  GJ 3470b is a warm Neptune transiting an M-dwarf star at the edge of the
evaporation desert. It offers the possibility of investigating how low-mass,
close-in exoplanets evolve under the irradiation from their host stars. We
observed three transits of GJ 3470b in the Lyman-alpha line with the Hubble
Space Telescope (HST) as part of the Panchromatic Comparative Exoplanet
Treasury (PanCET) program. Absorption signatures are detected with similar
properties in all three independent epochs, with absorption depths of 35+-7% in
the blue wing of the line, and 23+-5% in the red wing. The repeatability of
these signatures, their phasing with the planet transit, and the radial
velocity of the absorbing gas allow us to conclude that there is an extended
upper atmosphere of neutral hydrogen around GJ 3470 b. We determine from our
observations the stellar radiation pressure and XUV irradiation from GJ 3470
and use them to perform numerical simulations of the upper atmosphere of GJ
3470b with the EVaporating Exoplanets (EVE) code. The unusual redshifted
signature can be explained by the damping wings of dense layers of neutral
hydrogen that extend beyond the Roche lobe and are elongated in the direction
of the planet motion. This structure could correspond to a shocked layer of
planetary material formed by the collision of the expanding thermosphere with
the wind of the star. The blueshifted signature is well explained by neutral
hydrogen atoms escaping at rates of about 1e10 g s-1 that are blown away from
the star by its strong radiation pressure and are quickly photoionized,
resulting in a smaller exosphere than that of the warm Neptune GJ 436b. The
stronger escape from GJ 3470b, however, may have led to the loss of about 4-35%
of its current mass over its 2 Gyr lifetime.
