5 Binary frequency among HAeBe stars

In the course of this survey, we detected 6 binary systems through Li absorptions and 7 spectroscopic binaries. Before deriving any physical information, we need to address the important question of biases. Several biases have been identified and are therefore discussed below.

5.1 Possible biases

5.1.1 Rotational velocity

Herbig Ae/Be stars show usually a broad distribution in $v\!\sin \!i\,$, up to 300$\mathrm{km\,s}^{-1}$(Grady et al. 1996). The higher rotational velocity of the HAeBe primary the more difficult it is to detect radial velocity variations. The projected rotational velocities of our stars are displayed in last column of Tables 2 and 5 for HAeBe in T1 sample, and in Tables 4 and 6 for T2-T5 sample. $v\!\sin \!i\,$measurements were obtained by visually comparing some photospheric lines (mainly He I 4471 and 6678Å) with synthetic spectra broadened by rotation (Kurucz 1993; Hubeny et al. 1994). Error on such estimation should not exceed $\pm\,30$$\mathrm{km\,s}^{-1}$. For some stars, information was lacking (not enough spectral lines or imprecise spectral type). Our results were finally compared with previously published measurements (Davis et al. 1983; Finkenzeller 1985; Böhm & Catala 1995; Grady et al. 1996), when available. They appeared to be always consistent with them.

Restricting ourself to HAeBe from T1 sample, Fig. 22 shows the histogram of the $v\!\sin \!i\,$. The projected rotational velocity for the stars ranges from 10$\mathrm{km\,s}^{-1}$(TY CrA) to 200$\mathrm{km\,s}^{-1}$(V380 Ori, HD 141569, MWC 1080).

  

Figure 22: The distribution of $v\!\sin \!i\,$for the observed HAeBe from Table 1 of Thé et al. (1994). The bin size is 30$\mathrm{km\,s}^{-1}$, filled squared represent spectroscopic binaries with radial velocity variations from Table 2

Interestingly enough, we see that all stars with observed radial velocity variations (symbolized with a filled square) have a $v\!\sin \!i\,$below  100$\mathrm{km\,s}^{-1}$, but MWC 1080. So, among the 16 stars with $v\!\sin \!i\,$$\,<\,100\,$$\mathrm{km\,s}^{-1}$, 6 are spectroscopic binaries, i.e. a binary frequency of 37.5%. If we apply this ratio to the 20 remaining high-rotators ($100\,<\,$ $v\!\sin \!i\,$$\,< 200\,$$\mathrm{km\,s}^{-1}$), we should expect to detect 6 to 7 more spectroscopic binaries , in addition to MWC 1080. Note that we have not included in this scheme the 5 (apparently) non-binary stars with unknown $v\!\sin \!i\,$(probably larger than 100$\mathrm{km\,s}^{-1}$).

Finally, if the T Tauri companion is a fast rotator ($V_\mathrm{rot}\,\gt\,$50 - 100$\mathrm{km\,s}^{-1}$), its Li I line could be more difficult to detect. This argument may however be compensated by the fact that usually rapid rotators show a larger abundance of Li I than slow rotators do (see Soderblom et al. 1993; Martin et al. 1994; Cunha et al. 1995; Jones et al. 1996) at least for young G and early-K stars; on the other hand, Duncan & Rebull (1996) found no strong correlation between Li I and $v\!\sin \!i\,$for young stars in Orion.

If the system is composed of two HAeBe stars with similar luminosities, the blend of the lines (broadened by high rotational velocities) will make difficult their radial velocity measurement.

In conclusion, we estimate that we may have missed at least 50% of the spectroscopic binary with radial velocity variations.

5.1.2 Luminosity ratio

  If the primary HAeBe star is much more luminous than its T Tauri companion ($\Delta\,m_V\,<\,$4 - 5), the Li I line (among other lines) from the secondary companion is obviously very difficult to detect. So the binary criterion will be the radial velocity variations of the primary, if any.

  

Figure 23: The distribution of V magnitude for the observed HAeBe from Table 1 of Thé et al. (1994). Filled squared represent spectroscopic binaries with radial velocity variations from Table 2, while open triangles represent spectrum binaries with Li I line detection. Note that TY CrA (V=9.5) shows both radial velocity variations and Li I absorption from companions

Figure 23 shows the m_V histogram for stars in T1 sample. HAeBe binary systems with radial velocity variations (filled squares) are rather well distributed between m_V=6.5 and m_V=11. For spectrum binaries (with Li I line absorption from a cooler component), there may be a lack of detection if $m_V\,<\,8.5$. Keeping the same binary frequency as for fainter stars (7 spectrum binaries including TY CrA among 28 stars with $m_V\,\gt\,8.5$), up to 4 binaries may have been missed among the 14 remaining brightest stars.

