Linear polarization of submillimetre masers. Tracing magnetic fields
  with ALMA
  (Abridged) The goal of this work is to investigate if SiO, H2O and HCN maser
emission within the ALMA frequency range can be detected with observable levels
of fractional linear polarization in the regime where the Zeeman frequency
(gOmega) is greater than the stimulated emission rate (R) and the decay rate of
the molecular state (Gamma). We have used a radiative transfer code to
calculate the fractional linear polarization as a function of the emerging
brightness temperature for a number of rotational transition of SiO, H2O and
HCN which have been observed to display maser emission at submillimetre
wavelengths. We assume typical magnetic field strengths measured towards
galactic star forming regions and circumstellar envelopes of late-type stars
from previous VLBI observations. Since the Land\'e g-factors have not been
reported for the different rotational transitions we have modeled, we performed
our calculations assuming conservative values of the Zeeman frequency for the
different molecular species. Setting a lower limit for the Zeeman frequency
which still satisfies the criteria gOmega>R and gOmega>Gamma, we find
fractional polarization levels of up to 13%, 14% and 19% for the higher J
transitions analysed for SiO, H2O and HCN, respectively, without considering
anisotropic pumping or any other non-Zeeman effect. Such upper limits were
calculated assuming a magnetic field oriented perpendicular to the direction of
propagation of the maser radiation. According to our results SiO, H2O and HCN
maser emission within the ALMA frequency range can be detected with suitable
linear polarization to trace the magnetic field structure towards star forming
regions and late-type stars, even if the detected polarization has been
enhanced by non-Zeeman effects.
