Direct mapping of the temperature and velocity gradients in discs.
  Imaging the vertical CO snow line around IM Lupi
  Accurate measurements of the physical structure of protoplanetary discs are
critical inputs for planet formation models. These constraints are
traditionally established via complex modelling of continuum and line
observations. Instead, we present an empirical framework to locate the CO
isotopologue emitting surfaces from high spectral and spatial resolution ALMA
observations. We apply this framework to the disc surrounding IM Lupi, where we
report the first direct, i.e. model independent, measurements of the radial and
vertical gradients of temperature and velocity in a protoplanetary disc. The
measured disc structure is consistent with an irradiated self-similar disc
structure, where the temperature increases and the velocity decreases towards
the disc surface. We also directly map the vertical CO snow line, which is
located at about one gas scale height at radii between 150 and 300 au, with a
CO freeze-out temperature of $21\pm2$ K. In the outer disc ($> 300$ au), where
the gas surface density transitions from a power law to an exponential taper,
the velocity rotation field becomes significantly sub-Keplerian, in agreement
with the expected steeper pressure gradient. The sub-Keplerian velocities
should result in a very efficient inward migration of large dust grains,
explaining the lack of millimetre continuum emission outside of 300 au. The
sub-Keplerian motions may also be the signature of the base of an externally
irradiated photo-evaporative wind. In the same outer region, the measured CO
temperature above the snow line decreases to $\approx$ 15 K because of the
reduced gas density, which can result in a lower CO freeze-out temperature,
photo-desorption, or deviations from local thermodynamic equilibrium.
