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Astron. Astrophys. 334, 935-942 (1998)

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4. Discussion

4.1. The `enigmatic' CO source of [FORMULA]

Our CO (2-1) observations with the SEST should be directly comparable to the 1.3 mm continuum observations by Chini et al. (1991), since these were obtained with the same telescope and, hence, with the same beam size. Chini et al. modeled their results in terms of thermal dust emission from the circumstellar disk of [FORMULA]. The temperature and density of the dust were described by radial power laws. The size distribution of the grains includes particles as large as 4.3 mm. The lower limit to the dust mass of 0.44 [FORMULA] within the SEST beam ([FORMULA] 400 AU) was derived. According to these authors their derived dust mass is comparable to the mass of the gas in the disk, i.e. [FORMULA] would be of order unity and much lower than the average interstellar value of about one hundred (Hildebrand 1983).

Adopting the physical structure of the [FORMULA] disk from the model by Chini et al., we computed the expected CO ([FORMULA]) emission by varying the gas-to-dust mass ratio, but keeping the CO abundance relative to hydrogen fixed throughout the disk [at the interstellar medium value, [FORMULA] = 8 [FORMULA] ; van Dishoeck et al. 1993 and references therein]. The details of these calculations are presented by Liseau (in preparation), but a basic description of our treatment of the line emission from the disk model is provided in Appendix A. To be directly compatible with the results by Chini et al. we used the pre-Hipparcos distance to the star, viz. 16.4 pc, which will not, however, affect our general conclusions below. The parameters of the [FORMULA] disk model are presented in Table 2.


[TABLE]

Table 2. Adopted parameters for the [FORMULA] system


In Fig. 3, the CO line integral, [FORMULA], as function of the upper rotational level, J, is shown together with the observed upper limits, [FORMULA], for the (1-0) and (2-1) lines. As expected (Sect. 1), maximum line flux is generally found for transitions from [FORMULA], i.e. higher than those hitherto observed from the ground.

[FIGURE] Fig. 3. Integrated CO line intensity, [FORMULA], versus upper rotational quantum number, J, of the transition for the disk model described in the text. A telescope aperture of 15 m has been assumed for the calculations, depicted by the solid lines. The dashed curve corresponds to a fix beam size instead, viz. HPBW = 20''. The values of the parameter, [FORMULA], are indicated next to each curve. Observational results (in the main beam temperature scale) are indicated by the upper limit symbols, where (1-0) is from Savoldini & Galletta (1994) and (2-1) from the present investigation. For both models and observations, the integrations have been performed [FORMULA] km s-1 about the systemic velocity

Both model profiles and observations have been integrated over [FORMULA] km s-1 about the line center. The presented models have been computed for the gas-to-dust ratios [FORMULA] = 1.0, 0.1 and 0.01. For relatively high values, the gas densities in the disk are sufficiently high to drive the CO lines into LTE, whereas for [FORMULA] = 0.01, the excitation of the molecules is subthermal in most parts of the disk. It is evident from the figure that the observational results rule out any `normal' gas-to-dust mass ratio of 100. In particular, [FORMULA] [FORMULA] ([FORMULA], [FORMULA]) is implied by our measurement ([FORMULA] K km s-1, [FORMULA]).

In Fig. 4, we present the profiles of low-J CO lines most readily observable from the ground, i.e. (1-0), (2-1) and (3-2). In all cases, an antenna of 15 m aperture has been assumed (e.g. SEST, JCMT). The observed continuum fluxes are reasonably well reproduced by the model [ [FORMULA] mJy (observed: [FORMULA] mJy, Zuckerman & Becklin 1993) and [FORMULA] mJy (observed: [FORMULA] mJy, Chini et al. 1991)]. According to this particular disk model, kinetic temperatures are [FORMULA] K everywhere and the average column density of widespread CO in the gas phase is [FORMULA] cm-2 (3 [FORMULA] cm-2 for [FORMULA] = 0.05). This strict limit is not particularly sensitive to the choice of parameter values. For instance, in the figure, the dashed profiles refer to a change by [FORMULA] about the nominal value of the power law exponent of the density distribution (Table 2) in the two azimuthal halves of the disk, yielding still about the same [FORMULA]. However, the line profiles would, of course, change quite dramatically (and with time), as is exemplified in the figure. In principle, such non-axisymmetric matter distribution, if present (e.g. Kalas & Jewitt 1995), could thus be used to infer the sense (and rate) of rotation of the disk, which could be compared with the rotation of the host star (see the Solar System).

[FIGURE] Fig. 4. CO line profiles for the [FORMULA] disk model described in the text. The numerical resolution is 0.1 km s-1 in velocity and 1.25 AU in the spatial coordinates. An inner hole radius of 26 AU and [FORMULA] =0.1 have been assumed throughout. The beams of a 15 m telescope are taken as 46'' (1-0), 23'' (2-1) and 15'' (3-2) and the model continuum fluxes are 2.6 mJy (2.6 mm), 25 mJy (1.3 mm) and 83 mJy (0.8 mm), respectively. The curves drawn with solid lines assume axial symmetry for the density distribution. The dotted profiles refer to a non-symmetric disk model (at phase [FORMULA]), where the power law exponent of the density distribution has been changed by [FORMULA] in the two azimuthal halves of the disk

