We present results of a spectroscopic survey for new K- and M-type members of Scorpius-Centaurus (Sco-Cen), the nearest OB Association (~100-200 pc). Using an X-ray, proper motion and color-magnitude selected sample, we obtained spectra for 361 stars, for which we report spectral classifications and Li and Halpha equivalent widths. We identified 156 new members of Sco-Cen, and recovered 51 previously published members. We have combined these with previously known members to form a sample of 493 solar-mass (~0.7-1.3 Msun) members of Sco-Cen. We investigated the star-formation history of this sample, and re-assessed the ages of the massive main-sequence turn-off and the G-type members in all three subgroups. We performed a census for circumstellar disks in our sample using WISE infrared data and find a protoplanetary disk fraction for K-type stars of 4.4$^{+1.6}_{-0.9}$% for Upper Centaurus-Lupus and Lower Centaurus-Crux at ~16 Myr and 9.0$^{+4.0}_{-2.2}$% for Upper Scorpius at ~10 Myr. These data are consistent with a protoplanetary disk e-folding timescale of ~4-5 Myr for ~1 Msun stars, twice that previously quoted (Mamajek 2009), but consistent with the Bell et al. revised age scale of young clusters. Finally, we construct an age map of Scorpius-Centaurus which clearly reveals substructure consisting of concentrations of younger and older stars. We find evidence for strong age gradients within all three subgroups. None of the subgroups are consistent with being simple, coeval populations which formed in single bursts, but likely represents a multitude of smaller star formation episodes of hundreds to tens of stars each.
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