  We have embarked in a systematic study of the X-ray emission in a
volume-limited sample of M dwarf stars, in order to explore the full range of
activity levels present in their coronae and, thus, to understand the
conditions in their outer atmospheres and their possible impact on the
circumstellar environment. We identify in a recent catalog of the Gaia objects
within 10 pc from the Sun all the stars with spectral type between M0 and M4,
and search systematically for X-ray measurements of this sample. To this end,
we use both archival data (from ROSAT, XMM-Newton, and from the ROentgen Survey
with an Imaging Telescope Array (eROSITA) onboard the Russian
Spektrum-Roentgen-Gamma mission) and our own dedicated XMM-Newton observations.
To make inferences on the properties of the M dwarf corona we compare the range
of their observed X-ray emission levels to the flux radiated by the Sun from
different types of magnetic structures: coronal holes, background corona,
active regions and cores of active regions. At the current state of our
project, with more than 90\% of the 10pc M dwarf sample observed in X-rays,
only GJ 745 A has no detection. With an upper limit luminosity of log Lx
[erg/s] < 25.4 and an X-ray surface flux of log FX,SURF [erg/cm^2/s] < 3.6 GJ
745 A defines the lower boundary of the X-ray emission level of M dwarfs.
Together with its companion GJ 745 B, GJ 745 A it is the only star in this
volume-complete sample located in the range of FX,SURF that corresponds to the
faintest solar coronal structures, the coronal holes. The ultra-low X-ray
emission level of GJ 745 B (log Lx [erg/s] = 25.6 and log FX,SURF [erg/cm^2/s]
= 3.8) is entirely attributed to flaring activity, indicating that, while its
corona is dominated by coronal holes, at least one magnetically active
structure is present and determines the total X-ray brightness and the coronal
temperature of the star.
