations of the longitudinal magnetic field and the field of radial velocities in the photospheric Fe I λ 525.3 nm line. The periods of umbra and penumbra oscillations are 2.2–7.1 and 3.3–7.7 days, respectively. The spots at a greater solar latitude are characterized by a longer period of oscillations and a smaller axial strength of the magnetic field. The periods of umbra and penumbra oscillations increase with an increase in the period and amplitude of the sunspot umbra oscillations. The obtained results can point to a unitary mechanism of torsional oscillations of umbra and penumbra of single spots and a connection of these oscillations with the differential rotation of the Sun.     

The resonant excitation of transverse oscillations in coronal loops

We suggest a way of self-consistently solving the problem of the excitation and rapid damping of coronal loop oscillations observed from the TRACE (Transition Region and Coronal Explorer) satellite. Oscillations are excited on the dispersion branch of fast magnetoacoustic waves, which propagate mainly across the magnetic field. The rapid damping of the observed oscillations is governed by the dispersion spreading of the pulse of these waves that was produced, for example, by a solar flare. The fundamental oscillation period is close to the period of the fundamental mode. Dissipative processes attributable to the nonideality of the plasma and the coronal-loop footpoints play no fundamental role.     

Basic properties of sunspots: equilibrium,stability and long-term eigen oscillations

A number of fundamental questions as regards the physical nature of sunspots are formulated. In order to answer these questions, we apply the model of a round-shaped unipolar sunspot with a lower boundary consisting of cool plasma and with strong magnetic field at the depth of about 4 Mm beneath the photosphere, in accordance with the data of local helioseismology and with certain physically sound arguments (the shallow sunspot model). The magnetic configuration of a sunspot is assumed to be close to the observed one and similar to the magnetic field of a round solenoid of the appropriate size. The transverse (horizontal) and longitudinal (vertical) equilibria of a sunspot were calculated based on the thermodynamic approach and taking into account the magnetic, gravitational, and thermal energy of the spot and the pressure of the environment. The dependence of the magnetic field strength in the sunspot center, B ₀, on the radius of the sunspot umbra a is derived theoretically for the first time in the history of sunspot studies. It shows that the magnetic field strength in small spots is about 700 Gauss (G) and then increases monotonically with a, tending asymptotically to a limit value of about 4000 G. This dependence, B ₀(a) includes, as parameters, the gravity acceleration on the solar surface, the density of gas in the photosphere, and the ratio of the radius of the spot (including penumbra), a _p, to the radius of its umbra a. It is shown that large-scale subsurface flows of gas in the sunspot vicinity, being the consequence but not the cause of sunspot formation, are too weak to contribute significantly to the pressure balance of the sunspot. Stability of the sunspot is provided by cooling of the sunspot plasma and decreasing of its gravitational energy due to the vertical redistribution of the gas density when the geometric Wilson depression of the sunspot is formed. The depth of a depression grows linearly with B ₀, in contrast to the quadratic law for the magnetic energy. Therefore, the range of stable equilibria turns out to be limited: large spots, with radius a larger than some limit value (about 12–18 Mm, depending on the magnetic field configuration), are unstable. It explains the absence of very large spots on the Sun and the appearance of light bridges in big spots that divide the spot into a few parts. The sunspots with B ₀≈2.6÷2.7 kilogauss (kG) and a≈5 Mm are most stable. For these spots, taken as a single magnetic structure, the period of their vertical eigen oscillations is minimal and amounts, according to the model, to 10–12 hours. It corresponds well to the period derived from the study of long-term oscillations of sunspots using SOHO/MDI data.     

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.     

A search for acoustic amplitude deficit at the antipodes of sunspots

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

Solar convective zone and acoustic oscillations

The influence of the superadiabatic convection region and the hydrogen-helium ionization region on the spectrum of acoustic oscillations are considered. The spectrum peculiarities are studied by means of the phase-shift function which describes the reflection of the acoustic waves by the outermost layers of the Sun. This function permits us to investigate the influence of the envelope structure upon the oscillations without all the model data. It is shown that in spite of the strong influence of the superadiabatic convection upon acoustic oscillations, its structural changes cannot explain the discrepancy between observations and theory. It is emphasized that the explanation of the discrepancy between observations and standard model calculations requires taking into account the non-ideal nature of the plasma.     

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.     

Suppression of resonant field line oscillations by a turbulent background

Stochastic fluctuations of the magnetospheric plasma and background magnetic field, especially intense during geomagnetically active periods, can provide an additional mechanism of damping of Alfvén field line oscillations. To quantify this hypothesis, we consider a driven Alfvén field line resonator with stochastic fluctuations of the Alfvén resonant frequency. This problem is first considered analytically for a low level of fluctuations, then a more general numerical approach is introduced. The results of analytical calculations and numerical modeling both indicate the deterioration of resonant properties of the resonator owing to stochastic background fluctuations.     

