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.     

Acoustic Mode Frequencies of the Sun During the Minimum Phase Between Solar Cycles 23 and 24

We investigate the spatial and temporal variations of the high-degree mode frequencies calculated over localized regions of the Sun during the extended minimum phase between solar cycles 23 and 24. The frequency shifts measured relative to the spatial average over the solar disk indicate that the correlation between the frequency shift and magnetic field strength during the low-activity phase is weak. The disk-averaged frequency shifts computed relative to a minimal activity period also reveal a moderate correlation with different activity indices, with a maximum linear correlation of about 72?%. From the investigation of the frequency shifts at different latitudinal bands, we do not find a consensus period for the onset of solar cycle 24. The frequency shifts corresponding to most of the latitudes in the northern hemisphere and 30° south of the equator indicate the minimum epoch to be February 2008, which is earlier than inferred from solar activity indices.     

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.     

Some results of a statistical analysis of the S-component of solar radio emission

A statistical treatment of the mean daily solar radio flux between 9400 and 1000 MHz (cm-region) for two solar cycles leads to the following results: No differences have been found between the synodic rotation rates T _mon calculated for different single frequency time series as a whole (rigid rotation of emitting regions). From a piece-wise time series analysis it is concluded that T _mon averaged over all observed frequencies and over times belonging to related years of the two cycles shows a well-expressed dependence on cycle with a maximum of 28.8d following 2 y after the activity minimum and a minimum of 27d shortly after polar magnetic field reversal. Discrete spectral lines with periods smaller than T _mon point on the existence of elementary longitudinal regions of extension between 25° and 33°. The observed facts would support a relation between the sources of the large-scale magnetic field and the S-component.     

Solar p and g modes in a model with a convection layer above a sub-adiabatic interior

We study high-order acoustic modes which reside in the outer layers of the solar interior. Magnetic field effects are not taken into account in this paper as we wish first to filter out how the modal frequencies depend on physical characteristics of a particular model structure of the Sun. In particular, we are interested in how the modal frequencies of solar global oscillations depend on the thickness of the convection layer and on the temperature gradient of the solar interior below. The model we use consists of three planar layers: an isothermal atmosphere, while the convection layer and the interior have temperature gradients that are adiabatic and sub-adiabatic, respectively. The presence of a convection layer with a finite thickness brings in additional modes while the variations in temperature gradient of the interior cause shifts in eigenfrequencies that are more pronounced for the p modes than for the g modes. These shifts can easily be of the order of several hundreds of Hz, which is much larger than the observational accuracy.     

Global Oscillations at Low Frequency from the SOHO mission (GOLF)

The GOLF experiment on the SOHO mission aims to study the internal structure of the sun by measuring the spectrum of global oscillations in the frequency range 10^–7 to 10^–2 Hz. Bothp andg mode oscillations will be investigated, with the emphasis on the low order long period waves which penetrate the solar core. The instrument employs an extension to space of the proven ground-based technique for measuring the mean line-of-sight velocity of the viewed solar surface. By avoiding the atmospheric disturbances experienced from the ground, and choosing a non-eclipsing orbit, GOLF aims to improve the instrumental sensitivity limit by an order of magnitude to 1 mm s^–1 over 20 days for frequencies higher than 2.10^–4 Hz. A sodium vapour resonance cell is used in a longitudinal magnetic field to sample the two wings of the solar absorption line. The addition of a small modulating field component enables the slope of the wings to be measured. This provides not only an internal calibration of the instrument sensitivity, but also offers a further possibility to recognise, and correct for, the solar background signal produced by the effects of solar magnetically active regions. The use of an additional rotating polariser enables measurement of the mean solar line-of-sight magnetic field, as a secondary objective.     

