Optical variabilities in the Be/X-ray binary system

Aims.We present an analysis of long-term optical monitoring observations and optical spectroscopic observations of the counterpart to CXOU J205847.5+414637 (high-mass X-ray binary system). We search for variability in the light curve of Be star. Methods.We used differential magnitudes in the time-series analysis. The variability search in the optical light curve was made by using different algorithms. We used MIDAS and its suitable packages to reduce and analyse the spectra. Results.We have performed a frequency search that gave us the value 2.404 d-1. This value is attributed to the non-radial pulsation of the Be star. The Hα emission line profiles always show double-peaked emissions with a mean equivalent width of 2.31 ± 0.19 Å and a peak separation of 516 ± 45 km s-1. This suggests that the Be star disk is still present. CXOU J205847.5+414637 is in an X-ray quiescent state