Transit Timing Variation of K2-237b: Hints Toward Planet Disk Migration

Hot Jupiters should initially form at considerable distances from host stars and subsequently migrate towards inner regions, supported directly by transit timing variation (TTV). We report the TTV of K2-237b, using reproduced timings fitted from \textit{Kepler} K2 and \textit{TESS} data. The timings span from 2016 to 2021, leading to an observational baseline of 5 years. The timing evolution presents a significant bias to a constant period scenario. The model evidence is evaluated utilizing the Bayesian Information Criterion (BIC), which favours the scenario of period decay with a $\Delta$BIC of 14.1. The detected TTV induces a period decay rate ($\dot{P}$) of -1.14$\pm$0.28$\times$10$^{-8}$ days per day ($-$0.36 s/year). Fitting the spectral energy distribution, we find infrared excess at the significance level of 1.5 $\sigma$ for WISE W1 and W2 bands, and 2 $\sigma$ level for W3 and W4 bands. This potentially reveals the existence of a stellar disk, consisting of hot dust at 800$\pm$300 K, showing a $L_{dust}/L_{\ast}$ of 5$\pm$3$\times$10$^{-3}$. We obtain a stellar age of 1.0$^{+1.4}_{-0.7}$$\times$10$^{9}$ yr from isochrone fitting. The properties of K2-237b potentially serve as a direct observational support to the planet disk migration though more observation are needed.