The SNR of idealized radial velocity signals: RM curve grid based on Ohta+2005 and Hirano+2011 models

To derive the SNR equation for an ideal RM curve without second-order effects, including limb darkening, micro-turbulence, and macro-turbulence, we created an RM curve grid based on the Ohta+2005 and Hirano+2011 models. In the grid generation process, We fixed the projected stellar rotational velocity, vsini, to 3 km/s and transformed the limb-darkening coefficients, q1 and q2, to 0. For the Hirano+ model, the micro-turbulent and macro-turbulent velocities are set to 0. The grid spans sky-projected spin-orbit angles, lambda, from [0, 350] degrees in steps of 10 degrees, impact parameters, b, from [0,1] in steps of 0.1, and the base-2 logarithm of the ratio of the semi-major axis to the stellar radius, log_2(a/R_star) from [1, 8] in steps of 0.25. Thus, a total of 11,484 unique grid positions were defined. In each case, a/R_star and b are converted to T_14 and T_23 using the Seager & Mallen-Ornelas (2003) equations, assuming a circular orbit and a Solar bulk stellar density to obtain orbital period.