Context : The Spitzer Space Telescope has detected a powerful ( L _ { H _ { 2 } } \sim 10 ^ { 41 } erg s ^ { -1 } ) mid-infrared H _ { 2 } emission towards the galaxy-wide collision in the Stephan ’ s Quintet ( SQ ) galaxy group .
This discovery was followed by the detection of more distant H _ { 2 } -luminous extragalactic sources , with almost no spectroscopic signatures of star formation .
These observations place molecular gas in a new context where one has to describe its role as a cooling agent of energetic phases of galaxy evolution .

Aims : The SQ postshock medium is observed to be multiphase , with H _ { 2 } gas coexisting with a hot ( \sim 5 \times 10 ^ { 6 } K ) , X-ray emitting plasma .
The surface brightness of H _ { 2 } lines exceeds that of the X-rays and the 0-0 S ( 1 ) H _ { 2 } linewidth is \sim 900 km s ^ { -1 } , of the order of the collision velocity .
These observations raise three questions we propose to answer : ( i ) Why H _ { 2 } is present in the postshock gas ? ( ii ) How can we account for the H _ { 2 } excitation ? ( iii ) Why is H _ { 2 } a dominant coolant ?

Methods : We consider the collision of two flows of multiphase dusty gas .
Our model quantifies the gas cooling , dust destruction , H _ { 2 } formation and excitation in the postshock medium .

Results : ( i ) The shock velocity , the post-shock temperature and the gas cooling timescale depend on the preshock gas density .
The collision velocity is the shock velocity in the low density volume filling intercloud gas .
This produces a \sim 5 \times 10 ^ { 6 } ~ { } K , dust-free , X-ray emitting plasma .
The shock velocity is smaller in clouds .
We show that gas heated to temperatures less than 10 ^ { 6 } ~ { } K cools , keeps its dust content and becomes H _ { 2 } within the SQ collision age ( \sim 5 \times 10 ^ { 6 } ~ { } years ) . ( ii ) Since the bulk kinetic energy of the H _ { 2 } gas is the dominant energy reservoir , we consider that the H _ { 2 } emission is powered by the dissipation of kinetic turbulent energy .
We model this dissipation with non-dissociative MHD shocks and show that the H _ { 2 } excitation can be reproduced by a combination of low velocities ( in the range 5 - 20 km s ^ { -1 } ) shocks within dense ( n _ { H } > 10 ^ { 3 } ~ { } cm ^ { -3 } ) H _ { 2 } gas . ( iii ) An efficient transfer of the bulk kinetic energy to turbulent motions of much lower velocities within molecular gas is required to make H _ { 2 } a dominant coolant of the postshock gas .
We argue that this transfer is mediated by the dynamical interaction between gas phases and the thermal instability of the cooling gas .
We quantify the mass and energy cycling between gas phases required to balance the dissipation of energy through the H _ { 2 } emission lines .

Conclusions : This study provides a physical framework to interpret H _ { 2 } emission from H _ { 2 } -luminous galaxies .
It highlights the role that H _ { 2 } formation and cooling play in dissipating mechanical energy released in galaxy collisions .
This physical framework is of general relevance for the interpretation of observational signatures , in particular H _ { 2 } emission , of mechanical energy dissipation in multiphase gas .