Second Generation Stars in Globular Clusters from Rapid Radiative Cooling of Pre-Supernova Massive Star Winds

Following work by W\"unsch and collaborators, we investigate a self-enrichment scenario for second generation star formation in globular clusters wherein wind material from first generation massive stars rapidly radiatively cools. Radiative energy loss allows retention of fast winds within the central regions of clusters, where it fuels star formation. Secondary star formation occurs in $\sim3-5$ Myr, before supernovae, producing uniform iron abundances in both populations. We derive the critical criteria for radiative cooling of massive star winds and the second generation mass as a function of cluster mass, radius, and metallicity. We derive a critical condition on $M/R$, above which second generation star formation can occur. We speculate that above this threshold the strong decrease in the cluster wind energy and momentum allows ambient gas to remain from the cluster formation process. We reproduce large observed second generation fractions of $\sim30-80\%$ if wind material mixes with ambient gas. Importantly, the mass of ambient gas required is only of order the first generation's stellar mass. Second generation helium enrichment $\Delta Y$ is inversely proportional to mass fraction in the second generation; a large second generation can form with $\Delta Y\sim0.001-0.02$, while a small second generation can reach $\Delta Y\sim0.16$. Like other self-enrichment models for the second generation, we are not able to simultaneously account for both the full range of the Na-O anticorrelation and the second generation fraction.