The angular size of the dust, can be used to derive constraints on the dust properties and the geometry of the outflow. For simplicity we assume that the dust is optically thin at 10 m. The expected angular size of the dust shell around HR Car depends on the way the emissivity of the dust varies with wavelength. From ISO-SWS measurements (Lamers et al. 1996) we see that the spectrum of HR Car shows a pronounced bump near 10 m, which is interpreted as emission from silicates. Silicate dust has peculiar absorbing and emitting properties that can not be described by a power law dependence. In order to calculate the emission from an spherically symmetric silicate dust shell, we calculate the radiative equilibrium temperature structure of the shell and assume the dust particles to radiate according to the astrophysical silicate model of Draine and Lee (1984). We assume that the density varies with density as . The free parameters of the model are: the inner and outer radius of the dust shell and T , which determine the shape of the spectrum, and , which is used as a scaling factor. From the images it is clear that the dust shell is not spherically symmetric, but the approximation of spherical symmetry is suitable for obtaining a reasonable estimate of the size and the mass of the nebula.
The best fit model to the inner nebula for the ISO-SWS spectrum gives a well-defined inner radius of the shell of 4.5 104 R with a stellar temperature of 18500 K. This model also gives a good fit to IRAS photometry. With a luminosity of log = 5.63, this gives a stellar radius of 64 . The dust temperature at the inner radius of the shell is 150 K, which is slightly less than the BB-temperature fit of 165 K of McGregor et al. (1988) to IRAS data. In retrospect, the assumption of an optically thin approximation at 10 m was justified, as . The refractive properties of silicate grains are still not very well known, but if we extrapolate a fairly flat distribution, where , then the optical depth at the wavelength corresponding to the ionizing potential of Ne (21.564 eV 575 Å) equals 0.6. This shows that it is well possible that a substantial part of the radiation at 575 Å is blocked in certain parts of the nebula, so that Ne remains neutral. This is well reflected in the images, from which it is seen that the [Ne II ] flux SE of the star comes from a region slightly inside the arc seen in the N-band. An additional source of UV opacity will be the Lyman continuum, in the region where there is gas, but no dust present.
The outer radius is less well defined, but assuming a density distribution that is not steeper than , i.e. what is expected for a constant stellar outflow, the total dust mass of the shell is less than 8 10 . At a distance of 5.4 kpc, 4.5 104 R is equal to approx. 2 5, which coincides very well with what we see in the TIMMI images. We conclude that our simple spherically symmetric dust model can well explain the average distance at which we see the nebula in our TIMMI images.
We can set an upper limit to the grain size distribution using millimeter photometry. We have recently performed millimeter photometry of the dust emission from HR Car using the Swedish Sub-millimeter Telescope SEST at La Silla, at a wavelength of 1.1 mm for which we find an upper limit of 24 mJy (3 rms). Such a low flux rules out the possibility that the grains are grey out to 1.1 mm, i.e. a significant fraction of the grains must be smaller than 1 mm.
The irregular shape of the nebula complicates the explanation of the formation mechanism. In principle there are two possible origins for the peculiar shape; either the surrounding interstellar medium is highly inhomogeneous or the star itself ejects matter in a non-symmetric manner. The first possibility seems rather implausible in view of the fact that HR Car is considered to be a massive post main-sequence star. During its main sequence stage it has blown a large cavity around it by means of its high velocity stellar wind. This cavity is much larger than the size of the patchy nebula we observe. A filamentary nebula with an approximate radius of was noted by Nota et al. (1997). Its dynamics suggests it is physically connected to HR Car and the chemical composition which is approximately that of a regular H II region, suggests that it contains mainly swept-up material rather than chemically processed material, as could be expected in the case of an outburst. This means that the star itself ejects material in a very non-symmetric and non-spherical way, either as a result of a companion star or as a result of its internal instability. The presence of a companion, however, is expected to give rise to a more axisymmetric nebula than is seen in this case. We therefore conclude that the star itself ejects material into the surrounding medium in a non-symmetrical way, induced by its own instability. This should be taken into account in the modeling of the mass-loss of HR Car and of LBVs in general.
Comparing our results with those of optical investigations (Hutsemékers & van Drom 1991b and Clampin et al. 1995) we see that the dust and ionized gas distributions near the star () is "more asymmetric" than the gas distribution further away (). The roughly symmetric shape as noted by Clampin et al. (1995) suggests that the symmetry/geometry of the outflow changes with time. Almost all LBV nebulae show a clear symmetry axis and the inner nebula of HR Car is shown to be a rare exception to this rule. It is not immediately clear, however, if this apparent asymmetric shape is intrinsic or due to projection effects, such that light from one part of the nebula is blocked.
A determination of the kinematic age of the inner nebula can be obtained from high resolution [Ne II ] spectroscopy of the nebula (Waters and Voors 1997 in prep.). An outflow velocity of 46 10 kms-1 and a distance of 0.04 pc give an age of 850 185 yr. Projection effects are not taken into account and will affect the dynamic age of the nebula. The dynamic age of the outer nebula is estimated to be 5200 yr (Nota et al 1997). Therefore, the inner and outer nebula can only be of similar age if projection effects play a dominant role in determining the true age of the inner nebula. Apart from the nebulae of Car and P Cygni - stars of which the outbursts were observed that may have caused their surrounding nebula - this is the youngest LBV nebula known.
From the limited sample of LBV nebulae there appears to be a tight relation between the age and the mass of the nebula (Nota 1997). The small mass and its young age of the HR Car nebula agree with this relation. The existence of such a relation could indicate that the nebulae are not formed in a single outburst, but in a series of events, during which the mass continuously increases. However, there is a strong observational bias to this relation: a large nebula must contain a lot of mass if it is to be observed. The small nebula that now is observed may well have diluted in a few years to such an extent that it will not be visible anymore.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998