## 3. Parameters for WW Cet## 3.1. The state of WW Cet during the observationsIn Fig. 2, we present averaged spectra for each of the three of our observing periods. The typical properties of the lines are summarized in Table 2.
As stated in Sect. 2.1, the flux calibration proved to be very uncertain. However, it is still considered to be good enough to provide some information about the state of WW Cet at the time of our observations. For this reason, we have measured the continuum flux close to the H line. The first of the data points was taken as reference, while the other values were transformed into magnitudes. The results are plotted in Fig. 3.
These magnitudes show a scatter which amounts within each single data set to .8 in 1993 and .5 in 1994. However, the differences between the 1993 and the 1994 magnitudes are much larger than this, with the 1994 data being much brighter. Furthermore, the second night in 1994 shows WW Cet on a steady decline from the constant level maintained during the first night, almost down to the brightness observed in the 1993 data. We conclude that WW Cet was observed in quiescence in October 1993, and in outburst as well as in decline from outburst in October 1994. This is also supported by the observations of the Variable Star Section of the Royal Astronomical Society of New Zealand: our observations in 1993 lie between two registered outburst maxima on JD 2 449 264 and JD 2 449 276 (Jones et al. 1993), and 1 and 2 days after the outburst maximum (V = 11 .0) on JD 2 449 637 in 1994 (Cragg et al. 1994). ## 3.2. Radial velocitiesIn order to measure the Doppler shift of the observed line with
respect to the rest wavelength of H
, we applied the double Gaussian method as
outlined by Shafter (1983). Here, two Gaussians with the same FWHM separated by a
wavelength interval This method provides an important advantage over a single-Gaussian fit, which does not account for often observed dilution of the disk-born line profile by additional emission sources. However, their influence is irrelevant if we just want to derive the orbital period from the data. At this stage we therefore chose broad Gaussians with FWHM = 40 Å, measuring those parts of the line with good S/N. In order to derive the orbital period from these data, we applied
both the phase-dispersion minimization method of Stellingwerf (1978) as included in IRAF, and the analysis-of-variance (AOV)
algorithm by Schwarzenberg-Czerny (1989) as implemented in the In earlier radial velocity studies (Kraft & Luyten
1965, Thorstensen & Freed
1985, and Hawkins et al.
1990); these will be referred to hereafter as KL65, TF85, and HSJ90,
resp.), no unambiguous decision could be made between two periods
around 0.150 for the 1993 and 1994 data, respectively. The rather poor precision is probably due to the short overall coverage per orbit (only on 94/10/13 we observed the system for ). While the broad Gaussians are sufficient to derive the orbital period, greater care has to be taken when selecting the radial velocities which are used to determine the orbital parameters, i.e. the parameters of the function As the motion of the WD should be best represented by the variation of the line wings, we used narrow Gaussians with FWHM = 4 Å, which gave the best compromise between high resolution and high S/N for our data. To determine these parameters we used only the quiescence data. The H line in the outburst data is too narrow for the line wings to be resolved, and the radial velocities of the decline data are probably disturbed by non-orbital changes within the disk (Tappert et al. 1997). The diagnostic diagram for these extracted data is shown in Fig. 4.
In principle one can choose between two possibilities for selecting
the separation which corresponds to the correct parameters from this
diagram. The first is to look for the minimum value of
as this indicates the best fit to the data. In
our case, this separation is 5 Å which is of course much too
close to the line center. On the other hand, at some point the line
wings will be too much affected by the noise to yield reliable
parameters. This point is marked by the last
before the errors increase steeply. Note that
this does not For our data we have therefore chosen the parameters corresponding
to a separation The phase shift between line center and wings is
= 30 ## 3.3. Towards a more precise orbital periodThe publication of four previous radial velocity studies gives us
the possibility to determine the orbital period with a much greater
precision than before. This can be done by comparing the zero phases
of a set of functions from Eq. (2) which are fitted to the single data sets for a sample of periods
With the combined data of KL65 and our 1994 period spanning a range
of 30 years (11018 days), a precision of
days seems possible if an extrapolation with an
accuracy of 0.1 The published data of TF85 and R96 were obtained by using two broad
Gaussians with FWHM = 40 Å and 45 Å, respectively. Both
caught WW Cet in quiescence, and we therefore assume that our 1993
data measured with equally broad Gaussians are quite accurately in
phase with these data. On the other hand, HSJ90 measured the
absorption lines of the secondary which should show exactly opposite
phase to the motion of the WD and thus to our 1993 wings data (HSJ90
found no significant eccentricity in their radial velocities, and the
absorption lines seem thus undisturbed by irradiation effects). We
therefore expect that we are allowed to compare these data with an
accuracy of 0.1 To choose the frequency range to be searched, we took from all
published periods the most accurately determined one from TF85 and
allowed a deviation of 5
. With a precision of
cycles/day this gave us a range of 5.667 970 -
5.710 044 cycles/day. We then compared the data sets in pairs by
fitting functions of the form in Eq. (2) for each frequency and calculating the zero points according to Eq.
(4). The resulting frequencies, i.e. those which give the same phasing
(within 0.1
Further alias frequencies can be removed by including our 1994 and the KL65 data. However, the phasing of the 1994 data might be somewhat different from the quiescence data (Tappert et al. 1997) and we do not know, to which part of the line the radial velocities of KL65 correspond to. On the other hand, the phases of the line center and the wings in our 1993 data differ for less than 0.1 orbits, and thus we do not expect much bigger differences between any of the data sets. Therefore, we used for the extended comparison with the 1994 and
the KL65 data included an accuracy of 0.2
## 3.4. System parametersWith the now established period Warner (1995) gives semi-empirical relations for mass and radius of the secondary, ( The mass of the WD can be obtained from the semiamplitudes, Thus , where we used = 224(7) km/s from fitting the radial velocities of HSJ90 with respect to . The WD's radius is more difficult to determine, as the chemical composition is unknown, and therefore only rough estimates will be possible. Warner (1995) gives, for a non-rotating helium WD with a mass , the approximation where is the Chandrasekhar mass. This yields . However, we estimate this number a factor 1.5 too low when compared to Fig. 1 of Hamada & Salpeter (1961). Van Amerongen et al. (1987) use yielding which seems a more reasonable result. Finally, we can calculate the inclination which leads to . All derived parameters of WW Cet are summarized in Table 5.
© European Southern Observatory (ESO) 1997 Online publication: April 8, 1998 |