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 ejection-type nebula M1-67 around the runaway Population I Wolf-Rayet star WR124 ( = 209 BAC ) , which exhibits a WN8 spectrum .
With HST-WFPC2 we have obtained a deep , H \alpha image of M1-67 .
This image shows a wealth of complex detail which was briefly presented previously by Grosdidier et al . ( 1998 ) .
With the interferometer of the Université Laval ( Québec , Canada ) , we have obtained complementary Fabry-Perot H \alpha data using CFHT MOS/SIS . From these data M1-67 appears more-or-less as a spherical ( or elliptical , with the major axis along the line of sight ) , thick , shell seen almost exactly along its direction of rapid spatial motion away from the observer in the ISM .
However , a simple thick shell by itself would not explain the observed multiple radial velocities along the line of sight .
This velocity dispersion leads one to consider M1-67 as a thick accelerating shell .
Given the extreme perturbations of the velocity field in M1-67 , it is virtually impossible to measure any systematic impact of the present WR ( or previous 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 history .
In addition , either from the density field or the velocity field , we find 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 field 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 \times 10 ^ { -3 } pc ) , which can be attributed to turbulence in the nebula , and a strong scale break at larger scales .
Examination of the structure functions for different orders shows that the turbulent regime may be intermittent . Using our Fabry-Perot interferograms , we also present an investigation of the statistical properties of fluctuating gas motions using structure functions traced by H \alpha emission-line centroid velocities .
We find that there is a clear correlation at scales 0.02–0.22 pc between the mean quadratic differences of radial velocities and distance over the surface of the nebula .
This implies that the velocity field shows an inertial range likely related to turbulence , though not coincident with the small inertial range detected from the density field .
The first and second order moments of the velocity increments are found to scale as \langle| \Delta v ( r ) | \rangle \sim r ^ { 0.5 } and \langle| \Delta v ( r ) | ^ { 2 } \rangle \sim 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 turbulence .
Examination of the structure functions for different orders shows that the turbulent regime is slightly intermittent and highly multifractal with universal multifractal indexes \alpha \approx 1.90 –1.92 and C _ { 1 } \approx 0.04 \pm 0.01 .