UBV Photometry of the Massive Eclipsing Binary TT Aur

S. Oezdemir, H. Ak, M. Tanriver, H. Guelsecen, \\
S. Guelsecen,
A. T. Saygac, E. Budding, O. Demircan.
, PASA, 18 (2), in press.

Next Section: Absolute Parameters
Title/Abstract Page: UBV Photometry of the
Previous Section: Period Variation
Contents Page: Volume 18, Number 2

Subsections


The light curves

Figure 2: Simultaneous UBV TUG observations of TT Aur are here shown together with the semi-detached model discussed in Section 3.1. These (and subsequent) light curves plot relative flux levels against orbital phase.
\begin{figure} \centerline{ \psfig{figure=fig2.eps,height=10cm,width=15cm} } \end{figure}

The UBV light curves (Figure 2) were formed mainly from observations carried out using the 40 cm Cassegrain (Utrecht) telescope at the TUBITAK National Observatory (TUG) during 1997 (7 nights), supplemented by two nights with the 30 cm Maksutov telescope at the Ankara University Observatory in 1996. The 40 cm TUG telescope was used with a standard SSP-5 photometer and an SSP-5A on the 30 cm Maksutov. These single channel uncooled photometers have side-on Hamamatsu R1414 photomultipliers and near standard UBV filter sets. The control of the photometer heads, data acquisition and reduction functions were carried out with software prepared by Muyesseroglu (1992) (AUO) and Keskin (1996) (TUG). Further details of observational procedure are available on request (cf. also http://www.tug.tubitak.gov.tr/). The main comparison star (C1) was BD +39$^\circ$1191 (= SAO 57677), with occasional checks on BD +38$^\circ$1005 (= SAO 57581; C2). During the course of these observations, the star C2 was discovered to be variable, showing a light decrease of $\sim $1.5 mag (Ak, 1997). In addition to the new UBV data, IUE spectral data were also studied. Doppler shifts, equivalent widths, depths and areas of the bright lines were investigated. Derived values were found to show a phase dependence. Integration of the low dispersion continua between 1225Å$< \lambda < $ 1975 Å yields a very smooth light curve, where the primary is much deeper and the secondary shallower in comparison to the optical light curves.

Figure 3: Simultaneous light curve solutions of the system TT Aur with a semi-detached model, together with normalized observation points. The upper left panel shows the UV ($\sim $1600Å) light curve, extracted from IUE records; the lower left panel shows the radial velocity data of Popper and Hill (1991), fitted with the derived model. These are given as fractions of the total radial velocity amplitude of the close binary (430 km/s). The panel on the right shows a corresponding Wilson and Devinney (1971) (WD) type representation. This diagram was produced using Bradstreet's (1993) Binary MakerTM software.
\begin{figure} \centerline{ \psfig{figure=fig4_new.ps,height=10cm,width=15cm,angle=-90} } \end{figure}

Semi-detached model

These light curves have been fitted simultaneously, using a recent version of the Wilson-Devinney code (Wilson, 1992). During this curve-fitting, certain parameters were fixed to reliably known values. These parameters are: the spectroscopic mass ratio, q = 0.668 (Popper & Hill, 1991); the temperature of the primary, T1 = 23400K, appropriate to spectral type B2V (Wachmann et al., 1986); linear limb-darkening coefficients (Wade & Rucinski, 1985); bolometric albedo A1,2 = 1.0; gravity-brightening coefficients g1,2 = 1.0 and rotation parameter F1,2 = 1.0. We applied the semi-detached mode (W-D mode 5) in this analysis. Such a model is suggested by the long-term trend of period increase that can be associated with a Roche lobe overflow mechanism. Light curves of TT Aur also tend to show absorption effects in the primary minimum, which may also relate to mass transfer. The deeper primary minimum in the U filter may point to a hotter region on the secondary-facing hemisphere of the primary. The UV (IUE) light curve was also fitted with this model. Iterations were controlled visually, by inspection of the goodness of fit of the theoretical and observational light curves. The corresponding solution is listed in Table 3. The theoretical light curve corresponding to this solution is shown as Figure 2, together with normalized UBV data points, and also in Figure 3, which includes the UV (IUE) observations and corresponding radial velocity data. TT Aur has some resemblance to the early type close binary DM Per, whose period variation was interpreted in terms of a standard Case B type Roche lobe overflow process (Murad & Budding, 1984). In such a regime one may write, for the period variation due to mass transfer,

\begin{displaymath} \Delta P/P = - 9 \eta s\left((2x-1)/(1-x)/R_2\right) \times \left(P_d/365.25 \right) , \end{displaymath} (1)

where $\Delta P/P$ is the fractional change of period, $\eta$ is the density of the surface layer of the mass-losing star as a fraction of its mean density, R2 is the mean radius of this star, x is the value of M2 expressed in terms of the mass of the entire system, and s is the annual rate of surface expansion of the mass-losing star. If we substitute in the appropriate numbers, as in Murad & Budding, we will find a representative relative period variation $\Delta P/P$ of about

$3\times10^{-9}$. Period variations of this order can be observed for classical Case B Algols in the earlier stages of the semi-detached condition (cf. e.g. U Cep; Kreiner, 1978). However, this is considerably greater than the observed value for TT Aur of

$\sim6\times10^{-11}$ (Section 2). In considering the period variation in relation to the semi-detached hypothesis, we would note the following points. (i) The surface expansion rate s is a sensitive function of the initial mass of the loser (unknown but here assumed

$\sim7M_{\hbox{$\odot$}}$). (ii) The role of momentum exchange with the third body complicates the problem. (iii) Not all Algols necessarily follow the Case B model (cf. e.g. Tout & Eggleton, 1988). (iv) For spectral types earlier than mid-B the role of radiation pressure becomes increasingly dominant, whereupon the foregoing simple formula will no longer apply (cf. e.g. Plavec, 1989; Mazzali et al., 1992; Drechsel et al., 1995).

