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Astrometrically Registered Simultaneous Observations of the 22 GHz H$_2$O and the 43GHz SiO masers towards R Leonis Minoris using KVN and Source/Frequency Phase Referencing

Oxygen-rich Asymptotic Giant Branch (AGB) stars can be intense emitters of SiO ($v$=1 and 2, J=1$\rightarrow$0) and H$_2$O maser lines at 43 and 22 GHz, respectively. VLBI observations of the maser emission provide a unique tool to probe the innermost layers of the circumstellar envelopes in AGB stars. Nevertheless, the difficulties in achieving astrometrically aligned \water\ and $v$=1 and $v$=2 SiO maser maps have traditionally limited the physical constraints that can be placed on the SiO maser pumping mechanism. We present phase referenced simultaneous spectral-line VLBI images for the SiO $v$=1 and $v$=2, J=1$\rightarrow$0, and H$_2$O maser emission around the AGB star R\,LMi, obtained from the Korean VLBI Network (KVN). The simultaneous multi-channel receivers of the KVN offer great possibilities for astrometry in the frequency domain. With this facility we have produced images with bona-fide absolute astrometric registration between high frequency maser transitions of different species to provide the positions of the \water\ maser emission, and the centre of the SiO maser emission, and hence reducing the uncertainty in the proper motion for R\,LMi by an order of magnitude over that from Hipparcos. This is the first successful demonstration of source frequency phase referencing for mm-VLBI spectral-line observations and also where the ratio between the frequencies is not an integer.