An Energetic Consistency Test for Feedback-Driven Gas Loss in Milky Way Dwarf Satellites

Abstract: Dwarf spheroidal galaxies (dSphs) contain little detectable cold gas, but the relative roles of stellar feedback, reionization, and environmental effects in their gas loss remain uncertain. We apply an order-of-magnitude energy-budget test to nine Milky Way dwarf satellites using published color--magnitude-diagram star formation histories (SFHs), galaxy-level velocity dispersions, effective radii, and integrated $V$-band luminosities. For each galaxy and halo prescription, we define the energy-equivalence time $τ<em>{\mathrm{E}}$, when a crossing exists, as the first elapsed time at which the cumulative effective energy from core-collapse supernovae equals the adopted gas binding energy. This quantity is an energetic diagnostic rather than a direct measurement of wind launch. Under the fiducial parameters, all nine galaxies reach the nominal threshold under the kinematic--size prescription K+B16, yet star formation often continues long after threshold crossing. We compare the corresponding lookback time $t</em>{\mathrm{E,lb}}$ with $t_{90,\mathrm{lb}}$, the lookback time at which 90\% of the total initial stellar mass had formed. Because both times are derived from the same cumulative SFH, their temporal proximity is interpreted descriptively rather than as independent evidence of feedback-driven quenching. Whether the threshold is reached depends on the adopted halo mass, radius, retained gas fraction, and supernova--gas coupling efficiency. These results distinguish the availability of sufficient cumulative feedback energy from the processes that determine the timing of quenching.