Sensitivity analysis of the solar rotation to helioseismic data from GONG, GOLF and MDI observations

Accurate determination of the rotation rate in the radiative zone of the sun from helioseismic observations requires rotational frequency splittings of exceptional quality as well as reliable inversion techniques. We present here inferences based on mode parameters calculated from 2088-days long MDI, GONG and GOLF time series that were fitted to estimate very low frequency rotational splittings (nu < 1.7 mHz). These low frequency modes provide data of exceptional quality, since the width of the mode peaks is much smaller than the rotational splitting and hence it is much easier to separate the rotational splittings from the effects caused by the finite lifetime and the stochastic excitation of the modes. We also have implemented a new inversion methodology that allows us to infer the rotation rate of the radiative interior from mode sets that span l=1 to 25. Our results are compatible with the sun rotating like a rigid solid in most of the radiative zone and slowing down in the core (R_sun < 0.2). A resolution analysis of the inversion was carried out for the solar rotation inverse problem. This analysis effectively establishes a direct relationship between the mode set included in the inversion and the sensitivity and information content of the resulting inferences. We show that such an approach allows us to determine the effect of adding low frequency and low degree p-modes, high frequency and low degree p-modes, as well as some g-modes on the derived rotation rate in the solar radiative zone, and in particular the solar core. We conclude that the level of uncertainties that is needed to infer the dynamical conditions in the core when only p-modes are included is unlikely to be reached in the near future, and hence sustained efforts are needed towards the detection and characterization of g-modes.Comment: Accepted for publication in Astrophysical journal. 15 pages, 19 figure

Sensitivity of helioseismic gravity modes to the dynamics of the solar core

The dynamics of the solar core cannot be properly constrained through the analysis of acoustic oscillation modes. Gravity modes are necessary to understand the structure and dynamics of the deepest layers of the Sun. Through recent progresses on the observation of these modes -- both individually and collectively -- new information could be available to contribute to inferring the rotation profile down inside the nuclear burning core. To see the sensitivity of gravity modes to the rotation of the solar core. We analyze the influence of adding the splitting of one and several g modes to the data sets used in helioseismic numerical inversions. We look for constraints on the uncertainties required in the observations in order to improve the derived core rotation profile. We compute forward problems obtaining three artificial sets of splittings derived for three rotation profiles: a rigid profile taken as a reference, a step-like and a smoother profiles with higher rates in the core. We compute inversions based on Regularized Least-Squares methodology (RLS) for both artificial data with real error bars and real data. Several sets of data are used: first we invert only p modes, then we add one and several g modes to which different values of observational uncertainties (75 and 7.5 nHz) are attributed. For the real data, we include g-mode candidate, l=2, n=-3 with several splittings and associated uncertainties. We show that the introduction of one g mode in artificial data improves the rate in the solar core and give an idea on the tendency of the rotation profile. The addition of more g modes gives more accuracy to the inversions and stabilize them. The inversion of real data with the g-mode candidate gives a rotation profile that remains unchanged down to 0.2 R, whatever value of splitting we attribute to the g mode.Comment: Accepted for publication in A&A, 8 pages, 11 figure

An Upper Limit on the Temporal Variations of the Solar Interior Stratification

We have analyzed changes in the acoustic oscillation eigenfrequencies measured over the past 7 years by the GONG, MDI and LOWL instruments. The observations span the period from 1994 to 2001 that corresponds to half a solar cycle, from minimum to maximum solar activity. These data were inverted to look for a signature of the activity cycle on the solar stratification. A one-dimensional structure inversion was carried out to map the temporal variation of the radial distribution of the sound speed at the boundary between the radiative and convective zones. Such variation could indicate the presence of a toroidal magnetic field anchored in this region. We found no systematic variation with time of the stratification at the base of the convection zone. However we can set an upper limit to any fractional change of the sound speed at the level of $3 \times 10^{-5}$.Comment: 11 pages, 5 figures, to appear in Ap

Detection of periodic signatures in the solar power spectrum. On the track of l=1 gravity modes

In the present work we show robust indications of the existence of g modes in the Sun using 10 years of GOLF data. The present analysis is based on the exploitation of the collective properties of the predicted low-frequency (25 to 140 microHz) g modes: their asymptotic nature, which implies a quasi equidistant separation of their periods for a given angular degree (l). The Power Spectrum (PS) of the Power Spectrum Density (PSD), reveals a significant structure indicating the presence of features (peaks) in the PSD with near equidistant periods corresponding to l=1 modes in the range n=-4 to n=-26. The study of its statistical significance of this feature was fully undertaken and complemented with Monte Carlo simulations. This structure has a confidence level better than 99.86% not to be due to pure noise. Furthermore, a detailed study of this structure suggests that the gravity modes have a much more complex structure than the one initially expected (line-widths, magnetic splittings...). Compared to the latest solar models, the obtained results tend to favor a solar core rotating significantly faster than the rest of the radiative zone. In the framework of the Phoebus group, we have also applied the same methodology to other helioseismology instruments on board SoHO and ground based networks.Comment: Proceedings of the SOHO-18/GONG2006/HELAS I: Beyond the spherical Su

The Rotation Of The Deep Solar Layers

From the analysis of low-order GOLF+MDI sectoral modes and LOWL data (l > 3), we derive the solar radial rotation profile assuming no latitudinal dependance in the solar core. These low-order acoustic modes contain the most statistically significant information about rotation of the deepest solar layers and should be least influenced by internal variability associated with the solar dynamo. After correction of the sectoral splittings for their contamination by the rotation of the higher latitudes, we obtain a flat rotation profile down to 0.2 solar radius.Comment: accepted in ApJ Letters 5 pages, 2 figure