Astronomical Spectroscopy - Physics - University of Cincinnati

– 59 –
3.2.7. Radial velocities and Velocity Dispersions
Often the goal of the observations is to obtain radial velocities of the observed object.
For this, one needs to obtained sufficient calibration to make sure that any flexure in the
instrument is removed. Even bench-mounted instruments may “flex” as the liquid N 2 in
the CCD dewar evaporates during the night. The safe approach is to make sure that the
wavelength calibration spectra are observed both before and after a series of integrations,
with the wavelength scale then interpolated.
To obtain radial velocities themselves, the usual technique is to observe several radial
velocity standard stars of spectral type similar to the object for which one wants the velocity,
and then cross-correlate the spectrum of each standard with the spectrum of the object itself,
averaging the result.
Spectra are best prepared for this by normalizing and then subtracting 1 so that the
continuum is zero. This way the continuum provides zero “signal” and the lines provide
the greatest contrast in the cross-correlation. IRAF routines such as fxcor and rvsao will
do this, as well as (in principle) preparing the spectra by normalizing and subtracting the
continuum.
One way of thinking of cross-correlation is to imagine the spectrum of the standard and
the program object each contain a single spectral line. One then starts with an arbitrary
offset in wavelength and sums the two spectra. If the lines don’t match up, then the sum is
going to be zero. One then shifts the velocity of one star slightly relative to the other and
recomputes the sum. When the lines begin to line up, the cross-correlation will be non-zero,
and when they are best aligned the cross-correlation is at a maximum. In practice such
cross-correlation is done using Fourier transforms. The definitive reference to this technique
can be found in Tonry & Davis (1979).
The Earth is both rotating and revolving around the sun. Thus the Doppler shift of
an object has not only the object’s motion relative to the sun, but also whatever the radial
component is of those two motions. This motion is known as the heliocentric correction. The
rotation component is at most ± 0.5 km s −1 , while the orbital motion is at most ±29.8 km
s −1 . Clearly the heliocentric correction will depend both on latitude, date, time of day, and
the coordinates of the object. When one cross-correlates an observation of a radial velocity
standard star against the spectrum of a program object, one has to subtract the standard
star’s heliocentric correction from its cataloged value, and then add the program object’s
heliocentric correction to the obtained relative velocity.
It should be noted that cross-correlation is not always the most accurate method for
measuring radial velocities. Very early-type stars (such as O-type stars) have so few lines