4 Results

 

4.1 Stellar parameters

The properties of 45 observed stars are summarized in Table 2, which gives an identification number (Col. 1), source name (Col. 2) spectral type (Col. 3), distance (Col. 4), V-magnitude (Col. 5), (B-V) colour (Col. 6), effective temperature $T\rm _{eff}$ (Col. 7), and luminosity of the star (Col. 8). In Col. 9 we report the calculated age of the Herbig AeBe star (see Sect. 4.2), while the minimum mass limits corresponding to 0 and 2 magnitude of extinction in K are given in Cols. 10-11 (see Sect. 4.3). The stars are listed according to their spectral type, from the earliest to the latest. Spectral types, distances, V-magnitudes and (B-V) colors are taken from the literature, as specified in the comments on individual stars. We determined the effective temperature $T\rm _{eff}$ from the spectral type, using the scale of Cohen & Kuhi (1979). The luminosity was then computed by fitting a blackbody of temperature $T\rm _{eff}$ and varying radius to the de-reddened V-band magnitude and distance. In all cases, we have assumed a value of the total to selective extinction R_V=3.1. The bolometric corrections are from Schmidt-Kaler (1981). For variable stars, we have used the V-magnitude in the brightest state, assuming that the variability is due to circumstellar extinction.

 

Table 2:   Star parameters and mass sensitivities

4.2 Age estimates

 

The distribution in the H-R diagram of the 39 Herbig AeBe stars with a determination of temperature and luminosity is shown in Fig. 3. We have estimated the stellar ages from their location in the H-R diagram using the evolutionary tracks and isochrones from Palla & Stahler (1993). There is a clear distinction between Herbig AeBe stars of the earliest spectral types (O7 to B5) and those with types later than B5. For the former an age estimate based on the H-R diagram is not possible since they lie either on or above the ZAMS and do not have an optically visible PMS phase. These stars include number 1 to 14 of Table 2. There are two stars, R Mon (No. 4) and RNO 6 (No. 8), which lie far below the ZAMS, in a forbidden part of the diagram. This may be to due difficulties in deriving the correct stellar photometry and reddening in regions of heavy nebular emission.

 

Figure 3:  Distribution of 39 Herbig AeBe stars in the H-R diagram. Each star is labeled by its reference number as in Table 2. The solid lines are the evolutionary tracks for $M_\ast=$1.5, 2, 2.5, 3, 3.5, 4, 5 and 6 $M_\odot$ (from bottom to top). The dotted line is the birthline of Palla & Stahler (1990). The heavy solid line is the theoretical zero-age main-sequence

Herbig AeBe stars from B5 to A7 are well distributed at or below the birthline and an age estimate is thus possible. The individual ages (in million years) are listed in Table 2 and span a wide range from 0.1 Myr for stars near the birthline to 10 Myr for LkH$\alpha$ 198, the oldest of the whole sample. Our age estimates reflect the procedure adopted to compute the stellar parameters and are subject to several sources of uncertainty. In general, we obtain values of the luminosity that are on the low side of those published in the literature, resulting in greater ages for the Herbig AeBe stars. In a few cases, the difference can be quite substantial, up to factors greater than 10. Examples include LkH$\alpha$ 25, LkH$\alpha$ 198 and LkH$\alpha$ 233. A possible cause of the discrepancy in luminosity could be due to our assumption of a single value of R_V for all the stars. In fact, the bolometric luminosity depends sensitively on R_V and it is well known that many Herbig AeBe stars present anomalous extinction, suggesting higher values of R_V than for the standard interstellar case. As an example, a variation of R_V from 3.1 to 5.1 implies an increase of the luminosity of LkH$\alpha$ 198 from $\sim$10 $L_\odot$ to $\sim$45 $L_\odot$ with a corresponding decrease of age to a more realistic value of 1 Myr. Note that a larger value of R_V may also move close to the ZAMS the two stars R Mon and RNO 6.

In principle, a careful analysis of the appropriate value of R_V could be done on each Herbig AeBe star, but this exercise goes beyond the purpose of this section in which the stellar ages are only used to obtain the mass sensitivity limits of our survey, as illustrated in the next subsection. Moreover, it is important to point out that the age estimates do not affect the determination of the clustering properties of Herbig AeBe stars.

4.3 Limiting minimum mass

  Assuming that all the stars located around the Herbig AeBe star are coeval, it is possible to transform the K-completeness absolute magnitudes reported in Table 1 into an estimate of the lowest mass detectable in the field, the so-called minimum mass. For the transformation, we have used the method discussed in the Appendix (see also Meyer 1996), which allows one to derive at any given time a relation between the absolute K-magnitude and the mass of the star from a set of evolutionary tracks. For consistency, we should have used the same set of tracks employed for the age estimate. However, the models of Palla & Stahler (1993) do not extend below 0.6 $M_\odot$, whereas the IR images are deep enough to probe masses near the brown dwarf limit. Thus, these tracks cannot be used for the determination of the minimum mass, and we have used instead the evolutionary tracks of D'Antona & Mazzitelli (1994) which extend to substellar masses.

