*Astron. Astrophys. 348, 364-370 (1999)*
## 2. The theoretical linewidth/K vs mass ratio relation
The linewidth/K vs mass ratio relation is based on the assumption
that the emission lines are broadened by Doppler broadening in a
Keplerian disk. Since the linewidth and the radial velocity
semiamplitude *K* of the accreting primary have the same
dependence on the inclination angle, the ratio *R* between these
quantities is independent of *i*. If the accretion disk radius is
a constant fraction of the Roche lobe radius of the primary then
*R* should scale with the mass ratio.
The deduction by Warner (1973) assumes binary synchronus rotation,
circular orbits and that particles ejected from the inner Lagrangian
point at thermal velocities, conserve
their angular momentum about the primary and eventually take up a
circular orbit about the primary at a radius
. Using the Kepler's third law for
circular orbits along with the relation between *K* and the
orbital period, he found:
where *vsini* is the projected rotational velocity of the disk
at the radius , deduced from the width
of the emission lines at some intensity level and
is the distance from the center of
the primary to the inner Lagrangian point in units of the semi-major
axis of the orbit. Expressing this distance in units of the binary
separation as , Shafter (1983)
obtained:
Using the Roche approximation (Kopal 1959), an expression for
can be obtained:
which is accurate to 1% for 0.1
*q*
10, as deduced from the tables of
Plavec and Kratchovil (1964). From the above arguments, we should
expect a relationship:
where is a calibration parameter
depending on the line intensity level where *vsini* is measured.
The above relation has been used but almost always restricted to dwarf
novae above the period gap (Warner 1973, Piotrowski 1975, Robinson
1976, Shafter 1983 and Jurcevic et al. 1994). For example, Jurcevic et
al. (1994, hereafter J94) used =
*FWHM* (the full width at half maximum of the
emission line) and found
= 2.00
0.02 calibrating a sample of 12
dwarf novae, including only 2 SU UMa stars, viz. HT Cas and WZ Sge.
Looking in their Fig. 5, it is evident that their relationship is
relatively well established for above-the-gap dwarf novae, but a large
data gap is seen in the domain of SU UMa stars (the low *q*,
upper right corner of their Fig. 5). In fact, J94 extrapolated the
relationship to the domain of SU UMa stars basically using the data of
WZ Sge. They claim that removing this star from their sample
changes only by 5%. We think that
this extrapolation deserves an empirical confirmation, moreover
considering that the gas dynamics in the disks of dwarf novae above
and below the period gap could be substantially different.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999
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