4 Results

4.1 The orbit

The radial velocity measurements (given in Table 1) of the two components are well fitted by a circular orbit (Table 2). The scatter of the data points around the orbit is 0.54 and 0.57 $\rm km\,s^{-1}$ for the primary and secondary, respectively (Fig. 1). The fact that the scatter of the data is slightly larger than the accuracy of our measurement is possibly due to stellar activity. The upper limit of the eccentricity is 0.005. We also find a heliocentric systemic velocity of $+1.380\pm0.099$ $\rm km\,s^{-1}$, which is fully consistent with the value $+2.7\pm1.2$ $\rm km\,s^{-1}$ of the known members of the Lupus star-forming region (Wichmann et al. 1999).

 

 

Table 1: Radial-velocity measurements of RX J1603.8-3938

HJD	RV(A)	RV(B)
	[ $\rm km\,s^{-1}$]	[ $\rm km\,s^{-1}$]
2451263.7482	-14.18	18.30
2451290.8430	35.10	-33.10
2451331.7718	-14.33	18.50
2451332.7660	-36.63	43.06
2451333.7155	-34.46	40.38
2451335.7024	21.99	-21.24
2451355.8031	-38.90	45.60
2451621.7546	-13.26	16.09
2451621.7991	-11.89	14.36
2451622.7472	19.05	-17.07
2451623.7174	39.59	-40.36
2451623.8056	40.16	-40.72
2451624.6924	36.70	-37.15
2451625.7288	9.11
2451625.7636	7.28
2451733.4630	-38.33	44.26
2451737.7188	41.29	-40.99

 

 

Table 2: Orbital elements of RX J1603.8-3938

period	$7.55626\pm0.00021$ days
systemic velocity	$+1.380\pm0.099$ $\rm km\,s^{-1}$
$K_{\rm A}$	$40.33\pm0.19$ $\rm km\,s^{-1}$
$K_{\rm B}$	$43.53\pm0.20$ $\rm km\,s^{-1}$
$T_{\rm max}$ [HJD]	$2451525.8484\pm0.0044$
$a_{\rm A} \sin\,i$	$4.191\pm0.021$ Gm
$a_{\rm B} \sin\,i$	$4.523\pm0.022$ Gm
$M_{\rm A} \sin^3i$	$0.2396\pm0.0027$ $M_\odot$
$M_{\rm B} \sin^3i$	$0.2220\pm0.0025$ $M_\odot$
Mass-ratio q	$0.9265\pm0.0063$
eccentricity	0.0

4.2 Spectral types and brightness of the components

Figure 2 shows a small part of the spectra taken in five consecutive nights. Very prominent is the LiI 6708-line which is characteristic for pre-main sequence stars. We measured an apparent equivalent width for the LiI 6708-line of $0.251\pm0.018$ and $0.163\pm0.026$ Å, for the primary and secondary component, respectively.

Figure 2: Small part of the spectra taken of RX J1603.8-3938 in five consecutive nights. Clearly visible are the two sets lines of the two companions. The equivalent widths of the photospheric lines are clearly smaller in one component compared to the other

The most striking feature of this binary system is that although the masses of the two stars differ by only 7%, the line strength of the two components is clearly different (see Fig.2). We determined an average ratio of the equivalent widths of $EW_{\rm B} / EW_{\rm A}$ is $0.60 \pm 0.03$ for unblended photospheric lines in the spectral range between 5800 to 7800 Å. This value is the same for all spectra taken where the two components are well separated. This number does not directly reflect the brightness difference of the two stars at these wavelength bands as the equivalent width of spectral lines depends on temperature. Thus, the spectral types of the two components have to be determined first. In order to do this we compared the spectrum of RX J1603.8-3938 with template spectra of K2V, K3V, and K5V stars.

