Multiperiodic irradiance changes caused by r-modes and g-modes

More than 20 real periodicities ranging from 20 days to 2 years modulate the solar irradiance data accumulated since November 1978 by Nimbus 7. Many are quite strong during the first three years (solar maximum) and weak after that. There is a high correspondence between periods in irradiance and 28 periods predicted from the rotation and beating of global solar oscillations (r-modes and g-modes). Angular states = 1, 2, and 3 are detected as well as some unresolved r-mode power at higher . The prominence of beat periods implies a nonlinear system whose effective nonlinear power was measured to be about 2. This analysis constitutes a detection of r-modes in the Sun and determines from them a mean sidereal rotation rate for the convective envelope of 459 ± 4 nHz which converts to a period of 25.2 days (27.l^d, synodic).     

Properties of r-modes in the Sun

Global oscillations of the Sun (r-modes) with very long periods 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14^th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. Radial fine splitting which lifts the degeneracy in n is very small (20 nHz or less) for all n 14 trapped in the envelope. But, if splitting could be detected, we would have a valuable new constraint on solar convection theories.     

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.     

On properties of the fourier harmonics in the limit-cycle models of classical cepheids

The Fourier coefficients of the hydrodynamic variables are calculated for the limit-cycle models of classical Cepheids having periods from 7.2 to 10.9 days. In adiabatically pulsating layers of the stellar envelope, each Fourier harmonic of orderk 8 is shown to be identified with a corresponding standing wave, so that the pulsation motions of the adiabatic layers may be represented as a superposition of standing waves. Each Fourier harmonic of orderk may also be identified with the eigenfunction of orderl of the linear adiabatic wave equation when the resonance condition _l /₀ =k is fulfilled. The spectra of the oscillatory moment of inertia and the spectra of kinetic energy obey the power law for the Fourier harmonics of orderk 15, the spectrum slope being steeper for shorter pulsation periods. In the helium and hydrogen ionizing regions all of the Fourier harmonics drive the pulsation instability, whereas in the radiative damping region the mechanical work done by each Fourier harmonic is negative. In classical Cepheids having periods shorter than 10 days the period dependence of the secondary bump is due to phase changes of the second order Fourier harmonic in the outer nonadiabatic layers of the stellar envelope. At a pulsation period of II 9.7 days the second order Fourier harmonic is identified with the second overtone. At periods II > 10 days the second order Fourier harmonic tends to be attracted by the fundamental mode in such a way that their phases coincide in the outer layers of the stellar envelope.     

Low-Degree Low-Order Solar p Modes As Seen By GOLF On board SOHO

Data recovered from the GOLF experiment on board the ESA/NASA SOHO spacecraft have been used to analyze the low-order low-degree solar velocity acoustic-mode spectrum below =1.5 mHz (i.e., 1n9,l2). Various techniques (periodogram, RLAvCS, homomorphic-deconvolution and RLSCSA) have been used and compared to avoid possible biases due to a given analysis method. In this work, the acoustic resonance modes sensitive to the solar central region are studied. Comparing results from the different analysis techniques, 10 modes below 1.5 mHz have been identified.     

Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity _–/BNand absorptivity _– B/Nfor e-mode, effective temperature T _effand frequency of peak brightness _p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/_B). Their statistical error is, respectively, ±18% and ±29% for _–/BNand _– B/Nfor 10/_B100, ±128% and and ±170% for 2/_B10.     

Intermediate degree p-mode frequency splittings near solar maximum

We report on observations of global solar Ca K-line intensity oscillations taken in May 1991 from Mees Solar Observatory, Hawaii. We measurep-mode frequency splittings for modes of spherical harmonic degrees between 20 and 129 averaged over the radial order of the modes. Our measurement of the antisymmetric component of the splittings is comparable with previous measurements and thus indicates a decrease in the latitudinal differential rotation with depth into the convection zone and the upper radiative zone. We find evidence for a 1% variation in the rotation rate of the upper convection zone roughly in phase with the solar activity cycle. Our measurement of the symmetric component of the splittings is of the same order as was reported from the previous solar maximum and is an order of magnitude larger than has been measured near solar minimum. From the degree dependence of the symmetric component of the splittings, we find evidence for an aspherical fractional sound speed perturbation located at a depth of 0.85 ± 0.05 solar radii. This perturbation has a magnitude ofc/c +9 × 10^–4 at the equator relative to the poles. Additionally, there is evidence for a near-surface aspherical sound speed perturbation of smaller magnitudec/c +4 × 10^–4 at the equator relative to the poles. If an intense global magnetic field were the dominant source of the observed symmetric component of the splittings, instead of latitudinal gradients in the sound speed, then global fields of order 10⁵ G would be required in the convection zone.     

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.     

