The acceptance-corrected dielectron excess mass spectra, where the known hadronic sources have been subtracted from the inclusive dielectron mass spectra, are reported for the first time at mid-rapidity $|y_{ee}|<1$ in minimum-bias Au+Au collisions at $sqrt{s_{NN}}$ = 19.6 and 200 GeV. The excess mass spectra are consistently described by a model calculation with a broadened $rho$ spectral function for $M_{ee}<1.1$ GeV/$c^{2}$. The integrated dielectron excess yield at $sqrt{s_{NN}}$ = 19.6 GeV for $0.4<M_{ee}<0.75$ GeV/$c^2$, normalized to the charged particle multiplicity at mid-rapidity, has a value similar to that in In+In collisions at $sqrt{s_{NN}}$ = 17.3 GeV. For $sqrt{s_{NN}}$ = 200 GeV, the normalized excess yield in central collisions is higher than that at $sqrt{s_{NN}}$ = 17.3 GeV and increases from peripheral to central collisions. These measurements indicate that the lifetime of the hot, dense medium created in central Au+Au collisions at $sqrt{s_{NN}}$ = 200 GeV is longer than those in peripheral collisions and at lower energies.
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