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Broadband velocity modulation spectroscopy of ThF$^+$ for use in a measurement of the electron electric dipole moment

A number of extensions to the Standard Model of particle physics predict a permanent electric dipole moment of the electron (eEDM) in the range of the current experimental limits. Trapped ThF$^+$ will be used in a forthcoming generation of the JILA eEDM experiment. Here, we present extensive survey spectroscopy of ThF$^+$ in the 700 - 1000 nm spectral region, with the 700 - 900 nm range fully covered using frequency comb velocity modulation spectroscopy. We have determined that the ThF$^+$ electronic ground state is $X$ $^3Δ_1$, which is the eEDM-sensitive state. In addition, we report high-precision rotational and vibrational constants for 14 ThF$^+$ electronic states, including excited states that can be used to transfer and readout population in the eEDM experiment.