Fermi and eROSITA Bubbles as Persistent Structures of the Milky Way

The Fermi and eROSITA bubbles, large diffuse structures in our Galaxy, can be the by-products of the steady star formation activity. To simultaneously explain the star formation history of the Milky Way and the metallicity of $\sim$ Z$_\odot$ at the Galactic disk, a steady Galactic wind driven by cosmic-rays is required. For tenuous gases with a density of $\lesssim$10$^{-3}$ cm$^{-3}$, the cosmic-ray heating dominates over radiative cooling, and the gas can maintain the virial temperature of $\sim$0.3 keV ideal for escape from the Galactic system as the wind. A part of the wind falls back onto the disk like a galactic fountain flow. We model the wind dynamics according to the Galactic evolution scenario and find that the scale height and surface brightness of the X-ray and the hadronic gamma-ray emissions from such fountain flow region can be consistent with the observed properties of the Fermi and eROSITA bubbles. This implies that the bubbles are persistent structures of the Milky Way existing over (at least) the last $\sim$1 Gyr, rather than evanescent structures formed by non-trivial, $\sim$10 Myr past Galactic Center transient activities.