High-degree Oscillations Research Articles

Effects of differential rotation and meridional circulation in solar oscillations of high degree l

Helioseismic measurements at high degree l are sensitive to mode couplings induced by large-scale flows, with the largest contribution coming from the solar differential rotation. The coupling becomes strong at high degree l, when frequency spacings between interacting modes become small, calling for a more accurate theoretical prediction of the mode-coupling effects in helioseismic data analysis. In this paper, the currently available description based on the quasi-degenerate perturbation theory is developed to a higher order, and extended to include the possible contributing effects of solar meridional circulation. A semi-analytic asymptotic description is developed for effects of the centrifugal forces on the oscillation frequencies of high degree l. Numerical estimates of the corresponding effects in the observational data are discussed.

Properties of high-degree oscillation modes of the Sun observed with Hinode/SOT

Aims. With the Solar Optical Telescope on Hinode, we investigate the basic properties of high-degree solar oscillations observed at two levels in the solar atmosphere, in the G-band (formed in the photosphere) and in the Ca II H line (chromospheric emission). Methods. We analyzed the data by calculating the individual power spectra as well as the cross-spectral properties, i.e., coherence and phase shift. The observational properties are compared with a simple theoretical model, which includes the effects of correlated noise. Results. The results reveal significant frequency shifts between the Ca II H and G-band spectra, in particular above the acoustic cut-off frequency for pseudo-modes. The cross-spectrum phase shows peaks associated with the acoustic oscillation (p-mode) lines, and begins to increase with frequency around the acoustic cut-off. However, we find no phase shift for the (surface gravity wave) f-mode. The observed properties for the p-modes are qualitatively reproduced in a simple model with a correlated background if the correlated noise level in the Ca II H data is higher than in the G-band data. These results suggest that multi-wavelength observations of solar oscillations, in combination with the traditional intensity-velocity observations, may help to determine the level of the correlated background noise and to determine the type of wave excitation sources on the Sun.

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.

THE LINE-PROFILE VARIATIONS OF THETA2 TAURI

ABSTRACT With a 5.4-hour time series of high-resolution CFHT spectra, the oscillations of the rapidly-rotating delta Scuti star Theta2 Tauri (A7 IV + A5 V) are investigated. Line-profile variations are discovered and identified with the spectrum of the primary star of this binary system. Radial velocity variations are derived from the data and analyzed to reveal an oscillation frequency near 13.7 cycles day-1. Variations within the absorption profiles are analyzed with a Fourier-Doppler Imaging (FDI) technique to reveal that high-degree oscillations with a frequency of 16.1 cycles day -1 and an apparent degree of about ℓ = 8 are also present in the star. Whereas the low-degree variations of Theta2 Tau have been shown to be consistent with p-modes of radial order n=2 or 3, the identification of the high-degree variations in terms of pressure modes requires confirmation with theoretical models.

A NONRADIAL PULSATION MODEL FOR THE RAPIDLY ROTATING (DELTA) SCUTI STAR K2 BOOTIS

ABSTRACT A sectorial nonradial pulsation model is used to construct theoretical line profiles which mimic the variations for Kappa2 Boo. Synthetic spectra generated with the appropriate Teff and log g are used as input. It is found that the data can be reproduced by the combination of a high-degree l is approximately equal to 12 mode with Posc aproximately equal to 0.071 d, and a low-degree mode, l is approximately equal to 0-2 with Posc approximately equal to 0.071-0.079 d. The projected rotational velocity (v sin i - 115 ±5 km/s) was determined by fitting synthetic line profiles to the observed spectra. The velocity amplitude of the high-degree oscillations is estimated to be about 3.5 km/s. It is found that the ratio of the horizontal and radial pulsation amplitudes is small (about 0.02) and consistent with p-mode oscillations. Comparisons are made with models invoking starspots, and it is impossible to fit the observations of Kappa2 Boo by a starspot model without assuming unrealistic values of radius or equatorial velocity.

