Volume 543, July 2012
|Number of page(s)||13|
|Section||Interstellar and circumstellar matter|
|Published online||25 June 2012|
In this appendix some technical aspects are described of the modifications and extensions that were made to DUSTY. Some familarity with DUSTY and its manual is assumed. The modified code will be referred to as MoD (More of DUSTY). The core of MoD is DUSTY version 2.01, and the changes described below are w.r.t. that version.
In the process of developing MoD, one bug was found and corrected, namely in subroutine visi2d where the loop over the radial positions ran from 1 to Nin, but should run to (Nin-1).
The 2D array Elems, which has dimensions (25, npL). The second dimension was increased to npP.
In DUSTY it is possible to calculate intensity profiles (the *.itb files). From an observational point one would prefer intensity profiles convolved with the beam of the instrument/ telescope. In fact, this option was already present in DUSTY (subroutines Convolve and Conv2D ), but not described in the DUSTY user manual. The calculation requires parameters for the convolution, but also the angular diameter of the inner dust shell. In DUSTY this number is simply an input parameter, independent of any observational parameter (luminosity, effective temperature, dust condensation temperature, which basically set this value) because DUSTY is scale-free and hence does not require the luminosity as input. In MoD the angular diameter of the inner dust shell must be calculated self-consistently. In order to achieve this, the call to the subroutines that calculate the convolved intensity profiles (and visibilities as well) had to be moved to a different location in DUSTY.
A more general form of the piecewise power law for the density structure (density type = 1) was implemented in DUSTY, see Eq. (1) in the main text. With this density structure it is possible to model steps in the mass-loss rate. This implementation required modification in subroutine Ygrid to better resolve the different regions, and a change in subroutines ETA and Product. The parameter EtaRat, which is a control parameter on how much the normalized density profile may change between two radial gridpoints, was set to a high value.
For this mix, Figs B.1, B.2 show the visibility data for grains of size 0.15 and 0.25 μm, respectively. The visibility curve at the shortest wavelength is very sensitive to the adopted grain size, likely due to the effect of scattering. At 2.1 μm, Qabs/a is almost constant with values of 0.28, 0.30, 0.32 μm-1 for a = 0.15, 0.20, 0.25 μm, respectively, but Qsca/Qabs is 0.27, 0.58, 0.97, respectively. The effect is smaller at longer wavelengths; already at 4.9 μm the ratio of scattering to absorption is a factor of 2 lower.
Figure B.3 shows the best fit with pure olivine instead of the aluminosilicate. The best fit to the K-band visibility curve (not shown) is for a = 0.l8 μm. The fit is clearly poorer, and adding iron(-oxides) does not significantly improve the fit.
The standard model converged to a r-2.55 density distribution. The outer radius in this model is set to 1600 condensation radii where the dust temperature reached 20 K, corresponding to about 1.5′.
Non-standard models are now considered where the density distribution is fixed to r-2, as adopted in somestudies mentioned in Sect. 3.1.1. The dust is fixed to 100% aluminasilicates. It turns out that the outer radius has to be decreased significantly to obtain even an approximately good fit. Figures B.4–B.6 show the results for an outer radius of five condensation radii. Although the fit to the SWS spectrum is even slightly better than for the standard model, the fit to the intensity curves and visibility curves is worse. Such a small outer radius can in fact be excluded. Fong et al. (2002) mapped CO and detected it to 7 × 1017 cm correspoding to about 3.3′′. This should correspond to the CO photodissociation radius, and the outer radius of the dust should extent beyond this.
Best fit to the optical and NIR photometry and SWS spectrum of TT Cyg, with Teff = 3200 K, log g = −0.4, C/O = 1.10. The top panel shows the full SED, while the middle and lower panel show details of the SWS spectrum. The C3 feature near 5.4 μm is not well fitted in any of the Aringer et al. (2009) models and is excluded from the fit (as indictated by the line between 4.4 and 6.1 μm). This is likely related to the issue discussed in Jörgensen et al. (2000) about the parameter Kp(C3) that expresses the equilibrium between atomic carbon, C2 and C3 and that is not well known.
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In this section the influence of the different stellar parameters is illustrated. Figure C.1 shows the best-fit model from the
Aringer et al. (2009) set with solar metallicity, which has Teff = 3200 K, log g = −0.4, and C/O = 1.10 as parameters. Figures C.2–C.4 show models where one parameter is varied to Teff = 3000 K, log g = −0.0, and C/O = 2.0, respectively. Gravity is almost unconstrained by the SWS spectrum, but the strength of the 3.1 μm feature (due to HCN and C2H2) and 7.5 μm feature (mainly CS) strongly depend on effective temperature and C/O ratio (see Jörgensen et al. 2000). Based on these results error bars of 50 K in effective temperature and 0.15 in C/O are estimated.
© ESO, 2012
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