A&A 389, 547-555 (2002)
S. N. Hoogzaad1 - F. J. Molster2 - C. Dominik1 - L. B. F. M. Waters1,3 - M. J. Barlow4 - A. de Koter1
1 - Astronomical Institute "Anton Pannekoek'', University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam,
2 - ESTEC/ESA, RSSD-ST, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
3 - Instituut voor Sterrenkunde, K.U. Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium
4 - Department of Physics and Astronomy, University College London, Gower Street, London WC1E6BT, UK
Received 13 December 2001 / Accepted 14 March 2002
We have modeled the complete optical to millimeter spectrum of the Post-Asymptotic Giant Branch (Post-AGB) star HD 161796 and its circumstellar dust shell. A full 2-200 m spectrum taken with the Infrared Space Observatory was used to constrain the dust properties. A good fit is achieved using only 4 dust components: amorphous silicates, the crystalline silicates forsterite and enstatite, and crystalline water ice, contributing respectively about 63, 4, 6 and 27% to the total dust mass. The different dust species were assumed to be co-spatial but distinct, resulting in different temperatures for the different grain populations. We find a temperature for the crystalline H2O ice of 70 K, which is higher than thermal equilibrium calculations of pure H2O ice would give. This implies that the ice must be formed as a mantle on top of an (amorphous) silicate core. In order to form H2O ice mantles the mass loss rate must exceed some yr-1. With a water-ice fraction of 27% a lower limit for the gas to dust mass ratio of 270 is found. At a distance of 1.2 kpc (Skinner et al. 1994) and adopting an outflow velocity of 15 km s-1 (Likkel et al. 1991) an AGB mass loss rate of ( yr-1) is found, which lasted 900 years and ended 430 years ago. During this phase a total of 0.46 was expelled. The mass loss rate was high enough to account for the presence of the H2O ice.
Key words: stars: circumstellar matter, AGB and post-AGB - stars:
individual: HD 161796 - infrared: ISM -
ISM: lines and bands
In total four spectra of HD 161796 were obtained with ISO: two Short Wavelength Spectrometer (SWS; de Graauw et al. 1996) spectra covering the full SWS wavelength range (2.4-45 m) in revolution 71 and 342, one high spectral resolution SWS spectrum from 29.0 to 45.2 m during revolution 521, and one Long Wavelength Spectrometer (LWS; Clegg et al. 1996) spectrum covering its full spectral range (43-197 m) in revolution 80. In total we have a continuous spectrum from 2.4 up to 197 m. In the final spectrum the SWS data from revolution 71 was not used, although it was used to check for artifacts in the spectrum. The SWS spectra were reduced using the SWS off-line processing software, version 7.0. Each detector was checked for irregularities and if necessary bad sections of the spectrum of individual detectors were removed from the data. The main fringes were removed in the band 3 datasets. Finally, the 12 detectors of each sub-band were flat fielded and a sigma clipping procedure was used to remove deviating points; finally, the results were rebinned. Hereafter the different sub-bands were shifted or multiplied to match each other, when respectively the dark current or the flux calibration was expected to be the main source of error. The LWS spectrum was reduced by R. Sylvester using the LWS off-line processing software (version 7.0). The data from the different scans were averaged after sigma-clipping to remove deviating data points caused by cosmic-ray hits. The ten sub-spectra from the ten detectors were rescaled by small factors to give consistent fluxes in regions of overlap and merged for the final spectrum. The high galactic latitude of HD 161796 implies that contamination by cold interstellar dust in the LWS beam is negligible.
