  Recent observations have discovered an escape of ionizing Lyman-continuum
radiation from a population of compact, actively star-forming galaxies at
redshift z~0.3, also known as "green peas". We here study the peculiar green
pea Lyman-alpha (Lya) spectra, which are mostly double-peaked, unlike in any
other galaxy sample. We select a sample of twelve archival green peas and we
apply numerical radiative transfer models to reproduce the observed Lya
spectral profiles, using the geometry of expanding, homogeneous spherical
shells. We use ancillary optical and ultraviolet data to constrain the model
parameters, and we evaluate the match between the models and the observed Lya
spectra. As a second step, we allow all the fitting parameters to be free, and
examine the agreement between the interstellar medium parameters derived from
the models and those from ancillary data. The green pea double-peaked Lya line
profiles are not correctly reproduced by the constrained shell models.
Conversely, unconstrained models fit the spectra, but parameters derived from
the best-fitting models are not in agreement with the ancillary data. In
particular: 1) the best-fit systemic redshifts are larger by 10 - 250 km/s than
those derived from optical emission lines, 2) the double-peaked Lya profiles
are best reproduced with low-velocity (<150 km/s) outflows that contradict the
observed ultraviolet absorption lines of low-ionization-state elements with
characteristic velocities as large as 300 km/s, and 3) the models need to
consider intrinsic Lya profiles that are on average three times broader than
the observed Balmer lines. Differences between the modelled and observed
velocities are larger for targets with prominent Lya blue peaks. The blue peak
position and flux appear to be connected to low column densities of neutral
hydrogen, leading to Lya and Lyman-continuum escape.
