We investigate the circumstellar dust properties of the oxygen-rich bipolar proto-planetary nebula IRAS 18276–1431 by means of two-dimensional radiative transfer simulations of the circumstellar dust shell .
The model geometry is assumed to have a torus and an envelope which consists of a pair of bipolar lobes and a spherical AGB shell .
The parameters of the dust and the dust shell are constrained by comparing the spectral energy distribution ( SED ) and near-infrared intensity and polarisation data with the models .
The polarisation in the envelope reaches 50 – 60 % and is nearly constant in the H and K _ { S } bands in the observations .
This weak wavelength dependence of the polarisation can be reproduced with a grain size distribution function for the torus : 0.05 \mu m \leq a with n \left ( a \right ) \propto a ^ { - \left ( p = 5.5 \right ) } \exp \left ( - a / a _ { \mathrm { c } } = 0.3 ~% { } \mu \mathrm { m } \right ) .
The power index p is significantly steeper than that for interstellar dust ( p \sim 3 ) .
Similar results have also been found in some other PPNs and suggest that mechanisms that grind down large particles , such as sputtering , may also have acted when the dust particles formed .
The spectral opacity index \beta is found to be 0.6 \pm 0.5 from the 760 \mu m to 2.6 mm fluxes , which is characterised by the dust in the torus .
This low value ( < 2 ) indicates the presence of large dust grains in the torus .
We discuss two possible dust models for the torus .
One has a size distribution function of 1.0 \mu m \leq a \leq a _ { \mathrm { max } } = 5 000.0 ~ { } \mu m with n \left ( a \right ) \propto a ^ { - \left ( p = 2.5 \right ) } and the other is 1.0 \mu m \leq a \leq a _ { \mathrm { max } } = 10 000.0 ~ { } \mu m with n \left ( a \right ) \propto a ^ { - \left ( p = 3.5 \right ) } .
The former has \beta of 0.633 , but we are not able to find reasonable geometry parameters to fit the SED in the infrared .
The latter has \beta of 1.12 , but reproduces the SED better over a wide wavelength range .
With this dust model , the geometric parameters are estimated as follows : the inner and outer radii are 30 AU and 1000 AU and the torus mass is 3.0 M _ { \sun } .
Given that the torii are generally not found to be rotating , a large fraction of the torus material is likely to be expanding .
Assuming an expansion velocity of 15 kms ^ { -1 } , the torus formation time and mass-loss rate are found to be \sim 300 yrs and \sim 10 ^ { -2 } ~ { } M _ { \sun } yr ^ { -1 } respectively .