ExoMol line lists -- LII. Line Lists for the Methylidyne Cation (CH+)

Comprehensive and accurate rovibronic line lists for the X $^{1}\Sigma^{+}$ and A $^{1}\Pi$ states of $^{12}$C$^{1}$H$^{+}$ and $^{13}$C$^{1}$H$^{+}$ which should be applicable up to temperatures of 5000 K are presented. Available empirical potential energy curves and high-level ab initio dipole and transition dipole moment curves are used with the program LEVEL to compute rovibronic energy levels and Einstein $A$ coefficients. $\Lambda$-doubling is incorporated into the energy levels and $A$-coefficients involving the A $^{1}\Pi$ state using an empirical method. For $^{12}$C$^{1}$H$^{+}$, line positions are improved by using both laboratory and astronomical observational spectra as input to the MARVEL procedure. The $^{12}$C$^{1}$H$^{+}$ line list contains 1505 states and 34194 transitions over the frequency range of 0 - 33010 cm$^{-1}$ ($\lambda > 300$ nm). Comparisons with observed astronomical and laboratory spectra give very good agreement. The PYT CH$^{+}$ line lists and partition functions are available from the ExoMol database at www.exomol.com.