Astron. Astrophys. 331, 977-988 (1998)

5. Discussion

5.1. Comparison of the young star samples before and after ROSAT

Optimum use can be made of the results of this study if we combine our results with those of Leinert et al. (1993) who surveyed the young stars in Taurus-Auriga known before ROSAT. Their sample includes 104 stars, 39 of which are binaries, 3 triples, and 2 quadruple stars, giving a total of 51 companions.

Before combining the two samples, we have to compare whether the two samples lead to similar results and simply can be added to increase the statistical accuracy, or whether they are so different that they have to be treated separately. The comparison in Table 4 shows that indeed the observed multiplicity in the two samples is similar and that they can well be combined for statistical purposes.

Table 4. Comparison of multiplicity in the ROSAT-selected Taurus sample and in the sample studied by Leinert et al. (1993)

5.2. Pre-main-sequence vs. main-sequence stars

Now we are going to compare our data from the combined sample to the multiplicity survey of Duquennoy & Mayor (1991, DM91). Although other studies exist (e. g. Mayor et al. 1992; Fischer & Marcy 1992), this is not only the most comprehensive study, but also includes the spectral types most of our stars will have after evolution to the main sequence (F and G).

To do this comparison, we have to convert our measured angular separations into orbital periods. This is impossible for individual objects of our sample since the orbital parameters are not known. Instead, we use the same method as Leinert et al. (1993) and rely on statistical arguments. First, we convert the angular separation into a linear separation. To perform this, we use a distance to the Taurus star forming region of 140 pc (Elias 1978, Preibisch & Smith 1997). This choice is supported by new observations of the astrometry satellite Hipparcos, which measured the parallaxes of five T Tauri stars in Taurus, giving a weighted mean distance of (Wichmann et al. 1997).

The second step is to convert the projected separation into a semi-major axis, taking into account the probability for a binary to be observed in a particular position in its orbit and the inclination of the orbital plane. These two effects lead to a combined reduction factor of 0.95 (see Leinert et al. 1993for details). Finally, we use Kepler's third law with a system mass of to compute the orbital periods. With these numbers, the separation range to transforms into a range of periods from to days.

Fig. 5 shows the result of the comparison. The combined sample of Leinert et al. (1993) and this work contains 85 companions in 174 systems, corresponding to companions per 100 T Tauri stars. DM91 find companions per 100 main-sequence stars in the period interval covered by our survey. This means 100 T Tauri stars have additional companions compared to solar-type main-sequence stars. In other words, the multiplicity of pre-main-sequence stars in Taurus is enhanced by a factor of ().

Fig. 5. Binary frequency as a function of orbital period, resp. separation. By binary frequency, we mean the number of companion stars with orbital period in a given interval divided by the total number of systems. This implies that triples are represented as two pairs. The histogram shows the combined results of Leinert et al. (1993) and this work; the shaded curve is the distribution of binaries among solar-type main-sequence stars (Duquennoy & Mayor 1991). The number of companions with periods between and is only a lower limit since it is difficult to resolve binaries with such a small separation. This is why we are certain we did not discover all of them

DM91 claim to have detected all binaries down to mass ratios of 0.1. Our survey is complete for brightness ratios in K larger than 0.1 to about 0.01, depending on the separation. It is not obvious which relation should be used to convert the flux ratios of pre-main-sequence objects to mass ratios. A proportionality or near-proportionality of K brightness and mass for young stars has repeatedly been assumed and should be a good approximation for coeval binary components contracting along the Hayashi line (Simon et al. 1992, Zinnecker et al. 1992, Reipurth and Zinnecker 1993). As the stars contract down their evolutionary tracks, the relation between mass and the K luminosity for the lower main sequence, (Henry & McCarthy 1993), should be approached. This means our survey is propably not as complete as that of DM91. Therefore, the enhancement factor of 1.93 is rather a lower limit. Furthermore, DM91 added a correction for companions undetected because of detection biases, while we prefer to use only the number of binaries we actually are able to see.

5.3. Classical vs. weak-line T Tauri stars

The combined sample of Leinert et al. (1993) and this work contains 72 classical and 102 weak-line T Tauri stars. This allows us to compare the multiplicity of these two types of T Tauri stars.

