We survey the highly ionized circumgalactic media (CGM) of 29 blindly selected galaxies at 0.49 < z_(gal) < 1.44 based on high-S/N ultraviolet spectra of z > 1 QSOs and the galaxy database from the COS Absorption Survey of Baryon Harbors (CASBaH). We detect the Ne VIII doublet in nine of the galaxies, and for gas with N(Ne VIII) > 10^13.3 cm^-2 (> 10^13.5 cm^-2), we derive a Ne VIII covering fraction f_c = 75 +15/-25% (44 +22/-20%) within impact parameter (rho) < 200 kpc of M_* = 10^(9.5-11.5) Msol galaxies and f_c = 70 +16/-22% (f_c = 42 +20/-17%) within rho < 1.5 virial radii. We estimate the mass in Ne VIII-traced gas to be M_gas(Ne VIII) > 10^9.5 Msol (Z/Zsol)^-1, or 6-20% of the expected baryonic mass if the Ne VIII absorbers have solar metallicity. Ionizing Ne VII to Ne VIII requires 207 eV, and photons with this energy are scarce in the CGM. However, for the median halo mass and redshift of our sample, the virial temperature is close to the peak temperature for the Ne VIII ion, and the Ne VIII-bearing gas is plausibly collisionally ionized near this temperature. Moreover, we find that photoionized Ne VIII requires cool and low-density clouds that would be highly underpressured (by approximately two orders of magnitude) relative to the putative, ambient virialized medium, complicating scenarios where such clouds could survive. Thus, more complex (e.g., non-equilibrium) models may be required; this first statistical sample of Ne VIII absorber/galaxy systems will provide stringent constraints for future CGM studies.
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