D2 - Estimating the mass loss rate of OB stars
Task
Massive, hot stars (spectral types O and B) emit parts of their radiation in the Radio band. Wright & Barlow (1975) developed a simple model to calculate free-free-emission of stellar winds (see the script of the stellar atmospheres lecture!). At least of three OB stars (e.g. HD66811 ($\zeta$ Puppis), HD152408, HD169454) there are Radio measurements at different frequencies that show the predicted frequency profile. Multiple measurements show similar results (i.e. no variation with time). Both combined suggest that the model of Wright & Barlow is valid for these stars. A number of such measurements were taken with the most powerful Radio telescope in the world, the VLA (Very Large Array). (Data can e.g. be found in the Wendker 1995 catalog.)
Estimate the mass-loss rate $\dot{M}$ of the three stars mentioned before from the free-free Radio emission following the formula given by Wright & Barlow. The formula has three input parameters: The Radio flux at a given frequency, the distance and the “terminal velocity” of the stellar wind. Get the needed measurements from the acquainted databases in the internet (Simbad, VizieR).
Radio flux
First, find the Radio data for the given stars. See the database ViZieR of the Centre de Données astronomiques de Strasbourg, France. Select the wavelength/frequency range (Radio!) and enter the name of the star (Target field). Restrict the search radius to a useful value. A mission and a keyword don't need to be given. View the data by clicking Go!.
Distance
The distance (approximations) can be found at the SIMBAD database. On which basis were the given distances confined, what are their error margins? Discuss the reliability of the distance values.
Terminal velocity
The terminal velocity of the stellar wind is the third parameter needed. This is the (maximum) velocity of the radially expanding stellar wind. To simplify, it may be assumed that (a) the wind reaches its “terminal velocity” $v_{\infty}$ already in those layers where the saturated UV resonance lines form, and (b) this velocity remains constant up to the distances (several stellar radii from the star), where the free-free Radio emission forms. So the value of $v_{\infty}$ can be estimated from the UV spectrum.
A large number of UV spectra were obtained with the International Ultraviolet Explorer (IUE). Find the IUE database at VisieR or get the data directly. There are spectra in two wavelength ranges (SWP: $1150-1980\,\unicode{x212B}$ and LWP or LWR: $1850-3350\,\unicode{x212B}$). Furthermore, there are high and low resolution spectra, while the former has been rebinned to the lower resolution in the database. The C IV resonance doublet in the SWP range can serve as the saturated resonance line. The rest-frame wavelengths are $1548.188\,\unicode{x212B}$ and $1550.762\,\unicode{x212B}$. The middle of the steep blue wing of the P-Cygni absorption part shows the maximum blueshift, i.e. the maximum velocity, that can be used to calculate the “terminal velocity” ($v_{\infty}$) by the Doppler formula.
For this purpose, plot the IUE spectrum with a tool of your choice. On the website of the IUE database (IUE Search Results), this can be achieved by marking the corresponding spectrum and clicking on Plot marked spectra. Enlarge the blue wing of the C IV line by zooming into the plot, so that the wavelength can be precisely derived. The plot can be saved as a png image by clicking on the button Create PNG.
Correlation with the X-Ray luminosity
It's interesting to note, that OB stars also emit X-rays. X-ray count rates can also be found at Simbad. Also check (under the assumption of the distance used for the $\dot{M}$ estimation) if the X-ray luminosity scales with the mass-loss rate.
Prepare a laboratory course reprot, as usual (determine the mass-loss rate and deduce the necessary formula, plot the P-Cygni profile).