The high gas temperatures and the upper limit on the CO column density implied by this disk model, which fits the dust continuum observations, are both difficult to reconcile with the CO absorption features in the UV (Vidal-Madjar et al. 1994, Jolly et al. 1996). The UV-CO feature, which is at the systemic (stellar) radial velocity, has been persistent over the years since its discovery with the IUE and model fits to the observed profiles indicate the absorbing CO gas to be at very low temperatures. This gas should be, therefore, far away from the star and resides presumably in the outer regions of the disk ([FORMULA] AU). In addition, the UV models imply a relatively healthy column density of CO molecules [ [FORMULA] cm-2 ]. The apparent absence of molecular features at long wavelengths has commonly been explained in terms of photo-dissociation of the molecules (e.g. Dent et al. 1995). There are at least two difficulties with this explanation. First, dissociation should affect the `UV-CO' as much as the `mm-CO' - to the molecules, human observing mode should make little difference. Secondly, recent detailed model calculations made by Rentzsch-Holm et al. (1998) indicate that the stellar (and interstellar) UV field might not be sufficiently strong to largely dissociate the CO molecules in the [FORMULA] disk.

A more obvious solution to this enigma seems to be, then, that the CO gas is not widespread throughout the disk (as assumed in our model), but is confined to a relatively distant, localized region (cloud/ring etc.) in front of the star. Such CO `cloudlet' would be easily seen in absorption against the stellar continuum, but its emission impossible to be detected by our mm-wave observations because of heavy beam dilution.

4.2. An upper limit to the hydrogen mass of the [FORMULA] disk

For the assumed standard value of [FORMULA], the upper limit to the CO column density derived in the previous section implies an upper limit to the average column density of hydrogen through the disk, [FORMULA] cm-2 ([FORMULA] cm-2). This is of the same order as the value derived from optical/UV and radio work. From an LTE analysis of metal lines seen toward [FORMULA], Lagrange et al. (1995) estimated the hydrogen column at (1-2) [FORMULA] cm-2, assuming solar abundances. Based on HI 21 cm observations, also Freudling et al. (1995) arrived at an upper limit to the hydrogen column density of that order. In conclusion, there seems to be no need to invoke a CO-to-H2 ratio in the [FORMULA] disk, which is very much different from the canonical interstellar medium value. In other words, we do not find any convincing evidence that gaseous CO should be significantly (by orders of magnitude) depleted in the disk.

Based on the dust mass obtained by Chini et al. (1991), our CO (2-1) result implies then that the gas mass of the [FORMULA] disk (within 440 AU) is not likely to exceed a few hundredths of an Earth mass ([FORMULA] [FORMULA]). We conclude, therefore, that these results are suggestive of the fact that the [FORMULA] disk is largely devoid of primordial gaseous material such as hydrogen and carbon monoxide. This conclusion supports the idea that the early nebula around [FORMULA] indeed disappeared long ago, i.e. it has been consumed during planet formation and/or was blown out in an early, intense mass loss episode. Such scenario is heuristically purported by the CO detections of Vega-like systems by Zuckerman et al. (1995), all of which are considerably younger than [FORMULA], whose age is estimated at [FORMULA] 80 Myr (Crifo et al. 1997).

4.3. Presently produced SiO gas in the [FORMULA] disk

Artymowicz (in preparation) considers the possibility of the abundant presence of disk gas other than hydrogen or carbon monoxide, viz. silicon bearing molecular gas in particular. This gas is thought to be mainly produced during collision processes of the silicate grains, which constitute most of the mass of the particulate disk. Modeled gas production rates maintain, in the steady state, SiO masses of the order of [FORMULA] g. The disk model considered in the present context differs from the previous one (e.g., the disk extends to 1000 AU) and its parameters are listed in Table 2.

For the hydrogen gas in the disk we adopt the Chini et al. model for [FORMULA] = 0.1, which is considered an upper limit and when combined with the Artymowicz model results in the radial distribution of the SiO abundance, [FORMULA], shown in Fig. 5. From the figure it is evident that for the bulk of the [FORMULA] disk, SiO abundances are supposedly very much larger than what is normally found in the interstellar medium (van Dishoeck et al. 1993 and references therein). Proceeding as before for CO, we computed the expected SiO line emission within the beam of our observation, the result of which is presented in Fig. 6 (numerical resolution in velocity is 0.075 km s-1 and in the spatial coordinates 5 AU). For [FORMULA] 40 AU, densities are higher than the critical density of the transition ([FORMULA] 4 [FORMULA] cm-3), thermalizing the level populations, whereas in the outer parts of the disk the excitation becomes subthermal. The average SiO column density through the disk is [FORMULA] cm-2 and the emission is optically thin from most parts of the disk.

[FIGURE] Fig. 5. Radial distribution of the SiO gas abundance according to the collisional production model discussed in the text. The hydrogen density distribution follows the disk model by Chini et al. (1991) for [FORMULA] = 0.1

[FIGURE] Fig. 6. The predicted line profile for SiO (2-1), (v =0), (in the [FORMULA] scale) observed with a 15 m telescope (60'' beam) is shown by the solid line. The at 1 km s-1 rebinned SEST data are displayed as histogram

Although the rms level in our SEST observation of [FORMULA] in SiO (2-1) is very low, the predicted line would still be burried in the noise (see: Fig. 6). As such, these observations are neither in conflict with nor are they able to confirm the predictions of the SiO production model. The test of this model would require observations at significantly higher angular resolution. By matching the telescope beam to the size of [FORMULA] (see: Fig. 5), viz. to [FORMULA] 5'', a much higher beam filling could be achieved. This would, as such, require an operating mm-interferometer. For a 5'' beam, the SiO disk model predicts a peak line brightness temperature of nearly 5 K, which appears quite feasible for future testing.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998

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