We investigate the star formation histories (SFHs) of massive red spiral galaxies with stellar mass $M_ast>10^{10.5}M_odot$, and make comparisons with blue spirals and red ellipticals of similar masses. We make use of the integral field spectroscopy from the SDSS-IV/DR15 MaNGA sample, and estimate spatially resolved SFHs and stellar population properties of each galaxy by applying a Bayesian spectral fitting code to the MaNGA spectra. We find that both red spirals and red ellipticals have experienced only one major star formation episode at early times, and the result is independent of the adopted SFH model. On average, more than half of their stellar masses were formed $>$10 Gyrs ago, and more than 90% were formed $>6$ Gyrs ago. The two types of galaxies show similarly flat profiles in a variety of stellar population parameters: old stellar ages indicated by $D4000$ (the spectral break at around 4000AA), high stellar metallicities, large Mgb/Fe ratios indicating fast formation, and little stellar dust attenuation. In contrast, although blue spirals also formed their central regions $>$10 Gyrs ago, both their central regions and outer disks continuously form stars over a long timescale. Our results imply that, massive red spirals are likely to share some common processes of formation (and possibly quenching) with massive red ellipticals in the sense that both types were formed at $z > 2$ through a fast formation process.Possible mechanisms for the formation and quenching of massive red spirals are discussed.
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