The characteristics of circular motion and quasiperiodic oscillations around accelerating black hole

{This study explores the motion of massive test particles and associated quasi-periodic oscillations (QPOs) around an accelerating black hole. The acceleration factor $A$ suppresses the radial effective potential $V_{\text{eff}}$, thereby lowering the energy $E$ and angular momentum $L$ required for stable circular orbits. Stability demands $\partial_r^2 V_{\text{eff}} \geq 0$, setting an upper bound $AM$ $\leq 0.0161$. As $A$ increases, the innermost stable circular orbit (ISCO) radius grows, while $L_{\text{ISCO}}$ and $E_{\text{ISCO}}$ decrease. Radiative efficiency $ε$ rises with $A$, peaking at $6.9\%$. Fundamental frequencies show that $A$ accelerates the decay of the Keplerian $Ω_ϕ$ and vertical $Ω_θ$ frequencies, while suppressing the radial frequency. The divergence between $Ω_θ$ and $Ω_ϕ$ increases with $A$, differing from spherical black hole behavior. Using the RP, ER3, ER4, and WD QPO models, the WD model predicts the highest frequencies. The resonant radius of ER4 model remains fixed across frequency ratios, unlike ER3. Although $A$ suppresses twin-peak QPO frequencies, it enhances the nodal precession frequency $ν_{\text{nod}}$. Fitting observational data from GRO J1655-40 and XTE J1859+226 and applying the TOV limit, the ER4 model uniquely fits GRO J1655-40 with $(10^3A, M, r/M) \approx (4.31, 3.43 M_\odot, 8.08)$. For XTE J1859+226, three models yield $10^3A \approx 1.4$, excluding ER3, suggesting stronger acceleration in GRO J1655-40.}