Linear polarization of submillimetre masers Tracing magnetic fields with ALMA

Context. Once ALMA full polarization capabilities are offered, it will become possible to perform detailed studies of polarized maser emission towards star-forming regions and late-type stars, such as ( post-) asymptotic giant branch stars and young planetary nebulae. To derive the magnetic field orientation from maser linear polarization, a number of conditions involving the rate of stimulated emission R, the decay rate of the molecular state Gamma, and the Zeeman frequency g Omega need to be satisfied. Aims. 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 is greater than the stimulated emission rate. Methods. We 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 that have been observed to display maser emission at submillimetre wavelengths. We assumed typical magnetic field strengths measured towards galactic star-forming regions and circumstellar envelopes of late-type stars from previous VLBI observations. Since the Lande g-factors have not been reported for the different rotational transitions we modelled, we performed our calculations assuming conservative values of the Zeeman frequency for the different molecular species. Results. Setting a lower limit for the Zeeman frequency that still satisfies the criteria g Omega > R and g Omega > 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. These upper limits were calculated assuming a magnetic field oriented perpendicular to the direction of propagation of the maser radiation. Conclusions. 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