The reduced LWS and SWS spectra matched very well in their overlapping
region around 45 m, which is an indication for the quality of the
data reduction process. The final spectrum can be found in
Figs. 1 and 2; in
we also included the UV, optical and radio continuum
measurements of the star.
|Figure 1: Panel a) A pseudo-continuum has been subtracted from the spectrum (shown in panel B) to enhance the features. 1 = amorphous silicate, 2 = forsterite, 3 = enstatite, 4 = crystalline water ice (see Molster et al. 2002a for a more detailed description of the identifications). Panel b) A fit of the full radiative transfer model (dashed line) to the measured spectrum of HD 161796 (solid line). Panel c) The residual between the observed spectrum and the model is shown.|
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|Figure 2: A fit of the full radiative transfer model (dashed line) to the measured spectrum of HD 161796 (solid line) on log scales. The asterisks are the UV and optical data, and the observation at 1.3 mm is taken from Walmsley et al. (1991). We omit the ISO spectrum between 4 m and 9 m because of a too low signal to noise ratio. An interstellar reddening of E(B-V)=0.1 has been applied.|
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The ISO spectrum shows a broad continuum on top of which are two strong features at 43 and 60 m. This points to the presence of a large amount of crystalline water ice. The narrow features in the 23, 28, 33 and 40 micron complexes, indicate the presence of the crystalline silicates (Molster et al. 2002b). The wavelength position of these features is in agreement with very Fe-poor silicates, i.e. enstatite and forsterite (see e.g. Jäger et al. 1998). Broad amorphous silicate features around 10 m and 18 m are also present.
Several values for of HD 161796 are quoted in the literature. Fernie (1983) quotes 6300 K, while Hrivnak et al. (1989) use a value of 7000 K. We use a value of 6750, from an analysis of optical and UV photometry (van Winckel, private communication). A recent analysis of the optical absorption line spectrum however points to a somewhat higher value of 7300 K (van Winckel, private comm.). We estimate an uncertainty in of about 500 K. Using = 6750 K an extinction of E(B-V)=0.19 is found. This implies that 36% of the energy radiated by HD 161796 is absorbed by dust in the line of sight, assuming the standard interstellar extinction law applies (i.e. neglecting grey extinction). This extinction is caused by interstellar and/or circumstellar dust. From the infrared and millimetre observations (subtracting the stellar contribution in that range) we find that 40% of the total energy is emitted in the infrared. This suggests energy balance, which would be consistent with a spherical distribution of the dust and zero interstellar reddening. However, it is likely that a small amount of interstellar reddening exists, resulting in more IR emission from the circumstellar envelope than optical and UV absorption, thus implying a non-spherical distribution of dust. This is consistent with the observed optical and mid-infrared images that show an axisymmetric torus, typical for post-AGB stars (e.g. Skinner et al. 1994; Meixner et al. 1999). Note that we cannot exclude a grey extinction component due to the presence of large grains, which would underestimate the energy absorbed in the optical and UV (see e.g. AFGL4106, Molster et al. 1999).
As mentioned above, images of the dust surrounding HD 161796 indicate an axisymmetric geometry, and in principle a two-dimensional dust distribution is needed to fit both the images and the dust spectrum. However, we are interested in deriving quantitative mass fractions of the mineralogical components in the dust shell as well as an estimate of the mass loss history of the star. Since the ISO data show that the solid state bands are in emission and the central star shows relatively little reddening, it is reasonable to assume that the dust is optically thin. In that case, the infrared spectrum can be modeled using a spherical distribution of dust grains without losing accuracy. We note that the assumption of spherical symmetry leads to densities in the shell that are averaged over 4r2, while in reality a (significant) contrast between polar and equatorial densities may exist. We use a spherically symmetric radiative transfer model code (MODUST, Bouwman 2001) to model the complete spectrum of HD 161796. The dust is assumed to be distributed as r-2, corresponding to a constant velocity outflow. Below we will discuss the input parameters for the model.
We adopt an effective stellar temperature of 6750 K and a distance of 1.2 kpc (Skinner et al. 1994). The distance together with the observed flux and assumed interstellar extinction of about E(B-V)=0.1 (see Sect. 4) fixes the luminosity of the star to 3000 . The temperature and luminosity lead to the radius of the star, 41 . Both values are consistent with the post-AGB nature of HD 161796 but are uncertain due to the poorly determined distance to HD 161796.
