We present a comprehensive study of Z CVn , an RR Lyrae star that shows long-term cyclic variations of its pulsation period .
A possible explanation suggested from the shape of the O - C diagram is the light travel-time effect , which we thoroughly examine .
We used original photometric and spectroscopic measurements and investigated the period evolution using available maximum times spanning more than one century .
If the binary hypothesis is valid , Z CVn orbits around a black hole with minimal mass of 56.5 \mathfrak { M } _ { \odot } on a very wide ( P _ { orbit } = 78.3 years ) and eccentric orbit ( e = 0.63 ) .
We discuss the probability of a formation of a black hole–RR Lyrae pair and , although we found it possible , there is no observational evidence of the black hole in the direction to Z CVn .
However , the main objection against the binary hypothesis is the comparison of the systemic radial velocity curve model and spectroscopic observations that clearly show that Z CVn can not be bound in such a binary .
Therefore , the variations of pulsation period are likely intrinsic to the star .
This finding represents a discovery/confirmation of a new type of cyclic period changes in RR Lyrae stars .
By the analysis of our photometric data , we found that the Blazhko modulation with period of 22.931 d is strongly dominant in amplitude .
The strength of the phase modulation varies and is currently almost undetectable .
We also estimated photometric physical parameters of Z CVn and investigated their variations during the Blazhko cycle using the Inverse Baade-Wesselink method .