Journal of Cosmology and Astroparticle Physics       PAPER • OPEN ACCESS Bounds on neutrino-DM interactions from TXS 0506+056 neutrino outburst To cite this article: Gabriel D. Zapata et al JCAP07(2025)042   View the article online for updates and enhancements. You may also like Cascading Constraints from Neutrino- emitting Blazars: The Case of TXS 0506+056 Anita Reimer, Markus Böttcher and Sara Buson - The Blazar TXS 0506+056 Associated with a High-energy Neutrino: Insights into Extragalactic Jets and Cosmic-Ray Acceleration S. Ansoldi, L. A. Antonelli, C. Arcaro et al. - Lepto-hadronic -Ray and Neutrino Emission from the Jet of TXS 0506+056 Narek Sahakyan - This content was downloaded from IP address 45.231.80.27 on 23/09/2025 at 20:53 https://doi.org/10.1088/1475-7516/2025/07/042 /article/10.3847/1538-4357/ab2bff /article/10.3847/1538-4357/ab2bff /article/10.3847/1538-4357/ab2bff /article/10.3847/2041-8213/aad083 /article/10.3847/2041-8213/aad083 /article/10.3847/2041-8213/aad083 /article/10.3847/2041-8213/aad083 /article/10.3847/1538-4357/aadade /article/10.3847/1538-4357/aadade /article/10.3847/1538-4357/aadade /article/10.3847/1538-4357/aadade J C A P 0 7 ( 2 0 2 5 ) 0 4 2 ournal of Cosmology and Astroparticle Physics An IOP and SISSA journalJ Received: March 19, 2025 Revised: May 14, 2025 Accepted: June 11, 2025 Published: July 15, 2025 Bounds on neutrino-DM interactions from TXS 0506+056 neutrino outburst Gabriel D. Zapata ,∗ Joel Jones-Pérez and Alberto M. Gago Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Apartado 1761, Lima, Peru E-mail: gabriel.zapata@pucp.edu.pe, jones.j@pucp.edu.pe, agago@pucp.edu.pe Abstract: We constrain the neutrino-dark matter cross-section using the 13±5 neutrino event excess observed by IceCube in 2014–2015 from the direction of the blazar TXS 0506+056. Our analysis takes advantage of the dark matter overdensity spike surrounding the supermassive black hole at the center of the blazar. In our results, we take into account uncertainties related to the different types of neutrino emission models and the features of the dark matter spike, considering cross-sections that scale with energy as σ ∝ (Eν/E0)n, for values of n = 1, 0, −1, −2. In our best-case scenario, we obtain limits competitive with those derived from other active galaxies, tidal disruption events (TDEs), and the IC-170922A event. Keywords: active galactic nuclei, dark matter theory, ultra high energy photons and neutrinos ArXiv ePrint: 2503.03823 ∗Corresponding author. © 2025 The Author(s). Published by IOP Publishing Ltd on behalf of Sissa Medialab. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. https://doi.org/10.1088/1475-7516/2025/07/042 https://orcid.org/0000-0002-2419-8424 https://orcid.org/0000-0002-2037-6369 https://orcid.org/0000-0002-0019-9692 mailto:gabriel.zapata@pucp.edu.pe mailto:jones.j@pucp.edu.pe mailto:agago@pucp.edu.pe https://doi.org/10.48550/arXiv.2503.03823 http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/ https://doi.org/10.1088/1475-7516/2025/07/042 J C A P 0 7 ( 2 0 2 5 ) 0 4 2 Contents 1 Introduction 1 2 Neutrino flux from TXS 0506+056 2 3 DM spike 5 4 Neutrino attenuation by DM 8 4.1 Comparison with previous limits 15 5 Conclusions 17 1 Introduction The nature of dark matter (DM) has riddled the scientific community for more than half a century [1–4]. In fact, despite the compelling gravitational evidence favoring the existence of DM, its mass, spin, and possible interactions with Standard Model (SM) particles remain unknown. Furthermore, no direct or indirect detection experiments [5–13] have provided any firm evidence of DM interactions with charged SM particles. In front of this elusiveness of DM, one must also take into account what is probably the second most elusive particle we know of, that is, neutrinos. As is well known, for more than a decade neutrino oscillation experiments have indicated the need for non-zero neutrino masses [14–17], contrary to the firm prediction of the SM. Thus, neutrinos are a sure window towards physics beyond the SM. In this sense, the possibility that the neutrino sector is the principal portal through which DM interacts becomes increasingly attractive [18–21]. With this in mind, the observation of high-energy astrophysical neutrinos by detectors such as IceCube [22] presents a great opportunity to study these possible interactions. Neutrinos, unlike gamma rays and cosmic rays, interact only weakly with matter, allowing them to travel vast distances through space without being affected. However, if DM consists of particles that interact with