Turbulent gas-rich discs at high redshift: origin of thick stellar discs through 3D 'baryon sloshing'

In response to recent observations from JWST and ALMA, we explore a new class of dynamically self-consistent models using our AGAMA/Ramses hydrodynamic N-body framework (Nexus) that mimics a plausible progenitor of the Milky Way over a wide range of disc gas fractions ($f_{\rm gas} = 0-100\%$). The high gas surface densities encourage vigorous star formation, which in turn couples with the gas to drive turbulence. We show that this coupling through momentum recoil drives 'baryon sloshing,' i.e. a random walk of the baryonic potential minimum with respect to the centre of the total gravitational potential, $\Phi_{\rm tot}$. The amplitude of the bulk motion depends on the strength of the feedback, which in turn is directly associated with $f_{\rm gas}$. At its most extreme, when gas is the sole contributor to the disc potential ($f_{\rm gas}=100$%), the amplitude of the walk can reach up to $R\approx 5$ kpc and $\vert z\vert \approx 1$ kpc within $\Phi_{\rm tot}(R,\phi,z)$. Consistent with observations, the disc dominates over dark matter ($f_{\rm disc}\gtrsim 50$%) within $R_s=2.2 R_{\rm disc}$, where $R_{\rm disc}$ is the exponential disc scale length. For a lower $f_{\rm disc}$ and/or $f_{\rm gas}$, the 3D sloshing amplitude and velocity are reduced. The combination of strong feedback (which unbinds the disc) and sloshing leads to the newly formed stars being dynamically heated and settling to a more spatially extended disc population. The 3D heating process is isotropic but its effects are more noticeable in $\vert z\vert$ due to the initial dynamical coldness of the star-forming disc. Such a disc has enhanced [$\alpha$/Fe] stellar abundances and a vertical (but no radial) gradient in stellar age and metallicity, both consistent with the Milky Way's thick stellar disc. Contrary to earlier claims, star formation in a stationary turbulent disc does $not$ produce thick stellar discs.