Variations in Oscillation Frequencies From Minimum to Maximum of Solar Activity

The temporal variation in intermediate-degree-mode frequencies is analysed using helioseismic data which cover the minimum to the maximum phase of the current solar cycle. To study the variation in detail, the measured frequency shifts of f and p modes are decomposed into two components, viz., oscillatory and non-oscillatory. The f-mode frequencies exhibit prominent oscillatory behavior in contrast to p modes where the oscillatory nature of the frequencies is not clearly seen. Also, the oscillatory part contributes significantly to the f-mode frequencies while p-mode frequencies have maximum contribution from the non-oscillatory part. The amplitude of both oscillatory and non-oscillatory parts is found to be a function of frequency. The non-oscillatory part is observed to have a strong correlation with solar activity.     

Solar cycle variations inP-modes and chromospheric magnetism

The effect onp-mode frequencies of a horizontal chromospheric canopy field is studied theoretically and the results compared with Libbrecht and Woodard's observations of frequency changes. Combined changes in field strength and chromospheric temperature cause frequency shifts that are similar in form to those observed. Frequency shifts inp-modes offer the possibility of signatures of solar activity cycles distinct from sunspot numbers and butterfly diagrams.     

Theoretical Signature of Solar Meridional Flow in Global Seismic Data

Approximate expressions are derived for the perturbations in solar p- and f-mode oscillation eigenfunctions, due to large-scale, meridional flows which are symmetric about the equator. The essential signature of the perturbed eigenfunctions in global helioseismic data is derived and the prospects for detecting meridional flow using global seismic techniques are discussed.     

Solar Oscillation Frequency Changes on Time Scales of Nine Days

We establish that global solar p-mode frequencies can be measured with sufficient precision on time scales as short as nine days to detect activity-related shifts. Using ten years of GONG data, we report that mode-mass and error-weighted frequency shifts derived from nine days are significantly correlated with the strength of solar activity and are consistent with long-duration measurements from GONG and the SOHO/MDI instrument. The analysis of the year-wise distribution of the frequency shifts with change in activity indices shows that both the linear-regression slopes and the magnitude of the correlation varies from year to year and they are well correlated with each other. The study also indicates that the magnetic indices behave differently in the rising and falling phases of the activity cycle. For the short-duration nine-day observations, we report a higher sensitivity to activity.     

Realistic Solar Convection Simulations

We report on realistic simulations of solar surface convection that are essentially parameter-free, but include detailed physics in the equation of state and radiative energy exchange. The simulation results are compared quantitatively with observations. Excellent agreement is obtained for the distribution of the emergent continuum intensity, the profiles of weak photospheric lines, the p-mode frequencies, the asymmetrical shape of the mode velocity and intensity spectra, the p-mode excitation rate, and the depth of the convection zone. We describe how solar convection is non-local. It is driven from a thin surface thermal boundary layer where radiative cooling produces low entropy gas which forms the cores of the downdrafts in which most of the buoyancy work occurs. Turbulence and vorticity are mostly confined to the intergranular lanes and underlying downdrafts. Finally, we present some preliminary results on magneto-convection.     

Solar Radius at Subterahertz Frequencies and Its Relation to Solar Activity

The Sun emits radiation at several wavelengths of the electromagnetic spectrum. In the optical band, the solar radius is 695?700 km, and this defines the photosphere, which is the visible surface of the Sun. However, as the altitude increases, the electromagnetic radiation is produced at other frequencies, causing the solar radius to change as a function of wavelength. These measurements enable a better understanding of the solar atmosphere, and the radius dependence on the solar cycle is a good indicator of the changes that occur in the atmospheric structure. We measure the solar radius at the subterahertz frequencies of 0.212 and 0.405 THz, which is the altitude at which these emissions are primarily generated, and also analyze the radius variation over the 11-year solar activity cycle. For this, we used radio maps of the solar disk for the period between 1999 and 2017, reconstructed from daily scans made by the Solar Submillimeter-wave Telescope (SST), installed at El Leoncito Astronomical Complex (CASLEO) in the Argentinean Andes. Our measurements yield radii of \(966.5'' \pm2.8''\) for 0.2 THz and \(966.5'' \pm2.7''\) for 0.4 THz. This implies a height of \(5.0 \pm2.0 \times10^{6}\) m above the photosphere. Furthermore, we also observed a strong anticorrelation between the radius variation and the solar activity at both frequencies.     

