3 Results

3.1 Millimeter interferometry

The results of millimeter interferometry for the four stars are summarized in Table 2, which gives in Col.  1 the name of the star, in Cols. 2 and 3 the coordinates of the millimeter peak, in Cols. 4-7 the observed wavelengths and fluxes, in Col. 8 the spectral index $\alpha_{\rm mm}$ between the two wavelengths ( $F_\nu\propto \lambda^{-\alpha_{\rm mm}}$), in Col. 9 the FWHM size, in Col. 10 the disk mass derived from the observed flux assuming optically thin emission, in Cols. 11 and 12 the interferometer where the observations have been obtained and related references.

All the four stars have millimeter continuum emission which is well detected by the interferometers. This is a strong, albeit indirect, proof that the emitting dust must be distributed in a highly asymmetric manner, i.e., in a circumstellar disk (Beckwith et al. 1990). In the two nearest stars (AB Aur and CQ Tau), the continuum emission is resolved by the interferometers, confirming its disk-like structure (Dutrey et al., private communication). The existence of a disk in AB Aur is proved further by interferometric maps in the CO lines, which resolve the emission and show a velocity pattern typical of rotation (Mannings & Sargent 1997).

The disk mass (gas and dust) in Table 2 has been computed from the 1.3 mm flux assuming that the emission is optically thin:

$$M_{\rm D} = d^2 {F_{\rm 1.3~mm}\over{\kappa_{\rm 1.3~mm} B_{\rm 1.3~mm}(T_{\rm D})}}$$ (1)

where d is the distance of the star, $\kappa_{1.3~{\rm mm}}=0.01$ cm² g^-1, and $T_{\rm D}=28$ K for the three A stars and 16 K for CQ Tau (Natta et al. 2000a). The four stars have values of $M_{\rm D}$ between 0.02 and 0.05 $M_\odot$, typical of HAe stars. Note that in reality $M_{\rm D}$ depends also on the radial distributions of the disk surface density and temperature (see, for example, Beckwith et al. 1990). Also, the assumption that the millimetric emission is optically thin may not hold. Natta et al. (1999) discuss the possibility that UX Ori, which has a black-body-like millimeter emission ( $F_\nu\propto \lambda^{-2}$), has a disk which is optically thick at millimeter wavelengths and estimate the required disk mass to be 0.1 $M_\odot$.

The spectral index in the millimeter range probed by the interferometers is quite low when compared to the value of $\sim$4 expected for the optically thin emission of small grains, ranging from 2.1 in UX Ori to 3.1 in AB Aur. Note that there are no published interferometer measurements of AB Aur at 1.3 mm, so that the spectral index we computed combining a single-dish and an interferometric observation may be overestimated.

3.2 SEDs

The SEDs of the four stars are shown in Fig. 1. References for the observed fluxes are given in the figure caption. In Table 3, we give for each star the observed excess luminosity after subtraction of the stellar emission ( $L_{\rm IR}$), the excess luminosity between 1.25 and 7 $\mu$m, i.e., shortward of the silicate feature ( $L_{\rm NIR}$), the luminosity in the silicate feature $L_{\rm sil}$, computed by subtracting from the observed fluxes a power-law continuum between 7.7 and $\sim$13 $\mu$m, and the ratio of the flux at the peak of the feature to that at 7.7 $\mu$m ( $F_{\rm peak}/F_{7.7\,\mu {\rm m}}$).

Figure 1: SEDs of the four stars in the sample. For AB Aur, triangles and open dots plot ground-based fluxes (Mannings 1994 and references therein), while the thick line is the ISO SWS+LWS spectrum (Bouwman et al. 2000). For CQ Tau, visual (Rostopchina, private communication) and near-IR (Glass & Penston 1974) fluxes are shown by triangles, SWS points (Thi et al. 2001) by crosses, the LWS spectrum by small dots at $\lambda >40~$$\mu$m, the open dots are JCMT data from Mannings (unpublished data), the large filled dots from Dutrey et al. (private communication); at 10 $\mu$m, both ground-based photometry from this paper (small dots) and LRS-IRAS data are shown. For UX Ori, the symbols are as follows (see Natta et al. 1999 and references therein): visual and near-IR photometry (triangles), ISO-PHOT (squares), PHOT-S (small dots), SWS (crosses), PdB (large filled dots). For WW Vul, visual and near-IR photometry are from Rostopchina (private communication) and Glass & Penston (1974), crosses are SWS points from Thi et al. (2001); PHOT-S (thich line), PHOT (squares) and PdB (filled dots) fluxes from this paper. The observed fluxes have been de-reddened using the values of AV in Table 1. The thin lines show for each star the adopted photospheric spectrum (Kurucz 1979). Thick solid lines show the predictions of CG97 disk models (Sect. 4); dotted lines the separate contribution of the disk surface and midplane

Detailed aspects of the SEDs will be discussed in the following section. Here we want to note that the infrared excess of these stars is a large fraction of the stellar luminosity, varying between 35 and 44%. This is much more than the maximum fraction (25%) expected from a flat reprocessing disk extending from the stellar surface to infinity. It is possible in principle that additional excess luminosity is produced by viscous heating of an accreting disk. However, the "missing" luminosity ($\sim$20% $L_\star$) requires a very high accretion rate ($\sim$10^-6 $M_\odot$ yr^-1), much higher than current estimates in HAeBe stars (Ghandour et al. 1994; Tambovtseva et al. 2001). Accretion, as shown by Hartmann et al. (1993), cannot contribute significantly to the observed SEDs of HAe stars.

