There are several factors to be considered when a spectral line is selected for measuring rotation velocities.
Very few lines fulfil these conditions in the La Palma spectra, mainly
because of their moderate resolution which makes most of the lines appear blended. After a
careful selection, we have chosen two lines: 
and 
. The first one is stronger but it appears
slightly blended with the weak line 
and
it will be used only for 
where it is not
possible to use the weaker line 
. On the
contrary, this problem is not present in the McDonald spectra where the
spectral resolution is a factor of six higher. For these spectra, a set of nine
lines was used in the calculation of the rotational velocities: 
, 
, 
, 
, 
, 
, 
, 
and 
.
Different techniques have been developed to calculate rotational
velocities (e.g. Sletteback 1975; Tonry & Davis
1979; Gray 1992). Each one of these three methods
relies to some extent on the geometrical technique, suggested
originally by Shajn
& Struve (1929), that relates line profiles and line widths to apparent
rotational velocity, 
. Collins & Truax (1995) noted that this
technique implies the following three assumptions:
represents the
maximum broadening and 
is the limb darkening coefficient.
In this
paper we will follow the method described by Gray (1992) since
contrary to the Sletteback and Tonry & Davis methods which need
to build up a calibration of rotational velocities according to
some parameter (e.g. the FWHM in Sletteback), the Gray method provides
direct and independent measurements of 
. With this method
the projected rotational velocity (
) is calculated from the
Eq. (17.14) given in Gray (1992) which relates the frequencies
where the Fourier transform of
reaches a relative minimum and the wavelength of the
line considered. This method is independent of the instrumental profile
since the convolution of the intrinsic spectrum with the instrumental
profile may add relative minimum values but will not change the position of the
minima given by Eq. (17.14). Moreover, these minima introduced by the
instrumental profile appear at much higher frequencies than those of the
intrinsic spectrum used to calculate the rotational velocity. Projected
rotational velocities of the observed stars
are listed in Tables 3 and 4.
Table 3: Rotational velocities of observed 
Sct stars. The fourth
column indicates the
value of v sin i obtained using the method described in Gray (1992). For La
Palma spectra, the line chosen for the v sin i calculation appears in the last column. For McDonald spectra,
the mean rotational velocity and the standard deviation are given in the
forth column and the number
of lines used is shown in the last column. The absence of suitable lines
prevents the calculation of v sin i for VW Ari and CY Aqr
According to Eq. (1), one of the uncertainties in the
calculation of 
comes from the limb-darkening law. In our calculations, we have
assumed a linear limb-darkening law in the form
where 
with 
the angle formed
by the line of sight and the direction of the emerging flux, I(1)
represents the intensity at the stellar disk center and 
,
the linear limb-darkening coefficient, takes a value of 
.
Although some authors (Klinglesmith & Sobieski 1970; Manduca et
al. 1977; Díaz-Cordovés & Giménez 1992)
have proposed different non-linear laws for limb darkening,
Díaz-Cordovés & Giménez (1992) also showed that the
errors in the total emergent flux
assuming a linear law are less than 2% in the range of temperatures
where the 
Sct stars lie (
).
Wade & Rucinski (1985) have
tabulated the linear limb-darkening coefficient in terms of wavelength,
and 
. Assuming an interval of temperatures 
, 
and spectral ranges of 
(La Palma) and
(McDonald) we obtain 
for La Palma spectra and 
for McDonald spectra.
To see to what extent the limb-darkening coefficient affects the
calculated value of 
, we have convolved a synthetic line
(
), generated with ATLAS8 and with null
rotational broadening by definition, with a grid of rotational profiles
(
= 30, 60, 90, 120, 150, 180 
) and we have calculated the
rotational velocity for two values of 
(0.3, 0.6) which would correspond to the greatest difference in the
McDonald spectra. The results are given in Table 5. We can see how the influence
of the limb-darkening coefficient in the calculated value of 
increases when the rotational velocity increases. For McDonald
spectra, where 
is always 
, this effect is
negligible. On the other hand, for La Palma spectra, where the
difference (
) is, at worst, 0.07 this effect
can also be neglected.
Table 4: Rotational velocities for the sample of non-variable
stars. The value
of v sin i and the selected line(s) used for its determination
are given as in Table 3
The determination of the local continuum is another unavoidable source of
error: a displacement in the continuum level can change the line profile, especially
the wings, and thus distort the shape of the Fourier transform and modifying
the position of its zeroes. Despite of the excellent signal-to-noise
ratio of the La Palma spectra, their moderate resolution and the high
number of lines present in the spectral region considered make most of the
lines appear blended which makes difficult the continuum placement. The
error in the
continuum determination for these spectra has been estimated by comparing equivalent widths of
different lines in the observed spectrum of Procyon with those from the Atlas
of Procyon (Griffin & Griffin 1979). An error in the continuum
positioning of 
was adopted which correspond to an error of 8-10 
\
in 
for those stars with the highest rotational velocities, the
error being lower when 
is lower. For McDonald spectra, where the
continuum is much better defined, the error associated with the continuum
level indetermination is negligible.
The equivalent width of the line also plays an important role in
the accuracy of the 
value. This can be easily understood by considering that
the peak of the main lobe in the transform corresponds to the equivalent width of the
spectral line and the sidelobes are proportional to the main lobe. A large
equivalent width will thus mean large amplitudes in the data transform and
large relative height of the main lobe and sidelobes to the noise level.
The sampling frequency is another limiting factor in the
calculation of 
. Defining this frequency as
and considering La Palma and
McDonald spectral resolution
we can get a lowest 
value of 
and 
for La Palma and McDonald spectra respectively.
Hence, for stars with 
lower than these values it is not possible
to calculate their rotational velocities but only an upper limit.
The intrinsic nature of 
Sct stars is another source of
error: a pulsating star generates a velocity field in the line-forming
region which manifests itself as a distortion in the profiles of spectral
lines. Whereas radial pulsation will only produce a shift in the central
wavelength of the spectral lines, velocity perturbations whose phase is a
function of longitude (non-radial) will displace the contributions of the
various longitudinal strips causing bumps and dips in the line profile
(Walker et al. 1987). However and due to the small amplitudes of
the 
Sct stars, the influence of the line distortions on 
\
is
negligible compared to other sources of error: Kennelly et al. (1992) measured the rotational
velocities of a series of spectra of 
Boo obtaining an standard
deviation of only 
.