Mode Conversion of Solar p Modes in non-Vertical Magnetic Fields – i. two-Dimensional Model

Sunspots absorb incident p modes. The responsible mechanism is uncertain. One possibility is mode conversion to slow magnetoacoustic–gravity waves. In vertical field mode conversion can adequately explain the observed f-mode absorption, but is too inefficient to explain the absorption of p modes. In this investigation we calculate the efficiency of fast-to-slow magnetoacoustic–gravity wave conversion in non-vertical field. We assume two-dimensional propagation where the Alfvén waves decouple. It is found that resultant p-mode absorption is significantly enhanced for moderate inclinations at higher frequencies, whereas for p modes at lower frequencies, and the f mode in general, there is no useful enhancement. However, the enhancement is insufficient to explain the observed p-mode absorption by sunspots. Paper II considers the efficiency of mode conversion in non-vertical field with three-dimensional propagation, where fast and slow magnetoacoustic–gravity waves and Alfvén waves are coupled.     

FIRST RESULTS FROM VIRGO,THE EXPERIMENT FOR HELIOSEISMOLOGY AND SOLAR IRRADIANCE MONITORING ON SOHO

First results from the VIRGO experiment (Variability of solar IRradiance and Gravity Oscillations) on the ESA/NASA Mission SOHO (Solar and Heliospheric Observatory) are reported. The observations started mid-January 1996 for the radiometers and sunphotometers and near the end of March for the luminosity oscillation imager. The performance of all the instruments is very good, and the time series of the first 4–6 months are evaluated in terms of solar irradiance variability, solar background noise characteristics and p-mode oscillations. The solar irradiance is modulated by the passage of active regions across the disk, but not all of the modulation is straightforwardly explained in terms of sunspot flux blocking and facular enhancement. Helioseismic inversions of the observed p-mode frequencies are more-or-less in agreement with the latest standard solar models. The comparison of VIRGO results with earlier ones shows evidence that magnetic activity plays a significant role in the dynamics of the oscillations beyond its modulation of the resonant frequencies. Moreover, by comparing the amplitudes of different components ofp -mode multiplets, each of which are influenced differently by spatial inhomogeneity, we have found that activity enhances excitation.     

Empirical estimate of p-mode frequency shift for solar cycle 23

We have obtained empirical relations between the p-mode frequency shift and the change in solar activity indices. The empirical relations are determined on the basis of frequencies obtained from BBSO and GONG stations during solar cycle 22. These relations are applied to estimate the change in mean frequency for the cycle 21 and 23. A remarkable agreement between the calculated and observed frequency shifts for the ascending phase of cycle 23, indicates that the derived relations are independent of epoch and do not change significantly from cycle to cycle. We propose that these relations could be used to estimate the shift in p-mode frequencies for past, present and future solar activity cycles, if the solar activity index is known. The maximum frequency shift for cycle 23 is estimated to be 265±90 nHz, corresponding to a predicted maximum smoothed sunspot number 118.1±35.     

The Search for Solar Gravity-Mode Oscillations in the Solar Wind Using it Ulysses Plasma Data

A recent report that energetic particles measured in the solar wind may be influenced by solar gravity-mode ( -mode) oscillations motivated the search for -mode signatures in the Ulysses solar wind plasma data. Ulysses solar wind plasma data from 1 March 1992 through the 12 April 1996 were examined in this study for signs of possible solar oscillations. The multi-taper method for spectral analysis was used to look for significant spectral peaks in the entire four-year data set, as well as in the smaller, more heliographically homogenous data set over the solar poles. Several frequencies satisfying certain significance requirements were found in the -mode frequency range in both data sets that also agree with the previously published findings. However, these identifications are shown to be false detections, and hence the frequencies found cannot be identified as solar modes.     

