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

TL;DR

This work uses IceCube upper limits on GRB neutrinos to constrain prompt-emission jet properties for two bright bursts, GRB 221009A and GRB 240825A. It evaluates internal-shock (IS), baryonic photospheric (BPH), and magnetically dominated photospheric (MPH) models, plus a model-independent approach, by computing neutrino fluence via photo-hadronic interactions with a Band-function photon field and a proton spectrum $dN_p/dE_p \propto E_p^{-2}$; an empirical $\Gamma_0$--$E_{\gamma,\rm iso}$ relation with scatter sets the bulk Lorentz factor, enabling inference of the dissipation radius $R$ and baryon loading $f_p$ under each model. For GRB 221009A, IceCube limits favor high $\Gamma$ with relatively low $f_p$ in the IS case, while BPH and MPH are constrained at the minimum dissipation radius; for GRB 240825A, all three prompt-emission models remain viable with moderate $f_p$ and larger $R$, and a model-independent analysis points toward moderately high $R$ and $\Gamma$. These results narrow the allowed jet compositions and dissipation sites, inform the interpretation of high-energy photons, and highlight the capabilities and limits of current and near-future neutrino observatories for probing GRB jets.

Abstract

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.

Figures (4)

• Figure 1: Density plots of expected neutrino events in IceCube for GRB 221009A. (a) IS Model: The total number $N_{\rm tot}$ (muons + cascades) and $N_{\mu}$ (muons only) are calculated in the two-dimensional parameter space $\eta - \epsilon_{p}$. The colourbar corresponds to $N_{\rm tot}$. Contours where $N_{\rm tot} = 0.36$ and $N_{\mu} = 0.36$ are shown by solid and dashed lines, respectively. The other energy fractions are taken as constants, $\epsilon_{e} = 0.2$ and $\epsilon_{B} = 0.1$. The IceCube null result favours the darker (purple) regions, i.e., high $\eta$ (or $\Gamma$) with weak dependence on $\epsilon_p$. The blue horizontal line marks $\eta = \Gamma = 676$, intersecting the $N_{\rm tot} = 0.36$ contour at $\epsilon_{p} = 0.805$, constraining $f_{p}$. (b) BPH Model: Conventions are the same as (a). A high $\eta$ (or $\Gamma$) is favoured. The line $\eta = \Gamma = 676$ intersects $N_{\rm tot} = 0.36$ at $\epsilon_{p} = 0.18$, constraining $f_{p}$. (c) MPH Model: The result is insensitive to $\eta$ (or $\Gamma$) as the contours run almost parallel to the $\eta$-axis. The IceCube null result favours $\epsilon_{p} \lesssim 0.1 - 0.2$, roughly independent of $\eta$. The line $\eta = \Gamma = 676$ intersects $N_{\rm tot} = 0.36$ at $\epsilon_{p} = 0.03$, constraining $f_{p}$. (d) Model Independent: Density plot in the parameter space of dissipation radius $R_{13} = (R/10^{13} \rm cm)$ and Lorentz factor $\Gamma$. This uses the semi-analytical model in Section \ref{['IS-PH_Model']}, without assuming a specific scenario. Darker colours denote fewer events, while lighter colours indicate more. Dashed lines show contours for $N_{\rm tot} = 0.36$ with $f_{p} = 0.25, 0.5, 1$. Based on the IceCube null result abbasi2012Natur_I, the parameter space below each contour is likely ruled out for the corresponding $f_{p}$.
• Figure 2: Density plots of expected neutrino events in IceCube for GRB 240825A. (a) IS Model: Contours where $N_{\rm tot} = 0.196$ and $N_{\mu} = 0.196$ are shown by solid and dashed lines, respectively. The blue horizontal line marks $\eta = \Gamma = 242$, intersecting the $N_{\rm tot} = 0.196$ contour at $\epsilon_{p} = 0.08$, constraining $f_{p}$. The other energy fractions are fixed to $\epsilon_{e} = 10^{-2}$ and $\epsilon_{B} = 10^{-3}$. (b) BPH Model: Conventions are the same as (a). The blue line $\eta = \Gamma = 242$ intersects $N_{\rm tot} = 0.196$ at $\epsilon_{p} = 0.238$, setting the $f_{p}$ upper bound. (c) MPH Model: Results are insensitive to $\eta$, as contours run nearly parallel to the $\eta$-axis. IceCube non-detection favours $\epsilon_{p} \lesssim 0.1$ -- $0.3$, weakly dependent on $\eta$. The $\eta = 242$ line intersects $N_{\rm tot} = 0.196$ at $\epsilon_{p} = 0.073$. (d) Model Independent: Density plot in the dissipation radius $R_{13} = (R_{\rm dis}/10^{13})$ cm vs. $\Gamma$. Darker colours denote fewer events. Dashed lines show $N_{\rm tot} = 0.196$ contours for $f_{p} = 10, 15, 25$.
• Figure 3: $R_{\rm dis}-\Gamma$ curves for various models based on the baryon loading values. These curves are compared with the $\tau_{\gamma\gamma} =1$ curve for GRB 221009A and GRB 240825A.
• Figure 4: Predicted neutrino spectrum of GRB 221009A and GRB 240825A for the IS, BPH, and MPH models, along with IceCube-Gen2 ($\pm 500s$ time window) aartsen2021JPhG_A and KM3NeT/ARCA (1000s time window) sensitivities Palacios-Gonzalez:2021slw. The IceCube and KM3NET/ARCA upper limits are shown with the black and grey horizontal lines, respectively, for each GRB. (a) GRB 221009A: For $\Gamma = 676$ and $1000$, solid lines represent the value of dissipation radius as mentioned in Table \ref{['tab:GRBP']}, while the dashed lines represent $R = 4 \times 10^{15}$ cm for IS model, and $R = 4 \times 10^{14}$ cm for BPH and MPH models; the baryon loading values are $f_{p} = 8.05$ (IS), $1.8$ (BPH), and $0.3$ (MPH). (b) GRB 240825A: For $\Gamma = 242$ and $350$, solid lines represent the value of dissipation radius as mentioned in Table \ref{['tab:GRBP']}, while the dashed lines represent $R=4 \times 10^{14}$ cm for all models; the baryon loading values are $f_{p} = 16$ (IS), $47.6$ (BPH), and $14.6$ (MPH), respectively.