A Short-Timescale Optical Quasi-Periodic Oscillation in PKS\,0805$-$07 from High-Cadence TESS Observations

We present a timing analysis of the high-cadence optical light curve of the high-redshift flat-spectrum radio quasar PKS,0805$-$07 obtained during $\mathit{\text{TESS}}$ Sector~34 (MJD $59230.90$–$59239.90$). We search for short-timescale quasi-periodic oscillations (QPOs) using complementary time-series techniques, including the Lomb–Scargle periodogram (LSP) and the weighted wavelet $Z$-transform (WWZ), and evaluate their significance against red-noise variability using Monte Carlo simulations. The LSP reveals a dominant modulation at $f\approx 0.597{\mathrm{d}}^{-1}$ ($P\approx 1.7\mathrm{d}$) exceeding the $99.99\mathrm{\%}$ confidence level, while the WWZ independently recovers a consistent timescale at the $\sim 99.9\mathrm{\%}$ level and shows that the signal is temporally localized rather than persistent across the full light curve. The modulation spans $\sim 5$ coherent cycles, indicating a transient quasi-periodic feature. We discuss possible physical interpretations of the detected modulation. In a disk-based scenario, orbital motion of a hotspot near the innermost stable circular orbit implies a black hole mass of $M_{\mathrm{B}\mathrm{H}}\sim 7.2\times {10}^8{M}_{\odot }$, consistent with typical FSRQ values. Alternatively, magnetohydrodynamic kink instabilities in the relativistic jet can naturally produce day-scale variability for standard blazar parameters and account for the transient character of the signal. We conclude that the observed modulation is consistent with a compact, short-lived structure embedded within stochastic jet variability.