Long-period, low-amplitude radial velocity variations in the K giant star pi Herculis: rotation, substellar companion or non-radial pulsations?

Precise stellar radial velocity (RV) measurements (sigma approximate to 20 m s(-1)) spanning more than 2 yr are presented for the K giant star pi Herc ulis. These show variability with a period of 613 +/- 57 d and an amplitude of 150 +/- 12 m s(-1). Radial pulsations can be excluded as a mechanism fo r this variability because the observed period is more than an order of mag nitude greater than the expected period of the fundamental radial mode. Ten able hypotheses for the RV variability include rotational modulation by sur face structure, non-radial pulsations, or a substellar companion of mass at least 27 M-Jupiter in orbit 3 au from the star. An upper limit of 1400 d t o the rotational period for pi Herculis is determined using published value s of the angular diameter and distance to pi Herculis as well as an estimat e of the projected rotational velocity. Rotational modulation is thus a via ble mechanism for the RV variability. The RV variations were also fitted us ing two models: (i) a stellar surface covered with cool spots and (ii) non- radial pulsations. Both models could adequately reproduce the RV curve alth ough the spot model predicts photometric variations of Delta V similar to 0 .1 mag. As a result of the long period, non-radial pulsations may be g-mode or r-mode oscillations, which implies that most of the atmospheric motion of the star is in the horizontal direction. If these modes an indeed presen t then the corresponding photometric amplitude for non-radial pulsations ma y be quite small. The radial velocity variations were also measured using s ubsections of the spectral region. Weak spectral lines yielded an RV amplit ude of approximate to 140 ms(-1) whereas the stronger lines yielded an RV a mplitude of approximate to 220 m s(-1) with a phase shift of about 60 degre es with respect to the weaker lines. This seems to support the pulsation hy pothesis as the cause of the RV variability, although an analysis of more l ines is needed to confirm this. Also, a period of 90.3 d with an amplitude 50 m s(-1) is found in the residual RV measurements after subtracting the 6 13-d component. The presence of two periods also argues in favour of non-ra dial pulsations, although at the present time one cannot exclude low-mass c ompanions or surface structure as a cause for at least one of the observed periods. Photometric measurements as well as detailed analysis of the chang es in the spectral line shapes using high-resolution data may be required t o distinguish between the companion object and non-radial pulsation hypothe ses.