Seismological measurement of solar helium abundance

THE internal structure and evolution of the Sun depends on its chemical composition, particularly the helium abundance. In addition, the helium abundance in the solar envelope is thought to represent the protosolar value, making it a datum of cosmological significance. Spectroscopic measurements of the helium abundance are uncertain, and the most reliable estimates until now have come from the calibration of solar evolutionary models. The frequencies of solar acoustic oscillations are sensitive, however, to the behaviour of the speed of sound in the Sun's helium ionization zone, which allows a helioseismological determination of the helium abundance. Sound-speed inversion of helioseismological data can be used for this purpose1–3, but precise frequency measurements of high-degree oscillation modes are needed. Here we describe a new approach based on an analysis of the phase shift of acoustic waves4,5 of intermediate-degree modes. From the accurate intermediate-mode data now available6, we obtain a helium mass fraction Y = 0.25 ±0.01 in the solar convection zone, significantly smaller than the value Y = 0.27−0.29 predicted by recent solar evolutionary models7–9. The discrepancy indicates either that initial helium abundance was reduced in the envelope by downward diffusion9 or that the protosolar value was lower than currently accepted.

Glacial rebound and relative sea-level variations: a new appraisal

Summary. Late Pleistocene and Holocene changes in sea-level at technically stable shorelines contain information on the melting history of the ice sheets and on the response of the Earth to changes in surface loads on time scales of 104yr. Some separation of parameters defining the ice loads and the Earth's response can be achieved by examining sea-level change at different sites around the world and at different epochs. This paper examines the mathematical requirements for obtaining satisfactory solutions for the sea-level equation rather than emphasizing results for the Earth's response to the surface loads. an examination of the equation expressing the sea-level variation on a viscoelastic earth indicates that careful consideration needs to be given to both the definition of the ice load and the geometry of the redistributed water load if geophysically significant Earth-response parameters are to be deduced from observations of relative sea-level. the spectrum of the 5°x 5° area-mean description of the ice load, widely used in glacial rebound studies, contains significant power at high degrees (n > 30) and can result in substantial spatial variations in sea-level unless a thick lithosphere is introduced in the Earth's response function. A smoothed 1°× 1° description of the ice model avoids these high-degree oscillations in relative sea-level and produces satisfactory sea-level results without requiring a thick lithosphere. At far field sites, the Holocene sea-levels are sensitive to the Earth's response to the meltwater loading in the vicinity of the site and a high-degree spatial resolution of coastline geometry is required to model the mantle flow driven by the differential loading about the site. At some sites convergence of the solution to the sea-level equation is not obtained, even when the solution is expanded to degree 180. Convergent solutions at lower degrees can be achieved by introducing earth models with a moderately thick lithosphere. If high-resolution ice and meltwater load models are not used then the tendency will be to overestimate the effective elastic thickness of the lithosphere. Estimates of mantle viscosity are also of questionable value if these high resolution models are not used. A preliminary examination of sea-levels at sites in both the near- and far-field places an upper limit of about 50–80 km on the effective lithospheric thickness. These sea-level observations are also consistent with an upper mantle viscosity of about 1021 Pas with a lower mantle viscosity in the range of 1021-1023Pa s.

On the Detection of Subphotospheric Convective Velocities and Temperature Fluctuations

AbstractA procedure is outlined for estimating the influence of large-scale convective eddies on the wave patterns of five-minute oscillations of high degree. The method is applied to adiabatic oscillations, with frequency ω and wave number k, of a plane-parallel polytropic layer upon which is imposed a low-amplitude convective flow. The distortion to the k – ω relation has two constituents: one depends on the horizontal component of the convective velocity and has a sign which depends on the sign of ω/k; the other depends on temperature fluctuations and is independent of the sign of ω/k. The magnitude of the distortion is just at the limit of present observational sensitivity. Thus there is reasonable hope that it will be possible to reveal some aspects of the large-scale flow in the solar convection zone