Prospect of GRB-Neutrino Detection with Enhanced Neutrino Detectors

In the radiation zone of gamma-ray bursts (GRBs), a large number of gamma-ray photons are generated, either through thermal or non-thermal processes. Simultaneously, protons within the relativistic GRB jet are expected to be accelerated and acquire a relativistic random motion. Consequently, interactions between protons and gamma-ray photons, known as $p\gamma$ interactions, are unavoidable, leading to the production of high-energy neutrinos (e.g. Zhang, 2018). This, as well as the interactions between baryons, make GRB events a compelling candidate as a potential source of high-energy neutrinos (Waxman & Bahcall, 1997; Dermer & Atoyan, 2003; Razzaque et al., 2003; Guetta et al., 2004; Murase et al., 2006a; Murase & Nagataki, 2006; Hümmer et al., 2012; Murase et al., 2013; Bustamante et al., 2015; Tamborra & Ando, 2015; Biehl, D. et al., 2018; Pitik et al., 2021; Ai & Gao, 2023; Rudolph et al., 2023).

The predicted flux of high-energy neutrinos generated by GRB events through $p\gamma$ interactions depends significantly on the model used to describe the GRB prompt emission (e.g. Zhang & Yan, 2010; Pitik et al., 2021; De Lia & Tamborra, 2024). In the literature, three prominent models are often discussed: the dissipative photosphere model (Rees & Mészáros, 2005), the internal shock model (Rees & Meszaros, 1994), and the ICMART model (Zhang & Yan, 2010). In these models, different characteristic radii for the radiation regions are proposed. These radii determine the gamma-ray photon number density, which in turn influences the rate of $p\gamma$ interactions and, consequently, affects the resulting neutrino flux. The dissipative photosphere model requires a matter-dominated GRB jet, in which the gamma-ray photons are released at the photosphere radius as $R_{\rm ph}\sim 10^{11-12}~{}{\rm cm}$ (Mészáros & Rees, 2000; Pe’er et al., 2007). In the internal shock model, GRB photons are generated due to the collision of different layers inside the jet, which happens at a radius as $R_{\rm IS}\sim 10^{12-13}~{}{\rm cm}$ (Rees & Meszaros, 1994; Daigne & Mochkovitch, 1998). In the ICMART model, the GRB jet is assumed to be dominated by Poynting flux. The gamma-ray photons are generated at a much larger radius as $R_{\rm ICMART}\sim 10^{15}~{}{\rm cm}$ where significant magnetic dissipation occurs (Zhang & Yan, 2010; McKinney & Uzdensky, 2011; Lazarian et al., 2019). Joint observations of GRBs and neutrinos would offer an independent approach to test and distinguish between these competing models.

Theoretically, a considerable number of neutrinos could be produced by each GRB (Kimura, 2022). However, the immense distance from the source, coupled with the current technological constraints of neutrino detectors, significantly limits our capacity to detect these neutrinos. IceCube is currently the most sensitive detector for astrophysical neutrinos, located beneath the ice layer at the geographic South Pole (Aartsen et al., 2017a).

However, even for GRB 221009A, the brightest of all time burst, no associated neutrinos were detected by IceCube (Aiello et al., 2024) . The IceCube collaboration reported an upper limit on the neutrino flux associated with this event (IceCube Collaboration, 2022), leading to constraints on GRB models (Murase et al., 2022; Ai & Gao, 2023; Guarini et al., 2023; Rudolph et al., 2023; Veres et al., 2024). It is likely that the radiation radius of GRB 221009A is relatively far from the central engine, which is consistent with the ICMART model, featuring a jet dominated by magnetic fields (Yang et al., 2023). The internal shock model remains viable if the jet has a relatively high bulk Lorentz factor (Murase et al., 2022; Ai & Gao, 2023), whereas the dissipative photosphere model is disfavored (Ai & Gao, 2023).

