The universal acceleration scale from stellar feedback

It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale $g-{dagger }sim 10{-8}, rm {cm, s{-2}}$, a scale promoted to a new fundamental constant in MOND. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE ∼ς/ς_crit with $Sigma{rm crit} sim langle dot{p}/m-{ast }rangle /(pi , G)sim 1000, rm {M-{odot }, pc{-2}}$ (where $langle dot{p}/m-{ast }rangle$ is the momentum flux output by stellar feedback per unit stellar mass in a young stellar population). We argue that the SFE, more generally, should scale with the local gravitational acceleration, i.e. that SFE ${sim}g-{rm tot}/g-{rm crit}equiv (G, M-{rm tot}/R{2}) / langle dot{p}/m-{ast }rangle$, where M_tot is the total gravitating mass and $g-{rm crit}=langle dot{p}/m-{ast }rangle = pi , G, Sigma -{rm crit} approx 10{-8}, rm {cm, s{-2}} approx mathit{ g}-{dagger }$. Hence, the observed g_† may correspond to the characteristic acceleration scale above which stellar feedback cannot prevent efficient star formation, and baryons will eventually come to dominate. We further show how this may give rise to the observed acceleration scaling $g-{rm obs}sim (g-{rm baryon}, g-{dagger }){1/2}$ (where g_baryon is the acceleration due to baryons alone) and flat rotation curves. The derived characteristic acceleration g_† can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross-section): $g-{dagger }sim 0.1, G, m-{mathrm{ p}}/sigma -{rm T}$.