Another interesting aspect of the SEDs is the strong 10 $\mu$m silicate feature in emission shown by all four stars. The luminosity in the feature is between 2 and 4% of the stellar luminosity and the ratio $F_{\rm peak}/F_{7.7\,\mu {\rm m}}$ varies betwen 2.5 and 4.7. Both quantities are somewhat higher than observed in a sample of 9 T Tauri stars (TTS) in Chameleon by Natta et al. (2000b), who found that in 8/9 stars $F_{\rm peak}/F_{7.7\,\mu {\rm m}}$ ranges from 0.2 to 3.7 and $L_{\rm sil}$/$L_\star$ from 0.2 to 2%.

Figure 2 shows in detail the shape of the 10 $\mu$m silicate feature for the four stars, to which we have added GlassIa, a K4 star in Chamaleon with an unusually strong IR excess, discussed in Natta et al. (2000b). We overlay for comparison the spectrum of AB Aur to that of the other stars (thin lines). For UX Ori, Fig. 2 shows the three spectra, the 1997 ISOPHOT one and the two HIFOGS spectra of 1996 and 1997. The HIFOGS fluxes are about 25% lower than the PHOT-S values, with a peak ratio $F_{\rm peak}/F_{7.7\,\mu {\rm m}}$$\;\sim\;$4.0 and $L_{\rm sil}$/$L_\star$$\;\sim\;$0.03. The normalized profiles are very similar at short wavelength, but differ at long wavelength, especially around 11 $\mu$m, where the HIFOGS data indicate a narrower profile. The difference could be due to different beams (18 $^{\prime\prime}$ for PHOT-S and 3 $^{\prime\prime}$ for HIFOGS), or to time variabilty. At present, however, given the uncertainty on the absolute calibration, it is difficult to decide if the difference is significant or not.

The shape of the feature shows small variations from star to star, with AB Aur being somewhat narrower on the short wavelength side. The GlassIa silicate feature was fit by Natta et al. (2000b) with mixtures of amorphous pyroxene and olivine with radius 0.1-1 $\mu$m. In all of the stars, there is a hint of excess emission around 8.5 $\mu$m of uncertain identification. There is no convincing evidence of the 11.3 $\mu$m component due to cristalline silicates, seen in some isolated HAe stars (Bouwman et al. 2001). AB Aur shows PAH features at 6.2, 7.6 and 12.3 $\mu$m (Bouwman et al. 2000). No features of comparable intensity are seen in the other stars, although we cannot rule out the presence of low-intensity features at other PAH wavelengths (see, for example, the 6.9 $\mu$m bump in the spectrum of WW Vul, or the small, but significant variation of the shape of the silicate feature at 8.6 and 11.2 $\mu$m between the two HIFOGS spectra of UX Ori).

Figure 2: Profile of the 10 $\mu$m silicate feature for the four stars in this paper and Glass Ia. For each star we have subtracted a linear continuum between 7.7 and 13 $\mu$m and normalized to the peak intensity (Jy). For each star, the dots are the observed points: SWS data for AB Aur (Bouwman et al. 2000), PHOT-S for WW Vul (this paper) and Glass Ia (Natta et al. 2000b), HIFOGS for CQ Tau (this paper). For UX Ori we show PHOT-S data (Natta et al. 1999; squares) and the two spectra taken with HIFOGS in 1996 (circles) and 1997 (triangles) (this paper). The thin line shows the AB Aur profile, that we repeat on each panel to facilitate the comparison

 

 

Table 3: Infrared excess

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Star	$L_{\rm IR}$	$L_{\rm IR}/L_\star$	$L_{\rm NIR}$	$L_{\rm NIR}/L_\star$	$L_{\rm sil}$	$L_{\rm sil}/L_\star$	$F_{\rm peak}/F_{7.7\mu {\rm m}}$
	($L_\odot$)		($L_\odot$)		($L_\odot$)
AB Aur	21.3	0.44	11.1	0.23	1.0	0.02	2.5
CQ Tau	1.8	0.36	0.6	0.12	0.16	0.03	4.1
UX Ori	14.6	0.35	7.8	0.18	1.6	0.04	4.7
WW Vul	18.0	0.42	11.0	0.25	1.1	0.03	3.2