Measurement and assignment of $\it{J}$ $\geq$ 10 rotational energy levels in the 9510 to 9810 cm$^{-1}$ and 6590 to 6900 cm$^{-1}$ ranges of methane using optical frequency comb double-resonance spectroscopy

Accurate models of high temperature methane spectra are needed in astrophysics.

Previous measurements of methane hot-band transitions in the $\it{P}$6 $\leftarrow$ $\it{P}$2 polyad range have been limited to final rotational numbers of $\it{J}$ $\le$ 9, with theoretical predictions at higher $\it{J}$s remaining unvalidated.

Here, we use optical-optical double resonance spectroscopy (OODR) with a 3.3 ${\mu}$m narrow linewidth pump to excite the ${\nu}$${_3}$ P(12, A${_1}$$^{(2)}$) methane transition ($\it{P}$2 $\leftarrow$ $\it{P}$0) and a cavity-enhanced frequency comb centered around 1.68 ${\mu}$m to probe the sub-Doppler ladder-type ($\it{P}$6 $\leftarrow$ $\it{P}$2) and V-type ($\it{P}$4 $\leftarrow$ $\it{P}$0) transitions, as well as Doppler-broadened collision-induced four-level transitions ($\it{P}$6 $\leftarrow$ $\it{P}$2).

49 ladder-type transitions with final rotational states $\it{J}$ = 10-12 in the range of 9510 to 9810 cm$^{-1}$ (i.e., the $\it{P}$6 polyad) were assigned to effective Hamiltonian predictions and the ExoMol database, of which 6 reached vibrational states that had not been observed experimentally before.

19 sub-Doppler V-type transitions with final states $\it{J}$ = 11-13 in the range of 6590 to 6900 cm$^{-1}$ (i.e., the $\it{P}$4 polyad) were observed and assigned to the Hamiltonian and ExoMol, while only 2 of these V-type transitions could be unambiguously assigned to WKLMC and HITRAN line lists.

170 Doppler-broadened four-level double-resonance (4LDR) lines were observed, 7 of which were newly observed compared with our previous work when pumping transitions starting from the $\it{J}$ = 7 level in the ground state [Lehmann et al., J.

Chem.

Phys.

163, 144304 (2025)].

We could not assign these lines as they did not form combination differences with other observed 4LDR transitions.