Fire and Ice in the Whirlpool: Spatially Resolved Scaling Relations between X-Ray-emitting Hot Gas and Cold Molecular Gas in M51

The cold and hot interstellar medium in star-forming galaxies resembles the reservoir for star formation and associated heating by stellar winds and explosions during stellar evolution, respectively. We utilize data from deep Chandra observations and archival millimeter surveys to study the interconnection between these two phases and the relation to star formation activities in M51 on kiloparsec scales. A sharp radial decrease is present in the hot gas surface brightness profile within the inner 2 kpc of M51. The ratio between the total infrared luminosity (LIR) and the hot gas luminosity ( L0.5-2keVgas ) shows a positive correlation with the galactic radius in the central region. For the entire galaxy, a twofold correlation is revealed in the L0.5-2keVgas -LIR diagram, where L0.5-2keVgas sharply increases with LIR in the center but varies more slowly in the disk. The best fit gives a steep relation of log(L0.5-2keVgas/ergs-1)=1.82log(LIR/L circle dot)+22.26 for the center of M51. The similar twofold correlations are also found in the L0.5-2keVgas -molecular line luminosity ( Lgas ' ) relations for the four molecular emission lines CO(1-0), CO(2-1), HCN(1-0), and HCO+(1-0). We demonstrate that the core-collapse supernovae (SNe) are the primary source of energy for heating gas in the galactic center of M51, leading to the observed steep L0.5-2keVgas -LIR and L0.5-2keVgas - Lgas ' relations, as their X-ray radiation efficiencies (eta equivalent to L0.5-2keVgas / ESN ) increase with the star formation rate surface densities (Sigma SFR), where ESN is the SN mechanical energy input rate.