neutrinos, the corresponding attenuation of astrophysical neutrinos could serve as a probe for these interactions. The first object identified by IceCube as a high-energy neutrino source was blazar TXS 0506+056, following the observation of the IC-170922A neutrino event, which coincided with the direction of the blazar. Interestingly, observations by other experiments also indicated that TXS 0506+056 was experiencing a GeV gamma-ray flare [23], leading to a consistent description of the phenomena by blazar models [24–28]. The chance of coincidence of the neutrino with the flare of TXS 0506+056 is disfavored at the 3σ level. In a posterior analysis, IceCube also found evidence of a neutrino outburst from the direction of TXS 0506+056 during the 5-month period between September 2014 and March 2015, with an excess of 13 ± 5 high-energy muon neutrino events respect to atmospheric backgrounds [29]. However, this neutrino emission was not accompanied by an electromagnetic flare which, as we shall see, provides a challenge to blazar models. – 1 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 Other associations between high-energy neutrinos and astrophysical sources have since been made, including the active galaxy nuclei (AGN) NGC 1068 [30], the blazar PKS 1741-038 [31], and tidal disrupted events (TDEs) [32–34]. All of this data compels an evaluation of neutrino-DM interactions. The possibility of use the neutrino event IC-170922A to put bounds on the neutrino-DM cross-section was first introduced in [35], where the authors considered the path of neutrinos through both the cosmological DM background and the Milky Way’s DM halo.1 Stronger constraints were later obtained by accounting for the dense DM spike in the center of TXS 0506+056, increasing the DM column density along the neutrino path by several orders of magnitude [38, 39]. Additional limits on neutrino-DM interactions have been derived from other sources of high-energy neutrinos, such as the AGN NGC 1068 [40] and TDEs [41]. Bounds from such astrophysical neutrino sources have also been interpreted in specific models, see [42, 43] for examples. In this study we focus on the blazar TXS 0506+056, but instead of the single IC-170922A event, we consider the 13 ± 5 high-energy neutrino events from the 2014–2015 neutrino outburst. As mentioned earlier, this phenomenon has been difficult to reproduce in blazar models, so it is interesting to consider what information we can get from those few models that do so, taking also into account the uncertainties related to the features of the DM spike. In addition, previous studies of other astrophysical high-energy neutrino events have considered simplified setups for neutrino-DM interactions, assuming constant and linearly energy-dependent cross-sections. In this work we also contemplate situations where the cross-section is inversely proportional to the energy and to the square of the energy, as motivated by models involving light scalar mediators. This paper is organized as follows: in section 2, we describe the 2014–2015 neutrino outburst from TXS 0506+056 and the neutrino fluxes consistent with that observation. In section 3, we analyze the blazar’s DM density profile, emphasizing the properties of the DM spike and its effect on the column density. In section 4, we incorporate the fluxes from section 2 into the cascade equation to constrain the neutrino-DM cross-section under different energy-dependent cross-sections, accounting for uncertainties in the DM spike parameters. Here we also compare our constraints with existing limits in the literature. Finally, in section 5 we present our conclusions. 2 Neutrino flux from TXS 0506+056 Any bound placed on the neutrino-DM cross-section σνDM ultimately depends on the neutrino flux emitted by TXS 0506+056 during the 2014–2015 neutrino outburst [38, 40]. This means that the constraints will be inevitably tied to the specific blazar model for the flux. These models are usually either hadronic, leptonic or hybrid leptohadronic, depending on the dominant processes with the blazar jet. In our case, the observation of high-energy neutrinos points toward either a hadronic or leptohadronic description of the blazar, since leptonic models intrinsically produce too few neutrinos to be consistent with the outburst. However, in hadronic models the neutrino flux is generated via the decay of charged pions, while gamma rays are produced through the decay of neutral pions, resulting in similar numbers of 1See also [36] for an early constraint based on neutrino and photon arrival times, and [37] for a more