We present the results of an intensive campaign of spectroscopic and photometric monitoring of the peculiar Wolf-Rayet star WR 134 from 1989 to 1997. This unprecedentedly large data set allows us to confirm unambiguously the existence of a coherent 2.25 +/- 0.05 day periodicity in the line-profile changes of He II 4686, although the global pattern of variability is different from one epoch to another. This period is only marginally detected in the photometric data set. Assuming the 2.25 day periodic variability to be induced by orbital motion of a collapsed companion, we develop a simple model aiming at investigating (i) the effect of this strongly ionizing, accreting companion on the Wolf-Rayet wind structure, and (ii) the expected emergent X-ray luminosity. We argue that the predicted and observed X-ray fluxes can only be matched if the accretion on the collapsed star is significantly inhibited. Additionally, we performed simulations of line-profile variations caused by the orbital revolution of a localized, strongly ionized wind cavity surrounding the X-ray source. A reasonable fit is achieved between the observed and modeled phase-dependent line profiles of He II 4686. However, the derived size of the photoionized zone substantially exceeds our expectations, given the observed low-level X-ray flux. Alternatively, we explore rotational modulation of a persistent, largely anisotropic outflow as the origin of the observed cyclical variability. Although qualitative, this hypothesis leads to greater consistency with the observations.
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