Spectroscopic Data for the 6it s6it p 3 P1 level of Lu+ for the Determination of the Solar Lutetium Abundance

We report spectroscopic measurements on the 6s6p ³P₁ level of Lu⁺ at 28503.16 cm^-1. The radiative lifetime of this level was measured to be 37.4 ± 1.9 ns using time-resolved laser-induced fluorescence of a slow ion beam. Branching fractions were determined from Lu spectra recorded using the 1.0 m Fourier transform spectrometer at the National Solar Observatory. Thelog(gf) values determined by combining the radiative lifetime and branching fractions for the 3507.39, 5983.90, and 6221.87 (air wavelengths) lines are - 1.16 ± 0.03, - 1.16 ± 0.06, and -0.76 ± 0.04, respectively. The 6221.87 line has been identified by Bord, Cowley, and Mirijanian (1997) as the best candidate for the determination of the solar lutetium abundance because it is only slightly blended in the solar spectrum. The present 6221.87 transition probability measurement brings their solar lutetium abundance into good agreement with the CI chondrite abundance.     

Evidence for Long-term Retrograde Motions of Sunspot Patterns and Indications of Coupled g-mode Rotation Rates

Solar g-modes are global oscillations that would exist primarily in the radiative zone (RZ) and would be excited by either convective overshoot or nuclear burning in the core. Wolff and O’Donovan (Astrophys. J. 661, 568, 2007) proposed a non-linear coupling of g-modes into groups that share the same harmonic degree ℓ. Each group (denoted set(ℓ)) exhibits a unique retrograde rotation rate with respect to the RZ that depends mainly on ℓ. The coupling yields a standing wave (nearly stationary in longitude) that has two angularly defined hot spots offset from the equator on opposite sides of the Sun that would deposit energy asymmetrically in the lower convective envelope (CE). It is anticipated that when two or more groups overlap in longitude, an increase in local heating would influence the distribution of sunspots. In this paper, we scanned a multitude of rotational reference frames for sunspot clustering to test for frames that are concordant with the rotation of these g-modes sets. To achieve this, spherical harmonic filtering of sunspot synoptic maps was used to extract patterns consistent with coalesced g-modes. The latitude band, with minimal differential rotation, was sampled from each filtered synoptic map and layered into a stackplot. This was progressively shifted, line-by-line, into different rotational reference frames. We have detected long-lived longitudinal alignments, spanning 90 years of solar cycles, which are consistent with the rotation rate of the deep solar interior as well as other rotational frames predicted by the coupled g-mode model. Their sidereal rotation rates of 370.0, 398.8, 412.7, 418.3, 421.0, 424.2 and 430.0 nHz correspond, respectively, to coupled g-modes for ℓ = 2 through 7 and G, where G is a set with high ℓ values or a group of such sets (unresolved) that rotate almost as fast as the RZ. While the clustering in these reference frames offers new approaches for studying the longitudinal behavior of solar activity, it tentatively leads to the more profound conclusion that a portion of the driving force for sunspot occurrence is linked to energy extracted from the solar core and deposited at the top of the RZ by solar g-modes.     

Low-l 5-min oscillation observations

Medium resolution CCD-spectrograph observations have been obtained that are suitable for studying long spatial wavelength 5-min oscillations. We find evidence that at wavelengths of order one solar radius the oscillation field is not isotropic. It is also not well described by modes of uniform excitation. The velocity power density per spherical harmonic increases with decreasing l to 1.1 × 10³ cm² s^–2 per 3.5 × 10^–4 Hz angular frequency bandwidth at l = 4. These results are inconsistent with the data of Fossat and Ricort (1975) as analyzed by Christensen-Dalsgaard and Gough (1982), who found a substantially constant modal amplitude at intermediate l values. It is interesting that other calculations have seen a similar dependence at small l in the growth rate of p-modes due to the -mechanism.Visiting Astronomer, Sacramento Peak Observatory.     

Solar irradiance changes caused by g-modes and large scale convection

Solar irradiance measurements from the ACRIM experiment show a clear response to the rotation periods of g-mode oscillations (l = 1, 2, and 3) and their first harmonics. Peaks in the ACRIM spectrum at 16.6, 18.3, 20.7, 36.5, and - 71 days all lie within about 1% of periods arising from g-mode rotation. This means that the g-modes are a fundamental cause of irradiance fluctuations. On time scales of months and less they modulate the irradiance by means of transient flows of global scale which they stimulate in the Sun's convective envelope. Dimensional arguments indicate that the flows carry up heat at an average rate 10^-3 L which is not in conflict with observed changes in the irradiance. Five additional tests for g-modes and large-scale convection are given. An instability is described which undermines diffusion models of sunspot energy storage.     

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.     

Maximum temperatures for radiation from plasma waves

We derive upper limits to the radiation temperaturesT ^t(k) for emission near the fundamental and second harmonic of the electron plasma frequency in terms of the effective temperature for plasma wavesT ^l(k). We findT ^t(k)(c/(3)^1/2 V _e)³ T ^l(k) for emission near the fundamental which differs from the result of Melrose (1970b) by the factor in parentheses. This factor can exceed 4×10⁴ in some plasmas. The conditions under which this limit could be reached are delinated. For emission near the second harmonicT ^t(k)T ^l(k) since the absorption coefficient in this case can only be positive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Solar rotation as determined from OSO-4 EUV spectroheliograms

Spectroheliograms obtained in extreme ultraviolet (EUV) lines and the Lyman continuum are used to determine the rotation rate of the solar chromosphere, transition region, and corona. A cross-correlation analysis of the observations indicates the presence of differential rotation through the chromosphere and transition region. The rotation rate does not vary with height. The average sidereal rotation rate is given by (deg day^–1) = 13.46 - 2.99 sin² B where B is the solar latitude. This rate agrees with spectroscopic determinations of the photospheric rotation rate, but is slower by 1 deg day^–1) = 13.46 - 2.99 sin² than rates determined from the apparent motion of photospheric magnetic fields and from the brightest points of active regions observed in the EUV. The corona does not clearly show differential rotation as do the chromosphere and transition region.     