recent study in this direction. – 2 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 1−10 1 10 210 310 410 510 610 [TeV]νE 4−10 3−10 2−10 1−10 1 10 210 310 410]2 [m ef f A 1−10 1 10 210 310 410 510 610 [TeV]νE 15−10 13−10 11−10 9−10 7−10 /s ec ] -1 ) [T eV ν (E ef f ) A ν (E ν Φ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 Figure 1. Left: effective area Aeff from TXS 0506+056 in the sample IC86b, provided by IceCube [46]. Right: spectrum of events to be expected at IceCube, for each of the different fluxes considered. neutrinos and gammas. This represents a challenge in explaining the 2014–2015 neutrino outburst, as it occurred during a period of low gamma ray emission. Thus, for hadronic models it is very difficult to generate a sufficiently large enough neutrino flux explaining the outburst without saturating the bound on the electromagnetic emission of the blazar. Unfortunately, leptohadronic models suffer from similar difficulties [26, 28, 44, 45]. In the following, we will select models that address and overcome this incompatibility. As a first step, we need to assess which spectra are capable of describing the 13 ± 5 events at IceCube in the absence of neutrino-DM interactions. To this end, given a flux, the total number of muon neutrino events to be expected at IceCube can be calculated using: Npred = tobs ∫ dEν Φν(Eν) Aeff(Eν) (2.1) with Φν ≡ Φνµ+ν̄µ the neutrino flux arriving to the detector, and tobs the observation time. Furthermore, the effective detection area Aeff encapsulates the probability of a neutrino generating a muon within the detector via weak interactions, depending on the neutrino energy, the detector geometry, and source direction. Following [29], the 2014–2015 neutrino outburst occurred in the sample IC86b, with the effective area shown on the left panel of figure 1 [46]. With eq. (2.1), we can perform a consistency check following the conclusions of [29], where the collaboration reports that the 13 ± 5 events can be fit into an unbroken power-law of the form: Φνµ+ν̄µ(Eν) = Φref ( Eν 100 TeV )−γ , (2.2) where the best-fit parameters have γ = 2.2 ± 0.2 and Φref = 1.6+0.7 −0.6 × 10−15 TeV−1 cm−2 sec−1. These values are obtained with a time-dependent analysis with a box-shaped time window of duration tobs = 158 days, using an unbinned maximum likelihood ratio method to search for an excess on the number of neutrino events consistent with a point source, with γ, Φref and tobs being fitting parameters. Replacing the parameters above in eq. (2.1), we obtain Npred ≈ 15, integrating in the energy range Eν = 10−1–106 TeV. Our predicted number of events, with its uncertainties, is consistent with the 13 ± 5 neutrinos observed by IceCube, validating our procedure. – 3 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 In the literature, there exist several models claiming to be consistent with the neutrino outburst [47–53], managing to generate a large enough neutrino flux without exceeding the observed gamma ray emission. In the following, in order to place the most conservative bounds on σνDM, we focus on the three models giving the largest Npred for σνDM = 0, as calculated with eq. (2.1). The models under consideration all have Npred > 6.55, which is the 90% C.L. lower limit on the number 13 ± 5 of observed IceCube events, assuming a normal distribution. The first model is the two-zone radiation model, also called the inner-outer blob model, of Xue et al. [47, 49]. In this model, neutrino and gamma-ray emission occur in a first zone (inner blob) close to the Schwarzschild radius of the black hole, where X-ray photons from the hot corona absorb all gamma rays. The second zone (outer blob), located farther away, is responsible for the less energetic multi-wavelength electromagnetic emission observed. This flux is shown in figure 3 of [49] and has Npred = 11.5. The second model, from Wang et al. [50] considers the possibility of having the neutrinos being generated by the interactions between the jet of the blazar and a dense cloud, the latter originating from the envelope of a Red Giant star being tidally disrupted by the black hole. In this case, interactions of low-energy protons provide an electromagnetic spectrum that is spread out, and thus help respect the bounds, while the high energy undeflected protons lead to the neutrino flux. Case 2, shown in figure 2 of the paper, gives Npred = 6.83. The third model we consider is a recent work proposed by Yang et al. [51]. Here, similarly to [53], the neutrino emission is attributed to the accretion flow of the SMBH rather than the relativistic