4 Analysis

  
4.1 Spectral energy distributions

Using IRAS and published ISO observations obtained at other wavelengths we have determined the far-infrared spectral energy distributions of the excess stars. The spectral energy distributions after subtraction of the photospheric emission component have been plotted in Fig. 5. When the observed emission in the IRAS 12 $\mu$m band is within 5% of the estimated photospheric emission, an upper limit of 5% photospheric emission is presented.

The 12/25 flux ratio for HD 191408 yields a colour temperature of about 600 K assuming a $\lambda ^{-1}$ dust emissivity. In combination with the ISO upper limit at 60 $\mu$m we consider it more likely that the excess emission is due to coronal free-free emission. Also $F_{\nu}\propto{\lambda}^{-1.7}$ at 12-25 $\mu$m, a typical power law for free-free emission ( $F_{\nu}\propto{\lambda}^{-2}{-}{\lambda}^{0}$). We therefore exclude this star in the subsequent analysis.

Figure 5: The far-infrared spectral energy distributions of the 25 $\mu$m excess stars (cf. Table 2) after subtraction of the photospheric emission; open squares: the excess emission derived from IRAS data, filled squares: ISO data. The ISO data at 60 and 170 $\mu$m were taken from Paper I, for $\beta$ Leo we added 60 and 90 $\mu$m data from the ISO archive. The solid lines are $\lambda ^{-1}$ modified blackbody curves fitted to the 25/60 colour of the ISO excess emission. Except for the upper limits and HD 191408, all data points were colour corrected according to the corresponding modified blackbody.

Of the five remaining stars we have derived the 25/60 colour temperatures to analyse the temperature of the dust causing the 25 $\mu$m excess emission. Assuming a $\lambda ^{-1}$ dust emissivity, we find temperatures between 49 and 122 K. The inferred temperatures are included in Table 2. HD 38678 has the highest temperature (122 K) and is the only star for which the 25 $\mu$m excess flux density is higher than that at 60 $\mu$m.

4.2 Properties of the 25 $\mu$m excess stars

The fraction of Vega-like stars in our sample with a significant excess at 25 $\mu$m is 5 out of 81 or 6%. Did we overlook genuine 25 $\mu$m excess stars? There are two stars for which IRAS shows a significant excess which cannot be confirmed by ISO. The IRAS measurement of g Lup (HD 139664) at 25 $\mu$m (493 mJy) would indicate a strong excess above the photosphere. We find, however, an ISO flux ($253\pm32$ mJy) which is close to the predicted photospheric flux. This star shows one of the largest discrepancies between ISO and IRAS. HD74576 (see Table 1) is the other star where IRAS would indicate an excess higher than 120 mJy but is rejected because of an inconsistent ISO measurement. Based on these two cases we conclude that from our 25 $\mu$m sample, the uncertainty in the number of excess stars is at most two, giving a most probable fraction of Vega-like stars with 25 $\mu$m excess of 6% and a maximum possible fraction of 9%. This is smaller than the fraction found at 60 $\mu$m (18%) in Paper I.

4.3 Properties of the Vega-like disks

The non-detection of significant 25 $\mu$m excess emission for all other stars in the sample shows that the Vega-like disks are generally cool: the largest fraction of the dust in the disk must be colder than 120 K. The median 25 $\mu$m flux in our sample is $F^{\rm median}_{\nu}=310$ mJy ([25]=3.3 mag). To be detectable in our sample the typical contrast C₂₅ between emission from a presumed disk and the stellar photosphere must be greater than ${C_{25}~>3{\sigma}/F^{\rm median}_{\nu}}$, i.e. C₂₅> 0.3. Assuming a disk temperature of 120 K, the minimum detectable dust mass of the disk is estimated to be ${M_{\rm d}=2\times10^{-5}}$ ${M_{\oplus}}$for an A0 dwarf ( ${T_{\rm eff}=}$ 9600 K) and $2\times10^{-6}$ ${M_{\oplus}}$ for a G0 dwarf ( ${T_{\rm eff}=}$ 6000 K). See Appendix A for a description of the calculation. These masses increase for lower dust temperatures. For comparison, the minimum detectable mass in the survey at 60 $\mu$m is ${M_{\rm d}>1\times10^{-5}}$ ${M_{\scriptstyle\oplus}}$(Paper I). Our Vega-like candidates are all included in the list of Paper I. Since all Vega candidates in Paper I have inferred masses larger than ${1\times10^{-5}~M_{\scriptstyle\oplus}}$ we conclude that we have detected essentially the warmest disks at 25 $\mu$m.

Three stars in our sample ($\beta$ Leo, $\alpha$ Lyr, and $\beta$ Pic) show significantly more far-infrared emission at $\lambda>60~\mu$m than the modified black body energy distributions would predict, see Fig. 5. This could be an indication of the presence of colder dust material in the disk, presumably at larger radii from the stars.

The minimum detectable mass of ${\rm 2\times10^{-6}}$ ${M_{\oplus}}$ for a G0 dwarf assumes an arbitrarily chosen fixed distance between the disk and the star. The detection of only A stars suggests that only stars of this stellar type are sufficiently bright to heat the dust at a minimum distance of the star. For example, a 1 $\mu$m size silicate particle must be at $\sim$35 AU from an A0 star to be at a temperature of 120 K. At this distance, the temperature of a similar dust particle around a G0 star would be $\sim$86 K, yielding a minimum mass of ${M_{\rm d}=2\times10^{-5}}$  ${M_{\oplus}}$. It is therefore more likely that the minimum detectable mass in our sample is ${M_{\rm d}=2\times10^{-5}}$  ${M_{\oplus}}$.