From these spectra, we conclude that both stars have to have a spectral type earlier than K5, and later than K2. In the next step we selected a number of unblended spectral lines with different sensitivity to temperature. That is, lines where the equivalent width increases when going from a K3 to a K5-star, and lines where the equivalent width remains almost constant in this regime. For lines where the equivalent width remains constant within 20%, we find a ratio of $EW_{\rm B} /EW_{\rm A}=0.62\pm 0.05$ . For the lines that are relatively sensitive to the temperature in this regime, we derive $EW_{\rm B} /EW_{\rm A} = 0.59\pm 0.04$. Thus, within the errors, there is no difference between the two sets of lines, despite the fact that the equivalent width of some features such as FeI6750.164, and TiI6743.127 changes by a factor of three when going from a K3 to a K5 star. This is shown in Fig. 3, where we display the equivalent width ratios for our binary versus those between the K3 and K5 templates, for a number of spectral lines. The relatively small change in the ratios for the components of our binary stands in contrast to the broad range seen between the K3 and K5 templates. This is effectively a very sensitive test of the temperature difference between the stars in RX J1603.8-3938, and it indicates that there cannot be a large difference in their spectral types. Both must be between K3 and K5. However, we can narrow this range down even further. Since the sum of the equivalent width of the two components is slightly larger than the equivalent width of the K3V-template ( $EW_{\rm K3} /EW_{\rm A+B}=0.83\pm 0.03$), a K3V-template is actually not possible and the spectral types of the stars have to be very slightly later than K3. If the two stars had a spectral type of K5, a small amount of veiling would in principle be possible since the sum of the equivalent width of the two stars is smaller than that of the K5V-template ( $EW_{\rm K5}/EW_{\rm A+B}=1.37\pm 0.12$). However, even in this case the veiling would be too small to explain the large difference in the equivalent width of the two components. A substantial amount of veiling would also be highly unusual for weak-line TTauri stars, and we thus conclude that the veiling is unable to explain the difference in strength of the lines.

Figure 3: This figure shows the ratio of the equivalent width of the K3-template to the K5-template versus the ratio of the equivalent width of the two components of the object. Please note that the equivalent width of some lines changes by a factor of up to three when going from the K3-template to the K5-template. In contrast to this, there is no obvious difference of the ratio of the equivalent width between the two components for lines that are sensitive to the spectral type, and lines that are insensitive. Thus, the difference in spectral types between the two components has to be much smaller than the difference between the K3-template K5-template

The fact that the photospheric lines of the secondary are considerably weaker than those of the primary can be explained by a difference in the brightness of the stars. The precise difference in brightness of course depends on the accuracy with which the spectral types where determined. The brightness difference obviously becomes larger when the primary has an earlier spectral type than the secondary, and smaller, when the secondary has an earlier spectral type than the primary. In order to estimate the maximum amplitude of this effect let us take the K5 template as the secondary, and the K3 template as the primary. If the secondary were a K5 star, the brightness difference would be as large as 1.1 mag. In the hypothetical case that the secondary where a K2 star, the difference would be 0.4 mag. However, it is quite unreasonable to assume that the fainter component has the earlier spectral type. That the primary is a K2 star also is not possible, since the observed equivalent width of some lines in RX J1603.8-3938 are already larger than those of a K2 star, leaving no room for a secondary. We thus conclude that both stars have about the same spectral type (K3 to K4), and that the secondary is about 0.6 mag fainter than the primary.

If the difference between the equivalent width of the two components is interpreted as a difference in brightness than the values of the equivalent width for the LiI 6708-line has to be corrected correspondingly. Instead of $0.251\pm0.018$ and $0.163\pm0.026$ Å, the true equivalent width of the LiI 6708-line are $0.41\pm0.04$ Å, and $0.43\pm0.07$ Å, respectively. Since the upper limit of the equivalent width of the LiI 6708-line for stars in IC2602, IC2391, and IC4665 which have an age of 36 Myrs is 0.35 Å at the spectral type K3, RX J1603.8-3938 is correspondingly younger the stars in these clusters (Martín 1997).

4.3 Rotational periods and stellar activity

As mentioned before, both stars are weak-line TTauri stars. In all spectra, H$\alpha$ is seen in emission, all higher Balmer lines are in absorption. The average equivalent width (sum of both components) of H$\alpha$ is $0.21\pm0.07$ Å. The first interesting thing to find out about the components is, whether their axial rotation is synchronised with the orbital motion (synchronised rotation). Answering this question is in principle easy. One simply has to compare the rotational period of the stars, which is determined by monitoring some tracers on the stellar surface, with the orbital period. For example, if the stellar surface is covered with large spots, the photometric period can easily be compared with the orbital period. In a similar way, this can also be done by monitoring the variations of the equivalent width of photospheric lines.

Unfortunately, the variations of the equivalent width for the primary and secondary are too small to determine any period (0.006 to 0.008 Å for LiI 6708 line). The photometric variation of 0.167 magnitudes rms given in the TYCHO-2 catalog is too close to the photometric accuracy of this experiment. Thus, it would not be possible to derive any photometric period from these data either. Another possibility would be to use the emission components of the CaII lines. Since these features originate in plage regions, they can also be used as a tracer. However, although this feature is present, it is very small, and the equivalent width of the emission feature of the CaII IR triplet lines varies only by 12% and 21% in the primary and secondary. This feature also does not allow us to draw any conclusions on the rotational periods of the stars. Thus, the low level of stellar activity prevents us from determining the rotational periods of the stars.