Considering the difficulty of detecting neutrinos from a single source, stacked neutrino detection across multiple sources has become a more popular approach. As early as 2011, Abbasi et al. (2011) searched for neutrino emission within a one-day time window before and after GRBs from 2008 to 2010. Later, in 2015, Aartsen et al. (2015) analyzed the prompt emission phases of 506 GRBs from 2008 to 2012, placing constraints on the parameter space of the fireball model and estimating that GRBs could account for about 1% of the total astrophysical neutrino flux. Then, in 2017, Aartsen et al. (2017b) extended the data range by three years, including 1,172 GRBs from 2008 to 2015. In 2022, Abbasi et al. (2022) further extended the search window to 14 days before or after GRBs to account for the contribution of afterglows to neutrino production. Also in 2022, Lucarelli, Francesco et al. (2023) used ten years of IceCube data to search for neutrinos during both the GRB prompt and afterglow phases. To date, this stacked detection approach has not yet succeeded in detecting GRB neutrinos.

Several near-future neutrino detectors have been proposed or are already under construction, such as IceCube Gen 2 (Aartsen et al., 2021), Baikal-GVD in Lake Baikal (Avrorin et al., 2011), KM3NeT located in the Mediterranean Sea (Adrián-Martínez et al., 2016) and those in the Pacific Ocean, like P-One (Agostini et al., 2020) and TRIDENT (Ye et al., 2024). At this stage, it is of great interest to assess the prospects for detecting GRB neutrinos as detector sensitivity improves in the future. What is the detection probability for individual bright sources similar to GRB 221009A? After 5 to 10 years of cumulative observations, what is the likelihood of detecting GRB neutrinos through stacked neutrino detection methods? If GRB neutrino detection remains elusive, how constraining would this be for existing models? This work will delve into these questions. To ensure the generality of our research conclusions, we do not focus on the sensitivity of any specific proposed detector but instead calculate by increasing the effective area of IceCube IC86-II by a certain factor.

In the GRB environment, gamma-ray photons are produced concurrently with the acceleration of electrons and baryons (Waxman & Bahcall, 1997). These non-thermal protons interact with gamma-ray photons, as well as other protons and neutrons, producing high-energy neutrinos. Typically, the number density of photons is much higher than that of the baryons, making the $p\gamma$ interaction the dominant hadronic process. Here we focus on the $p\gamma$ process to generate high-energy neutrinos. In this section, we will introduce the theoretical models for GRB prompt emission and the $p\gamma$ neutrino production respectively.

The gamma-ray burst GRB 221009A is often referred to as the “brightest of all time”. This event was first triggered by the Fermi/Gamma-ray Burst Monitor at 3:16:59 UT on 2022 October 9, with a time-integrated energy flux within the 10–1000 keV range reported as $\left(2.912\pm 0.001\right)\times 10^{-2}\ \text{erg}\ \text{cm}^{-2}$. The peak photon number flux reached $\left(2385\pm 3\right)\ \text{cm}^{-2}\ \text{s}^{-1}$, sustaining this level for $1.024$ s. Using measurements from the Swift observatory, this event was localized at right ascension $\alpha=288.2645^{\circ}$ and declination $\delta=+19.7735^{\circ}$ (Dichiara et al., 2022), with a host galaxy identified at a redshift of $z=0.151$. Consequently, its isotropic energy reaches $\sim 10^{55}\ \text{erg}$ (An et al., 2023; Yang et al., 2023; Lan et al., 2023), making it a highly promising candidate to exhibit a neutrino counterpart, although it was not detected (Abbasi et al., 2023).

Given the predicted neutrino flux, the expected number of events recorded by the neutrino detector can be expressed as (IceCube Collaboration, 2021)

where $F_{\nu}=\phi_{\nu}/(E_{\nu}^{2}T)$ is the specific number flux of neutrinos, with $T$ as the duration of observation length. $A_{\rm eff}$ is the effective areas of the neutrino detector. Here we use IceCube IC86-II Effective Area (IceCube Collaboration, 2021), which depends on the neutrino energy and the declination of the source in the sky. The effective areas corresponding to several typical declinations as a function of neutrino energy are shown in Figure 1.

Given the expected number of neutrinos to be detected, the probability of actually detecting $N_{\nu}$ neutrinos is (Mukhopadhyay et al., 2024)

The predicted neutrino fluence associated with GRB 221009A from the dissipative photosphere, internal shock, and ICMART models, along with the corresponding $90\%$ upper limit under the non-detection condition with IceCube, is shown in Figure 2. Here, we adopt $\epsilon_{p}/\epsilon_{e}=3$ and $\epsilon_{B}/\epsilon_{e}=1$ for all models. For the internal shock model, $\delta t_{\text{min}}=0.01\,\text{s}$, and for the ICMART model, $R_{\rm ICMART}=10^{15}$ cm. With the predicted fluence, we can get the corresponding neutrino number to be detected by IceCube, that is $N_{\rm ph}=13.0132$, $N_{\rm IS}=3.5410$, and $N_{\rm ICMART}=0.2109$. Thus, for each model, the detection probability can be calculated as $P_{\rm ph}=99.99\%$, $P_{\rm IS}=97.10\%$, and $P_{\rm ICMART}=19.02\%$.

