Zusammenfassung
We analyze the equivalent widths of HI Ly-$\alpha$ ($W_Ly\alpha$) from the
inner (R < 160 kpc) circumgalactic medium (CGM) of 85 galaxies at $z 0$
with stellar masses $M*$ ranging $8 log M* / M_ødot 11.6$. Across
three orders of magnitude in stellar mass, the CGM of present-day galaxies
exhibits a very high covering fraction of cool hydrogen gas ($f_C = 86.6 \pm
3.6$%) indicating that the CGM is ubiquitous in modern, isolated galaxies.
These same galaxies show a decline in $W_Ly\alpha$ with increasing radius,
independent of mass, but the scatter in this trend correlates closely with
$M*$. Using the radial and stellar mass correlations, we construct a
fundamental plane describing the cool CGM of modern galaxies: $W^s_HI
1215 \; = \; (0.34 0.02) -( 0.0026 0.0005)*(R) + (0.286 0.002)*
(M_*/M_ødot)$. The RMS scatter around this bivariate relation is
$\sim$0.2 dex. We interpret the explicit correlation between $W_Ly\alpha$ and
$M*$ to arise from the underlying dark matter halo, i.e., $W_Ly\alpha$ traces
the gravitational potential whereas $M*$ tracks $M_halo$.
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