The influence of clumping on the infrared and radio continuum of early-type stars

Time-dependent hydrodynamical models predict that the stellar winds of early-type stars are clumped, due to the sweeping up of material into dense shells. In this paper we investigatewhether these shells can explain the longwavelength (≥ 10 μm) continuumfluxes of O and early B stars.We had previously found that, for some stars, smooth wind models failed to explain the infrared and millimetre fluxes. To calculate the continuum flux, we model the clumping by a single shell. This single shell can represent the joint effect of a number of shells and we discuss how multiple shells can be combined into a single shell. The shell strength parameter is introduced, which combines density contrast and width of the shell. From the 12, 25 and 60 μm IRAS observations of ζ Pup, we derive a shell strength and position. We find that the clumping is less extreme than predicted by the hydrodynamical models. This means that the strength of the shells is less than the models predict, that there are not as many of them or that they do not fill a complete solid angle. Considering such partial (i.e. filling a solid angle of < 4π) shells is a natural way tomake the time-dependent hydrodynamical models agree with the observations. That complete shells are found in the hydrodynamicalmodels is solely a consequence of present computational limitations.Whenwe introduce partial shells in our model for ζ Pup, we find that the IRAS observations can be explained if each shell is limited to a solid angle of ∼ 4π/3. The shells dissipate as they move away from the star, but reach the radio formation region before they damp out completely, thereby influencing the radio fluxes of the stars. In this case, applying a smooth wind model to the radio observations of an O or early B star could lead to an overestimate of the mass loss rate. In the case of ζ Pup this error turns out to be negligible. While clumping can explain the observed infrared continuumfluxesofOandearlyB stars, it cannot be excluded that other phenomena also contribute. Co-rotating interaction regions especially will influence the infrared flux formed in the wind.