We present Herschel SPIRE FTS spectroscopy of the nearby luminous infrared galaxy NGC 6240. In total 20 lines are detected, including CO J=4-3 through J=13-12, 6 H2O rotational lines, and [CI] and [NII] fine-structure lines. The CO to continuum luminosity ratio is 10 times higher in NGC 6240 than Mrk 231. Although the CO ladders of NGC 6240 and Mrk 231 are very similar, UV and/or X-ray irradiation are unlikely to be responsible for the excitation of the gas in NGC 6240. We applied both C and J shock models to the H2 v=1-0 S(1) and v=2-1 S(1) lines and the CO rotational ladder. The CO ladder is best reproduced by a model with shock velocity v_s=10 km s^-1 and a pre-shock density n_H=5 * 10^4 cm^-3. We find that the solution best fitting the H2 lines is degenerate: The shock velocities and number densities range between v_s = 17 - 47 km s^-1 and n_H=10^7 - 5 * 10^4 cm^-3, respectively. The H2 lines thus need a much more powerful shock than the CO lines. We deduce that most of the gas is currently moderately stirred up by slow (10 km s^-1) shocks while only a small fraction (< 1 percent) of the ISM is exposed to the high velocity shocks. This implies that the gas is rapidly loosing its highly turbulent motions. We argue that a high CO line-to-continuum ratio is a key diagnostic for the presence of shocks.
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