jet. To account for the 2014–2015 neutrino outburst, a super-Eddington accretion rate is required. The authors examine neutrino production in both the magnetically arrested disk (MAD) and the standard and normal evolution (SANE) accretion regimes. While both scenarios yield a neutrino flux consistent with observations, we adopt the flux from the SANE regime, as it is associated with less energetic jets, making it more compatible with the low gamma-ray emission observed during the 2014–2015 neutrino outburst.2 The SANE case, shown in the figure 6 of [51] with particle acceleration efficiency η = 300, gives Npred = 13.3. The spectra of events to be expected from each flux at IceCube is shown on the right panel of figure 1. This corresponds to the convolution of the flux and effective area, namely, the integrand of eq. (2.1). These are compared with the IceCube flux, eq. (2.2), where it is clear that the latter has a larger contribution from low-energy events than any of the models considered here, as well as a long tail. We find that the flux from Xue et al. [49] has a large contribution from medium energy neutrinos, peaking around Eν ∼ 10 TeV, but being around two orders of magnitude smaller than IceCube at low energy, and very strongly suppressed for energies above ∼ 103 TeV. In contrast, the flux from Wang et al. [50] leads to a much harder neutrino spectrum, peaking around Eν ∼ 100 TeV, and a tail going beyond that from Xue et al. [49]. Nevertheless, the noticeable lack of low-energy neutrinos leads to a relatively small Npred. Finally, The flux from Yang et al. [51] has a contribution from the low-energy neutrinos similar to the IceCube flux, peaking around Eν ∼ 1 TeV, but with a slightly shorter tail. It is worth noting that although the neutrino spectra have different shapes, given the 2In the recent work [54], the authors point out that the X-ray and proton luminosities assumed in these models are significantly higher than expected, and when realistic parameters are used, the resulting coronal neutrino emission from TXS 0506+056 is too low to account for the IceCube observation. – 4 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 significant fractional uncertainties in the energy reconstruction of the observed neutrinos (O(25%) in log10(Eν/TeV)),3 it is not possible to use the energy dependence of the IceCube flux to discriminate any of the considered models. 3 DM spike The second key element needed to constrain σνDM is the DM density profile of TXS 0506+056 and its host galaxy. If the growth of the black hole is adiabatic, an initially cuspy dark matter profile of the form ρ(r) = ρ0(r/r0)−γ , with 0 < γ < 2 and ρ0 a reference density at r = r0, evolves into a steeper distribution [55, 56]: ρ′(r) = ρR gγ(r) ( Rsp r )γsp , (4RS < r ≤ Rsp) . (3.1) Here, we have γsp = (9 − 2γ)/(4 − γ) as the spike slope, which is valid up to the spike radius Rsp = αγ r0(MBH/ρ0 r3 0)1/(3−γ). Apart from the black hole mass MBH, the spike radius depends on a normalization factor αγ , which must be obtained numerically (values are given in [55]). In addition, ρ′(r) depends on an additional function gγ(r), which is also obtained numerically in [55], and a further normalization factor ρR = ρ0(Rsp/r0)−γ designed such that ρ′(Rsp) = ρ(Rsp). Finally, eq. (3.1) is valid only if r ≥ 4RS , where RS is the Schwarzschild radius, with particles in smaller orbits being accreted into the SMBH, leading to a vanishing distribution. For definiteness, in the following we take γ = 1, which implies γsp = 7/3, αγ = 0.122 and gγ(r) ≈ (1 − 4RS/r)3. This election for the slope γ = 1 corresponds to an initial Navarro-Frenk-White (NFW) density profile [57, 58], given by ρNFW(r) = ρ0 r0 r ( 1 + r r0 )−2 . (3.2) We consider that outside the spike radius Rsp, the density of dark matter halo is still determined by the pre-existing NFW profile. For a fixed r0, γsp and MBH, the reference density ρ0 determines the spike size Rsp. The density can be estimated by requiring that the enclosed dark matter mass be roughly equal to the black hole mass [56, 59–61]∫ rmax rmin 4π ρ′(r) r2dr ≈ MBH (3.3) with rmin = 4RS and rmax = 105 RS , the radius of influence of the SMBH. Then ρ0 =  (3 − γsp)MBH 4π rγ 0 ξ(γsp−γ) ( r 3−γsp max − r 3−γsp min ) (4−γ) (3.4) with ξ = αγ r0 (MBH/r3 0)1/(3−γ). We adopt r0 = 10 kpc as the scale radius [39, 41], comparable to that of the Milky Way, for which r0 ∼ 20 kpc [62]. The mass of the black hole at 3Derived from the plot S6 in the ref. [29]. – 5 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 the center of TXS 0506+056 was estimated in [63] to