# Stellar feedback sets the universal acceleration scale in galaxies

Michael Y. Grudić*, Michael Boylan-Kolchin, Claude André Faucher-Giguère, Philip F. Hopkins

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

## 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-type theories. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE ∼ Σ/Σcrit with Σcrit ∼ (pÛ/m)/(π2 G) ∼ 1000 M pc−2 (where pÛ/m is the momentum flux output by stellar feedback per unit stellar mass formed). We show that the star formation efficiency, more correctly, scales with the gravitational acceleration, i.e. that SFE ∼ gtot/gcrit ≡ (G Menc/R2)/([pÛ/m]/π), where Menc(< r) is the total gravitating mass and gcrit = (pÛ/m)/π = π G Σcrit ≈ 10−8 cm s−2 ≈ g†. It follows that the characteristic galactic acceleration g corresponds to the acceleration scale above which SF is 'efficient' (and outflows 'inefficient'), and so baryons inevitably dominate the mass. This also explains the “deep MOND” scaling gobs ∼ (gbaryon g)1/2 (where gbaryon is the acceleration due to baryons alone) apparent at low accelerations. We further show that g can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross-section): g ∼ 0.1 G mp/σT.

Original language English (US) Unknown Journal Published - Oct 14 2019

## Keywords

• Cosmology: dark matter
• Galaxies: evolution
• Galaxies: formation

• General