Table 3: WD solutions for TT Aur.
Parameter Value p. e. ($\pm$)
     
a (R$\odot$) 11.64 0.07
i($^\circ$) 77.6 0.4
q 0.668 fixed
T1 23400 fixed
T2 18000 180
$\Omega_1$ 3.541 0.02
$\Omega_2$ 3.188 0.009

$r_{1,{\rm pole}}$

0.344 0.002

$r_{1,{\rm point}}$

0.387 0.003

$r_{1,{\rm side}}$

0.356 0.002

$r_{1,{\rm back}}$

0.372 0.003

$r_{2,{\rm pole}}$

0.323 0.001

$r_{2,{\rm point}}$

0.447 0.03

$r_{2,{\rm side}}$

0.337 0.002

$r_{2,{\rm back}}$

0.369 0.002

L1/(L1 + L2)(U,B,V)

0.69,0.66,0.64  

L2/(L1 + L2)(U,B,V)

0.31,0.34,0.35  
L1 (U,B,V) 8.7, 8.3, 8.1  
L2 (U,B,V) 3.95,4.35,4.45  
x1 (U,B,V) 0.31,0.28,0.24 fixed
x2 (U,B,V) 0.37,0.34,0.30 fixed
L3 (U,B,V) 0.0  
A1 = A2 1.0  
g1 = g2 1.0  
F1 = F2 1.0  
$\chi^2$ (mag) 0.04  

Figure 4: Light curve solutions of the system TT Aur with a detached model, derived by the ILOT curve-fitter and illustrated by means of Bradstreet's Binary Maker(TM), using the ILOT parameters. The light curve in the upper left panel is the B one of Fig. 2, otherwise the diagram follows the format of Fig. 3.
\begin{figure} \centerline{ \psfig{figure=fig5_new.ps,height=10cm,width=15cm,angle=-90} } \end{figure}

ILOT models

Superficially, TT Aur also has some likeness to the bright early-type system VV Ori (Budding & Najim, 1980). Although a semi-detached configuration is suggested by other evidence, as mentioned, we also examined the curve-fit of a detached model, utilizing the Information Limit Optimization Technique (ILOT) (cf. Budding, 1993). Previously fixed parameters were set to the same values as for the W-D fitting. It became clear that, whether or not the secondary photosphere is in contact with the surrounding Roche lobe, both stars must occupy large fractions of these lobes, so that some mass transfer, at least of coronal material, can be expected. The ILOT fittings are summarized in Table 4. Error estimates are derived from inverting the determinacy Hessian for four parameters in the vicinity of the $\chi^2$ minimum. Other things being equal, the SD configuration, entailing somewhat larger stars, requires a somewhat lower inclination to compensate for otherwise-introduced changes of shape to the light curves. Note here the difference between the inclination values of Tables 3 & 4 is appreciably bigger than their formal errors. This difference ($\sim $4$^\circ$) is a better indication of real uncertainties than the formal errors, which build in assumptions about the strict validity of the model.
Table 4: ILOT solutions for TT Aur
Parameter Value p. e. ($\pm$)
     
i($^\circ$) 81.6 0.8
q 0.668 fixed
T1 23400 fixed
T2 18000 180

$r_{1,{\rm side}}$

0.389 0.005

$r_{2,{\rm side}}$

0.280 0.005

$m_{0,{\rm ref}}(U,B,V)$

7.512,: 8.321,: 8.547 0.010

L1/(L1 + L2)(U,B,V)

0.81,: 0.79,: 0.75  

L2/(L1 + L2)(U,B,V)

0.19,:0.21,:0.25  
x1 (U,B,V) 0.31,:0.28,:0.24 fixed
x2 (U,B,V) 0.37,:0.34,:0.30 fixed
L3 (U,B,V) 0.0  
A1 = A2 black body 1.0  
g1 = g2 1.0  
$\chi^2$ (U,B,V) 189.4, 157.5, 180.0  
$N - \nu$ 168,168,168  
$\Delta l$ 0.008 (adopted)

The ILOT values of $\chi^2$, with the given number of degrees of freedom (168 for each light curve), and the given nominal accuracy of each datum (

$\Delta l = 0.008$), show that these detached model fittings are, statistically, as probable as the semi-detached one (cf. e.g. Pearson & Hartley, 1954). This adopted s.d. dispersion for the normal points (i.e. $\Delta l$) is in broad keeping with both the normal statistical expectation that

$\chi^2/(N-\nu) \sim 1$ and the observed scatter of individual observations of the comparison stars. Here it should be noted, however, that the greatest discrepancies in the light curves are systematic, and in certain regions of the light curves. Hence, neither the SD nor detached models are complete representations of the data. The detached model result was checked by Bradstreet's (W-D-based) Binary Maker(TM). Results are shown, for comparison, in Figure 4.


Next Section: Absolute Parameters
Title/Abstract Page: UBV Photometry of the
Previous Section: Period Variation
Contents Page: Volume 18, Number 2

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