Where are all of the nebulae ionized by supersoft X-ray sources?

Accreting, steadily nuclear-burning white dwarfs are associated with so-called close-binary supersoft X-ray sources (SSSs), observed to have temperatures of a few × 10⁵ K and luminosities on the order of 10³⁸ erg s^-1. These and other types of SSSs are expected to be capable of ionizing their surrounding circumstellar medium; however, to date only one such nebula was detected in the Large Magellanic Cloud (of its six known close-binary SSSs), surrounding the accreting, nuclear-burning WD CAL 83. This has led to the conclusion that most SSSs cannot have been both luminous (≳10³⁷ erg s^-1) and hot (≳few × 10⁴ K) for the majority of their past accretion history, unless the density of the interstellar medium (ISM) surrounding most sources is much less than that inferred for the CAL 83 nebula (4-10 cm^{- 3}). Here, we demonstrate that most SSSs must lie in much lower density media than CAL 83. Past efforts to detect such nebulae have not accounted for the structure of the ISM in star-forming galaxies and, in particular, for the fact that most of the volume is occupied by low density warm and hot ISM. CAL 83 appears to lie in a region of ISM which is at least ∼40-fold overdense. We compute the probability of such an event to be ≈18 per cent, in good agreement with observed statistics. We provide a revised model for the `typical' SSS nebula, and outline the requirements of a survey of the Magellanic Clouds which could detect the majority of such objects. We then briefly discuss some of the possible implications, should there prove to be a large population of previously undiscovered ionizing sources.