Model constraints based on the IceCube neutrino non-detection of GRB 221009A

GRB 221009A is a bright Gamma-ray burst (GRB) with isotropic energy being larger than $10^{54} ~{\rm ergs}$. Its fairly low redshift makes it a promising candidate for high energy neutrino detection. However, a neutrino search for this GRB reported by the IceCube collaboration yielded a null result. In this paper, we utilize the upper limit from IceCube observation to test different GRB prompt emission models. We find that, at least for this specific burst, the dissipative photosphere model could be ruled out in a large parameter space. The internal shock model can survive only with a large bulk motion Lorentz factor $\Gamma$, where the most stringent and conservative constraints are $\Gamma > \sim 450$ and $\Gamma > \sim 200$, respectively. Also, the ratio of the total dissipated energy that goes into the protons and electrons ($\epsilon_p / \epsilon_e$) can be constrained with a given $\Gamma$. For $\Gamma < 400$, $\epsilon_p / \epsilon_e < 10$ is required. For the Internal-collision-induced Magnetic Reconnection and Turbulence (ICMART) model, the constraint from GRB 221009A is modest. Under ICMART model, only for extreme situations when most dissipated energy deposit into protons and all accelerated protons are suitable for producing neutrinos, a slightly large bulk motion ($\Gamma > \sim 250$) is required.