The planetary nebula BD +30 3639: the infrared spectrum during post-AGB stellar evolution

We present a radiative-transfer calculation which reproduces the infraredspectrum of the planetary nebula BD~+30$^{\circ}$3639. We calculate thetransfer process through absorption and scattering in a spherical-symmetricmulti-grain dust shell. The emission of transiently heated particles is takeninto account, as well as polycyclic aromatic hydrocarbons. We obtain anacceptable fit to most of the spectrum, including the PAH infrared bands. Atsubmillimetre wavelengths the observed emission is larger than the modelpredicts, indicating that large dust conglomerates (``f{}luffy grains'') may beneeded as an additional constituent. The fit favours a distance of $\ge 2\,$kpc, which implies that BD~+30$^\circ$3639 has evolved from a massiveprogenitor of several solar masses. A low dust-to-gas mass ratio is found inthe ionised region. The calculations yield an original mass-loss rate of$2\times10^{-4} \msolar \peryr$ on the Asymptotic Giant Branch. Using thismass-loss rate, we calculate how the infrared spectrum has evolved during thepost-AGB evolution. We show in particular the evolution of the IRAS coloursduring the preceding post-AGB evolution.Comment: accepted for publication in MNRAS. LaTeX, 15 pages, hardcopy and 8 figures available from rsiebenm@isosa5.estec.esa.nl or azijlstr@eso.or