5 Discussion

The low fraction of 6% of main-sequence dwarfs exhibiting Vega-like excess emission at 25 $\mu$m gives force to the result by Aumann & Probst (1991) who carried out a similar survey at 12 $\mu$m. They found only 2 statistically significant excess candidates out of 548 nearby stars. These two stars ($\beta$ Pic and $\zeta$ Lep) are also found in our sample of excess candidates. Apparently, warm debris disks are rare.

A similar study by Fajardo-Acosta et al. (2000), where 2MASS data were combined with IRAS data for a sample of 296 main-sequence stars, yielded 8 systems which have a significant excess at 12 $\mu$m. None of their 8 stars is in our initial sample. This low fraction (<3%) is not inconsistent with our result at 25 $\mu$m. Only one of these 12 $\mu$m excess stars is detected at longer wavelengths, and the spectral energy distributions of the 8 stars indicate dust temperatures in excess of 200 K. The temperatures suggest that the systems detected by Fajardo-Acosta et al. (2000) are distinct from the systems we have detected at 25 $\mu$m which all have been detected at 60 $\mu$m (see Fig. 5).

From a survey of 38 main-sequence stars using IRAS and ISOPHOT data Fajardo-Acosta et al. (1999) found no star with a significant excess at 12 $\mu$m, and a fraction of $\sim$14% excess stars at 20 $\mu$m. It is difficult to interpret this fraction since the ISOPHOT data used in their study were inconclusive, and the 20 $\mu$m detections needed confirmation. In any case, the absence of 12 $\mu$m detections indicates that these disks are not warmer than 200 K.

The temperatures and the inferred upper limits for the dust emission at 25 $\mu$m put strong requirements to possible ground based photometric surveys of debris disks at 20 $\mu$m. In order to be able to detect disks below our detection limit of $2\times10^{-5}$  ${M_{\oplus}}$, the contrast between disk emission and photospheric emission is <0.3 (equivalent to larger than 1.3 mag). On the other hand, the accuracy of predicting the infrared photospheric flux is generally not better than 5% which limits the maximum contrast to 3.3 mag. Significant improvement can only be made by imaging the disk.

All five Vega-like candidates in our sample are young, less than 400 Myr (cf. Table 1) with spectral type A0-A3, confirming the finding by Habing et al. (1999) that debris disks are mostly found around stars that just entered the main-sequence. In fact, of the 8 stars in our sample younger than 400 Myr, 5 have a detectable dust disk at 25 $\mu$m, whereas none of the older stars show a significant excess.

The lower limits on the mass have been derived assuming that the size of the disk particles is much smaller than the wavelength. At 25 $\mu$m this corresponds to $a\la3~\mu$m, where a is the radius of a grain. Larger grain sizes yield relatively lower absorption cross sections which increase our minimum mass estimate. Detailed modelling by Krügel & Siebenmorgen (1994) and Dent et al. (2000) which includes the (observed) spatial distribution in the disk, suggests much larger grain sizes of the order of a few tens of $\mu$m. Such sizes could increase our lower limit of the disk mass by one order of magnitude or more.

The dust model calculations by Li & Greenberg (1998) for $\beta$ Pic assuming that the particles are made out of cometary material show that for a given temperature, the grains can span a whole range of distances from the star depending on the composition and mass. For $T_{\rm d}=120$ K they find D=20 AU for the biggest porous silicate aggregates (of 10^-4 g) to D=200 AU for the smallest ones (of 10^-14 g).