Detecting stellar activity cycles in p-mode travel times: Proof of concept using SOHO/VIRGO solar observations

The eleven year solar cycle is known to affect the global modes of solar acoustic oscillations. In particular, p mode frequencies increase with solar activity. We propose a new method to detect the solar cycle from the p-mode autocorrelation function, and we validate this method using VIRGO/SPM photometric time series from solar cycles 23 and 24. The p-mode autocorrelation function shows multiple wavepackets separated by time lags of $\sim$123 min. Using a one-parameter fitting method (from local helioseismology), we measure the seismic travel times from each wavepacket up to skip number 40. We find that the travel-time variations due to the solar cycle depend sensitively on the skip number, with the strongest signature in odd skips from 17 to 31. Taking the noise covariance into account, the travel-time perturbations can be averaged over all skip numbers to enhance the signal-to-noise ratio. This method is robust to noise, simpler to implement than peak bagging in the frequency domain, and is promising for asteroseismology. We estimate that the activity cycle of a Sun-like star should be detectable with this new method in Kepler-like observations down to a visual magnitude of $m_K \sim 11$. However, for fainter stars, activity cycles are easier to detect in the photometric variability on rotational timescales.