A Phase Dependent Comparison of the Velocity Parameters of SiO v=1, J=1-0 and J=2-1 Maser Emission in Long Period Variables

We have examined the relationship between the velocity parameters of SiO masers and the phase of the long period variable stars (LPVs) from which the masers originate. The SiO spectra from the v=1, J=1-0 (43.122 GHz; hereafter $J_{1\rightarrow0}$) and the v=1, J=2-1 (86.2434 GHz; hereafter $J_{2\rightarrow1}$) transitions have been measured using the Mopra Telescope of the Australia Telescope National Facility. One hundred twenty one sources have been observed including 47 LPVs contained in the American Association of Variable Star Observer Bulletin (2011). The epoch of maxima and the periods of the LPVs are well studied. This database of spectra allows for phase dependent comparisons and analysis not previously possible with such a large number of sources observed almost simultaneously in the two transitions over a time span of several years. The velocity centroids ($VCs$) and velocity ranges of emission ($VRs$) have been determined and compared for the two transitions as a function of phase. No obvious phase dependence has been determined for the $VC$ or $VR$. The results of this analysis are compared with past observations and existing SiO maser theory.