On measuring low-degree p-mode frequency splitting with full-disc integrated data

The standard method of measuring rotational splitting from solar full-disc oscillation data, based on maximum-likelihood fitting of multi-Lorentzian profiles to oscillation power spectra, systematically overestimates the splitting. One of the reasons is that the maximum likelihood estimators (MLE) become unbiased only asymptotically as the number of data tends to infinity; for a finite data set they are often biased, inducing a systematic error. In this paper we assess by Monte Carlo simulations the amount of systematic error in the splitting measurement, using artificially generated power spectra. The simulations are carried out for multiplets of degree     2 and 3 with various signal-to-noise ratios, linewidths and observing times. We address the possible use of non-MLE estimators that could provide a smaller or negligible systematic error. The implication for asteroseismology is also discussed.     

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 quest for the solar g modes

Solar gravity modes (or g modes)—oscillations of the solar interior on which buoyancy acts as the restoring force—have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well-observed acoustic modes (or p modes). The relative high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this article, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made—from both data and data-analysis perspectives—to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.     

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.     

On the effect of error correlation on linear inversions

We have examined the effect on linear helioseismic inversions of correlations in data errors, taking an example from one-dimensional rotational splitting inversion. Artificial data with correlated errors were generated and then inverted with or without using the proper covariance matrix. The effects of using incorrect covariance matrices, on solutions as well as on trade-offs, are discussed. It is found that improper account of the correlations can be deleterious to the faithfulness of the inversions, and yields incorrect error estimates, which under some circumstances can lead to misleading inferences.     

Phase inversion of one-dimensional artificial seismic data

Oscillations of an inhomogeneous one-dimensional loop have been simulated for the purpose of examining the effect of excitation and damping on the sound-speed inversion based on phase analysis. It has been demonstrated that the procedure is robust against the realization noise arising from frequent, stochastic excitation of weakly damped waves, but that strong damping can spoil the inversion.     

AsteroFLAG: First results from hare‐and‐hounds Exercise #1

We report on initial results from the first phase of Exercise #1 of the asteroFLAG hare and hounds. The asteroFLAG group is helping to prepare for the asteroseismology component of NASA's Kepler mission, and the first phase of Exercise #1 is concerned with testing extraction of estimates of the large and small frequency spacings of the low‐degree p modes from Kepler‐like artificial data. These seismic frequency spacings will provide key input for complementing the exoplanet search data. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)