be MBH ≈ 3 × 108M⊙, leading to ρ0 ≈ 2 × 105 GeV/cm3. This, in turn, implies that Rsp ≈ 0.3 pc. A more precise description of the DM spike would require the inclusion of relativistic effects. In [64] it was found that the relativistic effects reduce the inner radius of the spike from 4RS to 2RS , and increase significantly the density profile near the black hole. This enhancement of the density is larger for the case of a rotating black hole [65]. However, these relativistic effects are relevant only close to the SMBH, at r ≲ 20RS , while, as we will see, neutrinos are produced in more distant areas, so we will disregard such effects. Having defined the dark matter density profile for all values of r, we now consider the effects of dark matter self-annihilation. Such a possibility is to be expected once one allows ν DM → ν DM scattering, however, in the following we do not relate σνDM with the annihilation rate. In this case, the profile is suppressed by a factor ρsat = mDM/(⟨σv⟩ann tBH), where mDM is the DM mass, ⟨σv⟩ann is its velocity averaged annihilation cross section and tBH is the age of the black hole, for which we take the value tBH = 109 yr. In this situation, one needs to replace: ρDM(r) → ρDM(r) ρsat ρDM(r) + ρsat (3.5) where ρDM(r) represents either ρ′(r) or ρNFW(r), depending on r.4 It is important to note that the original profile is recovered when ρsat → ∞, which happens for vanishing ⟨σv⟩ann or very large mDM. To explore the range of possible outcomes for different annihilation cross-sections, we follow [59, 60] by considering three benchmark models BM1-BM3, with ⟨σv⟩ann = (0, 0.01, 3) × 10−26 cm3/s, respectively. As noted in [60], the first benchmark with ⟨σv⟩ann = 0 may be appropriate for asymmetric dark matter models [69, 70] and, more generally, for scenarios where no significant spike depletion is expected. The third benchmark with ⟨σv⟩ann = 3 × 10−26 cm3/s corresponds to thermal relic dark matter, while the second with ⟨σv⟩ann = 10−28 cm3/s represents an intermediate annihilation rate. In addition to annihilation effects, gravitational interactions between DM and stars surrounding the black hole may deplete the structure of the spike. Depending on the age of the galactic bulge, the spike can relax to a profile with an index as low as γsp = 3/2, without modifying aforementioned parameters, such as αγ and ρ0 [71]. To be conservative, we will consider the models BM1′-BM3′ using this less cuspy value γsp = 3/2, as was also done in [38]. In figure 2 we display the DM density profile of TXS 0506+056, for each of the benchmark models. On the left panel, we show γsp = 7/3 (3/2) in black (red), with the previously mentioned values of ⟨σv⟩ann in solid, dotted and dashed lines, respectively. It is clear that scenarios BM1 and BM1′, where ⟨σv⟩ann vanishes, have a very cuspy profile, while scenarios BM3 and BM3′, where the annihilation is largest, show an inner core-like structure. On the right panel, we compare the profile of benchmarks BM1-BM3 for different values of mDM. For BM2 and BM3, where ⟨σv⟩ann ≠ 0, we find that the peak of the density profile is more suppressed when the DM mass is small. 4Some works have pointed out that, considering general particle velocity distributions, the DM density profile cannot shallower than ∼ r−1/2 [66–68]. To simplify the discussion, we take the more cored DM profile as a conservative choice. – 6 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 5−10 4−10 3−10 2−10 1−10 1 10 210 310 r [pc] 710 910 1110 1310 1510 1710]3 [G eV /c m D M ρ BM1 BM2 BM3 BM1' BM2' BM3' emissionν 5−10 4−10 3−10 2−10 1−10 1 10 210 310 r [pc] 710 910 1110 1310 1510 1710]3 [G eV /c m D M ρ emissionν BM1 = 10 MeV DM BM2, m = 1 GeV DM BM2, m = 100 GeV DM BM2, m = 10 MeV DM BM3, m = 1 GeV DM BM3, m = 100 GeV DM BM3, m Figure 2. DM distribution around the black hole of TXS 0506+056, for the different considered benchmark models with ρ0 = 2 × 105 GeV/cm3. In the left figure, the dark matter mass is assumed to be mDM = 1 GeV. In light blue we show the region where neutrinos are likely emitted, see the text for details. Model BM1 BM2 BM3 BM1′ BM2′ BM3′ γsp 7/3 7/3 7/3 3/2 3/2 3/2 ⟨σv⟩ann 0 0.01 3 0 0.01 3 ΣDM 16.07 10.14 3.78 8.70 8.09 3.78 Table 1. Benchmark models consider in this work, with ⟨σv⟩ann in units of 10−26 cm3/s. We also include the column density ΣDM, in units of 1028 GeV/cm2, calculated taking Rem = RBLR and mDM = 1 GeV. The probability for neutrinos to scatter from DM in the spike of course depends on the amount of DM the neutrinos encounter on their path, which is encoded on the column density