We can see that with the current detection capabilities, at the declinations where GRB 221009A appears, the dissipative photosphere and internal shock models have a relatively high probability of detecting neutrinos, while the probability of detecting neutrinos under the ICMART model is relatively low. Therefore, the nondetection fact of high-energy neutrinos associated with GRB 221009A is consistent with the claim that it is driven by the ICMART model, combined with evidence from multiwavelength EM observations (Yang et al., 2023).

Despite GRB 221009A being referred to as a “once-in-a-millennium” GRB, it is not particularly unique. Lan et al. (2023) suggests that it is simply an ordinary nearby GRB with extraordinary observational properties. Therefore, in the future, if a GRB 221009A-like event occurs at different sky positions where the neutrino detector can achieve a larger effective area, neutrinos from such events may have chance to be detected.

It should be noted that, according to the conclusions of Ai & Gao (2023), for GRB 221009A, only if its internal shock originates from a region with a very large dissipation radius (a large variability timescale or a very large bulk Lorentz factor) can it match our expectation of not detecting neutrinos. Rudolph et al. (2023) presented a more sophysticated internal shock model, where the variability timescale is around $1$ s, and the final energy dissipation occurs at a radius of approximately $10^{16}\sim 10^{17}$ cm, which is even larger than that of the ICMART model. In this discussion, we adopt a conservative approach and assume that the minimum variability timescale is the classical $0.01$ s (Baerwald et al., 2011; Hümmer et al., 2012; Aartsen et al., 2017b). As shown in Figure 3, in the context of dissipative photosphere model, placing GRB 221009A at a redshift of 0.37 would still allow its generated neutrinos to be detectable by the current IceCube detector. With a less than twofold increase in the detector’s sensitivity, the neutrinos produced by GRB 221009A would remain observable even at a redshift of 0.5. In the context of the internal shock model, neutrinos from GRB 221009A can be detected within a redshift of $0.19$ without any increase in the detector’s effective area. A fivefold increase in the detector’s effective area would enable detection of neutrinos, provided the event occurs within a redshift of 0.5. In the case of the ICMART model, if the event occurs at the same redshift as GRB 221009A (z = 0.15), a tenfold increase in the detector’s effective area would be required to have a chance of detecting the neutrinos. It is worth noting that the above calculation are based on the effective area corresponding to the true declination angle of GRB 221009A. If the future event happens to occur at a declination where the detector’s effective area is maximized, the detection rate would increase significantly. In that case, only about 3 times increase of the detector’s sensitivity would be needed to detect the neutrinos from GRB 221009A-like bursts, at $z=0.15$ for ICMART model or at $z=0.5$ for internal shock model. The above conclusions are based on a 90% detection probability. Please note that the above discussion is based on the parameters used in Figure 2. The flux of neutrinos is influenced by these parameters, which may lead to potential uncertainties.

If we are not ”lucky” enough to encounter an event similar to GRB 221009A, we will have to rely on the stacked detection approach. Although the chance of detecting high-energy neutrinos associated with a single “normal” GRB event is low, the accumulation of GRB events increases the probability of detecting a high-energy neutrino associated with a GRB, which could eventually reach a considerably high level.

Here, we use data from GRBweb²²2For detailed data, see https://user-web.icecube.wisc.edu/~grbweb_public., an online platform that collects data from different telescopes, such as GBM (Hurley et al., 2013; von Kienlin et al., 2020), LAT (Ajello et al., 2019), Swift (Lien et al., 2016) and others. From 2019 to 2023, a total of 1503 gamma-ray bursts were recorded. We select those with fluence records and $T_{90}>2$ s for our calculations. If a source did not have a redshift measurement, we assigned a redshift value of $2.15$(Aartsen et al., 2017b). We adopt $E_{\text{break}}=200$ keV for all GRBs. For the bulk Lorentz factor ($\Gamma$) of GRBs, we derive it using the empirical relationship between the bulk Lorentz factor and the luminosity of the GRB (Liang et al., 2010; Lü et al., 2012; Zhang & Kumar, 2013), which is given by

For simplicity, the uncertainties connected with this relation, which may result from the orientation of the jets, are not considered. We exclude GRB 210518C and GRB 230614C, even though their fluences were well recorded. This is because, in the absence of redshift measurements, assuming a redshift of 2.15 for these sources would result in an unreasonably high luminosity. As a result, they would produce a number of neutrinos comparable to those of the remaining $\sim 1,000$ gamma-ray bursts. In addition, GRB 221009A is also excluded from the samples.

