6 V431 Pup

Figure 12: The He  I 4922 line of V431 Pup at phase 0.686, showing features of both binary components.

The star HD 69882 was discovered as an eclipsing variable with a period of 9$\fd$3634 by the HIPPARCOS satellite (ESA 1997). Our spectra were taken before the binary character of the star was known, and, of course, without knowledge of its ephemeris, so the phase coverage is not very good. An example of the He  I 4922 region is plotted in Fig. 12, H$\alpha$ in Fig. 7. The secondary line is only discernable - at favourable phases - as an extended wing of the 4922 primary line, and hence its position is only poorly determined. The profile shown in Fig. 12 was obtained from a CAT/CES spectrum. The ECHELEC spectra are noisier, and the secondary line positions are uncertain.

Figure 13: Radial velocity curve of V431 Pup; filled circles - ECHELEC data for He  I, squares - CAT/CES He  I data, x - CAT/CES H$\alpha$, crosses - H$\beta$ ECHELEC data, open circles - values by Feast et al. (1955); the curves correspond to the parameters listed in Table 7.

 

 

Table 6: Radial velocities of V431 Pup published by Feast et al. (1955).

JD	Velocity	Ph(HIP)	Ph(new)
-2 400 000	(km s-1)
34373.447	-115	0.391	0.770
34387.432	94	0.885	0.263
34392.472	-85	0.423	0.802
34396.363	135	0.839	0.217
34425.298	114	0.929	0.306
34428.349	-7	0.255	0.632

Feast et al. (1955) published radial velocities obtained in six nights. These velocities are listed in Table 6; the values are means formed from measurements made by various observers for a given plate. Secondary lines could not be recognized on these low-dispersion plates. In the column labeled "Ph(HIP)'' phases calculated according to the ephemeris by HIPPARCOS are given. However, such phases are incompatible with velocities measured in our spectra. We found that a phase shift of about +0.38 is needed to bring both sets in agreement. Such phase shift means that the true period should be longer than the HIPPARCOS value. Since the difference of epochs between the Feast et al. data and our data is approximately 1570, the period has to be longer by about 0$\fd$0024. However note that this corresponds only to the smallest possible phase shift; the phase shift might also be -0.62, or by one or more epochs larger, so that the true period could differ by more.

Figure 14: Our V measurements (crosses) and HIPPARCOS photometry (filled circles) of V431 Pup; the curve is the result of FOTEL.

 

 

Table 7: Parameters of V431 Pup.

Parameter	Value
i	$68.2 \degr$
K1	$118.2 \pm 0.6$ km s-1
K2	$149.2 \pm 0.6$ km s-1
$V_1\gamma$	$25.9 \pm 0.7$ km s-1
e	0.193
$\omega$	$300\fdg5$
$T_{\rm periastron}$	JD 2448509.038
Prim. min.	JD 2448512.553
r1	0.324
r2	0.125a
$a\sin i$	48.5  $R_{\odot}$
$m_1\sin^3 i$	9.16 $M_{\odot}$
$m_2\sin^3 i$	7.50 $M_{\odot}$

^a Assumed.

In April 1994, we obtained several UBV measurements of the star. The color indices were B-V = 0.316 and U-B = -0.605. The Vmagnitudes, together with the HIPPARCOS data, are plotted in Fig. 14. The HIPPARCOS data were transformed to V magnitudes using the formula by Harmanec (1998); 0$\fm$079 was subtracted.

To solve the light curve as well as the radial velocity curve, we applied the code FOTEL (Hadrava 1990, 1995), which solves the light and velocity curves simultaneously. The radial velocity curve is plotted in Fig. 13.

In our spectra, radial velocities from lines He  I 4922, H$\beta$(see below) and H$\alpha$ can be measured fairly well. However, in spectra where only the shorter wavelengths are covered and H$\beta$ is affected by a CCD defect (the first three spectra are concerned) the lines present are mostly blends, or are rather weak. The best line here is 4649, the blend of several C  III and O  II lines. Not knowing in advance the representative laboratory wavelength of this blend, we measured this line and by comparison with He  I lines 4713 and 4922 and H$\beta$ obtained a central wavelength of this feature of 4649.66. Due to the uncertainty of this value we however did not use the corresponding velocities in our solution.

Radial velocities as well as photometry do not provide sufficient constraints to define the system. It is clear that the deeper minimum is the secondary minimum, in the sense that the smaller, less luminous (and probably also less massive) star with nearly invisible spectral lines is eclipsed. At the phase when the more luminous star is behind the secondary component, the mutual distance of both components is so large that practically no eclipse occurs.

The minima are not well covered by photometry, and the ratio of radii is nearly impossible to obtain; but the ratio of luminosities of both components might be estimated using the CAT/CES spectrum where the secondary line is visible as a deformation of the line wing (see Fig. 12). EWs are 1.249 and 0.147 Å, i.e. their ratio is 8.5. Assuming that the EWs represent the luminosities of components, the solution given in Table 7 was obtained. With the assumed value of r₂ = 0.125 the temperatures do not differ much, and the assumed ratio of luminosities seems appropriate.

In the solution in Table 7 only the secondary line measured in the CAT/CES spectrum was considered. Taking into account also the features visible in the ECHELEC spectra would increase K₂ to a considerably larger value with a corresponding primary mass of about 20 $M_{\odot}$.

The minimum time of the deeper minimum derived from the FOTEL solution comes out very close to the time determined by HIPPARCOS data. The following ephemeris results:

$${\rm Sec.~min.} = {\rm HJD}~~2448508.517 + 9\fd36575 \cdot E .$$

This ephemeris has been used through this paper, since the time of the deeper minimum is well defined and independent of any orbital solution.

Of course the mass ratio is poorly known, being only based on the mentioned deformation of the He  I 4922 line. Nevertheless the basic parameters of the system appear acceptable: a somewhat evolved more massive star accompanied by a main sequence component, both of similar temperatures. From the width of the He  I line 4922 we find $v \sin i = 180$  km s^-1(primary component). This is considerably more than what would correspond to synchronous rotation; according to Hut (1981) the pseudosynchronous velocity is 116  km s^-1.

 

 

Table 8: Absolute parameters of four binaries.

Parameter	V337	V649	V382a	V431
	Aql	Cas	Cyg	Pup
M1 ( $M_{\odot})$	17.2	12.9	29.2	11.4
R1 ( $R_{\odot})$	9.4	6.1	10.1	16.9
M2 ( $M_{\odot})$	6.8	5.5	21.2	9.4
R2 ( $R_{\odot})$	7.2	4.4	8.4	6.5

^a Inclination, r₁ and r₂ according to Degirmenci et al. (1999).