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Limited by the sensitivities of the current gravitational wave (GW)detectors, the central remnant of the binary neutron star (NS) mergerassociated with GW170817 remains an open question. Considering the relativelylarge total mass, it is generally proposed that the merger of GW170817 wouldlead to a shortly lived hypermassive NS or directly produce a black hole (BH).There is no clear evidence to support or rule out a long-lived NS as the mergerremnant. Here we utilize the GW and electromagnetic (EM) signals tocomprehensively investigate the parameter space that allows a long-lived NS tosurvive as the merger remnant of GW170817. We find that for some stiffequations of state, the merger of GW170817 could, in principle, lead to amassive NS, which has a millisecond spin period. The post-merger GW signalcould hardly constrain the ellipticity of the NS. If the ellipticity reaches$10^{-3}$, in order to be compatible with the multi-band EM observations, thedipole magnetic field of the NS ($B_p$) is constrained to the magnetar level of$\sim10^{14}$ G. If the ellipticity is smaller than $10^{-4}$, $B_p$ isconstrained to the level of $\sim10^{10}-10^{12}\,$G. These conclusions weaklydepend on the adoption of equations of state.

The allowed parameter space of a long-lived neutron star as the merger remnant of GW170817