Investigation of Shock Wave Dynamics in An Inhomogeneous Solar Atmosphere

The shock front (SF) propagation in the solar atmosphere with a power-law decrease of density is studied in the Kompaneets approximation. It is shown that the SF part moving from the Sun in the radial direction speeds up at the exponent n > 3 and slows down at n < 3. When passing from the lower corona with n = 6 to the solar wind with n = 2, the acceleration in the front part changes into deceleration. This result allows us to understand the kinematics of the SF obtained from the observational data on type II bursts at low frequencies. Besides, in the region of solar wind, new analytical solutions of the Kompaneets equation (KE) for SF have been obtained. One of them describes SF as an expanding sphere with the center moving from the Sun (plain case). Another solution has been obtained for the case of the inverse near-square law density depending on radius with the singularity at a given levelR.     

Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission (SMM) satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0–2) is approximately 1.3 parts in 10⁴ higher in 1980, near the time of sunspot maximum, than in 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.     

A New Way to Model the Solar Oscillation ℓ−ν Power Spectrum

We present a new approach for the precise and accurate forward modeling of the solar oscillation ℓ−ν power spectrum. The approach is designed to provide the basis for a streamlined solar seismic inversion without measurements of the p-mode frequencies. The new strategy represents a paradigm change in how information is extracted from the oscillation spectrum. It also represents a step toward the ideal case of inferring the Sun's properties directly from the raw observations.     

Supergranulation rotation

Simple convection models estimate the depth of supergranulation at approximately 7500 km which suggests that supergranules would rotate at the rate of the plasma in the outer 1% of the solar radius. The supergranulation rotation obtained from MDI dopplergrams shows that supergranules rotate faster than the outer 5% of the convection zone and show zonal flows matching results from inversions of f-mode splittings. Additionally, the rotation rate depends on the size scale of the features.     

Mode Conversion of Solar <Emphasis Type="Italic">p</Emphasis>-Modes in Non-Vertical Magnetic Fields

Sunspots absorb and scatter incident f- and p-modes. Until recently, the responsible absorption mechanism was uncertain. The most promising explanation appears to be mode conversion to slow magnetoacoustic-gravity waves, which carry energy down the magnetic field lines into the interior. In vertical magnetic field, mode conversion can adequately explain the observed f-mode absorption, but is too inefficient to account for the absorption of p-modes. In the first paper of the present series we calculated the efficiency of fast-to-slow magnetoacoustic-gravity wave conversion in uniform non-vertical magnetic fields. We assumed two-dimensional propagation, where the Alfvén waves decouple. In comparison to vertical field, it was found that mode conversion is significantly enhanced in moderately inclined fields, especially at higher frequencies. Using those results, Cally, Crouch, and Braun showed that the resultant p-mode absorption produced by simple sunspot models with non-vertical magnetic fields is ample to explain the observations. In this paper, we further examine mode conversion in non-vertical magnetic fields. In particular, we consider three-dimensional propagation, where the fast and slow magnetoacoustic-gravity waves and the Alfvén waves are coupled. Broadly speaking, the p-mode damping rates are not substantially different to the two-dimensional case. However, we do find that the Alfvén waves can remove similar quantities of energy to the slow MAG waves.     

