Pulsars are known to emit non-thermal radio emission that is generally a
power-law function of frequency. In some cases, a turnover is seen at
frequencies around 100~MHz. Kijak et al. have reported the presence of a new
class of ''Gigahertz Peaked Spectrum'' (GPS) pulsars that show spectral
turnovers at frequencies around 1 GHz. We apply a model based on free-free
thermal absorption to explain these turnovers in terms of surrounding material
such as the dense environments found in HII regions, Pulsar Wind Nebulae
(PWNe), or in cold, partially ionized molecular clouds. We show that the
turnover frequency depends on the electron temperature of the environment close
to the pulsar, as well as the emission measure along the line of sight. We
fitted this model to the radio fluxes of known GPS pulsars and show that it can
replicate the GHz turnover. From the thermal absorption model, we demonstrate
that normal pulsars would exhibit a GPS-like behaviour if they were in a dense
environment. We discuss the application of this model in the context of
determining the population of neutron stars within the central parsec of the
Galaxy. We show that a non-negligible fraction of this population might exhibit
high-frequency spectral turnovers, which has implications on the detectability
of these sources in the Galactic centre.Comment: 7 pages, 3 figures, Accepted for publication in MNRA
