Parameter Effects on the Total Intensity of H i Ly\(\alpha \) Line for a Modeled Coronal Mass Ejection and Its Driven Shock

The combination of the H i Ly $\alpha$ $\alpha $ (121.6 nm) line formation mechanism with ultraviolet (UV) Ly $\alpha$ $\alpha $ and white-light (WL) observations provides an effective method for determining the electron temperature of coronal mass ejections (CMEs). A key to ensuring the accuracy of this diagnostic technique is the precise calculation of theoretical Ly $\alpha$ $\alpha $ intensities. This study performs a modeled CME and its driven shock via the three-dimensional numerical magneto-hydrodynamic simulation. Then, we generate synthetic UV and WL images of the CME and shock within a few solar radii to quantify the impact of different assumptions on the theoretical Ly $\alpha$ $\alpha $ intensities, such as the incident intensity of the solar chromospheric Ly $\alpha$ $\alpha $ line ( $I_{disk}$ $I_{disk}$ ), the geometric scattering function ( $p(\theta )$ $p(\theta )$ ), and the kinetic temperature ( $T_{\mathit{n}}$ $T_{ \boldsymbol{n}}$ ) assumed to be equal to either the proton ( $T_p$ $T_{p}$ ) or electron ( $T_e$ $T_{e}$ ) temperature. By comparing differences of the Ly $\alpha$ $\alpha $ intensities of the CME and shock under these assumptions, we find that: (1) Using the uniform or Carrington maps of the disk Ly $\alpha$ $\alpha $ emission underestimates the corona Ly $\alpha$ $\alpha $ intensity (with relative uncertainties below 10%) compared to the synchronic map, except for a slight overestimate (<4%) observed in the partial CME core. The Carrington map yields lower uncertainties than the uniform disk. (2) Neglecting the geometric scattering process has a relatively minor impact on the Ly $\alpha$ $\alpha $ intensity, with a maximum relative uncertainty of no more than 5%. The Ly $\alpha$ $\alpha $ intensity is underestimated for the most part but overestimated in the CME core. (3) Compared to the assumption $T_{\mathit{n}}=T_p$ $T_{\boldsymbol{n}}=T_{p}$ , using $T_{\mathit{n}}=T_e$ $T_{\boldsymbol{n}}=T_{e}$ leads to more complex relative uncertainties in CME Ly $\alpha$ $\alpha $ intensity. The CME core and void are both overestimated, with the maximum relative uncertainty in the core exceeding 50% and in the void remaining below 35%. An appropriate increasing proton-to-electron temperature ratio can reduce the uncertainty in the CME core and void. In the CME front, both overestimates and underestimates exist with relative uncertainties of less than 35%. The electron temperature assumption has a smaller impact on the shock, with an underestimated relative uncertainty of less than 20%.