Stellar feedback sets the universal acceleration scale in galaxies

Abstract

It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale g†∼10⁻⁸ 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 Σ_(crit)∼⟨p˙/m∗⟩/(πG)∼1000 M_⊙ pc⁻² (where ⟨p˙/m∗⟩ 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 ∼g_(tot)/g_(crit) ≡ (GM_(tot)/R²)/⟨p˙/m∗⟩⁠, where M_(tot) is the total gravitating mass and g_(crit) = ⟨p˙/m∗⟩ = πGΣ_(crit) ≈ 10⁻⁸ cm s⁻² ≈ g†. 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_(obs) ∼ (g_(baryon)g†)^(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†∼0.1Gmp_/σ_T⁠.

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