For spectrum binary systems composed of two HAeBe stars, Li I criterion is not anymore valid to probe the duplicity. Bouvier and collaborators (Bouvier et al. 1998; Corporon 1998) have detected at least 5 pairs of gravitationally linked HAeBe among the 30 visual binary systems (separation $\rho\,\gt\,0.13\hbox{$^{\prime\prime}$}$) observed with Adaptive Optics. Assuming a similar ratio for much smaller binary separations, we could expect to detect 1 or 2 new spectroscopic binaries composed of two HAeBe stars (this estimate is however a lower limit as not all spectral type for visual companions in Bouvier et al. study could have been determined).

5.1.3 Branch effect:

This effect has already been described and we showed that it was not important for binaries with one high mass component and one low mass companion. The 6 systems detected through Li absorptions belong to this category. For the 7 other spectroscopic binary systems, the secondary spectral type is unknown in most cases. However, the total luminosity of those systems is much lower than our limiting magnitude (m_V<11), except for the faintest star MWC 1080: we may have included this spectroscopic binary in our survey because the secondary contributes to a non-negligible part of the system luminosity. This issue deserves further studies.

Considering our whole sample, we claim finally that the Branch effect won't affect our preliminary binary frequency estimate for HAeBe stars.

5.1.4 Conclusion on biases:

In conclusion, at least 50% of the spectroscopic binaries could have been missed because of either rotational difficulties measurements or the luminosity ratio.

5.2 Derived binary frequency

Table 2 contains 13 Herbig Ae/Be spectroscopic binaries. If we only consider the Doppler shift of the lines criterion, we have 7 spectroscopic binary systems (6 stars from the second group of our Table 2 plus the TY CrA system) among the 42 HAeBe stars of our principal sample: so our observed binary frequency fb is $\approx$ 17%. This is a lower limit: for reasons stated above, the true spectroscopic binary frequency for HAeBe may be as high as 35%.

Restricting ourself to secure or candidate spectroscopic binary systems with $P\,<\,100$days (namely T Ori, AS 442, MWC 1080 and TY CrA), the binary frequency is 10%. For short-period ($P\,<\,100$days) WTTS spectroscopic binaries, Mathieu (1992) found a binary frequency $fb=11\pm4$%, slightly higher than for MS solar-mass stars $fb=7\pm2$% found by Duquennoy & Mayor (1991). Our present binary frequency estimate for short period systems seems comparable to the one for T Tauri or MS stars. However, as our number are small and the biases important, this binary frequency for short-period systems should be regarded as a lower limit: future observations (e.g. using interferometric technics) will certainly help to detect new close systems.

5.3 Is X-ray emission a binary criterion?

We address now the puzzling issue of X-ray emission in HAeBe stars. We may wonder if this property could also be used to identify double stars and thus give an other way of determining the binary frequency.

Herbig Ae/Be are known to be strong X-ray emitters (Zinnecker & Preibisch 1994; Damiani et al. 1994). However, the existence of X-ray emission intrinsical to Herbig Ae/Be stars is still doubtful: these stars indeed lack convective zones that could create a solar-type dynamo and heat a corona via strong magnetic field.

A non-solar dynamo model has been proposed by Tout & Pringle (1995) and applied to the HAeBe star HD 104237 by Skinner & Yamauchi (1996): if this shear dynamo model may generate an active corona, the X-ray luminosity $L_\mathrm{X}$ predicted seems to be lower than observed. However, many parameters in this model remain free and are not known empirically.

Another possibility is that the X-ray emission detected arises from a cooler T Tauri companion associated to the HAeBe star (Zinnecker & Preibisch 1994; Damiani et al. 1994), possibly through a process of colliding winds (Zhekov et al. 1995). In our limited sample of HAeBe binaries (Table 2), 4 stars are known to be X-ray emitters (V380 Ori, TY CrA, MWC 361 and MWC 1080); 2 other binaries (T Ori and HD 53367) have not been detected by EINSTEIN nor ROSAT, while the 7 remaining stars have no known X-ray properties. Thus the apparent trend is that X-ray emission is a possible indicator of binarity for HAeBe stars: this conclusion has also been found in the case of visual HAeBe binaries (Bouvier et al. 1998; Corporon 1998). Nevertheless, it would be worth to observe the 7 remaining binary stars in the X-ray domain.