4. Results for the X-ray selected sample
4.1. Uncorrected data
Table 1 lists all the binary and multiple stars we find in our sample. Table 2 lists all stars where we did not find a companion and gives limits for the brightness of an undetected companion. Fig. 2 shows the results in a plot of flux ratio and magnitude difference vs. binary star separation. In total, we find 29 binary, 6 triple and 1 quadruple star with separations in the range between and .
Table 1. New binary WTTS in Taurus. The first column gives the number of the star as in Table 4 of Wichmann et al. (1996); the second gives the official designation; the third column specifies to which pair of a higher-order multiple system the following parameters apply; the fourth column gives the total system brightness in K. The following columns contain the date of the observation and the position and brightness of the companion relative to the primary (i. e. the star brighter in K). For a description of the way the errors were determined see text. If a companion was observed more than once, the different observations are listed in separate rows. Stars marked with were found with pointed ROSAT observations
Table 1. (continued)
Table 2. Unresolved stars in our sample and limits for undetected companions. Objects marked with were found with pointed ROSAT observations
The lower separation limit is the diffraction limit of the telescope at K for binary stars. In principle, it is possible to discover binaries with even smaller separations (Table 1 shows that we actually do find some). However, we cannot distinguish with certainty a close binary star below the diffraction limit from an elongated structure.
The upper limit was chosen so that contamination with background stars has little effect (see the following section for a detailed discussion of this problem). Leinert et al. (1993) chose the same value of in their survey.
Fig. 2 also shows the sensitivity of our survey, i. e. the maximum brightness ratio of a possible undetected companion as a function of the separation. On average our survey is sensitive to companions brighter than of the primary for all separations larger than . All observations are sensitive to companions brighter than . Based on the curves for individual observations and the number of companions actually found, we expect about 0.14 additional companions above brightness ratio at separations . Thus, we are confident we have found all companions brighter than of their primary. This corresponds to a magnitude difference of .
4.2. Confusion with background stars
We expect a certain number of our wide binaries to be no physically bound pairs, but appear to be binaries due to chance projections of background stars. To quantify this effect, we count the field stars in the 32 images taken at the telescope. We exclude a circular area with a radius of around the T Tauri star in each image. The remaining area is per field, giving a total area of . These are the same images as used in our search for companions, which ensures that we have exactly the same magnitude limit.
Fig. 3 shows the results of this procedure. The measured distribution of field stars is approximately the same as a Poisson distribution with a mean of 9.5. This corresponds to a background star density of stars per . Leinert et al. (1993) find stars brighter than per . The difference is partly due to the different magnitude limit, and partly due to the different spatial distributions of the two samples: the stars of Leinert et al. (1993) are more concentrated towards the dark clouds where the extinction is higher and therefore less background stars are visible.
Given the background star density, we can calculate the expected number of background stars with a projected distance of at most to one of our 74 T Tauri stars:
In other words: the probability for a background star with a projected distance of at most to one object is .
To estimate the number of physically bound companions, we have to subtract the number of chance projections from the total number of companions. This yields companions. To correct the numbers of binaries, triples, and quadruples, we have to take into account the relative numbers of single, binary, and triple stars (a binary caused by a nearby background object is in fact a single star, thus the number of "false" binaries depends on the number of single stars). This way, we arrive at about 2.4 binaries and 1.7 triple stars caused by chance projections. The corrected numbers of physically bound objects are consequently 29 binaries, 4 triples, and 1 quadruple star.
Unfortunately, we cannot say which companions are bound and which are chance projections. We do know, however, that the star 40C is one of the chance projections as Rainer Wichmann took a spectrum of it (priv. comm.). This spectrum shows no Lithium line, thus we know this star is no pre-main-sequence object. To identify further background stars it would be necessary to carry out additional spectroscopic observations.
4.3. Bias induced through X-ray selection
Brandner et al. (1996) pointed out that ROSAT-unresolved binaries are statistically brighter X-ray sources than single stars. Since the ROSAT All-Sky Survey is X-ray-flux limited, this induces a detection bias. Binaries with component X-ray luminosities below, but combined luminosity above the cut-off, will cause an overestimate of the actual binary frequency.
The X-ray luminosities of our stars are known so we can check which binaries could have been detected only because of this bias. The worst case would be if all binaries consisted of two components with equal luminosities. Then all binaries with luminosity between and would have been detected only because of the detection bias.
In reality, only a small fraction of the binaries consist of two equally bright components. We would over-correct the bias if we excluded all binaries with . We need an estimate for the number of binaries with both components below . To obtain this, we start with the X-ray luminosity function given by Brandner et al. (1996). They used the X-ray luminosities of 47 detected TTS associated with the dark cloud Chamaeleon I to derive the following relation:
We use this as a reasonable approximation for the luminosity function of single stars.
We now consider a binary with total X-ray luminosity and component luminosities and , where and . Therefore we have . The probability for both components to be fainter than is identical to the probability for the brighter component to be fainter than :
We obtain the proportional constant by using the fact that for . Thus,
This is a linear relationship between P and .
In this derivation, we assume that the probability for a second component with the correct is independent of , i. e. we neglect the (unknown) distribution of X-ray flux ratios in binaries. This does not change the general trend, but it simplifies the calculation.
The probability that both components of a binary are fainter than is 33 % if . We decide to use this value of as borderline and to consider all fainter binaries as discovered because of the detection bias. This means we have to exclude them from our survey to obtain an unbiased sample.
It is possible to derive a relation for triple stars similar to Eq. (4) by replacing the factor 2 by 3. This yields a borderline for triples of .
Fig. 4 shows the numbers of unresolved, binary, triple, and quadruple stars vs. their X-ray luminosities. The luminosity limit of the RASS in Taurus-Auriga, (Wichmann et al. 1996), and the corresponding limits for binaries and triples are also shown. In a few cases ROSAT could measure only the combined X-ray flux of two stars due to its limited spatial resolution. However, they are too far apart from each other to be considered a binary. Therefore, we assign half of the combined flux to each star in these cases.
The upper panel of Fig. 4 clearly shows that one of the binaries and all of the unresolved stars fainter than the limiting luminosity of the RASS have been discovered in pointed observations. However, there are two binary and two triple stars from the all-sky survey below their corresponding limit. Table 3 lists the names and X-ray luminosities of these four stars.
Table 3. Binaries and triples we think have only been discovered because of the X-ray selection bias
To correct the X-ray selection bias, we have to subtract six companions from the result derived in Sect. 4.2. Furthermore, we have to subtract four from the total number of systems, since these stars have been detected only because their combined luminosity is above the limit. This yields a corrected sample with 70 systems, 27 binaries, 2 triples, and 1 quadruple star, giving a total of 34 companions. This corresponds to companions per 100 systems.
Since the pointed ROSAT observations were performed with different integration times, it is difficult to determine their luminosity limit. Therefore, and because of the small number of stars involved, we do not try to correct a possible detection bias of binaries found with pointed observations. However, we would like to point out that the multiplicity of our sample does not change significantly if we exclude all sources found with pointed observations.
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998