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Strong Gravitational Lensing of Quasi-Kerr Compact Object with Arbitrary Quadrupole Moments

We study the strong gravitational lensing on the equatorial plane of a quasi-Kerr compact object with arbitrary quadrupole moments which can be used to model the super-massive central object of the galaxy. We find that, when the quadrupolar correction parameter $ξ$ takes the positive (negative) value, the photon-sphere radius $r_{ps}$, the minimum impact parameter $u_{ps}$, the coefficient $\bar{b}$, the relative magnitudes $r_m$ and the angular position of the relativistic images $θ_{\infty}$ are larger (smaller) than the results obtained in the Kerr black hole, but the coefficient $\bar{a}$, the deflection angle $α(θ)$ and the angular separation $s$ are smaller (larger) than that in the Kerr black hole. These features may offer a way to probe special properties for some rotating compact objects by the astronomical instruments in the future.