Semi-regular red giants as distance indicators I. The period-luminosity
  relations of semi-regular variables revisited
  Semi-regular variables (SRVs) are similar to Miras in brightness, and they
also follow PLRs, though not necessarily the same as Miras. As potential
standard candles they are more challenging than Miras due to their smaller
variability amplitudes and less regular light curves, but they are
substantially more numerous and especially promising to probe old stellar
populations.
  We aim to characterize the variability of SRVs, with focus on their
connection with Miras, in order to prepare the ground for investigating their
potential as distance indicators.
  We examine SRVs and Miras in the Magellanic Clouds from OGLE-III
observations, with data from Gaia and 2MASS. After cleaning the sample from
variability periods unrelated to pulsation, we classify each source by chemical
type and combination of pulsation modes. We examine the results in terms of
global photometric and pulsation properties.
  We identify four SRVs groups that fit the general evolutionary scenario
predicted by theory. SRVs dominated by fundamental-mode pulsation are very
similar to Miras, especially if mono-periodic. They further split into two
sub-groups, one of which follows the same sequence as Miras in the
period-luminosity and period-amplitude diagram, without discontinuity.
  The similarities between Miras and SRVs suggest that the latter can be
adopted as complementary distance indicators to the former, thereby at least
doubling the available number of LPVs suitable for use as distance indicators.
The traditional amplitude-based separation between Miras and SRVs is not
necessarily appropriate, and a more physically sound criterion should also
involve pulsation periods. While this would require comparatively longer time
series, they are expected to become accessible in the coming years even for
weak sources thanks to current and future large-scale surveys. The table of
reclassified LPVs is made public.
