Long-term optical variability of the Be/X-ray binary GRO J2058+42

Context. GRO J2058+42 is a transient hard X-ray pulsar that occasionally goes into outburst. The optical counterpart is a poorly studied OB-type companion.Aims. We investigate the long-term optical variability of the Be/X-ray binary GRO J2058+42 and the possible connection with periods of enhanced X-ray activity.Methods. We performed an optical spectroscopic and photometric analysis on data collected during about 18 yr. We also present the first optical polarimetric observations of this source.Results. The long-term optical light curves in the BVRI bands and the evolution of the H alpha equivalent width display a sinusoidal pattern with maxima and minima that repeat every & SIM;9.5 yr. The amplitude of this variability increases as the wavelength increases from 0.3 mag in the B band to 0.7 in the I band. The H alpha equivalent width varied from about -0.3 to -15 & ANGS;. We found a significant decrease in the polarization degree during the low optical state. The intrinsic polarization degree changed by & SIM;1% from maximum to minimum. The optical maxima occur near periods of enhanced X-ray activity and are followed by a drop in the optical emission. Unlike many other Be/X-ray binaries, GRO J2058+42 does not display V/R variability.Conclusions. The long-term optical variability agrees with the standard model of a Be/X-ray binary, where the circumstellar disk of the Be star grows and dissipates on timescales of 9-10 yr. We find that the dissipation of the disk started after a major X-ray outburst. However, the stability of the H alpha line shape as a double-peak profile and the lack of asymmetries suggest the absence of a warped disk and argue against the presence of a highly distorted disk during major X-ray outbursts.