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One of the most important sources for the space-borne gravitational wavedetectors such as TianQin and LISA, is the merger of massivie black holebinaries. Using the inspiral signals, we can probe the properties of themassive black holes, such as the spin-induced multipole moments. By verifyingthe relation among the mass, spin and quadrupole moment, the no-hair theoreomcan be tested. In this work, we analysed the capability on probing thespin-induced quadrupole moment with the inspiral signal of massive black holebinaries using space-borne gravitational wave detectors. Using the Fisherinformation matrix, we find that the deviation of quadrupole moment can beconstrained to the level of $10^{-1}$, and the events with higher mass-ratiowill give a better constraint. We also find that the late inspiral part willdominate the result of parameter estimation. The result of Bayesian analysisshows that the capability will be improved by a few times due to theconsideration of higher modes. We also calculate the Bayes factor, and theresults indicate that the model of black hole and Boson star can bedistinguished undoubtedly.

Probing the Spin-Induced Quadrupole Moment of Massive Black Holes with the Inspiral of Binary Black Holes