Lifetimes of High-Degree <Emphasis Type="Italic">p</Emphasis> Modes in the Quiet and Active Sun

We study variations of the lifetimes of high-ℓ solar p modes in the quiet and active Sun with the solar activity cycle. The lifetimes in the degree range ℓ=300 – 600 and ν=2.5 – 4.5 mHz were computed from SOHO/MDI data in an area including active regions and quiet Sun using the time – distance technique. We applied our analysis to the data in four different phases of solar activity: 1996 (at minimum), 1998 (rising phase), 2000 (at maximum), and 2003 (declining phase). The results from the area with active regions show that the lifetime decreases as activity increases. The maximal lifetime variations are between solar minimum in 1996 and maximum in 2000; the relative variation averaged over all ℓ values and frequencies is a decrease of about 13%. The lifetime reductions relative to 1996 are about 7% in 1998 and about 10% in 2003. The lifetime computed in the quiet region still decreases with solar activity, although the decrease is smaller. On average, relative to 1996, the lifetime decrease is about 4% in 1998, 10% in 2000, and 8% in 2003. Thus, measured lifetime increases when regions of high magnetic activity are avoided. Moreover, the lifetime computed in quiet regions also shows variations with the activity cycle.     

The subsurface radial gradient of solar angular velocity from MDI f-mode observations

We report quantitative analysis of the radial gradient of solar angular velocity at depths down to about 15 Mm below the solar surface for latitudes up to 75° using the Michelson Doppler Imager (MDI) observations of surface gravity waves (fmodes) from the Solar and Heliospheric Observatory (SOHO). A negative outward gradient of around –400 nHz/R , equivalent to a logarithmic gradient of the rotation frequency with respect to radius which is very close to –1, is found to be remarkably constant between the equator and 30° latitude. Above 30° it decreases in absolute magnitude to a very small value at around 50°. At higher latitudes the gradient may reverse its sign: if so, this reversal takes place in a thin layer extending only 5 Mm beneath the visible surface, as evidenced by the most superficial modes (with degrees l>250). The signature of the torsional oscillations is seen in this layer, but no other significant temporal variations of the gradient and value of the rotation rate there are found.     

The Effect of Abnormal Granulation on Acoustic Wave Travel Times and Mode Frequencies

Observations indicate that in plage areas (i.e. in active regions outside sunspots) acoustic waves travel faster than in the quiet Sun, leading to shortened travel times and higher p-mode frequencies. Coupled with the 11-year variation of solar activity, this may also explain the solar cycle variation of oscillation frequencies. While it is clear that the ultimate cause of any difference between the quiet Sun and plage is the presence of magnetic fields of order 100 G in the latter, the mechanism by which the magnetic field exerts its influence has not yet been conclusively identified. One possible such mechanism is suggested by the observation that granular motions in plage areas tend to be slightly “abnormal”, dampened compared to the quiet Sun. In this paper we consider the effect that abnormal granulation observed in active regions should have on the propagation of acoustic waves. Any such effect is found to be limited to a shallow surface layer where sound waves propagate nearly vertically. The magnetically suppressed turbulence implies higher sound speeds, leading to shorter travel times. This time shift Δ τ is independent of the travel distance, while it shows a characteristic dependence on the assumed plage field strength. As a consequence of the variation of the acoustic cutoff with height, Δ τ is expected to be significantly higher for higher frequency waves within the observed regime of 3 – 5 mHz. The lower group velocity near the upper reflection point further leads to an increased envelope time shift, as compared to the phase shift. p-mode frequencies in plage areas are increased by a corresponding amount, Δ ν/ν=ν Δ τ. These characteristics of the time and frequency shifts are in accordance with observations. The calculated overall amplitudes of the time and frequency shifts are comparable to, but still significantly less than (by a factor of 2 to 5), those suggested by measurements.     

How Good are the Predictions for Oscillation Frequencies

We have used available intermediate degree p-mode frequencies for solar cycle 23 to check the validity of previously derived empirical relations for frequency shifts (Jain et al., 2000). We find that the calculated and observed frequency shifts during the rising phase of cycle 23 are in good agreement. The observed frequency shift from minimum to maximum of this cycle as calculated from MDI frequency data sets is 251±7 nHz and from GONG data is 238±11 nHz. These values are in close agreement with the empirically predicted value of 271±22 nHz.     

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.     