ΣDM. To this end, we define the accumulated column density: Σ̃DM(r) = ∫ r Rem dr′ ρDM(r′) , (3.6) where Rem is the location where the neutrinos are produced, measured from the center of the black hole. The column density for the DM density profile then follows ΣDM = Σ̃DM(r → ∞). Contributions from the intergalactic DM and the Milky Way halo to ΣDM are about five orders of magnitude lower than the spike and TXS halo contribution [35], so in the following are disregarded. For clarity, in table 1 we show the column density values obtained with the six different benchmark models, considering mDM = 1 GeV and Rem = RBLR = 0.0227 pc, the broad-line region (BLR), where the neutrinos are likely to be produced [63]. As expected, for a fixed γsp, the column density decreases with increasing ⟨σv⟩ann. Our results are consistent with figure 2, in the sense that larger density profiles correspond to larger values of ΣDM. Notice that scenarios BM3 and BM3′ have practically identical profiles, regardless of the different γsp, leading to the same ΣDM in both cases. To finalize this section, let us comment on the values of Rem predicted by the models of Xue et al. [49], Wang et al. [50] and Yang et al. [51], described earlier. We follow the treatment – 7 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 made in [38] and estimate the emission radius as Rem = R′ δ, where R′ is the comoving size of the emission region and δ is the Doppler factor. Then, for the jet-cloud interaction model from Wang et al. [50], we obtain Rem = 1018 cm ≈ 0.3 pc. For the two-zone model of Xue et al. [49], we find Rem = 6 × 1015 cm ≈ 0.002 pc. For the accretion flow neutrinos model from Yang et al. [51], we get Rem ≈ 1.3 × 1015 cm ≈ 4 × 10−4 pc. These values define the neutrino emission region, shown in light blue in figure 2. From this calculation, one finds that the flux from Wang et al. [50] has Rem ≈ Rsp, so their flux will not be subject to the spike. This does not mean that these neutrinos shall not be subject to interactions with DM, but that one should expect a relatively small ΣDM. In contrast, the emission region for the fluxes by Xue et al. [49] and Yang et al. [51] lies closes to the peak of the spike, implying a large value of ΣDM. 4 Neutrino attenuation by DM Having defined the neutrino fluxes to be considered in our study, as well as the DM distribution around the SMBH, we now turn to describe the neutrino flux attenuation due to their scattering with DM along the journey to the detector. Assuming that neutrino-DM interactions are flavour-universal, this can be described by a form of the Boltzmann equation known as the cascade equation [38, 40]: dΦ dτ (Eν , τ) = −σνDM(Eν)Φ(Eν , τ) + ∫ ∞ Eν dE′ ν dσνDM dEν (E′ ν → Eν)Φ(E′ ν , τ) , (4.1) where τ = Σ̃DM(r)/mDM is proportional to the accumulated column density from Rem up to a point r. Here, Φ(Eν , τ) is the neutrino flux after traversing a distance corresponding to a column density equal to τ mDM. On eq. (4.1), the first term on the right hand side describes the neutrino loss in the beam, depending directly on σνDM. Furthermore, the second term represents the redistribution of energy due to the neutrino-DM interaction, where an initial neutrino energy E′ ν is decreased to the observed energy Eν by the dσνDM/dEν factor. To solve this equation we must make an assumption about the energy dependence of both σνDM and dσνDM/dEν . In order to illustrate how the bound on the cross-section is placed, we first assume an energy independent cross-section, σνDM = σ0, and neglect the energy redistribution term in eq. (4.1). This leads to a flux Φobs arriving to IceCube with an exponential attenuation: Φobs(Eν) = Φem(Eν) e−µ (4.2) where µ = σ0ΣDM/mDM and Φem(Eν) = Φ(Eν , τ = 0) corresponds to the emitted neutrino flux. Then, using eq. (2.1), we can relate the parameter µ with the number of predicted and observed events: µ = ln Npred Nobs (4.3) where Npred = tobs ∫ dEν Φem(Eν) Aeff(Eν) Nobs = tobs ∫ dEν Φobs(Eν) Aeff(Eν) (4.4) – 8 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 For this example, we take Φem to be the IceCube flux, as shown in eq. (2.2), so Npred ≈ 15. Requiring that the observed events lie above the 90% C.L. lower limit by IceCube (Nobs ≥ 6.55), we obtain µ ≲ 0.83, so the energy independent cross section must satisfy: σ0 ≲ 0.83mDM ΣDM . (4.5) In this case, the limit on the cross-section depends linearly on the ratio between DM mass and column density. From table 1, which assumes mDM = 1 GeV, we see that the limit ranges from 5.2 to 22 × 10−30 cm2. Let us now proceed with our full analysis. In the