Multiwavelength Analysis of GRB 250101A: From Gamma-ray Prompt Emission to Optical Afterglow

The interaction between the relativistic jet and the circumburst medium produces a multiwavelength afterglow of a gamma-ray burst (GRBs). In this work, we present multiwavelength properties of GRB~250101A based on the observations of Swift, Fermi and Mephisto. The spectral analysis of Swift/BAT and Fermi/GBM reveals a soft prompt spectrum with a low-energy photon index of $-1.18$ and a peak energy of 33 keV, and the isotropic energy is $1.4\times10^{52}~{\rm erg}$. The prompt emission of GRB 250101A aligns with Type II GRBs in the Amati relation. Meanwhile, our analysis indicates that GRB 250101A is an X-ray-rich or X-ray-dominated GRB, with intrinsic properties suggesting that it is relatively softer than most classical GRBs. Optical observation with Mephisto, beginning 197 s post-trigger, shows a single power-law decay in $uvgriz$ bands, with $F_{\nu,\mathrm{obs}} \propto t^{-0.76} \nu^{-1.21}$. The observed spectral index significantly exceeds theoretical predictions under standard afterglow models, suggesting a color excess of $\sim0.216$ mag. However, combining X-ray and optical afterglow, we find that GRB 250101A is more likely a ``normal burst'' rather than an ``optical-dark burst'', and the dust extinction effect plays an important role in the optical blue bands. Furthermore, there is a structural change at $T_0+2924$ s in the optical light curve, indicating a density drop of $\sim50$ \% in the interstellar medium at a distance of $\sim0.13~{\rm pc}$. Our analysis shows that this GRB clearly shows some unique characteristics in its observed X-ray rich prompt emission as well as the circumburst environment, implying a special progenitor.