An analysis of the low-degree p-mode frequency shifts over more than a solar cycle has been carried out. Time dependence of the resonant frequencies and the total velocity power have been studied with several, old and new, methods, yielding a correlation and an anti-correlation with the solar activity cycle respectively which confirms previous results. Moreover, quantitative parameters have been introduced which yield the sensitivities of such variations with respect to a given activity index, in our case the radio flux at 10.7 cm. The existence of a hysteresis behavior between both parameters seems to imply different direct causes for them.
Also, the frequency shifts have been obtained as a function of frequency
and degree. These studies make use of data taken from two experiments
(Mark-I and LOWL) which confirm each other results, when they coincide
(at very low 
modes), and complement their findings otherwise.
Indeed, the main source for the variation of the frequencies with the cycle is
located near the surface while a secondary, deeper rooted source, seems to be
very weak if it exists at all.
Interesting details such as the oscillation found for very low-
p-modes
and the surprisingly small frequency shift for
even modes need
further investigation.
The results obtained and methods used in this work will also be useful in the analysis of very long time-series covering more than half the solar activity cycle, since both resonant frequencies and, to a lesser extent, amplitudes vary cyclically with time, providing wrong results if only data taken at parts of the cycle are used. In the following paper (second part of this work) we will use these methods to minimize the effects of solar activity on these parameters in annual power spectra, allowing an average of all data thus improving the signal to noise ratio. Using this power spectra we will be able to give a new estimation of the solar rotational splitting, which combined with LOWL data, will be used to infer the solar rotation close to the core.
Finally we note that the hysteresis between frequencies of odd and even modes or between mode frequencies and magnetic flux is not addressed in this work based on yearly time series. These studies are however of considerable importance (see e.g. Moreno-Insertis & Solanki 2000) but would require shorter time series and better data (e.g. higher duty cycle) in order to reliably confirm previous analysis. This should probably be addressed in the future using long term observations of low degree modes from the ground based networks BiSON and IRIS++ (i.e. IRIS + LOWL +Mark-I, Salabert 2001).
Acknowledgements
We are deeply thankful to the all members, past and present, of the helioseismology group at the IAC for doing Mark-I observations and maintenance. The use of Birmingham University resonant scattering spectrophotometer at Observatorio del Teide is also deeply acknowledged. We are extremely grateful to Tom Bogdan and Mausumi Dikpati for useful discussions and additional comments. T. Corbard acknowledges support from NASA grant S-92678-F and PPARC grant PPA/A/S/2000/00171. The High Altitude Observatory of the National Center for Atmospheric Research is sponsored by the National Science Foundation.
Copyright ESO 2001