  We present an analysis of the far-infrared and submillimetre molecular
emission line spectrum of the luminous M-supergiant VY CMa, observed with the
SPIRE and PACS spectrometers aboard the Herschel Space Observatory. Over 260
emission lines were detected in the 190-650-micron SPIRE FTS spectra, with
one-third of the observed lines being attributable to H2O. Other detected
species include CO, 13CO, H2^18O, SiO, HCN, SO, SO2, CS, H2S, and NH3. Our
model fits to the observed 12CO and 13CO line intensities yield a 12C/13C ratio
of 5.6+-1.8, consistent with measurements of this ratio for other M
supergiants, but significantly lower than previously estimated for VY CMa from
observations of lower-J lines. The spectral line energy distribution for twenty
SiO rotational lines shows two temperature components: a hot component at 1000
K, which we attribute to the stellar atmosphere and inner wind, plus a cooler
~200 K component, which we attribute to an origin in the outer circumstellar
envelope. We fit the line fluxes of 12CO, 13CO, H2O and SiO, using the SMMOL
non-LTE line transfer code, with a mass-loss rate of 1.85x10^-4 Msun yr^-1
between 9 R* and 350 R*. To fit the observed line fluxes of 12CO, 13CO, H2O and
SiO with SMMOL non-LTE line radiative transfer code, along with a mass-loss
rate of 1.85x10^-4 Msun yr^-1.
  To fit the high rotational lines of CO and H2O, the model required a rather
flat temperature distribution inside the dust condensation radius, attributed
to the high H2O opacity. Beyond the dust condensation radius the gas
temperature is fitted best by an r^-0.5 radial dependence, consistent with the
coolant lines becoming optically thin. Our H2O emission line fits are
consistent with an ortho:para ratio of 3 in the outflow.

Astrophysics of Galaxies;Solar and Stellar Astrophysics