Terahertz Water Masers: II. Further SOFIA/GREAT Detections toward
  Circumstellar Outflows, and a Multitransition Analysis
  Following up on our discovery of terahertz water masers, reported in 2017, we
report two further detections of water maser emission at frequencies above 1
THz. Using the GREAT instrument on SOFIA, we have detected emission in the
1.296411 THz $8_{27}-7_{34}$ transition of water toward two additional
oxygen-rich evolved stars, omicron Ceti (Mira) and R Crateris, and obtained an
upper limit on the 1.296 THz line emission from U Orionis. Toward these three
sources, and toward the red supergiant star VY Canis Majorae from which 1.296
THz line emission was reported previously, we have also observed several
lower-frequency (sub)millimeter water maser transitions using the APEX 12-m
telescope along with the 22 GHz transition using the Effelsberg 100-m
telescope. We have used a simple model to analyse the multi-transition data
thereby obtained. Adopting, as a prior, independent literature estimates of the
mass-loss-rates in these four sources and in W Hydrae, we infer water
abundances in a remarkably narrow range: $n({\rm H_2O})/n({\rm H_2}) = 1.4 -
2.5 \times 10^{-4}$. For o Cet, VY CMa, and W Hya, the model is successful in
predicting the maser line fluxes to within a typical factor $\sim 1.6 - 3$. For
R Crt and U Ori, the model is less successful, with typical line flux
predictions lying an order of magnitude above or below the observations; such
discrepancies are perhaps unsurprising given the exponential nature of maser
amplification.
