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The COS-Halos Survey: Physical Conditions and Baryonic Mass in the Low-Redshift Circumgalactic Medium

We analyze the physical conditions of the cool, photoionized (T $\sim 10^4$ K) circumgalactic medium (CGM) using the COS-Halos suite of gas column density measurements for 44 gaseous halos within 160 kpc of $L \sim L^*$ galaxies at $z \sim 0.2$. These data are well described by simple photoionization models, with the gas highly ionized (n$_{\rm HII}$/n$_{\rm H} \gtrsim 99\%$) by the extragalactic ultraviolet background (EUVB). Scaling by estimates for the virial radius, R$_{\rm vir}$, we show that the ionization state (tracked by the dimensionless ionization parameter, U) increases with distance from the host galaxy. The ionization parameters imply a decreasing volume density profile n$_{\rm H}$ = (10$^{-4.2 \pm 0.25}$)(R/R$_{\rm vir})^{-0.8\pm0.3}$. Our derived gas volume densities are several orders of magnitude lower than predictions from standard two-phase models with a cool medium in pressure equilibrium with a hot, coronal medium expected in virialized halos at this mass scale. Applying the ionization corrections to the HI column densities, we estimate a lower limit to the cool gas mass M$_{\rm CGM}^{\rm cool} > 6.5 \times 10^{10}$ M$_{\odot}$ for the volume within R $<$ R$_{\rm vir}$. Allowing for an additional warm-hot, OVI-traced phase, the CGM accounts for at least half of the baryons purported to be missing from dark matter halos at the 10$^{12}$ M$_{\odot}$ scale.