Estimating LuSEE-Night's Sensitivity to Cα Radio Recombination Lines
Carbon radio recombination lines (CRRLs) arising from the cold neutral medium (CNM) of the interstellar medium are potential foregrounds in the 1-50 MHz band that LuSEE-Night will observe from the lunar far side. CRRLs are sensitive probes of the temperature, density, and radiation field of the CNM, and LuSEE-Night will provide sky-averaged measurements in a poorly explored frequency range. We model CRRLs across this band, accounting for doppler, collisional, and radiation broadening, and we estimate line strengths using two independent methods - fixing either the peak or the frequency-integrated optical depth - applied both uniformly across the sky and with region-dependent values informed by prior low-frequency observations. We simulate LuSEE-Night's expected response to these CRRLs and further convolve the beam-diluted spectra with LuSEE-Night's polyphase-filter-bank spectrometer response, including its zoomed-mode frequency resolution of $\sim$390 Hz, to obtain the expected observed brightness temperature. Using these simulated spectra, we estimate the integration time required to detect individual CRRLs at SNR=5 across the six sky models considered. Required integration times range from as short as 30 hours (in the most optimistic model where the optical depth across the sky is $\sim$10$^{-3}$) to 27.6 years (in the most conservative models where the optical depth across the sky is $\sim$10$^{-4}$). Stacking the 361 simulated C$α$ lines between 10 and 50 MHz reduces the integration time needed for an SNR=5 detection to $\sim$11 minutes and $\sim$151 hours respectively, indicating that LuSEE-Night has realistic chances of making a stacked detection of C$α$ RRLs within a realistic mission lifetime, even under the most conservative optical-depth assumptions.