STATISTICAL PROPERTIES OF THE PULSES IN THE SOLAR p-MODE POWER

We have revealed the periods of good visibility for each individual mode of low spherical degree using irradiance data from the IPHIR experiment. Their statistical properties and the influence on the resulting line shapes are discussed. The analysis of the temporal change of each mode power by Fourier transform with a running temporal window was performed. The running mean power of p-modes (=0, n=17–24 and =1, n=16–23) apparently changes with the rotation of the Sun. There is well visible an anticorrelation of the p-mode power with the mean solar magnetic field and less significant correlation with daily sunspot number.     

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.     

The unusual anisotropic solar particle event of November 18, 1968

The ground level event of November 18, 1968, was unusual in that pronounced anisotropy persisted essentially until the cessation of the arrival at the earth of relativistic protons. Real and significant differences were observed in the intensity profiles at different neutron monitor stations. By a method of successive approximations, the geographical coordinates of the axis of symmetry were determined as: latitude = - 25° ± 10° and longitude = -35° ± 10°. The exponent in a power law spectral representation over the narrow range covered by the nucleonic intensity measurements was 5.The onset times of the GLE were related to the angular differences between the mean directions of viewing and the axis of symmetry. The event differed markedly from earlier isotropic events that were well described by diffusion theory, but was compatible with the predictions of a model envisaging diffusion only in the vicinity of the Sun (radius R of solar envelope 34 solar radii). The diffusion coefficient D 3 × 10²¹ cm²/s is consistent with that deduced for earlier isotropic events, but the values of other parameters are smaller than those derived for the only previously observed event to which the model of diffusion in an inhomogeneous medium was applicable (May 4, 1960).It is concluded that the observed one hundred percent anisotropy was a direct consequence of the propagation mechanism rather than other postulated causes. Furthermore, the observed large pitchangle distribution was produced by scattering from small scale field irregularities.This research was sponsored by the National Science Foundation and Air Force Cambridge Research Laboratories, Office of Aerospace Research, under Contract No. F19628-70-C-0190, but the report does not necessarily reflect endorsement by the sponsor.     

Correlation of Solar Indices with Solar euv Fluxes

The paper presents a more extensive comparison of Extreme Ultraviolet (EUV) irradiances during AE-E (1977–1980), Pioneer Venus (1979–1992) and SEM/SOHO (1996 onwards) with other solar indices than has been discussed previously. For long-term changes (solar cycle), all indices had similar trends and inter-correlations were high, so that any one could serve as a proxy for the other. For intermediate time-scales (monthly means), only L, F10 (2800 MHz) and Mgii had reasonably high correlations with EUV. The 2695 MHz radio emission also had a high correlation. For daily values, data for many indices are intermittant and these cannot serve as proxies. Again, only L, F10 (and 2695 MHz), Mgii stand out as possible proxies for EUV, particularly during intervals of strong 27-day sequences.     

The observed intermediate-degreef-mode eigenfrequency spectrum of the sun and tests of the mode classification proficiency

Power spectra of the 1979 solar differential observations (Bos, 1982) have been analyzed for evidence of intermediate-degreef-modes. A set of 19 intermediate-degreef-mode multiplets has been identified and classified based on more than 300 classified modes of oscillation. The angular degree of the multiplets ranges from 18 to 36. Them=0 eigenfrequency spectrum, measured with an accuracy of typically 0.01–0.02 Hz, was found to be on the average 10 Hz greater than that predicted by the standard solar model of Saio (1982). Rotational splitting effects up to fifth order inm were obtained. The multiplet fine structure that is linear inm was found to be consistent with the internal rotation curve obtained by Hillet al. (1986a). The multiplet fine structure that is described by terms that are cubic and fifth order inm were found to be consistent with the differential rotation curve of Hillet al. (1986b). The probability that this set of 19 Zeeman-like frequency patterns were obtained from a set of peaks randomly distributed in frequency was estimated to be 10^–9. The effectiveness of the mode detection and classification program in this work has been established in part by observing the horizontal spatial properties of thef-mode eigenfunctions. One consequence obtained from the study of the horizontal spatial properties of the modes is the estimate, obtained observationally, of the number of correct mode identifications: these results indicate that 73±6% of the 374 modes are correctly classified.SCLERA is an acronym for Santa Catalina Laboratory for Experimental Relativity by Astrometry, a facility operated by the University of Arizona.