following, we take a cross section σνDM with a power-law dependence with neutrino energy σνDM(Eν) = σ0 ( Eν E0 )n , (4.6) with a reference energy E0 = 100 TeV. For the scaling, we consider n = 1, 0, −1, −2, as motivated by simplified models such as those discussed in appendix C of [18].5 Moreover, for the differential cross section we consider a scattering isotropic in the center of mass frame, and approximate: dσνDM dEν (E′ ν → Eν) ≈ σνDM(E′ ν) E′ ν = σ0 E0 ( E′ ν E0 )n−1 . (4.7) This assumption for the neutrino-DM cross-section allows us to solve the cascade equation, following the algorithm presented in [72]. For this, we evaluate the flux at specific values of energy Ei, such that Φi(τ) ≡ Φ(Ei, τ). The chosen Ei are logarithmically spaced, that is, Ei = 10xi , with constant ∆x. This allows us to discretize eq. (4.1), taking the form: dΦi dy = µ N∑ j=i ( − ( Ei E0 )n δij + ∆x ln 10 ( Ej E0 )n) Φj (4.8) where we have defined a dimensionless evolution parameter y = (mDM/ΣDM)τ ∈ [0, 1]. With this, eq. (4.8) can be written in terms of a matrix M , such that: dΦ⃗ dy = µM Φ⃗ . (4.9) Since the equation is linear, the eigenvectors ϕ̂i of M satisfy the differential equation ϕ̂′ i = µ λi ϕ̂i, where λi are the corresponding eigenvalues. With the ϕ̂i forming a complete basis, the solution of eq. (4.8) is Φ⃗(y) = ∑ ci ϕ̂i eµ λi y , (4.10) where the coefficients ci are determined by the initial neutrino flux, at y = 0. The observed flux Φobs(Eν) is an interpolation of the solved Φi(y = 1), which can be used to calculate Nobs in eq. (2.1). We also checked we got the same results when solving eq. (4.8), by evolving the initial flux with small increments in y, from y = 0 to y = 1. 5The scaling index n is derived by taking the high- and low-energy limits of various cross sections. The cases n = −1 and n = −2 correspond, respectively, to models with fermionic and scalar dark matter, both with scalar mediators, in the limit of very high neutrino energy. A more detailed discussion on simplified models and their impact on neutrino flux attenuation will be presented in an upcoming paper. – 9 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 Reference flux Φν µmax n = 1 n = 0 n = −1 n = −2 IceCube [29] 9.32 1.54 0.318 0.0801 Xue et al. [49] 1.89 1.13 0.505 0.228 Wang et al. [50] 0.0157 0.0977 0.173 0.134 Yang et al. [51] 2.62 1.08 0.267 0.0664 Table 2. Maximum allowed value for the attenuation parameter µ = σ0ΣDM/mDM for the different neutrino flux models, assuming σνDM = σ0(Eν/E0)n. Constraints on µ are then placed by requiring Nobs ≥ 6.55, as done earlier. The largest allowed values, µmax, are reported in table 2, for n = 1, 0, −1, −2 and the four assumed fluxes. For the IceCube flux in eq. (2.2), constraints are weakest for σνDM ∝ (Eν/E0), (n = 1), and strongest for σνDM ∝ (Eν/E0)−2, (n = −2). This can be understood by analyzing how each cross-section affects the low-energy and high-energy parts of the neutrino spectrum at IceCube, illustrated in black lines on figure 3. For n = 1, shown in figure 3(a), the high-energy tail of the flux is strongly suppressed, particularly for energies above 10 TeV. However, since the peak of the spectrum lies at Eν ≈ 1 TeV, losing the high-energy tail affects Nobs only marginally, allowing then large values for µmax. In contrast, as seen on figure 3(d), setting n = −2 affects heavily the low-energy part of the spectrum. The small value of µmax in this case already decreases the peak by more than one order of magnitude, shifting it to Eν ≈ 30 TeV, thus suppressing Nobs down to 6.55 events. Still concentrating on the IceCube flux, the cases with n = 0 and n = −1, on black lines in figures 3(b) and 3(c) respectively, show in-between scenarios. The energy-independent cross-section affects the whole spectrum without shifting the position of the peak, with the maximum value diminished by a factor ∼ 2. Since this time the low-energy part of the spectrum is affected, µmax cannot be as large as the one for n = 1. In contrast, when the cross-section is proportional to the inverse of Eν , the peak is suppressed and shifted, similar to the n = −2 scenario, implying a smaller µmax. Table 2 and figure 3 also show results for the three blazar models [49–51]. Before giving details, it is worth noting that for σνDM = 0 the models by Xue et al. [49] and Yang et al. [51] predict over 50% more events than the one from Wang et al. [50], so it is natural to expect the former two to be less constraining than the latter. Furthermore, the prediction from Wang et al. [50] in this case is very close to our threshold, Nobs ≥ 6.55, so