The average stacked neutrino fluxes produced by all-sky GRB events from 2019 to 2023, assuming the dissipative photosphere, internal shock, and ICMART models, are shown in Figure 4. Here, we also adopt $\epsilon_{B}/\epsilon_{e}=1$ and $\epsilon_{p}/\epsilon_{e}=3$ for all models. For the internal shock model, $\delta t_{\text{min}}=0.01\ \text{s}$ is adopted. For the ICMART model, $R_{\rm ICMART}=10^{15}$ cm is adopted. Based on these fluxes, we calculate the expected number of neutrinos detected by IceCube for the three models as $N_{\rm ph}\approx 2.65$, $N_{\rm IS}\approx 1.62$, and $N_{\rm ICMART}\approx 0.0439$, corresponding to the detection probabilities of $P_{\rm ph}\approx 92.90\%$, $P_{\rm IS}\approx 80.19\%$, and $P_{\rm ICMART}\approx 4.293\%$, respectively. We can see that for the ICMART model, there is still a significant gap to reach a 90% detection probability, whereas for the dissipative photosphere and internal shock models, the probability of detecting neutrinos is approximately 90%. Please note that we have assumed uniform benchmark microphysical parameters for all GRBs and employed an approximate relation to determine the bulk Lorentz factor of the jet. Various parameter settings might lead to different outcomes.

We assume that GRBs will continue to be observed in the coming years at the same detection rate as during the period from 2019 to 2023. Using the same parameters as those applied in the models shown in Figure 4, we calculate the evolution of the probability of detecting neutrinos from GRBs over the detector’s operational time. The results are shown in Figure 5. Assuming the detector’s effective area remains unchanged, the dissipative photosphere model and the internal shock model require 4.35 years and 7.11 years, respectively, to achieve a $90\%$ detection probability. In contrast, the ICMART model can only reach a detection probability of $58\%$, even with an accumulation time of 100 years.

With next-generation neutrino detectors, the increase in the effective area will significantly enhance the probability of jointly detecting GRBs and neutrinos. If the detector’s effective area is increased fivefold relative to IceCube IC86-II, the dissipative photosphere and internal shock models would require only one year of accumulation to achieve detection probabilities of 80% and 93%, respectively. In contrast, the ICMART model would require 52 years of accumulation to reach a 90% detection probability. With a tenfold expansion of the detector’s effective area, the dissipative photosphere and internal shock models would quickly approach a 100% detection probability. However, even with 10 years of accumulation,the ICMART model would only achieve a 58% detection probability.

On the other hand, even if the neutrino counterparts of GRBs remain undetected, much more stringent constraints can be placed on the free parameters of different GRB models. If the parameters are constrained to an unacceptable range, it can be concluded that the corresponding GRB model can be rule out. Inspired by observations of GRBs and their afterglows, we assume reasonable parameters to be $\epsilon_{p}/\epsilon_{e}>1$, $\epsilon_{B}/\epsilon_{e}<1$ (Gao et al., 2015). And we still adopt $\delta t_{\rm min}=0.01$ s and $R_{\rm ICMART}=10^{15}$ cm. In the future, assuming the events accumulated over five years, similar to those from 2019 to 2023, using the non-detection results from an enhanced neutrino detector and the parameter space shown in Figure 6, one may conclude that:

• •

  For the dissipative photosphere model, if the effective area has been increased by a factor of 4 relative to IceCube IC86-II, then for $\epsilon_{p}/\epsilon_{e}>1$, $\epsilon_{B}/\epsilon_{e}>1.18$ is required, suggesting that this model is not generally applicable to GRBs.

