From Common Envelope Evolution to Luminous Red Novae I: A One-dimensional Radiation Hydrodynamic Model

The acceleration and unbinding of the common envelope during the plunge-in phase are governed by complex physical processes that often manifest observationally as luminous red novae. We investigate the dynamics of this phase using one-dimensional radiation hydrodynamic simulations evolved with the code {\tt Guangqi}. We perform a parameter survey to quantify the impact of key physical conditions on the unbound mass fraction, $\eta$, and the resulting light curves. Our survey spans a range of radiation-to-gas internal energy ratios ($\mathcal{E}/e_{\text{g}}\in[0.2,3.2]$), ratios of total envelope energy to gravitational binding energy ($\zeta\in[0.54,2.87]$), and mass injection rates ($\dot{M}\in[2.5,10]M_{\odot}/\rm{yr}$), while covering both subsonic and supersonic expansion regimes ($v_{\rm ej}/v_{\rm esc}\in[0.3,0.6]$). We demonstrate that: (1) radiation pressure becomes the dominant driver of mass ejection in the high-opacity, high-luminosity region immediately below the recombination front; (2) $\eta$ exhibits a nonlinear dependence on $\zeta$, which is modulated by the mass injection rate and gravitational potential; and (3) the recombination of atomic to molecular hydrogen ($\ce{H}\to\ce{H2}$) releases latent heat that sustains a secondary plateau in the late-time light curve. These findings are substantiated by detailed error analysis and convergence testing presented in the Appendices.