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

We present a radiative-transfer calculation which reproduces the infrared spectrum of the planetary nebula BD +3003639. We calculate the transfer process through absorption and scattering in a spherically symmetric, multigrain dust shell. The emission of transiently heated particles is taken into account, as well as polycyclic aromatic hydrocarbons (PAHs). We obtain an acceptable fit to most of the spectrum, including the PAH infrared bands. At submiiiimetre wavelengths the observed emission is greater than the model predicts, indicating that large dust conglomerates (`fluffy grains') may be needed as an additional constituent. The fit favours a distance of > 2 kpc, which implies that BD + has evolved from a massive progenitor of several solar masses. A low dust-to-gas mass ratio is found in the ionized region. The calculations yield an original mass-loss rate of 2 x 10- M0 yr -1 on the asymptotic giant branch (AGB). Using this mass-loss rate, we calculate how the infrared spectrum has evolved during the post-AGB evolution. We show, in particular, the evolution of the IRAS colours during the post-AGB evolution. Key words: radiative transfer - stars: AGB and post-AGB - circumstellar matter - dust, extinction - planetary nebulae: individual: BD +3003639 - infrared: stars.