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

Variations of the solar granulation motions with height using the GOLF/SoHO experiment

Below 1 mHz, the power spectrum of helioseismic velocity measurements is dominated by the spectrum of convective motions (granulation and supergranulation) making it difficult to detect the low-order acoustic modes and the gravity modes. We want to better understand the behavior of solar granulation as a function of the observing height in the solar atmosphere and with magnetic activity during solar cycle 23. We analyze the Power Spectral Density (PSD) of eleven years of GOLF/SOHO velocity-time series using a Harvey-type model to characterize the properties of the convective motions in the solar oscillation power spectrum. We study then the evolution of the granulation with the altitude in the solar atmosphere and with the solar activity. First, we show that the traditional use of a lorentzian profile to fit the envelope of the p modes is not well suitable for GOLF data. Indeed, to properly model the solar spectrum, we need a second lorentzian profile. Second, we show that the granulation clearly evolves with the height in the photosphere but does not present any significant variation with the activity cycle.Comment: Paper accepted in A&A. 7 pages, 4 figures, 2 table

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

Distributed cooperative control for stepper motors synchronization

This paper describes the design and simulation of a distributed cooperative control algorithm based on multi-agents to synchronize a group of stepper motors. Modeling of the two-phase hybrid stepper motor in closed loop is derived in d-q rotary reference frame, based on field-oriented control techniques to provide torque control. The simulation obtained by MATLAB-Simulink shows that the distributed cooperative control effectiveness depends on the network topology defined by the graph.Postprint (published version