Galaxy Structure, Stellar Populations, and Star Formation Quenching at 0.6 ≲ z ≲ 1.2

We use both photometric and spectroscopic data from the {\it Hubble Space Telescope} to explore the relationships among 4000 \AA\ break (D4000) strength, colors, stellar masses, and morphology, in a sample of 352 galaxies with log$(M_{*}/M_{\odot}) > 9.44$ at 0.6 $\lesssim z \lesssim$ 1.2. We have identified authentically quiescent galaxies in the $UVJ$ diagram based on their D4000 strengths. This spectroscopic identification is in good agreement with their photometrically-derived specific star formation rates (sSFR). Morphologically, most (that is, 66 out of 68 galaxies, $\sim$ 97 \%) of these newly identified quiescent galaxies have a prominent bulge component. However, not all of the bulge-dominated galaxies are quenched. We found that bulge-dominated galaxies show positive correlations among the D4000 strength, stellar mass, and the S\'ersic index, while late-type disks do not show such strong positive correlations. Also, bulge-dominated galaxies are clearly separated into two main groups in the parameter space of sSFR vs. stellar mass and stellar surface density within the effective radius, $\Sigma_{\rm e}$, while late-type disks and irregulars only show high sSFR. This split is directly linked to the `blue cloud' and the `red sequence' populations, and correlates with the associated central compactness indicated by $\Sigma_{\rm e}$. While star-forming massive late-type disks and irregulars (with D4000 $<$ 1.5 and log$(M_{*}/M_{\odot}) \gtrsim 10.5$) span a stellar mass range comparable to bulge-dominated galaxies, most have systematically lower $\Sigma_{\rm e}$ $\lesssim$ $10^{9}M_{\odot}\rm{kpc^{-2}}$. This suggests that the presence of a bulge is a necessary but not sufficient requirement for quenching at intermediate redshifts.