Up: Apsidal motion in eccentric Ophiuchi
The detached eclipsing binary TV Cet
(also HD 20173, BD
502, SAO 111068,
HIP 15090, PPM 146367, AN 270.1934, FL 266;
,
,
mag; Sp. F2+F5)
is a rarely investigated binary with an eccentric orbit
(e = 0.055) and relatively long orbital period of about 9.1 days.
It was discovered to be a variable by Martynov (1951),
who derived the first light elements
Spectroscopically TV Ceti was studied by Popper (1967, 1968), who obtained
the radial velocity curves with semiamplitudes
K1 = 67.4 kms-1 and
K2 = 73.8 kms-1.
Four-color ubvy photometry was obtained by Jørgensen (1979)
at ESO, Chile, between November 1972 and December 1974.
He derived photometric elements and absolute dimensions of this binary
(
,
).
He also presented three new times of minimum and refined light elements
From its spectral type and other known properties, TV Cet was listed by
Giménez (1985) as a good candidate for the study of the contribution
of general relativity to the secular displacement of the line of
apsides, given that the relativistic effect is expected to be dominant
in this particular case.
More moments of minimum light obtained photoelectrically were published
by Meyer (1972) and later by Caton & Hawkins (1987), Caton et al. (1989)
and Agerer & Hübscher (1998).
Aside from these occasional measurements of the times of eclipse, TV Ceti
has remained a rather neglected system until recently.
More than 20 years have elapsed since its last study, thus
TV Cet was also included in our photometric program.
From the Hipparcos photometry (Perryman 1997), we were able to determine
one additional moment of minimum light. It is also given in Table 1,
where epochs are calculated according to the light
elements given by Jørgensen (1979).
All photoelectric times of minimum light published in Meyer (1972),
Jørgensen (1979), Caton & Hawkins (1987), Caton et al. (1989)
as well as Agerer & Hübscher (1998) were incorporated in our analysis.
A total of 20 times of minimum light were used in our analysis,
with 9 secondary eclipses among them.
![\begin{figure}
\par\includegraphics[width=8.8cm,clip]{TVCET.EPS} \end{figure}](/articles/aa/full/2001/28/aa1229/Timg18.gif) |
Figure 1:
O-C graph for the times of minimum of TV Cet. The continuous
and dashed lines represent predictions for primary and secondary
eclipses, respectively. The individual primary and secondary
minima are denoted by circles and triangles, respectively. Larger
symbols correspond to the photoelectric measurements
which were included in calculations with higher weight. |
The eclipse timings listed partially in Table 1 allow the determination
of linear ephemerides indepedently for primary and secondary eclipses
with the following results(numbers between parentheses indicate errors
in the last digits and E is the number of cycles):
These linear ephemerides we propose also for current use.
The difference in the apparent periods is of course a clear indication
of the presence of significant apsidal motion.
The method described by Giménez & García-Pelayo (1983),
with equations revised by Giménez & Bastero (1995), was used for
a more accurate calculation of the apsidal motion rate.
The apsidal motion resulting from the final fit is
deg cycle-1, which is significant at the
3
level.
Adopting the orbital inclination derived from the light curve
solution of
(Jørgensen 1979), the apsidal motion
elements can be computed. The parameters found and their internal
errors of the least squares fit (in brackets) are given in Table 2.
In this table
denotes the sidereal period,
the anomalistic
period, e represents the eccentricity and
is the rate
of periastron advance (in degrees per cycle or in degrees per year).
The zero epoch is given by T0 and corresponding position of
the periastron is represented by
.
The relation between the sidereal and the
anomalistic period,
and
,
is given by
and resulting apsidal motion period U, directly given
by
is,
The O-C residuals for all times of minimum with respect to the
linear part of the apsidal motion equation are shown in Fig. 1.
The quasi-linear predictions, corresponding to the
fitted parameters, are plotted as continuous and dashed lines for
primary and secondary eclipses, respectively.
![\begin{figure}
\par\includegraphics[width=8.8cm,clip]{tv3.eps} \end{figure}](/articles/aa/full/2001/28/aa1229/Timg30.gif) |
Figure 2:
O-C2 diagram for the times of minimum of TV Cet
after substraction the terms of apsidal motion. The curve
represents a light-time effect for the third body orbit
with a period of 28.5 years and an amplitude of about
0.003 days. The individual primary and secondary minima
are denoted by circles and triangles, respectively. |
Subtracting the influence of apsidal motion, the O-C2 diagram
in Fig. 2 can be plotted. The sinusoidal variation of these values
are remarkable and could be caused by a light-time effect.
A preliminary analysis of the possible third body orbit gives the
following parameters:
P3 (period) |
=
days |
|
= 28.5 years |
T3 (time of periastron) |
= JD
 |
A (semiamplitude) |
=
 |
e3 (eccentricity) |
=
 |
(lenght of periastron) |
=
 |
These values were obtained together with the new
mean linear ephemeris
by the least squares method.
Assuming a coplanar orbit (
)
and a total mass
of the eclipsing pair
(Jørgensen 1979), we can obtain a lower limit for the mass of the
third component
.
The value of the mass function
is
,
from which the minimum mass
of the third body follows as
.
A possible third component of spectral type M8 with the bolometric
magnitude about +12 mag could be practically invisible in the system with
a F2 primary (
mag, Harmanec 1988). Therefore, new
high-accuracy timings of this eclipsing binary are necessary in order
to confirm the light-time
effect in this system.
The acceleration of the rate of apsidal motion
caused by the presence of the third body
(Martynov 1973) is
 |
(1) |
where
 |
(2) |
This correction for the apsidal motion is
negligible in this system due to the relatively
long period P3 of the third body orbit.
More precise non-linear light elements of the eclipsing pair including
the term of the light-time effect with the circular orbit are
where
is a mean anomaly of the third body.
Up: Apsidal motion in eccentric Ophiuchi
Copyright ESO 2001