Hubble Space Telescope imagery and Canada-France-Hawaii Telescope Fabry-Perot two-dimensional spectroscopy in H alpha of the ejected nebula M1-67: Turbulent status

Bright circumstellar nebulae around massive stars are potentially useful to derive time-dependent mass-loss rates and hence constrain the evolution of the central stars. A key case in this context is the relatively young ejec tion-type nebula M1-67 around the runaway Population I Wolf-Rayet star WR 1 24 (=209 BAC), which exhibits a WN 8 spectrum. With HST-WFPC2 we have obtai ned a deep, H alpha image of M1-67. This image shows a wealth of complex de tail that was briefly presented previously by Grosdidier et al. With the in terferometer of the Universite Laval (Quebec, Canada), we have obtained com plementary Fabry-Perot Ha data using Canada-France-Hawaii Telescope (CFHT) MOS/SIS. From these data M1-67 appears more or less as a spherical (or elli ptical, with the major axis along the line of sight), thick, shell seen alm ost exactly along its direction of rapid spatial motion away from the obser ver in the ISM. However, a simple thick shell by itself would not explain t he observed multiple radial velocities along the line of sight. This veloci ty dispersion leads one to consider M1-67 as a thick accelerating shell. Gi ven the extreme perturbations of the velocity field in M1-67, it is virtual ly impossible to measure any systematic impact of the present WR (or previo us LBV) wind on the nebular structure. The irregular nature of the velocity field is likely due to either large variations in the density distribution of the ambient ISM or large variations in the central star mass-loss histo ry. In addition, either from the density field or the velocity field, we fi nd no clear evidence for a bipolar outflow, as was claimed in other studies . On the deep H alpha image we have performed continuous wavelet transforms to isolate stochastic structures of different characteristic size and look for scaling laws. Small-scale wavelet coefficients show that the density f ield of M1-67 is remarkably structured in chaotically (or possibly radially ) oriented filaments everywhere in the nebula. We draw attention to a short , marginally inertial range at the smallest scales (6.7-15.0 x 10(-3) pc), which can be attributed to turbulence in the nebula, and a strong scale bre ak at larger scales. Examination of the structure functions for different o rders shows that the turbulent regime may be intermittent. Using our Fabry- Perot interferograms, we also present an investigation of the statistical p roperties of fluctuating gas motions using structure functions traced by H alpha emission-line centroid velocities. We find that there is a clear corr elation at scales 0.02-0.22 pc between the mean quadratic differences of ra dial velocities and distance over the surface of the nebula. This implies t hat the velocity field shows an inertial range likely related to turbulence , though not coincident with the small inertial range detected from the den sity field. The first- and second-order moments of the velocity increments are found to scale as [\Deltav(r)\] similar to r(0.5) and [\Deltav(r)\(2)] similar to r(0.9). The former scaling law strongly suggests that supersonic , compressible turbulence is at play in the nebula; on the other hand, the latter scaling law agrees very well with Larson-type laws for velocity turb ulence. Examination of the structure functions for different orders shows t hat the turbulent regime is slightly intermittent and highly multifractal w ith universal multifractal indexes alpha approximate to 1.90-1.92 and C-1 a pproximate to 0.04 +/- 0.01.