Experimental study of the removal of excited state phosphorus atoms by H$_{2}$O and H$_{2}$: implications for the formation of PO in stellar winds

The reactions of the low-lying metastable states of atomic phosphorus, P($^2$D) and P($^2$P), with H$_{2}$O and H$_{2}$ were studied by the pulsed laser photolysis at 248 nm of PCl$_{3}$ , combined with laser induced fluorescence detection of P($^2$D), P($^2$P) and PO. Rate coefficients between 291 and 740 K were measured, along with a yield for the production of PO from P($^2$D or $^2$P) + H$_{2}$O of (35$\pm$15)%. H$_{2}$ reacts with both excited P states relatively efficiently; physical (i.e. collisional) quenching, rather than chemical reaction to produced PH + H, is shown to be the more likely pathway. A comprehensive phosphorus chemistry network is then developed using a combination of electronic structure theory calculations and a Master Equation treatment of reactions taking place over complex potential energy surfaces. The resulting model shows that at the high temperatures within two stellar radii of a MIRA variable AGB star in oxygen-rich conditions, collisional excitation of ground-state P($^4$S) to P($^2$D), followed by reaction with H$_{2}$O, is a significant pathway for producing PO (in addition to the reaction between P($^4$S) and OH). The model also demonstrates that the PN fractional abundance in a steady (non-pulsating) outflow is under-predicted by about 2 orders of magnitude. However, under shocked conditions where sufficient thermal dissociation of N$_2$ occurs at temperatures above 4000 K, the resulting N atoms convert a substantial fraction of PO to PN.