Wind Inhomogeneities in Wolf-Rayet Stars. I. Search for Scaling Laws Using Wavelet Transforms

We describe a new technique involving wavelet transforms for analyzing discrete stochastic components like those found on the tops of emission lines in Wolf-Rayet stars. A wavelet power spectrum is used to characterize the variable component of the emission line we believe arises from the superposition of many individual Gaussian-like subpeaks. This was applied to emission-line spectra of eight Wolf-Rayet stars obtained at the Canada-France-Hawaii Telescope and European Southern Observatory. Where the data show the most power we identify a dominant scale, which is found to be very similar in all but one of the stars in our sample. We present a phenomenological model where the variable structure on top of the emission line is represented by a sum of individual subpeaks of the same simple shape (Gaussian or triangular) and various scales. This model is used to introduce the idea of scaling laws. The amplitude A and number density N of subpeaks on a given scale are related to their characteristic width σ (i.e., velocity dispersion) by scaling relations, of which the simplest form is a power law: A ∼ σα and N ∼ σβ. The wavelet power spectrum is used to verify the consistency of this model with the data. Synthetic signals are generated, and their wavelet spectra are compared to those of the data. This provides a constraint on the value of 2α + β, which is found to be 2.7±0.5(s.d.) for the model involving Gaussians, or ≈3.4±0.6(s.d.) for the model involving triangles. The implications provided by this new constraint are discussed.