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Astron. Astrophys. 318, 472-484 (1997)

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6. Multiplicity

After the discussion of the individual systems we now give a statistical overview of the data. Among the 26 Herbig Ae/Be stars in our sample, 8 have a companion with a projected separation between 50 AU and 1300 AU. In addition there are three cases where the projected separation of the companion falls between 2000 AU and 3600 AU. These latter are not free of the suspicion to be chance projections, given the fact that many Herbig Ae/Be stars are situated in small clusters of stars. We measure the binarity by the degree of multiplicity (also called "fractional multiplicity"), which we define as (number of binary or multiple systems)/(total number of systems in sample), as we did in our previous similar study on the low-mass young stars in Taurus (Leinert et al.  1993). The resulting degree of multiplicity for our sample then is 31 [FORMULA] 10% (42 [FORMULA] 13%), where the number in parentheses includes the more doubtful companions with separations [FORMULA] 2000 AU.

Recent studies of the multiplicity of T Tauri stars (Ghez et al.  1993, Leinert et al.  1993) have shown a distinct overabundance of young binaries with respect to their main-sequence counterparts. We want to see whether this effect can also be found in our sample. Therefore we compare to what appears the best data set on the duplicity on the main sequence (Duquennoy and Mayor 1991). Since these authors give their results in logarithmic bins of orbital period, we convert our measured projected separations to periods by the following assumptions: a system mass of 4 [FORMULA], a uniform distribution of orbital planes and longitudes of perihelia, a "relaxed" excentricity distribution of [FORMULA]. Then on the average, the semimajor axis is a =1.02 [FORMULA], where d is the projected separation (see Leinert et al.  1993). The statistically predicted orbital periods in our sample then range from 320 to 20000 years ([FORMULA] 105 years for the three wide systems), which we take to correspond to the logarithmic intervals of period P = 105 - 107 days (105 - 107.5 days). In these period ranges, Duquennoy and Mayor (1991) found a duplicity of 15 [FORMULA] 3% (18 [FORMULA] 3%). We should not overemphasize a statistical result for such a small and somewhat heterogeneous sample, but it appears that there is an excess of duplicity in Herbig Ae/Be stars by about a factor of two (1 [FORMULA] -2 [FORMULA]) with respect to G type main sequence stars.

We briefly consider the importance of two systematic effects. First, our results could be incomplete. We may have missed a few close, faint companions. Indeed we know that we could not have seen close ([FORMULA] [FORMULA]) companions, which are fainter by more than a factor of twenty than the primary. As possible indication that this effect actually may occur in our sample, we note that only one of the five subarcsecond binaries has a brightness difference of [FORMULA] K [FORMULA] 1 mag, while the five widest binaries all have [FORMULA] K [FORMULA] 3 mag. Second, among the wider binaries we may have included one or two spurious companions due to chance projections. These two systematic effects counteract each other and, depending on the actual statistics of companion brightness and separation, may even cancel. We therefore take our results as an acceptable estimate of the duplicity in our sample. Our results could also represent a lower limit on duplicity only. This would be the case if the wide binaries in our sample represent true physical associations and at the same time there are some undetected faint close companions.

The above comparison to main sequence G stars is informative, but it would be more meaningful to compare our results to the duplicity for intermediate mass main-sequence stars of spectral types A and B. We are not aware of a recent survey of duplicity for a A and B stars of similar quality and completeness like the survey of G stars by Duquennoy and Mayor. But Abt (1983) concludes that binary frequency, period distribution and secondary mass distribution do not vary drastically along the main sequence from B to G stars. Indeed, the degree of multiplicity of 51% given by him for the B stars compares well with the values found for G dwarfs of 48% (Duquennoy and Mayor 1991) or 55% (Abt 1983). The same is true for the number of companions per primary star, given as 0.69 for the B stars (as observed, upper limit) and as 0.60 (Duquennoy and Mayor 1991) or 0.54 (Abt and Willmarth 1992) for G dwarfs. We conclude that in terms of duplicity the study of Duquennoy and Mayor is also representative for intermediate mass A and B stars and that our sample of Herbig Ae/Be stars therefore shows an excess in duplicity by a factor of about two (1 [FORMULA] -2 [FORMULA]) also with respect to their counterparts of spectral type A and B on the main sequence.

The distribution of brightness ratio of the binary components in our sample is sharply increasing towards small companion brightnesses. Nine out of 11 of the binaries in Table 4 have near-infrared brightness ratios at K of [FORMULA] 2 mag, and if a couple of them had to be rejected as chance projections, the fraction would still be 6 out of 9. We will see that this distribution in brightness ratio is more steeply rising towards faint companion brightnesses than found for T Tauri stars.

Most of the binary Herbig Ae/Be stars in Table 5 have strong infrared excess or even SED's rising with wavelength through the near- to mid-infrared, i.e. they belong mostly to class II, partly to class I in the classification scheme of Lada (1987). There is the possibility that companions to these infrared emitters will look systematically too faint relative to their primaries compared to the ratio of the 'stellar' brightnesses. To largely avoid this bias, we compare only to those T Tauri stars in the list of Leinert et al.  (1993) which also belong to class I and class II according to Kenyon and Hartmann (1995). Out of these 32 pairs, only 8 companions have a brightness ratio [FORMULA] 2 mag at 2.2 µm. Although the involved number of Herbig Ae/Be binaries is small, and although the conversion from K brightness to mass may be different for the typical companions to T Tau or Herbig Ae/Be stars, we see in these data an indication that the mass ratio distribution for Herbig Ae/Be binaries is also more peaked towards small masses than for T Tauri stars. Such a steep distribution has been found for main sequence B star binaries by Abt and Willmarth (1992).

We note that qualitatively such relations would be expected if the mass distribution in binaries were the result of random association from a Miller-Scalo (1979) initial mass function. Then for a 3 [FORMULA] Ae/Be star 75% of the companions would have a mass less than 1/6 of the primary, while for a T Tauri star of 1.2 [FORMULA] this percentage would be only 45%. Given the the statistical uncertainties due to the small number of binaries in our sample all we can conclude is that the present results do not obviously contradict the concept of random association from an initial mass function as a summary description of binary mass ratios. In detail, as discussed in Sect. 5.13, luminosity (and perhaps also mass) of the primaries and companions may be correlated.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998