|dust species||wavelength range [m]||reference|
|crystalline water ice||0.1-1.3||Warren (1984) (compilation of amorphous ice data)|
|1.3-333||Bertie et al. (1969) (crystalline water ice at 100 K)|
|amorphous water ice||0.1-2.5||Warren (1984)|
|2.5-200||Hudgins et al. (1993) (the 10 K data)|
|0.4-1300||Ossenkopf et al. (1992) (cool oxygen rich data)|
|0.4-333||amorphous silicate and crystalline water ice data|
|forsterite||0.1-4.0||Scott & Duley (1996)|
|4.0-250||Servoin & Piriou (1973)|
|enstatite||0.1-7.5||Scott & Duley (1996)|
|7.5-100||Jäger et al. (1998) (MgxFe1-xSiO3 with x=0.96)|
We used four dust components for our radiative transfer calculations: crystalline water ice, amorphous silicates, enstatite and forsterite (see Table 1 for an overview of the optical constants used in our modeling). These components were previously identified by comparison of the ISO data to laboratory spectra of cosmic dust analogues (e.g. Molster et al. 2002a). We cannot exclude that more dust components are present (it is even likely); however, these four dust species dominate the spectrum. We assumed that all grains are spherical with a size distribution of , with q fixed at 3.5, which is commonly used.
The H2O ice is assumed to be in the form of a mantle surrounding an amorphous silicate core: the ice will only condense at a significant distance from the star, well outside the region where all refractory materials have been formed, using the silicates as condensation sites. If we would assume pure H2O ice grains, the low opacity of H2O ice would result in temperatures that are much lower than derived from the band strength ratios of the 43 and 60 m bands; this supports the core-mantle model. We checked the heat transfer in a 1 m core-mantle grain and found, with the thermal conductivity of crystalline water ice (Ross & Kargel 1998), that the crystalline ice can indeed be very efficiently heated by the silicate core. However, for amorphous ice the thermal conductivity is nine orders of magnitude lower (Kouchi et al. 1992). So for amorphous water ice heating by a silicate core will not work. Crystalline water ice and amorphous water ice can therefore have very different temperatures even if both are found in the same mantles. We calculate the optical properties of a core-mantle grain with the aid of Lorentz oscillators (Bohren & Huffman 1983). In our calculations we assumed that only a fraction of the amorphous silicates have ice mantles; we will return to this point in Sect. 4. Due to the low abundance of crystalline silicates and their low temperature, we did not include water ice mantles for this grain component, as the contribution of this water ice fraction would be negligible.
We allowed for a different upper and lower size cut-off for the amorphous and crystalline silicates. Finally, we assume co-spatial distributions for all dust species, but without thermal contact, except for the core-mantle grains.
For the crystalline water ice mantle of the core-mantle grains, we used the optical constants measured by Bertie et al. (1969) extended to the UV with the compilation of measurements done by Warren (1984). The data for the amorphous water ice used to find the maximum amount possible to be hidden in the spectrum (see Sect. 4) is also taken from Warren (1984).
The optical properties of amorphous silicate are taken from the cool oxygen rich amorphous silicate data of Ossenkopf et al. (1992). The optical properties of forsterite are from Servoin & Piriou (1973) extended to the UV with the data of Scott & Duley (1996). The optical properties of enstatite are from Jäger et al. (1998), MgxFe1-xSiO3 with x=0.96 again extended to the UV with the data of Scott & Duley (1996) (see also Table 1).
The results of the modelling are listed in
Tables 2 and 3
and the best fit is shown in Figs. 1
and 2. The best fit has been
determined by eye, because several of our assumptions
(spherical instead of irregularly shaped grains,
only four dust species, Kurucz 1979
model) forced us to neglect some of the apparent mismatches or shifts,
which cannot satisfactorily be done by a
method. In order to estimate the errors in our modelling we changed
the different parameters (even in combination) up to a point were a
fit was rejected.
|Best fit model parameters|
|value||at 1.2 kpc|
|Inner shell radius||7100 +600-2000 R*||1400 AU|
|Outer shell radius||22000 +13000-3000 R*||4200 AU|
|Dust mass ()|
|Shell mass ()||0.46|
|Interstellar E(B-V)||0.1 -0.06+0.02|
A fit to a spectral energy distribution from dust heated by a central star suffers from degeneracies which can only be resolved by including spatial information about the distribution of the dust (see e.g. Bouwman et al. 2000). This analysis also suffers from this difficulty, but due to the detailed spectral information the ISO data provide, we can constrain certain parameters well. Below we describe the spectral regions that were used to constrain certain model parameters.
