Astron. Astrophys. 361, L9-L12 (2000)

4. Results

Since the dataset in J band is more accurate (because of a larger integration time, better observing conditions, and a better sensitivity of the whole system) than in Ks band, the geometrical parameters and the disk model are based on the J band image. We checked in a second step that the results are compatible with the Ks band data.

4.1. Disk geometrical parameters

Given a disk inclination with respect to the line of sight which is 45^o, we expect to observe some deviations from the perfect ellipse case. Indeed, particles relatively large with respect to the wavelength produce non-isotropic scattering. One simple way to reduce this effect is to symmetrize the disk i.e. construct an isotropic-like virtual disk by averaging the original disk image and its symmetrical image with respect to the major axis. Best ellipse fitting on this symmetrized images gives the following results:

• disk position angle on the sky of degrees with respect to east direction.

• ellipse major to minor axis ratio of 1.2 implying a disk inclination of degrees with respect to the line of sight (or from the edge-on case).

• disk extension: 2.0 arcsec from the star corresponding to a distance to the star around 200 AU (assuming a distance to the Earth of 103 parsecs (van den Ancker et al. 1998) and a limiting sensitivity of 5 mJy/arcsec².

4.2. Photometry

Using the stars HD 101713 (B9V) and HD 97218 (G8) as references whose V magnitude is known and using appropriate V-J and V-Ks color indices, we derived the following photometry for the disk in J and Ks band: a disk flux in J band of Jy outside the coronograph mask and a maximum surface brightness of Jy/arcsec². From images of HD 100546 and corresponding reference star images (HD 101713 and HD97218) obtained when shifting the targets outside of the mask, we can deduce a total of scattered flux in the J band around 1 Jy; note that we get also a disk-shaped emission when removing a scaled reference to the HD 100546 image obtained outside the mask, but its signal to noise is very low. This result is compatible with the infrared excess computed considering a Kurucz model of the star (B9V spectral type). Consequently, the disk flux outside the coronograph mask represents roughly 30% of the total disk emission.

In the Ks band, we find an emission of Jy outside the coronograph mask and a maximum surface brightness of Jy/arcsec²

4.3. Model and observation fit

In order to derive physical parameters of the disk, we built a numerical model of starlight scattering by an optically thin disk made of dust particles. Assuming that no multiple scattering is occurring in the disk, and since the exact physical properties of the particles are poorly known (composition, shape, size distribution), we chose to use a global, single-parameter, scattering phase function. The most practical one, although not realistic, is the Henyey-Greenstein phase function (Henyey & Greenstein 1941). The disk is assumed to be seen with an inclination derived above, and to have a proper thickness similar to the one of Pic parameterized following Artymowicz et al. 1989. The disk midplane density is described by a scattering area which follows a series of broken power laws. We start with a first guess deduced from the radial surface brightness, and we iterate on the parameters until we obtain a satisfactory fit along the four directions defined on Fig. 2.

Fig. 2. Fit of the data profiles. Upper plot, full lines: the modeled profiles, stars and diamonds represent the data profiles 1 and 3 defined on the disk image inserted. Lower plot, dashed line: model of profile 4 (dominant forward scattering), plain line: model of profile 2. As seen on the lower plot, the scattering asymmetry is well reproduced by an anisotropic phase function (Henyey-Greenstein, see the text) with , corresponding to a particle size around 0.1 µm.

4.4. Fit results

The best fit model provides the following parameters (one must keep in mind that they are model-dependent):

• The Henyey-Greenstein phase function parameter found is corresponding to dominant spherical particles with size around 0.1 micron.

• A radial normal optical thickness fitted by a series of broken power laws whose exponents are: 0.6 in the range [10,45]AU, -0.4 in the range [45,70]AU, -1.35 in the range [70,100]AU, -5 outwards from 100 AU, see Fig. 3.

• An exponentially decreasing vertical profile, and an opening angle around 0.1 radian.

• A total scattering area of 10²⁹ cm² and a dust mass of 0.02 .

• An approximate disk surface density at maximum around particles/m² assuming single-sized particles of 0.1 µm, or an equivalent maximum scattering area of the order of the unity/m².

Fig. 3. The normal optical thickness of the disk deduced from model fitting of the data (diamonds). We have overplotted (stars) the normal optical thickness found in the case of the disk around Pictoris (Pantin, Lagage & Artymowicz 1998)

© European Southern Observatory (ESO) 2000

Online publication: September 5, 2000
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