Discovery of a Barred-Spiral Galaxy at $z_{spec}$ = 3.16 II. The Star Formation History
We present a detailed analysis of a massive barred galaxy at $z_{spec}=3.1591$ using deep multi-band imaging from HST and JWST. For the first time, we resolve its morphology and stellar structures thanks to the JWST/NIRCam NIR and MIR photometry. The galaxy possesses two distinct components with significantly different colors. Through careful image decomposition and masking, we isolate and characterize the flux contribution from each component. The galaxy exhibits a clear spiral morphology, and in a separate companion paper, we present evidence suggesting the presence of a stellar bar. Based on spatially resolved spectral energy distribution modeling with Prospector, we derive the star formation history and other physical properties of the bar and the surrounding regions. The total stellar mass of the galaxy is constrained as $\log(M_*/M_{\odot}) = 10.63\pm0.13$. We find that the bar region contains around 30% of the total stellar mass, but only accounts for around 8% of the recent star formation rate. The region containing the potential bar shows a significantly older mass-weighted stellar age, supporting the inside-out scenario for galaxy formation, and providing tentative evidence for bar quenching in the early stage. The quick onset of a stellar bar at this redshift requires a low dark matter fraction, suggesting the baryon-dominated nature of high-$z$ massive galaxies, and offering rare insight into galaxy evolution at around two billion years after the Big Bang.