Further Evidence Suggestive of a Solar Influence on Nuclear Decay Rates

Recent analyses of nuclear decay data show evidence of variations suggestive of a solar influence. Analyses of datasets acquired at the Brookhaven National Laboratory (BNL) and at the Physikalisch-Technische Bundesanstalt (PTB) both show evidence of an annual periodicity and of periodicities with sidereal frequencies in the neighborhood of 12.25 year^?1 (at a significance level that we have estimated to be 10^?17). It is notable that this implied rotation rate is lower than that attributed to the solar radiative zone, suggestive of a slowly rotating solar core. This leads us to hypothesize that there may be an ??inner tachocline?? separating the core from the radiative zone, analogous to the ??outer tachocline?? that separates the radiative zone from the convection zone. The Rieger periodicity (which has a period of about 154 days, corresponding to a frequency of 2.37 year^?1) may be attributed to an r-mode oscillation with spherical-harmonic indices l=3,m=1, located in the outer tachocline. This suggests that we may test the hypothesis of a solar influence on nuclear decay rates by searching BNL and PTB data for evidence of a ??Rieger-like?? r-mode oscillation, with l=3,m=1, in the inner tachocline. The appropriate search band for such an oscillation is estimated to be 2.00??C?2.28 year^?1. We find, in both datasets, strong evidence of a periodicity at 2.11 year^?1. We estimate that the probability of obtaining these results by chance is 10^?12.     

Millisecond radio spikes on long centimetre and short decimetre wavelengths and occurrence frequency

High time-resolution data observed in two periods, respectively, by three frequencies (1.42, 2.84, and 3.67 GHz) or four frequencies (1.42, 2.00, 2.84, and 4.00 GHz) of fast sampling radiotelescopes were processed. Obtained were some significant results showing that during the obviously rising or maximum phases of solar cycle 22, the occurrence frequency of millisecond radio spikes at three or four frequencies decreased with the frequency increase and the highest occurrence frequency was at 1.42 GHz. If we assume the secondx-mode is pre-dominant in the growth rate of ECM instability, we calculate the magnetic intensity of source regions with spike bursts at the four frequencies and interpret the occurrence frequency of millisecond radio spikes on long centimetre and short decimetre wavelengths. Finally, this paper suggests that, owing to the Razing effect, whenf126 MHz the occurrence frequency of millisecond radio spikes starts to decrease.     

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.     

On Short-Term Periodicity of the Solar Radius Measurements

The aim of the present study is to investigate the short-term periodicity in the solar radius measurements and to compare with the short periods in sunspot numbers, sunspot areas and flare index data. The spectral analysis of data sets covering a time interval from 26 February 2000 to 26 October 2007 during Solar Cycle 23 were made by using the Date Compensated Discrete Fourier Transform (DCDFT). The power spectrum of solar radius data corrected for the seeing effect gives an evident peak at 25.7 days with the amplitude of 0.034 arcsec, which is slightly different from the peaks of 26.2 and 26.7 days produced by sunspot numbers and sunspot areas data, respectively. Besides, the main peak of 25.7 days detected in the power spectrum of solar radius data is in agreement with the period of 25.5 days, suggested to be the fundamental period of the Sun by Bai and Sturrock (in Nature 350, 141, 1991).     

Toward Waveform Heliotomography: Observing Interactions of Helioseismic Waves with a Sunspot

We investigate how helioseismic waves that originate from effective point sources interact with a sunspot. These waves are reconstructed from observed stochastic wavefields on the Sun by cross-correlating photospheric Doppler-velocity signals. We select the wave sources at different locations relative to the sunspot, and investigate the p- and f-mode waves separately. The results reveal a complicated picture of waveform perturbations caused by the wave interaction with the sunspot. In particular, it is found that for waves originating from outside of the sunspot, p-mode waves travel across the sunspot with a small amplitude reduction and slightly higher speed, and wave amplitude and phase get mostly restored to the quiet-Sun values after passing the sunspot. The f-mode wave experiences some amplitude reduction passing through the sunspot, and the reduced amplitude is not recovered after that. The wave-propagation speed does not change before encountering the sunspot and inside the sunspot, but the wavefront becomes faster than the reference wave after passing through the sunspot. For waves originating from inside the sunspot umbra, both f- and p-mode waves show significant amplitude reductions and faster speed for all propagation paths. A comparison of positive and negative time lags of cross-correlation functions shows an apparent asymmetry in the waveform changes for both the f- and p-mode waves. We suggest that the waveform variations of the helioseismic waves interacting with a sunspot found in this article can be used for developing a method of waveform heliotomography, similar to the waveform tomography of the Earth.