Calculating Rotational Velocities (vsini)

Now that I have a library of echelle spectra, I can measure rotational velocities for those stars without measurements in the literature.

To calculate rotational velocities from our Hamilton Echelle spectra, we will use the following technique from Fekel 1997:





(1) Calculate the instrumental broadening by measuring the FWHM of several lines in the arclamp (ThAr) spectra in a wavelength regime corresponding to an order with several strong stellar lines (~6430 A)

(2) For several (at least 5) lines in the order  including 6430 A, measure the FWHM (I used 6394, 6400, 6412, 6420, 6421, 6431, 6439, 6439, and 6450).

(3) Calculate the corrected FWHM: FWHM = sqrt(FWHM_obs^2 - FWHM_inst^2)

(4) calculate the vsini from the equation provided by Fekel (1997):

where X is the total broadening (velocity).

(5) the macroturbulent velocity (broadening due to the motion of the stellar atmosphere) is then removed (vsini=sqrt(X^2-M^2)) where M = 3km/s for spectral types G5 and later, and 5 km/s for spectral types earlier than G5 (from Strassmeier et al. 1990)

Now Strassmeier et al. have their own prescription for calculating the rotational velocities:

where chi is the macroturbulent velocity. We can calculate the vsini inferred by each line in the 6430 A order and average them together to get a total vsini.

Comparing Fekel and Strassmeier velocities, it seems that Strassmeier's vsini values are almost always lower than Fekel's.

Without convincing evidence to use one method vs another, I chose to use the Strassmeier velocities, since they list errors (2-3km/s).