The detectability of baryonic acoustic oscillations in future galaxy surveys

We assess the detectability of baryonic acoustic oscillation (BAO) in the power spectrum of galaxies using ultralarge volume N -body simulations of the hierarchical clustering of dark matter and semi-analytical modelling of galaxy formation. A step-by-step illustration is given of the various effects (non-linear fluctuation growth, peculiar motions, non-linear and scale-dependent bias) which systematically change the form of the galaxy power spectrum on large scales from the simple prediction of linear perturbation theory. Using a new method to extract the scale of the oscillations, we nevertheless find that the BAO approach gives an unbiased estimate of the sound horizon scale. Sampling variance remains the dominant source of error despite the huge volume of our simulation box  (=2.41  h ⁻³ Gpc³)  . We use our results to forecast the accuracy with which forthcoming surveys will be able to measure the sound horizon scale, s , and, hence constrain the dark energy equation of state parameter, w (with simplifying assumptions and without marginalizing over the other cosmological parameters). Pan-STARRS could potentially yield a measurement with an accuracy of  Δ s / s = 0.5–0.7  per cent (corresponding to Δ w ≈ 2–3 per cent), which is competitive with the proposed WFMOS survey (  Δ s / s = 1  per cent Δ w ≈ 4 per cent). Achieving Δ w ≤ 1 per cent using BAO alone is beyond any currently commissioned project and will require an all-sky spectroscopic survey, such as would be undertaken by the SPACE mission concept under proposal to ESA.     

Mixing-length theory and the excitation of solar acoustic oscillations

The stability of radial solar acoustic oscillations is studied using a time-dependent formulation of mixing-length theory. Though the radiation field is treated somewhat simplistically with the Eddington approximation, and we appreciate that any coupling of the pulsation to the radiation field is important, for the lower frequency radial modes that have been computed this should not produce too serious an error. Instead, we have concentrated upon treating the coupling with convection as accurately as is currently possible with generalized mixing-length theory in order to learn something about its pertinence. Our principal conclusion is that, according to this theory, solar radial acoustic oscillations are expected to be stable and generated by turbulence. Moreover, the theory predicts changes in mode frequency that may, in part, explain the discrepancy between solar observations and the adiabatic pulsation frequencies of theoretical models. We also compute the amplitudes of the modes using a theory of stochastic excitation. These are in good agreement with observed power spectra.     

Overstability of acoustic modes and the solar five-minute oscillations

The stability of linear convective and acoustic modes in solar envelope models is investigated by incorporating the thermal and mechanical effects of turbulence through the eddy transport coefficients. With a reasonable value of the turbulent Prandtl number it is possible to obtain the scales of motion corresponding to granulation, supergranulation and the five-minute oscillations. Several of the acoustic modes trapped in the solar convection zone are found to be overstable and the most unstable modes, spread over a region centred predominantly around a period of 300 s with a wide range of horizontal length scales, are in reasonable accord with the observed power-spectrum of the five-minute oscillations. It is demonstrated that these oscillations are driven by a simultaneous action of the -mechanism and the radiative and turbulent conduction mechanisms operating in the strongly superadiabatic region in the hydrogen ionization zone, the turbulent transport being the dominant process in overstabilizing the acoustic modes.     

Structure of sunspots

The sunspot models published so far do not reproduce the observed run of the umbral continuum intensities over the entire spectral range 0.5 < < 4 m. Moreover, in several previous models is the temperature gradient smaller than both the adiabatic and the radiative equilibrium gradient.Agreement between intensities computed from acceptable models and measured intensities can be obtained by introducing an additional opacity for 0.8 m, which is probably caused by the crowding of atomic and molecular lines. We present a new umbral model atmosphere with a wavelength dependent opacity enhancement factor which explains the continuum intensities and also reproduces plausible center-to-limb variations and line profiles. This model is in radiative equilibrium down to _0.5 = 1.5, with an effective temperature of 4000 ± 100K. For the deeper superadiabatic layers a small but probably significant departure from radiative equilibrium is indicated by the intensities in the range 1.5 < < 2.4 m.The uncertainties in the present model and the effect of the additional opacity on line profiles are briefly discussed.     

On molecules in sunspots

Spectra of umbrae of several sunspots in the wavelength region 4000–8000 Å scanned photoelectrically at the Göttingen Locarno Observatory were used in order to search for absorption lines of molecules. Several thousands of lines of known molecules were reidentifled (see Table II and Table III). Newly identified molecules are CoH, NiH and H₂O (see Table IV and Wöhl (1969a)). The Zeemann effect on molecular lines (of MgH and CaH; see Table V and Wöhl (1969b)) in spectra of umbrae was detected.     

Lithium abundance in sunspots

The observations of lithium were carried out with the TST-2 telescope at CrAO on August 15–20, 2006. A sunspot model was calculated for the dates of observations. The lithium abundance in a sunspot and in the undisturbed photosphere was determined. It is log(N _Li) = 1.35 for the sunspot and log (N _Li) = 1.05 for the undisturbed photosphere.     

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.     

Material flow in sunspots

Observations nowadays reveal more and more details about the small‐scale structure of the penumbra and umbra. Recent measurements of the motions in the penumbra indicate that (i) the Evershed flow is confined to a thin photospheric layer and (ii) the material rises from and sinks to subphotospheric layers within the penumbra. This flow pattern solves the question of the mass budget of the Evershed flow in a natural way. The nature of umbral dots and their role for the spot's energy budget remains unclear, since they are obviously unresolved even in the best existing measurements.