In the zero-rotation approximation, our model of the line-profile variations has six parameters. In the slow-rotation model, the relative rotation rate is the seventh parameter. Of course, real line profiles and their variations also depend on and . These two parameters can be removed from the model by proper scalings, which are described in Sects. 4.1 (click here) and 5.5 (click here). A single representation of the line-profile variability is then applicable to a wide range of rotational velocities and line strengths.

Following AW, we use values for up to 0.5 for
the slow-rotation model. The parameters *k* and
are closely related because of their joint dependence on
. Nevertheless, we have chosen to keep them as separate
parameters, and consequently, every combination corresponds to a star
with different mass, radius and/or rotational frequency. For a given
rotational velocity, a large value for
corresponds to a large *k*-value. This implies that certain domains
in the -()-plane become irrelevant,
depending on the ratio, , of the centrifugal force to the
gravitational force at the equator of the star

In our work we only use combinations of and
that satisfy . This corresponds
to an equatorial rotation velocity that is at most of the
equatorial break-up velocity. Clement (1994) has found that the
spheroidal part of axisymmetric modes (zonal, *m* = 0), does
not maintain its basic zero-rotation spatial distribution. Therefore,
our model might be inaccurate for zonal modes with high
.

The frequencies that we use for our line-profile calculations are
those as observed in the corotating frame of the star. In this way the
retrograde modes lead to bumps that move from red to blue in the line
profiles, while the bumps of prograde modes move from blue to red.
This makes it easier to distinguish prograde and retrograde modes in
our figures. In the zero-rotation approach, the line-profile
variations associated with prograde (*m* < 0) and retrograde
(*m* > 0) modes behave symmetrically in time (see Fig. 8 (click here),
right two columns). This symmetry is broken by the effects of
rotation on the mode, which necessitates a separate investigation of
prograde and retrograde modes in the case of the slow-rotation model.

Symmetries in the expressions of the displacement field allow us to
restrict the inclination angle *i* to the interval
(Aerts 1993).

A comparative study of line profiles with different values of ,
*m*, , or , in which the model amplitude
is kept constant, is not convenient, since this
implies physical situations with substantially different velocities,
and correspondingly different amplitudes of the line-profile
variations. To facilitate a fair comparison between the line-profile
variations resulting from different parameter settings, we adjust the
displacement amplitude in each case such that the
calculated maximum pulsational surface velocity

is kept the same whereas the other parameters may vary.

Two profiles will have identical shapes if the combination of and is the same for both profiles. Such profiles differ only in velocity (wavelength) and intensity scale. We therefore use as a scaling factor for the velocity amplitude, for the width of the intrinsic profile, and for the velocity scale of the line profile. We adopt only one specific value of and vary the pulsation amplitude and intrinsic width to investigate the response in the line-profile variations.

The amplitude of pulsation and the intrinsic profile
width *W* have a broad range of physically relevant values. The more
rapid rotators are best accounted for by relatively small values of
and , while
the slower rotators have values of and *W* of order
.

Theoretically, the value for *k* can range from approximately zero up
to infinity (Eq. 22 (click here)). If we keep the
same for each calculated mode, the profiles do not change much for *k*
values higher than a certain value . Above this value,
the magnitude of the velocity vector is almost proportional to *k*,
because the radial velocity component becomes negligible. For all
investigated modes we found 1 , depending somewhat
on the considered value. In Figs. 10 (click here) and 15 (click here),
where is one of the two running parameters, we adjust the
range of according to the value of . The
line-profile characteristics for the highest values that we use for
can be considered as representative for all higher values as
well.

For the calculation of line profiles, we have chosen to use
as model parameter and to calculate the corrected *k* from
Eq. (22 (click here)). Such an approach allows to separate the
effect of the rotation on *k*, and to study the line profiles by
comparing different rotation rates for the same -value
(Fig. 14 (click here)).

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