  The majority of baryons reside beyond the optical extent of a galaxy in the
circumgalactic and intergalactic media (CGM/IGM). Gaseous halos are
inextricably linked to the appearance of their host galaxies through a complex
story of accretion, feedback, and continual recycling. The energetic processes,
which define the state of gas in the CGM, are the same ones that 1) regulate
stellar growth so that it is not over-efficient, and 2) create the diversity of
today's galaxy colors, SFRs, and morphologies spanning Hubble's Tuning Fork
Diagram. They work in concert to set the speed of growth on the star-forming
Main Sequence, transform a galaxy across the Green Valley, and maintain a
galaxy's quenched appearance on the Red Sequence. Most baryons in halos more
massive than 10^12 Msolar along with their high-energy physics and dynamics
remain invisible because that gas is heated above the UV ionization states. We
argue that information on many of the essential drivers of galaxy evolution is
primarily contained in this "missing" hot gas phase. Completing the picture of
galaxy formation requires uncovering the physical mechanisms behind stellar and
SMBH feedback driving mass, metals, and energy into the CGM. By opening
galactic hot halos to new wavebands, we not only obtain fossil imprints of >13
Gyrs of evolution, but observe on-going hot-mode accretion, the deposition of
superwind outflows into the CGM, and the re-arrangement of baryons by SMBH
feedback. A description of the flows of mass, metals, and energy will only be
complete by observing the thermodynamic states, chemical compositions,
structure, and dynamics of T>=10^6 K halos. These measurements are uniquely
possible with a next-generation X-ray observatory if it provides the
sensitivity to detect faint CGM emission, spectroscopic power to measure
absorption lines and gas motions, and high spatial resolution to resolve
structures.
