Astron. Astrophys. 329, L53-L56 (1998)

3. Discussion

3.1. Determination of the excess

In order to determine the infrared excess, we quantify the stellar component of the spectral energy distribution by fitting a Kurucz atmosphere model (Kurucz 1979) through the available visible, near-infrared and IRAS data of  Cnc up to 12 µm. We used optical magnitudes from the Bright Star catalogue and infrared magnitudes from Gezari et al. (1993). A very satisfactory fit is obtained for the parameters T K, , . Subtracting the infrared flux of this model from the observations, we derive no significant excess at 25 µm, an excess of mJy at 60 µm and an upper limit of mJy for the excess at 90 µm.

3.2. Nature of the excess

We examine various possibilities that may cause such an excess. They have been discussed in detail by by Aumann et al. (1984) and Backman & Paresce (1993) and we test them for  Cnc.

1. The companion M5 star can be excluded as a source for the 60 µm excess. At infrared wavelength the radiation from an M5 dwarf is typically less than 10% of the radiation of a G8 dwarf at the same distance. This is less than the errorbars on our measurements and can be neglected. In addition, the companion is about 90 arcsec away from  Cnc. It is possible that it was visible in one of the two off-source positions of the 25 µm measurement. However, in the critical 60 µm measurement the position of the companion was always at the edge of the C100 array, thus not contaminating the detection in the central pixel 5.
2. The planet near  Cnc can also be excluded. A planet with radius 1 would capture of the stellar radiation. This is one order of magnitude less than the we see in the 60 µm flux. Furthermore, the planet would re-radiate at a temperature near 1000K where it will be completely hidden in the stellar flux. At infrared wavelengths, the power of a 1000K Jupiter is typically only 10^-3 of the stellar radiation.
3. Chance alignment with a cirrus knot. This cannot be ruled out completely, but alignment within 46 arcsec (the pixel size of the C100 array) is unlikely.

Therefore we believe that the excess is due to the presence of a Vega-like disk.

3.3. A physical model for the disk

We now use the fluxes given in Sect. 3.1to model a Vega-like disk. We calculate the emission from dust grains distributed in an optically thin disk around the star. We assume that the size distribution of the dust grains follows a power law as is commonly used for grains derived from collisional grinding. We use optical properties for cometary dust grains taken from Li & Greenberg (1997) with silicate core, organic refractory mantle, ice mantle (volume ratio 1:1:2), packed in fluffy aggregates with a porosity of 0.9. Grain masses in the model range from 10^-11 and 10^-8 g, corresponding to aggregate sizes between 2.2 and 22 µm. We distribute the grains in the disk with a surface density , similar to what has been found for the Pictoris disk (Artymowicz et al. 1989). In order to reproduce the observed excess, we fit the total grain mass and the distance of the disk from the star.

Even though there is currently only an excess measured at 60 µm, the limits at 25 and 90 µm help to constrain the model. The temperature of the dust grains surely cannot exceed 100K since this would produce an excess at 25 µm. Therefore, the grains have to be located outside AU. On the other hand the temperature cannot be lower than 40K since this would require the 90 µm flux to be as high as the 60 µm flux. Also, the grains cannot be large compared to the 60 µm wavelength of the observation since this again would produce too much flux at 90 µm.

We can match the observations with a total dust mass of M , in a disk ranging from 50 to 60 AU from the star. The spectral energy distribution of this model is shown in Fig. 2. The fractional luminosity of the dust relative to the star is . Disk mass and fractional luminosity are consistent with the results for other Vega-like disks. The mass estimate has to be seen as a lower limit since there could be larger bodies present but undetectable in the infrared.

Fig. 2 also shows for comparison the best fit with a similar dust grain model where the ice component has been left out (to the effect that the aggregate porosity increases to 0.95). The grains become warmer and have to be moved out to larger distances from the star (90 AU) in order to reach the same temperature as icy grains at 60AU. Also we need more material ( M ) to reproduce the 60 µm flux. This model produces a less convincing fit, indicating that the ice model is more suitable to match the data.

3.4. Grain lifetimes

The radiation field of a G8 star is generally too weak to expel dust grains by radiation pressure. An upper limit for the lifetime of dust grains orbiting a star can always be given by the Poynting-Robertson time scale which is (Burns et al. 1979, Backman and Paresce 1993)

where is the grain radius in µm, is the radiation pressure transfer efficiency of the grains, averaged over the stellar spectrum, their specific density in g cm^-3, the distance from the star in AU and the luminosity of the star in solar units. At a distance of 60 AU and a grain size of 10 µm ( g cm^-3, , L ) we find Myr, much smaller than the age of the star (5 Gyr). Thus, also in  Cnc the dust grains producing the excess need to be replenished in some way.

© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
helpdesk.link@springer.de