The temperature as a function of mass T(M) of the hottest particles determines the spectral shape in the 10-20 m wavelength range. This T(M) is influenced by the inner radius and the size of the dust particles; moving the inner radius outwards and simultaneously decreasing the grain size will result in a similar spectrum. If particles become much smaller than the optical wavelength at which they absorb stellar light, their temperature and therefore their emitted spectrum becomes fairly independent of size (Bohren & Huffman 1983). We determined an upper limit of 104 R* for the inner radius of the dust shell assuming small hot grains.
To constrain the lower size cut-off of the amorphous silicate grains we took into account the effects of grain size on the shape and strength of the 18 m amorphous silicate feature. When we lowered the lower size limit below the range indicated in Table 3 this resulted in an excess (8% with a lower cut-off of 0.06 m) in the region between 16 and 21 m (the amorphous silicate feature).
With this constraint on the lower size cut-off of the most abundant
grains, the inner radius was found to be smaller than 7700 R*. The
lower cut-off of the less abundant crystalline grains had less
influence on the model spectrum and is therefore much less accurately
|Dust type||dust mass||min. particle||max. particle||Temperature|
|[%]||size [m]||size [m]||range [K]|
|Cryst. water ice||27||-||-||-|
The outer radius should be constrained by the width of the spectral energy distribution. Increasing the outer radius will increase the width of the SED, and visa versa. However, large changes in the outer radius made relatively small changes in the width of the resulting energy distribution. Furthermore, there is a correlation between the width of the SED and the upper size cut-off of the size distribution. For an upper size cut-off of amorphous silicates larger than 6 m, an excess in the 95-260 m wavelength range was found, in addition to a widening of the SED. We could determine the outer radius of the dust shell with 30 per cent accuracy.
For crystalline silicates the upper limit to the grain size was found by looking at the width of the features, especially the forsterite complex around 33 m. For an upper limit larger than 3 m, the crystalline features are wider than observed. We adopted the same upper and lower grain size limits for both crystalline silicate species, i.e. 0.1 and 3.0 m respectively.
Most accurately determined are the mass ratios of the different dust species. The strength of the different complexes, which often are dominated by one type of dust species, naturally limits the freedom in the mass ratios. We could change the water fraction of the core-mantle grains slightly, hereby changing the temperature of these grains. This changes the continuum at the longer (>20 m) wavelengths and resulted in slightly different mass fractions.
The total amount of dust could be determined within 50%. The error is influenced by the relatively large error in the lower limit of the grain size. A systematic error in the total dust mass could exist if the particles are not spherical. Non-spherical particles have a different absorption coefficient per unit mass than spherical particles.
We find that about 10% of all the silicate grains are crystalline (see Table 3) a fraction which is not uncommon for oxygen-rich circumstellar envelopes (Molster 2000). The derived mass-averaged temperature for crystalline water ice is found to be 70 K and amorphous silicates are about 110 K. Crystalline pyroxene grains were found to be about 15 K warmer than forsterite grains, which is in agreement with the results found by Molster (2000).
The inner and outer shell radius of our best fit model agree well with the observations. We adopt a distance of 1.2 kpc, resulting in an outer radius of the dust shell of 3.5 arcsec. This is consistent with the upper limit of 6.5 arcsec derived from CO observations by Bujarrabal et al. (1992) and equal to the size of derived from the optical observations of the scattered light by Ueta et al. (2000). We note that the outer radius is mostly determined by the position of the cold dust. In a non-spherical (torus) distribution of the dust, the shielding in the equatorial plane can become very efficient and thus the dust colder than we have derived from our 1-D analysis. This might bring the outer radius closer to the star. Because this requires a 2-D modeling we did not investigate this further.
