Sensitivity of 1670 GHz east and west limb line profiles to (top) torus central position and (bottom) gas dispersion velocity. Top: model calculations, performed here for a radially infinitely narrow torus located at 2, 3, 4, and 6 Saturn radii (R_S), confirm that the absorbing material is located near 4 R_S, and not e.g. in Saturn’s main rings at  <2 R_S. Bottom: model calculations for several values of molecule dispersion velocity V_rms. Best fits are obtained for V_rms = 2.3 km s^-1 (resp. 2.0 km s^-1) for the east (resp. west) limb spectrum. Dynamically colder models with V_rms = 0.8 km s^-1 or V_rms = 0.5 km s^-1 (typical of plume material ejection conditions) produce too narrow absorptions.

Additional model fits of the 1670 GHz north, center and south observations. Determination of the torus vertical scale height H. Assuming that the column density falls as N(z) = N_eq e^−z/H, where z is the distance from the equatorial plane, the red, green, and dark blue curves correspond to H = 0.8, 0.4, and 0.2 R_S, and N_eq = (2.5, 4, 8) × 10¹³ cm^-2, respectively. The lower absorption in the northern spectrum compared to center and south indicates that R_S. Test of a physical model. The light blue curves are based on the distribution of N_H2O predicted from the Cassidy & Johnson (2010) model for a 0.85 × 10²⁸ s^-1 Enceladus source rate (and shown in the left panel of Fig. 3, main text). This model provides an overall good match of all H₂O lines, including the sorth-south asymmetry. Although not shown here, this physical model also gives a good match of the 557 and 1113 GHz absorption, and also underestimates the 987 GHz absorption by a factor  ~1.7.