Do the observed relations of the global seismic parameters depend on the magnetic activity level?

It has been known that the global asteroseismic parameters as well as the stellar acoustic mode parameters vary with stellar magnetic activity. Some solar-like stars whose variations are thought to be induced by magnetic activity, however, show mode frequencies changing with different magnitude and phase unlike what is expected for the Sun. Therefore, it is of great importance to find out whether expected relations are consistently manifested regardless of the phase of the stellar magnetic cycle, in the sense that observations are apt to cover a part of a complete cycle of stellar magnetic activity unless observations span several decades. Here, we explore whether the observed relations of the global seismic parameters hold good regardless of the phase of the stellar magnetic cycle, even if observations only cover a part of the stellar magnetic cycle. For this purpose, by analyzing photometric Sun-as-a-star data from 1996 to 2019 covering solar cycles 23 and 24, we compare correlations of the global asteroseismic parameters and magnetic proxies for four separate intervals of the solar cycle: solar minima ±2 years, solar minima +4 years, solar maxima ±2 years, and solar maxima +4 years. We have found that the photometric magnetic activity proxy, S_ph, is an effective proxy for the solar magnetic activity regardless of the phase of the solar cycle. The amplitude of the mode envelope correlates negatively with the solar magnetic activity regardless of the phase of the solar cycle. However, relations between the central frequency of the envelope and the envelope width are vulnerable to the phase of the stellar magnetic cycle.