Period-luminosity diagram of long period variables in the Magellanic
  Clouds. New aspects revealed from Gaia Data Release 2
  Context: The period-luminosity diagram (PLD) has proven to be a powerful tool
for studying populations of pulsating red giants. Gaia Data Release 2 (DR2)
provides a large data set including many long-period variables (LPVs) on which
this tool can be applied.
  Aims: We investigate the location of LPVs from the Large and Small Magellanic
Clouds in the PLD using various optical and infrared luminosity indicators from
Gaia and 2MASS, respectively. We thereby distinguish between stars of different
masses and surface chemistry.
  Methods: The data set taken from the Gaia DR2 catalogue of LPVs allows for a
homogeneous study from low- to high-mass LPVs. These sources are divided into
sub-populations of asymptotic giant branch (AGB) stars according to their mass
and their O- or C-rich nature using the Gaia-2MASS diagram developed by our
group. This diagram uses a Wesenheit index Wrp based on Wesenheit functions in
the Gaia and 2MASS photometric bands. Four different luminosity indicators are
used to study the period-luminosity (P-L) relations.
  Results: We provide the first observational evidence of a P-L relation offset
for both fundamental and 1O pulsators between low- and intermediate-mass O-rich
stars, in agreement with published pulsation predictions. Among the luminosity
indicators explored, sequence C' is the narrowest in the P-Wrp diagram, and is
thus to be preferred over the other PLDs for the determination of distances
using LPVs. The majority of massive asymptotic giant branch (AGB) stars and red
supergiants form a smooth extension of sequence C of low- and intermediate-mass
AGB stars in the P-Wrp diagram, suggesting that they pulsate in the fundamental
mode. All results are similar in the two Magellanic Clouds.