Distribution of magnetic flux on the solar surface and low-degree p-modes

The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs between the rising and falling phases of the solar cycle, leading to a hysteresis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree ( l ≤3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of modes with different order and degree as a function of time. The resulting curves are periodic functions (in simple cases just sine curves) shifted in time by different amounts for the different modes. We show how this may easily lead to hysteresis cycles comparable to those observed. Our models suggest that high-latitude fields are necessary to produce a significant difference in hysteresis between odd- and even-degree modes. Only magnetic field distributions within a small parameter range are consistent with the observations by Jiménez-Reyes et al. Observations of p-mode frequency shifts are therefore capable of providing an additional diagnostic of the magnetic field near the solar poles. The magnetic distribution that is consistent with the p-mode observations also appears reasonable compared with direct measurements of the magnetic field.     

Solar cycle changes in the high frequency spectrum

We present observations of high frequency, intermediate degree, Ca-K line solar intensity oscillations. We compare the peak frequencies determined from these 1991.4 observations with the peak frequencies from 1987.9 South Pole observations (Duvallet al., 1991) in that portion of the spatio-temporal diagram where the two datasets overlap (degrees between 30 and 150 and frequencies between 4 and 6.6 mHz). We find that temporal changes are detectable in the high frequency spectrum and are particularly large near 5.4 mHz. The m-averaged high frequency peaks decreased in frequency in 1991.4 compared to the peak frequencies measured in 1987.9. The magnitude of the frequency shift is of the order of 10 μHz near 5.4 mHz, increases with degree, and decreases to near zero both above and below 5.4 mHz. It is unlikely that these temporal changes in the high frequency spectrum are due to a change in the height of the subphotospheric acoustic source layer. A physical mechanism for these frequency shifts has not yet been identified.     

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.     

Lunar photometric properties at wavelengths 0.5-1.6 μm acquired by SELENE Spectral Profiler and their dependency on local albedo and latitudinal zones

The lunar photometric function, which describes the dependency of the observed radiance on the observation geometry, is used for photometric correction of lunar visible/near-infrared data. A precise photometric correction parameter set is crucial for many applications including mineral identification and reflectance map mosaics. We present, for the first time, spectrally continuous photometric correction parameters for both sides of the Moon for wavelengths in the range 0.5-1.6 μm and solar phase angles between 5° and 85°, derived from Kaguya (SELENE) Spectral Profiler (SP) data. Since the measured radiance also depends on the surface albedo, we developed a statistical method for selecting areas with relatively uniform albedos from a nearly 7000-orbit SP data set. Using the selected data set, we obtained empirical photometric correction parameter sets for three albedo groups (high, medium, and low). We did this because the photometric function depends on the albedo, especially at phase angles below about 20° for which the shadow hiding opposition effect is appreciable. We determined the parameters in 160 bands and discovered a small variation in the opposition effect due to the albedo variation of mafic mineral absorption. The consistency of the photometric correction was checked by comparing observations made at different times of the same area on the lunar surface. Variations in the spectra obtained were lower than 2%, except for the large phase angle data in mare. Lastly, we developed a correction method for low solar elevation data, which is required for high latitude regions. By investigating low solar elevation data, we introduced an additional correction method. We used the new photometric correction to generate a 1° mesh global lunar reflectance map cube in a wavelength range of 0.5-1.6 μm. Surprisingly, these maps reveal that high latitude (?75°) regions in both the north and south have much lower spectral continuum slopes (color ratio r_1547.7nm/r_752.8nm ? 1.8) than the low and medium latitude regions, which implies lower degrees of space weathering.     

