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Register a new userCalculation of Solar P-mode Oscillation Frequency Splittings Based on a Two-dimensional Solar Model
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Linghuai Li
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We compute the p-mode oscillation frequencies and frequency splittings that arise in a two-dimensional model of the Sun that contains toroidal magnetic fields in its interior.
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The solar rotation profile is well constrained down to about 0.25 R thanks to the study of acoustic modes. Since the radius of the inner turning point of a resonant acoustic mode is inversely proportional to the ratio of its frequency to its degree, only the low-degree p modes reach the core. The higher the order of these modes, the deeper they penetrate into the Sun and thus they carry more diagnostic information on the inner regions. Unfortunately, the estimates of frequency splittings at high frequency from Sun-as-a-star measurements have higher observational errors due to mode blending, resulting in weaker constraints on the rotation profile in the inner core. Therefore
A new fitting methodology is presented which is equally well suited for the estimation of low-, medium-, and high-degree mode parameters from $m$-averaged solar oscillation power spectra of widely differing spectral resolution. This method, which we call the Windowed, MuLTiple-Peak, averaged spectrum, or WMLTP Method, constructs a theoretical profile by convolving the weighted sum of the profiles of the modes appearing in the fitting box with the power spectrum of the window function of the observing run using weights from a leakage matrix that takes into account both observational and physical effects, such as the distortion of modes by solar latitudinal differential rotation. We demonstrate that the WMLTP Method makes substantial improvements in the inferences of the properties of the solar oscillations in comparison with a previous method that employed a single profile to represent each spectral peak. We also present an inversion for the internal solar structure which is based upon 6,366 modes that we have computed using the WMLTP method on the 66-day long 2010 SOHO/MDI Dynamics Run. To improve both the numerical stability and reliability of the inversion we developed a new procedure for the identification and correction of outliers in a frequency data set. We present evidence for a pronounced departure of the sound speed in the outer half of the solar convection zone and in the subsurface shear layer from the radial sound speed profile contained in Model~S of Christensen-Dalsgaard and his collaborators that existed in the rising phase of Solar Cycle~24 during mid-2010.
The variations of the frequencies of the low-degree acoustic oscillations in the Sun induced by magnetic activity show a dependence with radial order. The frequency shifts are observed to increase towards higher-order modes to reach a maximum of about 0.8 muHz over the 11-yr solar cycle. A comparable frequency dependence is also measured in two other main-sequence solar-like stars, the F-star HD49933, and the young 1-Gyr-old solar analog KIC10644253, although with different amplitudes of the shifts of about 2 muHz and 0.5 muHz respectively. Our objective here is to extend this analysis to stars with different masses, metallicities, and evolutionary stages. From an initial set of 87 Kepler solar-like oscillating stars with already known individual p-mode frequencies, we identify five stars showing frequency shifts that can be considered reliable using selection criteria based on Monte Carlo simulations and on the photospheric magnetic activity proxy Sph. The frequency dependence of the frequency shifts of four of these stars could be measured for the l=0 and l=1 modes individually. Given the quality of the data, the results could indicate that a different physical source of perturbation than in the Sun is dominating in this sample of solar-like stars.
We analyze and interpret SOHO/MDI data on oscillation frequency changes between 1996 and 2004 focusing on differences between activity minimum and maximum of solar cycle 23. We study only the behavior of the centroid frequencies, which reflect changes averaged over spherical surfaces. Both the f-mode and p-mode frequencies are correlated with general measures of the suns magnetic activity. However, the physics behind each of the two correlations is quite different. We show that for the f-modes the dominant cause of the frequency increase is the dynamical effect of the rising magnetic field. The relevant rise must occur in subphotospheric layers reaching to some 0.5 - 0.7 kG at a depth of about 5 Mm. However, the implied constraints also require the field change in the atmosphere to be so small that it has only a tiny dynamical effect on p-mode frequencies. For p-modes, the most plausible explanation of the frequency increase is a less than 2 percent decrease in the radial component of the turbulent velocity in the outer layers. Lower velocity implies a lower efficiency of the convective transport, hence lower temperature, which also contributes to the p-mode frequency increase.
As a part of an on-going program to explore the signature of p-modes in solar-like stars by means of high-resolution absorption lines pectroscopy, we have studied four stars (alfaCMi, etaCas A, zetaHer A and betaVir). We present here new results from two-site observations of Procyon A acquired over twelve nights in 1999. Oscillation frequencies for l=1 and l=0 (or 2) p-modes are detected in the power spectra of these Doppler shift measurements. A frequency analysis points out the dificulties of the classical asymptotic theory in representing the p-mode spectrum of Procyon A.
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