The inner radius of the best fit model is 1 arcsec, which is about twice the value of 0.4 arcsec estimated by Skinner et al. (1994) based on N band images. Two effects will likely explain this apparent discrepancy. First, we assumed spherical symmetry, while as discussed before, the real shape is more likely to be a torus. A smaller angular size of the inner radius of the dust shell may partially be a projection effect. Furthermore, we assumed spherical particles in our calculations. Non-spherical particles have a relatively larger surface area. Therefore, real particles are likely to be a little colder (at the same distance) than the ones in our calculations and are therefore expected to be closer to the central star.
The E(B-V) of the full radiative transfer model is only 0.06, which is less than the value of 0.19 determined from the stellar SED, implying an interstellar E(B-V) of order 0.1 (see Fig. 2).
We included both "bare'' amorphous silicate grains and core-mantle grains consisting of an amorphous silicate core and a crystalline H2O ice mantle. If all silicates would be equally covered with an H2O ice mantle, the strength of the 43 and 60 m bands can only be fitted by using relatively thin mantles. Thin mantles on top of large cores result in too high temperatures of the core-mantle grains. We resolved this discrepancy by assuming that only a fraction of the silicates have a relatively thick mantle. While in a spherical shell the co-existence of bare and core-mantle grains may be hard to explain, the torus geometry of the dust shell surrounding HD 161796 provides a natural spatial separation of these two components, with the core-mantle grains concentrated more in the equatorial regions of the torus.
Kouchi et al. (1992) measured the speed of amorphization of crystalline water ice under UV radiation. The UV radiation field around HD 161796 would under normal conditions transform the crystalline water ice into amorphous water ice within a day. So, we must conclude that the crystalline water-ice is efficiently shielded from the harsh UV radiation field, for example by the density enhancement in the torus. This again leads to the conclusion that most if not all of the crystalline water ice is located in the torus.
Our fit shows a small offset for the 43 m and a larger offset for the 60 m water ice features. Part of these errors are due to the fact that the measurements of the optical constants from Bertie et al. (1969) were done at 100 K and at a poor spectral resolution. Higher spectral resolution measurements at the right temperature of 70 K would give a better fit as the features tend to move to shorter wavelength when measured at lower temperatures. The large discrepancy at 60 m is not solved using the 70 K data from Smith et al. This indicates that additional solid state components may contribute in this wavelength range, such as diopside (CaMgSiO3, Koike et al. 2000) or dolomite (CaMg(CO3)2, Kemper et al. 2002b).
Our best fit model shows a weak absorption at 3.1 m due to H2O ice, which is not observed (see Fig. 3). This indicates that we have slightly overestimated the amount of H2O ice in the line of sight towards the star. This may have several reasons: (1) blends of the 43 and 60 m ice bands with other species (see above), or (2) deviations from spherical symmetry.
We also investigated the possibility that amorphous H2O ice is
present. Amorphous H2O ice has a broad resonance near 45 m but
lacks the 60 m band. We find that about 10% of the dust mass
could be pure amorphous water ice (or core-mantle) at the
expense of slightly decreasing the mass of
the crystalline H2O ice (see Fig. 4).
We note that the amorphous H2O ice is very cold due to its poor
conductivity and mainly contributes in the 60-100 m wavelength
|Figure 3: A detail of the best fit of the full radiative transfer model (dashed line) compared to the spectrum of HD 161796 (solid line). A 3.1 m absorption feature of water ice is visible in the model. The small apparent absorption in the measured spectrum near 3 m is caused by an anomaly in the measured spectrum.|
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With the amount of water ice found we can derive a estimate of the lower limit for the gas to dust mass ratio. We find that about 27% of all dust mass in the shell consists of water ice (see Table 3). An estimate of the water fraction per mass, can be derived from the water vapour fraction by number relative to H2. González-Alfonso & Cernicharo (1999) found that the water fraction by number in oxygen rich circumstellar environments is about . We will use and an average mass for the atoms in outflow of an AGB star (mainly H and He) to be 1.4 , with the proton mass. This makes the mass fraction of water in an outflow ( )) and gives for HD 161796 a gas to dust mass ratio after the water ice condensation of 270. Since we find a water ice mass of 27% this makes the gas to dust ratio before the ice condensation 370. This number is a lower limit since we assumed in deriving this number that all water vapour present in the outflow has become ice, which does not have to be the case.