First, we compare the total numbers of binary orbits. We find 39 companions among the CTTS, or companions per 100 systems. Among the WTTS, we find 45 companions, corresponding to companions per 100 systems. The errors have been estimated by taking the square root of the number of companions. Within the errors, there is no systematic difference between classical and weak-line T Tauri stars.

Fig. 6 shows the distributions of companions as a function of their orbital period separately for companions to CTTS and WTTS. We performed an test, resulting in a reduced of 0.66. If both samples were drawn from the same distribution, one would find larger values of with a probability of . We take this as confirmation of the assumption that the distributions of CTTS and WTTS binaries are indeed essentially identical.

Fig. 6. Binary frequency as a function of orbital period, broken down into classical (shaded histogram) and weak-line T Tauri stars (lined histogram). The Gaussian curve denotes the distribution of binaries among solar-type main-sequence stars (Duquennoy & Mayor 1991)

This is in contrast to the result of Ghez et al. (1993) who reported a difference in the distributions of WTTS and CTTS binary stars as a function of the separation: they find that the WTTS binary star distribution is enhanced at smaller separation ( or ) relative to the CTTS binary star distribution. Our data (Fig. 6) do not support their finding.

5.4. Surface density of companions

In a study of clustering of young stars in different star forming regions, Simon (1997) found that the differential surface density of companions followed a power law as a function of the angular separation with the exponent b close to 2.0 in all three regions studied. Since our combined sample in Taurus is considerably larger than the sample based on lunar occultations used by Simon (1997), we recalculated the exponent for the surface density distribution on the basis of the enlarged sample. The resulting exponent (, see Fig. 7) is essentially the same as given by Simon (). In descriptive terms, this means that in the diagram the distribution of companions is flat (because then and the area of the annuli as a function of is proportional to ). As far as the range of separations studied here is concerned, a flat distribution in apparently is consistent with the data and is a reasonable first approximation for the separation distribution of companions to young stars in Taurus.

Fig. 7. Differential surface density of companions for the combined sample. To determine this, the separations have been binned in non-overlapping annular areas starting at and increasing by factors of until the outer limit is reached. The number of companions in each annulus divided by the area of the annulus gives the surface density shown. The straight line shows the best fit to the points

5.5. Is there a difference between close and wide companions?

In Fig. 8 we plot the distribution of flux ratios for the companions in the ROSAT-selected sample and the sample of Leinert et al. (1993), split into close pairs with the companion separated to ( - ) from their primary and wide pairs with companions separated to ( - ). The dividing line has been set somewhat arbitrarily at what we consider is a typical accretion disk radius ( - 200 AU, or 1.1" - 1.5"). In triple systems, we use the ratio of the combined flux of the inner pair to the flux of the third component as flux ratio of the outer pair.

Fig. 8. Distribution of flux ratios for close companions (between and or and separated from the primary) and for distant companions (between and or and from the primary). The hatched histogram shows the numbers of companions to WTTS, the open histogram those of companions to CTTS. The star 40C has been excluded here because we know it is probably a background star

The distributions for close and wide pairs are not identical: the wide binaries preferentially have small flux ratios, while the distribution of close pairs is flat with a possible slight increase towards equal flux ratios. A test for the combined sample yields a probability of only that the two samples have been drawn from the same distribution. The histogram of wide pairs still contains three background stars, however, we do not know their flux ratios (one background star has already been excluded since we know that the star 40C is one). If we subtract these three background stars from the bin for flux ratios between 0.0 and 0.2, we get a probability of . We take this as indication that there is a difference between the brightness ratios in close and wide pairs.

On the other hand, one can argue that the difference at the lowest brightness ratios simply reflects our inability to detect faint companions close to the primary. We certainly admit that we may have missed some companions with these properties. But we note that making the difference in the lowest brightness ratio bin disappear would require adding about 10 unseen companions, i. e. would require to double the number of companions. It therefore seems unlikely to us that the difference at the lowest brightness ratios is caused by the above-mentioned bias. Nevertheless, in order to not have to consider this bias at all, we also performed a test for the upper four bins only, negelecting the bin with the lowest brightness ratios. The result is a probability of still only that the two distributions are identical. This maintains our conclusions that there is a difference between the brightness ratio distributions of close and wide pairs.

