Testing the Lense-Thirring Precession Origin of the QPO in Swift J1727.8$-$1613

We present a comprehensive spectral and timing analysis of the newly discovered black hole transient Swift J1727.8$-$1613, based on broadband (2$-$150 keV) observations from $Insight$-HXMT during its 2023 outburst. We use the flexible, energy-conserving SSsed model to model both the outer disc and inner, complex Comptonisation, using the expected disc emissivity to constrain the corona radius, $r_{cor}$. This decreases from 45 $R_{\rm g}$ to 9 $R_{\rm g}$ during the transition from the hard to hard intermediate and then soft intermediate state. We plot $r_{cor}$ versus the centroid frequency of the strong quasi-periodic oscillations (QPOs; $ν_{\rm c}$) seen in these data to test the inner hot flow Lense-Thirring (LT) precession model. The overall slope of the observed trend is in strong agreement with the predictions of LT precession, despite the complexities of accretion behavior, though there is an offset in absolute value which may indicate that the system parameters are still not well determined. The inner radius of the hot flow is consistent with a constant value throughout most of the outburst, indicating that changes in the jet (e.g. the discrete ejections) do not strongly affect the radiated power. Either the jet kinetic power is not a large fraction of the accretion power or the jet is instead mostly powered by the spin energy of the black hole.