The Impact of Circumgalactic Rotation on Ly$\alpha$ Radiative Transfer

Abstract

Hydrogen Lyman-alpha (Ly$\alpha$) is a prominent emission line from the circumgalactic medium (CGM). Due to its resonant nature, Ly$\alpha$ carries imprints of the physical properties and kinematics of the cold CGM. In particular, CGM rotation can modify the Ly$\alpha$ peak separation, which is often interpreted as a tracer of H I column density. We present 3D Monte Carlo Ly$\alpha$ radiative-transfer simulations in a CGM-like rotating medium and examine how the emergent spectra depend on rotational velocity ($V_{\rm rot}$), H I column density ($N_{\rm HI}$), viewing angle, clumpiness, and intrinsic source width. We find that rotation broadens the integrated spectra and increases the peak separation, with the strongest viewing-angle dependence when rotational Doppler shifts dominate over frequency diffusion. At high $N_{\rm HI}$, numerous scatterings reduce the sensitivity of integrated spectra to rotation, producing a degeneracy between $V_{\rm rot}$ and $N_{\rm HI}$. Consequently, Ly$\alpha$ peak separation alone can overestimate $N_{\rm HI}$ in a rotating medium. Spatially resolved halo spectra provide a clearer diagnostic: opposite sides of the rotating medium show systematic redshifted and blueshifted asymmetries associated with the line-of-sight velocity of the last-scattering gas. Such rotation-driven signatures can also contribute to velocity-map patterns often interpreted in terms of inflow or outflow, highlighting the need to consider rotation in spatially resolved Ly$\alpha$ observations. We further show that the main signatures persist in simple clumpy media, while the halo signatures are largely insensitive to the intrinsic source width. Our results demonstrate that spatially resolved Ly$\alpha$ observation is essential for disentangling CGM rotation from radiative-transfer effects.