Astron. Astrophys. 359, 181-190 (2000)

5. Mean distance

Given the rotational period as well as and , it is possible to compute the stellar radius R as

With photometric data available, the distance r of the star then might be estimated as

Here, denotes the flux of a blackbody of temperature at the frequency , the observed flux from the star, and the effective temperature of the star (as inferred from the spectral type). is a correction factor of order unity obtained from model spectra (Hauschildt et al. 1998), to account for deviation of the stellar flux from the blackbody law.

For several stars of our sample, has been measured by Bouvier et al. (1997). As individual inclination angles are unknown, we set to its mean value of (for an isotropic distribution of inclination angles), and evaluate the mean distance for the whole sample. The resulting distance is pc (for stars with ).

However, as already discussed by Wichmann et al. (1999), where this method is applied to ROSAT LRSs in Lupus, period detection may introduce a bias towards stars with high inclination angle. Wichmann et al. (1999) estimated that this could lead to an overestimate of the mean distance by some 13 per cent (the effect is not very high, as high inclinations are more frequent than low inclinations even for an isotropic distribution). This estimate was based on the fraction of period non-detections in the Wichmann et al. (1999) sample. A similar estimate for the Bouvier et al. (1997) sample would not be very meaningful, as many non-detections in this sample presumably are due to bad weather during the observing runs of this study. Thus, we adopt the bias estimate by Wichmann et al. (1999). This would lead to a mean distance in the range 130-180 pc for the stars of our sample.

Fig. 5 shows a histogram of the distribution of individual distances (which are, of course, subject to large errors due to the unknown inclination). As one can see, the computed mean distance might be somewhat biased by two outliers at about 300 pc.

Fig. 5. Distribution of distances computed for mean value of for .

A different method to get an idea about the distances, in the absence of direct distance determinations, is to look at the offset from the ZAMS that one obtains for some fixed distance estimate, or equivalently (as isochrones are more or less parallel to the ZAMS), at the distribution of ages one obtains.

Fig. 6 shows a box-plot of the age distributions for the stars in our sample, both for stars classified as PMS and as ZAMS. Ages (and masses), as listed in Table 2, were estimated using the evolutionary tracks from D'Antona & Mazzitelli (1994). Following Wichmann et al. (1997a), extinctions were estimated from the colours, bolometric luminosities were computed from the dereddened magnitudes, and effective temperatures were estimated from spectral types (for details see Wichmann et al. 1997a). A distance of 140 pc was assumed to compute bolometric luminosities from apparent magnitudes. (In a few cases, where only B and V were measured, extinctions are from the colours and bolometric luminosities from the dereddened V magnitudes.)

Fig. 6. Box-plot of ages estimated for an assumed distance of 140 pc, both for stars classified as PMS and as ZAMS. (The boxes mark the range between the upper and lower quartile, while the whiskers extend to the smallest and largest values less distant from the quartile points than one interquartile distance. The bold line within the box is the group median.)

While the PMS sample should exhibit young ages, possibly with some intrinsic spread, the ZAMS stars should show a narrow distribution near the ZAMS age, if their distances were correctly estimated. From Fig. 6 we can infer that their distances are, on average, overestimated. The median age estimate of for an assumed distance of 140 pc is equivalent to an offset of some 0.4 dex with respect to the ZAMS, thus their true mean distance should be some 60 per cent lower to place them on the ZAMS.

We also note a significantly larger spread in ages for the ZAMS sample with respect to the PMS sample. As we would expect a rather narrow spread for correct distances, given that these stars should be on the ZAMS, this large spread in estimated ages is an indication that this sample shows a correspondingly large spread in true distances, significantly larger than those stars classified as PMS.

We therefore conclude that the stars classified as PMS are consistent with a rather narrow distance distribution at a mean distance similar to that of the Taurus-Auriga SFR, while those stars classified as ZAMS show evidence of a more widespread distance distribution with typically lower values.

© European Southern Observatory (ESO) 2000

Online publication: June 30, 2000
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