Four-month chromospheric and coronal activity cycle in τ Boötis

We have used our robotic TIGRE facility to closely monitor the star tau Boo during the last three observing seasons 2013-2016 and to determine its S-index variability from the strength of its Ca II H and K line cores in order to study its characteristic cyclic chromospheric variations and determine its rotation period. We furthermore reanalyze archival X-ray data of tau Boo taken with the XMM-Newton satellite. Using Lomb-Scargle periodograms, we find a strong periodic signal in our data with a period of about 122 days with extremely high significance, which is also consistent with the observed long-term X-ray variability. Furthermore, the epochs of magnetic field reversals observed in tau Boo with the technique of Zeeman Doppler imaging are consistent with the hypothesis that they are produced at activity maximum. In line with previous studies of tau Boo, we therefore interpret our data as evidence of a very short activity cycle in analogy to the solar cycle, but the cycle period of tau Boo may also show some slight variability and may show substantial phase shifts. The chromospheric signal of tau Boo is found to vary on the rotational timescale of somewhat more than three days only during one out of the available three observing seasons. The available data suggest that persistent cyclic magnetic activity can occur on timescales much shorter than the decadal timescale observed for the Sun and many other late-type stars.