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Register a new userInfluence of Low-Degree High-Order p-Mode Splittings on the Solar Rotation Profile
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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
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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.
Context: A number of pulsating stars with rotational splittings have been observed thanks to the CoRoT and Kepler missions. This is particularly true of evolved (sub-giant and giant) stars, and has led various groups to investigate their rotation profiles via different methods. Aims: We would like to set up some criteria which will help us to know whether a decreasing rotation profile, or one which satisfies Rayleighs stability criterion, is compatible with a set of observed rotational splittings for a given reference model. Methods: We derive inequalities on the rotational splittings using a reformulated version of the equation which relates the splittings to the rotation profile and kernels. Results: These inequalities are tested out on some simple examples. The first examples show how they are able to reveal when a rotation profile is increasing somewhere or inconsistent with Rayleighs criterion in a main sequence star, depending on the profile and the $ell$ values of the splittings. The next example illustrates how a slight mismatch between an observed evolved star and a reference model can lead to erroneous conclusions about the rotation profile. We also show how frequency differences between the star and the model, which should normally reveal this mismatch, can be masked by frequency corrections for near-surface effects.
Using full-disk observations obtained with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) spacecraft, we present variations of the solar acoustic mode frequencies caused by the solar activity cycle. High-degree (100 < l < 900) solar acoustic modes were analyzed using global helioseismology analysis techniques over most of solar cycle 23. We followed the methodology described in details in Korzennik, Rabello-Soares and Schou (2004) to infer unbiased estimates of high-degree mode parameters (see also Rabello-Soares, Korzennik and Schou, 2006). We have removed most of the known instrumental and observational effects that affect specifically high-degree modes. We show that the high-degree changes are in good agreement with the medium-degree results, except for years when the instrument was highly defocused. We analyzed and discuss the effect of defocusing on high degree estimation. Our results for high-degree modes confirm that the frequency shift scaled by the relative mode inertia is a function of frequency and it is independent of degree.
The observed power spectrum of high-degree solar p-modes (l>200) shows discrepancies with the power spectrum predicted by the stochastic excitement and damping theory. In an attempt to explain these discrepancies, the present paper is concerned with the influence of the observed subsurface flows on the trapped acoustic modes (p-modes). The effect of these inhomogeneous background flows is investigated by means of a non-modal analysis and a multi-layer model. It is shown that the rotational and meridional components of the velocity field change the wavelengths of the oscillation modes which, in turn, results in modifications of the corresponding modal frequencies. The magnitudes of the frequency residuals depend on the spatial scales of the modes and on the gradients of the different components of the flow velocity. Together with other mechanisms (e.g. the scattering of modes by the large scale convection (Goldreich & Murray 1994), the non-modal effect of the variation of the frequencies in time may contribute: 1) to the observed widening of the corresponding peaks in the observed power spectrum with increasing angular degree; 2) to the partial dissipation of spectral power, and, as a result, 3) to the discrepancies between the predicted and the observed power spectrum of solar p-modes.
We compute the rates P at which acoustic energy is injected into the solar radial p modes for several solar models. The solar models are computed with two different local treatments of convection: the classical mixing-length theory (MLT hereafter) and Canuto et al (1996)s formulation (CGM hereafter). Among the models investigated here, our best models reproduce both the solar radius and the solar luminosity at solar age and the observed Balmer line profiles. For the MLT treatment, the rates P do depend significantly on the properties of the atmosphere whereas for the CGMs treatment the dependence of P on the properties of the atmosphere is found smaller than the error bars attached to the seismic measurements. The excitation rates P for modes associated with the MLT models are significantly underestimated compared with the solar seismic constraints. The CGM models yield values for P closer to the seismic data than the MLT models. We conclude that the solar p-mode excitation rates provide valuable constraints and according to the present investigation clearly favor the CGM treatment with respect to the MLT, although neither of them yields values of P as close to the observations as recently found for 3D numerical simulations.
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