Based on the inner and outer radius of the dust shell (See Table
2), the distance of 1.2 kpc (Skinner et al. 1994)
and the outflow velocity of 15 km s-1 (Likkel et al. 1991)
we find that the mass loss episode stopped about 430
years ago after it had lasted for about 900 years. In this
period a total dust mass of about
has been lost. This results in a mean dust mass loss rate
With the assumed gas to dust ratio of 270 after the water condensation,
we find a total shell mass of (
and a total
mass loss rate of
yr-1. The uncertainty
in the mass loss rate is about a factor 2.
|Figure 4: The full radiative transfer model with 11% of amorphous water ice (dotted line) compared with the preferred model (dashed line) and the observed spectrum (solid line). The grain size of the pure amorphous water ice grains is the same as the core-mantle grains. This way we model that some grains have an amorphous water ice mantle which is thermally insulated from the grain, but has an equal size as the crystalline grains. The amorphous ice data used is the 10 K data from Hudgins et al. (1993).|
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The most prominent spectral bands in the ISO spectrum of HD 161796 are the crystalline H2O ice features. The presence of ice mantles on the silicate grains poses restrictions on possible models. Water molecules can only condense onto the grains in significant amounts if the grains are cold and the gas densities are high enough for water ice to be stable. In this section we will quantify this constraint.
We assume that the ice condenses on pre-existing silicate grains.
Therefore, the process of nucleation (seed formation) is not relevant.
In a gas-grain mixture, gas molecules collide with grains because of
thermal motions and because of drift motions between gas and dust.
For the estimates in this section we assume that the relative speed of
gas and dust particles is given by a collision speed
also assume that the grain is cold, so that the evaporation of ice
molecules from the grain can be neglected. The rate of change of the
is then given by
The high quality ISO spectrum, with its wide wavelength coverage, allows a detailed analysis of the dust composition of this high latitude post-AGB star. We find a modest amount (10 per cent) of crystalline silicates, which is typical for similar stars (e.g. Molster et al. 1999; Kemper et al. 2002a). These crystalline silicates are Fe-poor, in contrast to the amorphous silicates.
The ISO spectrum of HD 161796 is unique in that it shows very strong crystalline H2O bands. This must imply that the conditions to form H2O ice in the envelope were very favourable, compared to other oxygen-rich AGB stars. We showed that core-mantle grains, consisting of a silicate core and a water ice mantle, must exist, since this is the only way to get the water ice at the right temperature without assuming a strange geometry of the dust shell.
The critical parameter which determines the formation of H2O ice is the density of water vapour at the condensation point in the outflow. It is possible that the H2O condensation radius in HD 161796 was smaller than in other AGB stars, leading to efficient H2O ice deposition. In view of the high mass loss rate of HD 161796, and considering the modest luminosity of HD 161796 compared to typical OH/IR stars, the density in the outflow may have been substantially higher and the ice condensation radius accordingly smaller at high densities. From the preference of water ice to form in a high density regime we expect that most water ice is present in the torus. Since crystalline water ice becomes amorphous when exposed to UV radiation, the torus is also the likely place where the crystalline water ice can survive.
We find that the mass loss episode of HD 161796 lasted for about 900 years and stopped about 430 years ago. In this period a total dust mass of about has been lost. This results in a mean dust mass loss rate of yr-1. We were able to derive a lower limit to the gas to dust ratio of 270 from the amount of water ice. A total shell mass of 0.46 and a total mass loss rate of yr-1 result. These numbers are similar to those found by e.g. Skinner et al. (1994).
In order to fit the spectrum we had to assume a particle size distribution which lacks small grains: the grains around HD 161796 are (on average) much larger than in the ISM. A similar result was obtained by Molster et al. (1999) for AFGL4106.
We would like to thank R. Sylvester for the use of his reduced LWS spectrum of HD 161796 and H. van Winckel for his measurement of the reddening. FJM acknowledges support from NWO under grant 781-71-052 and under the talent fellowship program. LBFMW, AdK and CD acknowledge financial support from NWO "Pionier'' grant number 616-078-333. This work was partly supported by NWO Spinoza grant 08-0 to E. P. J. van den Heuvel.