Solar coronal streamers

The solar disk locations of 13 coronal streamers were determined from a combination of eclipse, K-coronameter (1 1/8r1 1/2 R ), and balloon-borne coronagraph (2<r<6 R ) observations taken during 1964 and 1965. Of this sample, three were observed twice on photographs taken over intervals of four and 28 days. Most of these streamers could be structurally associated with K-coronameter enhancements to establish their disk locations.Those features having known disk locations all lay above some stage of chromospheric disk activity in the form of active regions and prominences. The average lifetime of three K-coronameter streamer-enhancements, for which all or nearly all of their lifetimes were known, was about 4 solar rotations. Rotation rates for the lower latitude streamer-enhancements (30°) were essentially identical to the underlying surface. One high latitude feature ( 50°) which overlay a quiescent prominence had a rate equivalent to the surface rate at 30° latitude. In general those K-coronameter enhancements associated with streamers came into existence over time periods of 14 days and disappeared by gradually blending into the background coronal pattern. All the observed structures are explained by a model consisting of localized, high density features (streamers) which overlie disk activity and are imbedded in a uniform but weaker azimuthally-symmetric quiet corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A new observational strategy in search for solar g-modes

The aim of the present work is the detection of solar g-modes, by means of a new observational strategy based on the exploitation of their spatial and temporal properties. The basic data, obtained at the Observatorio del Teide in 1993, consists of daily solar velocity measurements taken continuously and sequentially at six different and symmetric positions on the solar disk. By correlating the time series resulting from the reduction process, from different solar disk positions and considering the geometrical properties of different modes (l,m) on the Sun's surface, some of these can be selectively eliminated or enhanced. Moreover, the main spectral features present in the resulting power spectra must have precise phase relations if they correspond to global solar g-modes. The severe constraints established by the above properties have been applied to the best observed series (summer 1993). As a result, a discrete series of peaks have been selected that fulfill all the imposed conditions and which can therefore be interpreted as being of solar origin.     

The emission and propagation of ∼40keV solar flare electrons

Electrons of ~ 40 keV energy observed at 1 AU are used as tracers to map the emission structure of a large active region, McMath plage 8905, which crossed the visible disk in July–August, 1967.The acceleration of 10–100 keV electrons is found to be a property of active regions with a certain stage of development, and is signaled by the emission of 20 keV X-rays. The emission of electrons into the interplanetary medium may be separate from the acceleration of the electrons. Type III radio emission at long wavelengths appears to indicate the escape of the electrons into the interplanetary medium.The subsequent electron propagation in the interplanetary medium is essentially scatter-free, and the profile of the electron appears to be determined predominantly by transport/storage processes in the solar corona. The emission structure for active region McMath plage 8905 consists of (1) an open cone of ~ 70° extent in solar longitude where electrons have direct access to interplanetary field lines; (2) a cone of propagation of 100° width in solar longitude, surrounding and including the open cone in which impulsive electron events are observed; and (3) an overall ~ 200° extent of solar longitude over which low, non-impulsive fluxes from the active region are observed. A model is presented to account for the observed structure. This type of emission structure may be present in other electron-active regions.     

Negative Energy And Angular Momentum Modes Of Thin Accretion Disks

This work derives the linearized equations of motion, the Lagrangian density, the Hamiltonian density, and the canonical angular momentum density for general perturbations [∝ exp (imφ) with m = 0, ± 1, ...] of a geometrically thin self-gravitating, homentropic fluid disk including the pressure. The theory is applied to “eccentric,” m = ± 1 perturbations of a geometrically thin Keplerian disk. We find m = 1 modes at low frequencies relative to the Keplerian frequency. Further, it is shown that these modes can have negative energy and negative angular momentum. The radial propagation of these low-frequency m = 1 modes can transport angular momentum away from the inner region of a disk and thus increase the rate of mass accretion. Depending on the radial boundary conditions there can be discrete low-frequency, negative-energy, m = 1 modes.     

Relation between the mode of oscillation and the velocity amplitude of chromospheric waves

The distribution of oscillation-amplitude for Doppler shifts in chromospheric lines is computed as a function of position on the disk and time frequency. High amplitude regions are restricted to a small part of the solar surface. Propagation modes are investigated with respect to the oscillation amplitude in the K line. Waves seem to be standing or evanescent for most of the points (small amplitude in K) and progressive for some other ones, with perhaps upward and downward motions (partial reflections). Mechanical energy could only escape into corona from narrow chromospheric structures.