Spatially-Resolved Dense Molecular Gas and Star Formation Rate in M51

We present the spatially-resolved observations of HCN J = 1 -- 0 emission in the nearby spiral galaxy M51 using the IRAM 30 m telescope. The HCN map covers an extent of $4\arcmin\times5\arcmin$ with spatial resolution of $28\arcsec$, which is, so far, the largest in M51. There is a correlation between infrared emission (star formation rate indicator) and HCN (1--0) emission (dense gas tracer) at kpc scale in M51, a natural extension of the proportionality between the star formation rate (SFR) and the dense gas mass established globally in galaxies. Within M51, the relation appears to be sub-linear (with a slope of 0.74$\pm$0.16) as $L_{\rm IR}$ rises less quickly than $L_{\rm HCN}$. We attribute this to a difference between center and outer disk such that the central regions have stronger HCN (1--0) emission per unit star formation. The IR-HCN correlation in M51 is further compared with global one from Milky Way to high-z galaxies and bridges the gap between giant molecular clouds (GMCs) and galaxies. Like the centers of nearby galaxies, the $L_{\rm IR}$/$L_{\rm HCN}$ ratio measured in M51 (particularly in the central regions), is slightly lower than what is measured globally in galaxies, yet is still within the scatter. This implies that though the $L_{\rm IR}$/$L_{\rm HCN}$ ratio varies as a function of physical environment in the different positions of M51, IR and HCN indeed show a linear correlation over 10 orders of magnitude.