• •

  For the internal shock model, if the effective area has been increased by a factor of $5.5$ relative to IceCube IC86-II, then for $\delta t_{\rm min}=0.01$ s, $\epsilon_{p}/\epsilon_{e}$ must be less than approximately $0.96$. This implies that the internal shock model with $\delta t_{min}=0.01$s is not generally applicable to GRBs. In addition to the conservative case, some also suggest that the minimum variability timescale could be 0.1 s (Zhang & Kumar, 2013). We have also considered this scenario and find that if the detector’s effective area is increased by a factor of 19 and neutrinos are still not detected, then for $\delta t_{\rm min}=0.1$ s, $\epsilon_{p}/\epsilon_{e}$ must be less than 1. Therefore, to rule out this scenario, the detector’s effective area would need to be increased by a factor of 19.

• •

  For the ICMART model, if the effective area has been increased by a factor of $10$ relative to IceCube IC86-II, then for $R_{\rm ICMART}=10^{15}~{}{\rm cm}$, $\epsilon_{p}/\epsilon_{e}<15$ is required. This is consistent with the theoretical description, so we cannot impose strong constraints on the ICMART model.If we want to constrain $\epsilon_{p}/\epsilon_{e}$ to below 1 without detecting neutrinos for $R_{\rm ICMART}=10^{15}$ cm, the detector’s effective area would need to be increased by a factor of 150. This is far beyond the detection capabilities of both our current and near-future detectors.

GRBs are potential sources of high-energy neutrinos. However, despite extensive studies, including the exceptionally bright GRB 221009A and over a decade of cumulative neutrino searches, no definitive association has been confirmed.

The lack of neutrino detections provides meaningful insights into models of GRB prompt emission. Stringent constraints have been placed on the physical parameters of the dissipative photosphere and internal shock models, while the parameter space for the ICMART model remains broad.

In this work, we first calculate the neutrinos produced in a GRB 221009A-like event under the dissipative photosphere, internal shock, and ICMART models, respectively. Our calculations indicate that, under typical parameters, if GRB 221009A originated from either the dissipative photosphere model or the internal shock model, its neutrinos should have already been detected.

Thus, the lack of neutrinos associated with GRB 221009A is consistent with implications from multiband EM observations suggesting that a magnetically dominated jet was launched. With future enhanced neutrino detectors, if the effective area is approximately $10$ times larger than that of IceCube IC86-II, we would be able to detect neutrinos from such a GRB event which have the same redshit with GRB 221009A, even if produced under the ICMART model. If we are particularly lucky, and the event occurs at a declination corresponding to the effective area of maximum detector efficiency, then increasing the effective area by a factor of $3$ would be sufficient to detect the neutrinos it produces.

We then calculated the cumulative neutrino flux from stacked GRBs and analyzed 1,142 sources from 2019 to 2023. We considered a scenario where future detectors with an increased effective area observing these $1,142$ sources over a 5-year period. If the effective area is increased $4$ times relative to IceCube IC86-II and no neutrinos are detected, the general applicability of the dissipative photosphere model would be strongly questioned. If expanded $5.5$ times, the same issue appears to the internal shock model. For the ICMART model, even if the detector’s effective area is increased by a factor of $10$ and no associated neutrinos are detected, the model can still survive.

Here are three cautions: (1) For the internal shock model, we assume the minimum variability timescale of the GRB light curve is $\delta t_{\rm min}\sim 0.01$ s, which is a classical theoretical value. However, if $\delta t_{\rm min}$ is much greater (like $0.1$ s inferred from some of observed minimum variability timescale (Golkhou et al., 2015; Camisasca et al., 2023)), the internal shock model should have a radiation radius comparable to that of the ICMART model (Rudolph et al., 2023), making neutrinos production in the internal shock model also very inefficient. (2) When we rule out models using stacked GRB observations, we mean ruling out the possibility that a single model applies to all GRBs. In fact, there may be multiple channels responsible for producing GRBs. (3) Our discussion is valid only in the “one-zone” scenario, where protons are accelerated in the same region where the gamma-ray photons are emitted.

Studies predict that low-luminosity GRBs might be more efficient generators of high-energy neutrinos (Murase et al., 2006b; Gupta & Zhang, 2007). Similarly, short GRBs with relatively lower bulk Lorentz factors in their jets could also be potential sources of high-energy neutrinos (Rudolph et al., 2024). Currently operating powerful gamma-ray and X-ray detectors could detect more of these relatively faint events, thereby providing better constraints on GRB models.