4 Orbital ephemeris and light curve

According to an estimate of GB83 the time-scale for the decrease of the orbital period of MT Ser due to gravitational radiation is comparatively short. Therefore, they urge other observers to obtain timings. The present light curves permit us to measure the epochs of six minima (a further minimum occurred a few minutes before the end of the observations, making an accurate timing difficult; therefore it is not considered here).

The individual light curves were fitted by a spline which was then evaluated to find the minima. The corresponding timings are listed in Table 2 which also includes the minimum epochs measured by GB83.

 

 

Table 2: Times of minimum for MT Ser.

HJD	E	O-C $_{\rm lin}$	O-C $_{\rm quad}$
2444703.9734	-3347	-0.003785	-0.002478
2444705.9029	-3330	+0.000868	+0.002168
2445082.9480	0	+0.001618	+0.001618
2445084.8715	17	+0.000267	+0.000261
2445087.9277	44	-0.000651	-0.000667
2445115.6691	289	+0.000250	+0.000145
2445115.7829	290	+0.000823	+0.000718
2445117.7061	307	-0.000825	-0.000937
2445117.8197	308	-0.000450	-0.000562
2445118.7249	316	-0.001065	-0.001180
2450683.4683	49463	-0.002120	-0.002217
2450686.4165	49489	+0.002232	+0.002145
2450686.5278	49490	+0.000334	+0.000247
2450687.4341	49498	+0.000772	+0.000688
2450687.5454	49499	-0.001127	-0.001210
2450688.4521	49507	-0.000201	-0.000281

The ephemeris determined by GB83 are accurate enough so that no cycle count ambiguities occur at the epoch of our measurements. The cycle numbers of the minima observed here are also quoted in Table 2. Combining the present minimum timings with those of GB83, the much longer time base permits us to determine a considerably more accurate period for MT Ser. Improved values for the minimum epoch, T₀, and the period, P, were determined by minimizing $\chi^2$ of the O-C values of the minimum times. The revised ephemeris is:

HJD (min)	=	2445082.9461	+	0.113226533	$\times$	E
		$\pm$ 4		$\pm$ 15

The O-C values of the individual minima with respect to this ephemeris are also given in Table 2.

Although according the to model of GB83 a change of the period due to gravitational radiation should only become detectable on time scales of 100 years or more, we also fitted a quadratic ephemeris to the minimum timings:

HJD(min)=	2445082.94638	+	0.11326899	E-	7.36$\times$10-12	E2
	$\pm 37$		$\pm 12$		$\pm 25$

Table 2 contains the O-C values also for this case. As can be seen, the quadratic term is highly significant within the formal error. The issue of the period derivative will be discussed further in Sect. 7.

The combined light curves, folded on the period P₁ = 0.113226533 days (linear ephemeris), are shown in the upper panel of Fig. 1. Since it cannot be excluded that the true period is twice as long, the light curves were also folded on $2 \times P_1 \equiv P_2$, as shown in the upper panel of Fig. 2. In the P₂ curve the minimum at phase 0.5 appears to be slightly less deep than the one at phase 0. Moreover, there is no indication of flat topped maxima as were seen by GB83 and taken by them as an argument against an ellipticity effect and thus against the longer period. Therefore, the present results appear to be slightly in favor of a true period twice as long as originally assumed. In this case the variations are expected to be due to an elliptical shape of the hotter star (which we will refer to as the primary regardless of its mass being higher or lower than that of the cooler star) and - as it turns out, see Sect. 5.2 - to eclipses, while in the other case they would be explained as a reflection effect off the illuminated face of the less luminous star. Evidently, this has a tremendous bearing on any model of MT Ser. We will not try to decide the question of the true period based on a visual inspection of the light curves alone. We will rather try to find solutions using light curve synthesis for both cases.

Figure 1: Top: Light curve of MT Ser folded on the nominal orbital period, P=P1, (dots) and two different model light curves (solid and dashed lines). Centre and bottom: O-C curve between the observations and the model light curves; for details, see text.