The dynamics of the Wolf-Rayet ring nebula M1-67
Undergraduate research of Marc
van der Sluys
Supervisor: Henny Lamers
Astronomical Institute, Utrecht
Article Status: 2003A&A...398..181V
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Figure 1. HST image of M1-67.
|M1-67 is a nebular structure around the Wolf-Rayet star WR 124.
The star is of spectral type WN8, which indicates that the star has probably
just recently entered the Wolf-Rayet phase. The nebula around it
is very chaotic and clumpy (see Figure 1), but in the same time, (parts
of) rings and arcs are clearly visible. These indicate that the nebula
is probably caused by a number of discrete outbursts, possibly during a
Luminous Blue Variable phase. The goal of my undergraduate research was
to find the number, geometries and dynamical timescales of these outbursts.
|However, we found that the situation was more complicated than we had
thought. We found that the star is moving with a velocity of about 180
km s-1 with respect to the local Interstellar Medium (ISM). In stead of a nice wind-blown
bubble with a radius of about 30 pc, the star is surrounded by a bow shock and
is as close as only 1.3 pc away from the front of the bow shock. Because
the star moves away from us, at an inclination of less than 30° from the
line of sight, we cannot see this bow shock in Figure 1, but it is visible
from radial velocity observations. In Figure 2, the emission distribution
in the Right Ascension - Radial velocity plane is displayed, derived from
Fabry-Pérot observations by Grosdidier et al. 
The star has a radial velocity of about 199 km s-1 and sits
at 0" in this image.
Figure 2. Emission distribution of M1-67
in the RA-v plane.
Figure 3. A 3D bow shock model for i=50°,
Left: position-position plot. Right: position-velocity
|To model this bow shock, we used simple analitical expressions derived by Canto,
Raga and Wilkin.  They give the geometry and
velocity along the surface of a 2D bow shock. From this, we created
a 3D model, that can be rotated to any orientation. After that,
the radial coordinate is converted to a radial velocity, so that we have
two spatial coordinates and a radial velocity coordinate, that can be compared to the observational
data like in Figure 2. An example of such a 3D bow shock model, again
in the RA - velocity plane, is shown in Figure 3.
|To obtain likely values for the star-ISM velocity, inclination and
position angle, we used models of galactic rotation to obtain the ISM velocity
and subtracted the known velocity of WR 124. Together with the observed
stellar mass loss and terminal wind velocity  and an assumed ISM
density, these quantities define the geometry and orientation of the bow shock.
We did this for different distances and different possible proper motions
(there is a large error in the proper motion of WR 124, because of its distance of about 6.5 kpc)
and found that the model output resembles the data remarkably well, as shown in Figure 4. The thick
line represents a countour around the model output mesh as in the right panel of Figure 3. The underlying
grey scaled image and its thin contours are the data from Figure 2.
Figure 4. Position-velocity plot of the
model output (thick line) plotted over
the data (grey scales and thin contours).
 Grosdidier, Y., Moffat, A.F.J., Blais-Ouelette,
S., 1999, Proc. IAU Symp. 193, 356.
 Canto, J., Raga, A.C. & Wilkin, F.P.,
1996, ApJ 469, 729.
 Nugis, T. & Lamers, H.J.G.L.M., 2000,
A&A 360, 227.