We assume that an unperturbed disk is steady, axisymmetric,
and nearly Keplerian.
For simplicity, the disk was assumed to be isothermal;
the disk temperature adopted
was 2/3 of the effective temperature of the central star.
In addition, we assumed that the disk extends from the surface of
the central star (
) to
the outer radius (
).
The adopted value of the mean molecular weight was 0.6.
We took a B0 main-sequence star as being a typical central star,
because many Be stars exhibiting long-term V/R variations are
early B stars (Hirata, Hubert-Delplace 1981).
The quantities characterizing the central star were from Allen (1973)
(see table 1 of Paper I).
We used a cylindrical coordinate system
to describe the disk;
the origin is at the center of the star and
the z-axis is perpendicular to the disk midplane.
For convenience's sake, we assume in later sections that
the projection of the observer's direction onto the equatorial plane
is at 
.
From the equation describing the hydrostatic balance of the disk in the vertical direction, we obtain the density distribution in the vertical direction,
where 
is the unperturbed density,
is the unperturbed density on the equatorial plane,
and H is the vertical scale-height of the disk, given by
Here, 
and 
are
the isothermal sound speed and the Keplerian angular frequency,
respectively.
At present, the density profiles of the Be-star disks are
not well determined observationally.
Hence, we adopt a simple power-law form for 
,
where the index 
is a constant.
The surface density is then proportional to 
.
In the present model, the angular frequency of disk rotation
and
the epicyclic frequency 
are written in the form
and
Here, 
is the apsidal motion constant and
f is a measure of the central star's rotation rate, defined by
where 
is the angular frequency of the central star
(Papaloizou et al. 1992; Savonije, Heemskerk 1993).
Note that the second and third terms in each square brackets
in equations (4) and (5) denote
the contribution due to the pressure-gradient force in the disk and
the quadrupole contribution to the potential of
the rotationally distorted central star, respectively.
In the remainder of this subsection we discuss the effect of the rotational deformation of the central star. Papaloizou et al. (1992) and Savonije and Heemskerk (1993) claimed that m=1 oscillations are confined to the inner part of Be-star disks by including the quadrupole contribution to the potential of a rotationally distorted central star. In Okazaki (1991), since the m=1 oscillations were not confined naturally, truncation of the disk was assumed. We show in the following paragraphs that the above conclusions obtained by Papaloizou et al. (1992) and Savonije and Heemskerk (1993) do not generally hold for Be-star disks. For Be stars, the effect of the rotational deformation of the central star is comparable even in the innermost region of the disk, and decreases rapidly with increasing r.
Papaloizou et al. (1992) adopted 
,
which corresponds to the disk temperature,
, for a B0-type star and
for a B5-type star.
This temperature is too low as a model for the Be-star disks.
Savonije and Heemskerk (1993) studied m=1 oscillations
in disks with 
and
around a star of 
and 
.
These parameter ranges cover
and
.
Here, we normalized 
using the value adopted in
Papaloizou et al. (1992).
The value of 
strongly depends on the internal structure
of the star,
and is not determined well (Claret, Giménez 1991).
If 
, the above range of the stellar rotation rate
covers that for actual Be stars.
However, the temperature range in their study was still too low
to apply to the Be-star disks.
We can evaluate the effects by the pressure force and the rotational deformation of the central star for the present disk model by studying the free-particle precession frequency,
Here, 
and 
, the measures of
these effects, are given by
and
For the present model, the ratio of these two quantities is
For B0-type Be stars, 
0.2--0.6
(see figure 4 of Kogure, Hirata 1982).
Consequently, the effect of the rotational deformation
of the central star is comparable to
the pressure effect, even in the innermost region of the disk.
For 
, the former is much weaker than the latter.
Thus, we conclude that since the effect of the rotational deformation
of the central star is not generally important in the disks of Be stars,
including this effect does not qualitatively change
the results obtained by Okazaki (1991).
It is important only for the cases 
and 
.