If we take the flux ratios in K as an approximation for the mass ratios, then our findings match the prediction of the model calculations of Bate and Bonnell (Bate 1997, Bate & Bonnell 1997). They studied accretion from a collapsing cloud onto a protobinary at its center. For a close system, the infalling material has comparatively high angular momentum, which leads to accretion onto the secondary and therefore drives the mass ratio to higher values. For a wide binary system, the opposite is true, and in the outcome such long-period systems are more likely to have small mass ratios. However, mass outflows are not considered in their models. These may change the results significantly.

As we already mentioned in Sect. 5.2, the relation between mass and the K luminosity for our pre-main-sequence stars is somewhere between and . The latter relation would distort the scale of the abscissa in Fig. 8, but not alter the result. In classical T Tauri stars, the contribution to the K brightness from an accretion disk is non-negligible and may be strong. Probably, this effect would smear out intrinsic differences in the brightness ratios of the stars alone and not mimic them. This could explain why the difference between close and wide pairs is more clearly observed in the weak-line T Tauri stars. Therefore, we still accept that the difference we see in the brightness ratios translates into a difference in the mass ratio distribution for close and wide pairs.

5.6. Consequences of the controversy on the age of ROSAT-selected stars

Briceño et al. (1997) claim that the majority of ROSAT-detected sources are not pre-main-sequence objects, but  years old, essentially zero-age main-sequence stars. We are not going to contribute to this discussion. In particular, we hesitate to use the binary frequency to determine the age of a stellar group; this would be premature and questionable: multiplicity may depend on several parameters, and none of these possible relations has been firmly established so far, Therefore, our measurement of the binary frequency can not answer the question about the status of these stars. Instead, we will show that it does not weaken our conclusions if the stars have already reached the main sequence.

For the purpose of this discussion we assume with Briceño et al. (1997) that a sizeable fraction of the ROSAT-detected sources are about  years old and not certainly associated with the Taurus clouds. There would be nothing to discuss if all of these sources belonged to Taurus, and there is sufficient evidence for young WTTS in Taurus to reject the possibility that all ROSAT-detected sources could be zero-age main-sequence objects. To study the influence which a different age of a fraction of the stars would have on our multiplicity survey, we consider two limiting cases: either the multiplicity of the zero-age main-sequence stars is as high as that of the pre-main-sequence stars in Taurus, or it is similar to that of the main-sequence stars surveyed by Duquennoy and Mayor (1991).

The first case leads to the conclusion that there is no evolution of multiplicity while the stars evolve from their pre-main-sequence phase to the main-sequence. This would only emphasize the discrepancy in multiplicity, making it a discrepancy between different groups of stars on the main sequence. The prediction of Briceño et al. (1997) that the -year-old stars are somewhat nearer to us than the Taurus star forming region (100 - instead of ) is not important in this respect. Even changing the distance by a factor of 2 would shift the histogram in Fig. 5 by only one bin. A high binary frequency among zero-age main-sequence stars would be in remarkable contrast to the findings of Bouvier et al. (1997), who have searched for binaries among G and K dwarf members of the Pleiades cluster, which are also about years old. They derive a multiplicity similar to that of main-sequence stars. The way out of this discrepancy between stars of similar age could be given by the hypothesis that the local environment has a decisive influence on the binary frequency.

In the second case, if the multiplicity of the old stars in our sample is the same as on the main sequence, there have to be even more binaries and multiples among the ROSAT-selected pre-main-sequence objects in order to yield the high multiplicity we observe in the full ROSAT-selected sample. If, for example, half of the ROSAT-selected sample showed the multiplicity properties of main-sequence stars, the remaining 37 young stars would need to have 25 companions in the range of separations 0.13" - 13", almost three times the value found on the main sequence.

If we assume that the majority of the ROSAT-selected stars are indeed zero-age main-sequence stars, then the question of how to explain the differences in multiplicity between ROSAT-selected and main-sequence stars would only be rendered more difficult, however necessary and interesting the discussion on the age of these stars may be.

© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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