Equilibrium States of Galactic Atmospheres. I. The Flip Side of Mass Loading

Abstract This paper presents a new framework for understanding the relationship between a galaxy and its circumgalactic medium (CGM). It focuses on how imbalances between heating and cooling cause either expansion or contraction of the CGM. It does this by tracking all of the mass and energy associated with a halo’s baryons, including their gravitational potential energy, even if feedback has pushed some of those baryons beyond the halo’s virial radius. We show how a star-forming galaxy’s equilibrium state can be algebraically derived within the context of this framework, and we analyze how the equilibrium star formation rate depends on supernova feedback. We consider the consequences of varying the mass loading parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>η</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≡</mml:mo> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>wind</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> </mml:math> relating a galaxy’s gas mass outflow rate ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>wind</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) to its star formation rate ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> </mml:math> ) and obtain results that challenge common assumptions. In particular, we find that equilibrium star formation rates in low-mass galaxies are generally insensitive to mass loading, and when mass loading does matter, increasing it actually results in more star formation because more supernova energy is needed to resist atmospheric contraction.