Lyman $\alpha$ Absorption as a Sensitive Probe of the H I Column in Cooling Flows

X-ray spectra of a significant fraction of cooling flow (CF) clusters of galaxies indicate the presence of a large column of ``cold'' absorbing gas. The physical nature of the absorbing medium remains a mystery. Searches for H I absorption using the 21 cm hyperfine structure line yielded null results in most cases. The purpose of this contribution is to point out that the Lyman $\alpha$ absorption cross section is ~10^7 times larger than for the 21 cm line, it can therefore be used as a very sensitive probe of the H I column in clusters, and can thus place stringent constraints on the nature of the X-ray absorber. This method is applied to the Perseus CF cluster where a medium resolution (~250 km/s) UV spectrum is available. The upper limit on the H I column obtained using Lyman $\alpha$ is at least ~50 times smaller than the 21 cm detection, and ~5,000 smaller than implied by X-ray spectra, indicating that the X-ray absorber is exceedingly devoid of H I. Higher resolution UV spectra with HST may improve the H I column limits by an additional factor of ~4,000. This method can be applied to strongly constrain the nature of the X-ray absorbing medium in a significant fraction of CF clusters .