Simulating the diversity of shapes of the Lyman-$\alpha$ line

The Ly$\alpha$ line is a powerful probe of distant galaxies, which contains information about inflowing/outflowing gas through which Ly$\alpha$ photons scatter. To develop our understanding of this probe, we post-process a zoom-in radiation-hydrodynamics simulation of a low-mass ($M_* \sim 10^9 M_\odot$) galaxy to construct 22500 mock spectra in 300 directions from $z = 3$ to 4. Remarkably, we show that one galaxy can reproduce the variety of a large sample of spectroscopically observed Ly$\alpha$ line profiles. While most mock spectra exhibit double-peak profiles with a dominant red peak, their shapes cover a large parameter space in terms of peak velocities, peak separation and flux ratio. This diversity originates from radiative transfer effects at ISM and CGM scales, and depends on galaxy inclination and evolutionary phase. Red-dominated lines preferentially arise in face-on directions during post-starburst outflows and are bright. Conversely, accretion phases usually yield symmetric double peaks in the edge-on direction and are fainter. While resonant scattering effects at $< 0.2\times R_{\rm vir}$ are responsible for the broadening and velocity shift of the red peak, the extended CGM acts as a screen and impacts the observed peak separation. The ability of simulations to reproduce observed Ly$\alpha$ profiles and link their properties with galaxy physical parameters offers new perspectives to use Ly$\alpha$ to constrain the mechanisms that regulate galaxy formation and evolution. Notably, our study implies that deeper Ly$\alpha$ surveys may unveil a new population of blue-dominated lines tracing inflowing gas.