Constraints on GRB Jet Properties from IceCube Upper Limits: Insights from GRB 221009A and GRB 240825A

The IceCube neutrino telescope has provided upper limits on neutrino emission from gamma ray bursts. These constraints provided by the IceCube detector have been instrumental in investigating the properties of the GRB jet and its emission models. During the prompt phase of gamma ray burst emission, intense radiation components are generated that interact with the shock-accelerated particles within the jet. We study various GRB emission models, such as the internal shock model, the photospheric models, and also include a model-independent case. Based on these models, we calculate the neutrino fluence using the photo-hadronic interaction process. We estimate the bulk Lorentz factor using the well-known correlations between prompt phase observables, which is then used to calculate the emission site for the model-dependent scenarios. For GRB 221009A, we find that a low baryon loading scenario is consistent with the IceCube upper limits; however, for GRB 240825A, a higher value of baryon loading is preferred. Also, the values of the microphysical parameters $ε_e$ and $ε_B$ for GRB 240825A are lower by factors of approximately 10 and 100, respectively, compared to those of GRB 221009A. Further, using neutrino upper limits for these two sources, we estimate the lower limits on the dissipation radius for our models. The current TeV PeV upper limits for GRB 221009A are already useful for constraining parameter space for the BPH and MPH models.