High-resolution far-infrared and sub-millimetre spectroscopy of water lines is an important tool to understand the physical and chemical properties of cometary atmospheres .
We present observations of several rotational ortho- and para-water transitions in comet C/2008 Q3 ( Garradd ) performed with HIFI on Herschel .
These observations have provided the first detection of the 2 _ { 12 } – 1 _ { 01 } ( 1669 GHz ) ortho and 1 _ { 11 } – 0 _ { 00 } ( 1113 GHz ) para transitions of water in a cometary spectrum .
In addition , the ground-state transition 1 _ { 10 } – 1 _ { 01 } at 557 GHz is detected and mapped .
By detecting several water lines quasi-simultaneously and mapping their emission we can constrain the excitation parameters in the coma .
Synthetic line profiles are computed using excitation models which include excitation by collisions , solar infrared radiation , and radiation trapping .
We obtain the gas kinetic temperature , constrain the electron density profile , and estimate the coma expansion velocity by analyzing the map and line shapes .
We derive water production rates of 1.7 \textrm { - - } 2.8 \times 10 ^ { 28 } \mathrm { s } ^ { -1 } over the range r _ { \mathrm { h } } = 1.83 – 1.85 AU .