The minimum mass depends on the extinction at K band. Even though the K extinction is a factor $\sim10$ (in magnitudes) less than in the visual and the extinction toward the Herbig AeBe star itself is usually $\le 5$ mags in the visual, some of the colour-colour diagrams shown in the following section reveal that several stars in the fields are affected by a substantial amount of extinction ($A_V\sim 10-20$ mags in some cases). We give in Table 2 the minimum mass in each field for A_K=0 and 2 mags (Cols. 10 and 11). Clearly, the calculation of the minimum mass is possible only for those fields where an age estimate of the Herbig AeBe star exists. A value $<0.1~M_\odot$ in Table 2 means that the mass limit is smaller than the minimum mass available from the PMS evolutionary tracks of D'Antona & Mazzitelli (1994).

Note that the derivation of the minimum mass assumes that all the observed emission at K-band is due to the stellar photosphere (i.e. the infrared excess is not considered and corrected for).

4.4 Cluster indicators

Several methods of measuring the richness of an embedded cluster of stars associated to the visible Herbig AeBe stars have been discussed in Paper I. We compute for each of the observed fields two such indexes, namely ${\cal N}_{K}$ and $I_{\rm C}$ which are given in Table 2, Cols. 12 and 13.

${\cal N}_{K}$ is defined as the number of stars detected in the K-band image of the field within a distance of 0.21 pc from the Herbig AeBe star with an absolute magnitude M_K< 5.2 mag. The first of these two constraints is set to match the size of the best-studied clusters (e.g., BD+40$^\circ$4124: Hillenbrand et al. 1995; Palla et al. 1995). The threshold at M_K = 5.2 mag is low enough to include at least some stars in most of the fields. In fact, there are 5 fields (those centered on Elias 1, MWC 758, MWC 480, AB Aur and XY Per) which have been imaged with a field of view smaller than 0.21 pc, and 7 (centred on Z CMa, MWC 300, AS 310, MWC 1080, V 645 Cyg, RNO 6 and MWC 137) which have $M_{K}\rm ^c$<5.2 mag. The values of ${\cal N}_{K}$ in Table 2 for these 12 objects should be considered as lower limits. Note that ${\cal N}_{K}$ can be directly compared to the results in Hillenbrand (1995).

The second, more reliable richness indicators is the quantity $I_{\rm C}$, which corrects for the "local'' background/foreground contamination. $I_{\rm C}$ is computed by integrating the source surface density profile centered on the Herbig AeBe star n(r) and by subtracting the average surface density measured at the edge of each field $n_\infty$:

$${I_{\rm C}}=\sum_{i=0}^{i_{\rm max}}\pi(n(r_i)-n_\infty)(r^2_{i+1}-r^2_i)$$ (1)

where n(r_i) is the local source surface density (i.e. the number of stars between r_i and r_i+1 arcsec from the Herbig AeBe star divided by the area $\pi(r^2_{i+1}-r^2_i)$). $i_{\rm max}$ is chosen to contain all the members of the cluster and $n_\infty$ is the mean value of n(r_i) in the outer parts of the plot. In all fields $\Delta r\equiv r_{i+1}-r_i= 12^{\prime\prime}$, which ensures a good "resolution'' and (in most cases) a reasonable number of stars per annulus. The uncertainty on $I_{\rm C}$ has been computed by propagating the error in the determination of $n_\infty$ on the sum defined in Eq. (1).

The two indexes $I_{\rm C}$ and ${\cal N}_{K}$ suffer from different biases. In the case of $I_{\rm C}$, the main source of errors in comparing values for different fields arises from the fact that all sources detected within the completeness limit $M_{K}\rm ^c$ have been included, in spite of the fact that $M_{K}\rm ^c$ varies from field to field. A second error derives from possible local extinction variations within the cluster (note that since $n_\infty$ is derived from observations of the same field, line-of-sight extinction does not affect $I_{\rm C}$). This effect leads to a systematic underestimate of the number of cluster members when a compact (with size of the order of the cluster size), high column density molecular clump is localized at the position of the Herbig AeBe star. In the case of ${\cal N}_{K}$, as we have already pointed out, the main uncertainty derives from background/foreground contamination. These points have been extensively examined in Paper I, and will not be discussed any further in here.

Both $I_{\rm C}$ and ${\cal N}_{K}$ are affected by the presence of bright reflection nebulosities associated to the Herbig AeBe star, which may "hide'' low-luminosity companion stars. It is difficult to quantify this effect. We suggested in Paper I that it could provide an explanation for the very negative values of $I_{\rm C}$ in LkH$\alpha$ 198 and R Mon. Among the new fields observed in this paper, it certainly affects to an unknown degree the star counts in V645 Cyg.

In the last column of Table 2 we report an estimate of the stellar group radius, $r\rm _c$, for the fields in which a source density enhancement is detectable around the Herbig Ae/Be star. This typical size has been derived as the radius at which the sources density peak reachs the background level in the K-band sources surface density profiles presented below.