for this model we should expect small modifications to the spectrum shown on the right panel of figure 1. As can be seen in table 2, for the fluxes by Yang et al. [51] and Xue et al. [49] the bounds on µ becomes more constraining as one moves from n = 1 to n = −2. The underlying reason for this is similar to that for the IceCube flux, to pass the Nobs threshold these models rely mostly on low- and medium-energy events (around 1 and 10 TeV, respectively), as can be corroborated in figure 3. The n = 1 interactions affect mainly the tail of the spectrum, so these models can afford a larger µ, while the n = −2 interactions suppress the low and medium energies, forcing µ to lower values. Notice that, except for n = 1, the flux by Yang et – 10 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 1−10 1 10 210 310 410 510 610 [TeV]νE 15−10 13−10 11−10 9−10 7−10 /s ec ] -1 ) [T eV ν (E ef f ) A ν (E ν Φ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 ν E∝ σ (a) 1−10 1 10 210 310 410 510 610 [TeV]νE 15−10 13−10 11−10 9−10 7−10 /s ec ] -1 ) [T eV ν (E ef f ) A ν (E ν Φ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 = constσ (b) 1−10 1 10 210 310 410 510 610 [TeV]νE 15−10 13−10 11−10 9−10 7−10 /s ec ] -1 ) [T eV ν (E ef f ) A ν (E ν Φ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 ν 1/E∝ σ (c) 1−10 1 10 210 310 410 510 610 [TeV]νE 15−10 13−10 11−10 9−10 7−10 /s ec ] -1 ) [T eV ν (E ef f ) A ν (E ν Φ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 ν 2 1/E∝ σ (d) Figure 3. Neutrino spectrum at IceCube, allowing interactions with DM. The solid lines show the spectra for all the considered fluxes with a cross section σνDM ∝ En ν for a) n = 1, b) n = 0, c) n = −1 and d) n = −2. All curves are consistent with Nobs = 6.55. The spectrum representing the case where σνDM = 0, also presented on the right panel of figure 1, is shown in dashed lines. al. [51] puts stronger bounds on µ than the one by Xue et al. [49], which is indicative of the higher importance of the lowest energy part of the spectrum for this model. Let us now turn to the model by Wang et al. [50] which, as mentioned previously, already has a small number of events in absence of interactions with DM, leading to µmax values that are usually small. However, contrary to the previous cases, it is less constraining as one moves from n = 1 to n = −1. As one can see in figure 3, this happens because the flux presents a hard spectra, peaking at ∼ 100 TeV, with a small contribution to Nobs coming from low-energy events. Thus, n = −1 tends to affect a sector of the spectrum that does not contribute much to the final number of events. Interestingly, n = −2 is less constrained than n = −1, here the suppression of low-energy events is so strong that it starts affecting the 100 TeV peak. We can also see in figure 3, for the cases n = 0 and n = −1, that the observed flux becomes slightly larger than the initial flux for Eν ∼ 10 TeV. This is due to the effect of the second term in the cascade equation (4.8), which enhances the low-energy neutrino flux at the expense of the high-energy flux. Given the hard spectrum of the Wang flux, this effect becomes more pronounced. – 11 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ BM1 BM1' BM2 BM2' BM3 BM3' = 100 TeV0 E ν E∝ σ (a) 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ BM1 BM1' BM2 BM2' BM3 BM3' const∝ σ (b) 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ BM1 BM1' BM2 BM2' BM3 BM3' = 100 TeV0 E ν 1/E∝ σ (c) 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ BM1 BM1' BM2 BM2' BM3 BM3' = 100 TeV0 E ν 2 1/E∝ σ (d) Figure 4. 90% C.L. bounds on DM-neutrino cross section obtained with Rem = RBLR and flux given by eq. (2.2), considering (a) σ ∝ Eν (n = 1), (b) σ = σ0 (n = 0), (c) σ ∝ 1/Eν (n = −1) and (d) σ ∝ 1/E2 ν (n = −2). It is important to notice that these results are independent of any assumption taken regarding the DM mass and spike profile, as all this information is contained within µ.6 Nevertheless, the latter become relevant when translating the limit on µ to a limit on σ0, the reference cross-section at Eν = E0 = 100 TeV: σ0 ≤ µmax mDM ΣDM . (4.11) Such a bound is shown in figure 4 as a function of mDM, assuming the IceCube flux and setting the neutrino emission region Rem = RBLR. Each panel shows one of the four assumed behaviors for the cross-section, and places constraints based on the benchmark models for the DM spike profile, as detailed in table 1. Let us first focus on benchmarks BM1 and BM1′, shown on all panels in solid black and red lines, respectively. These two benchmarks assume no DM self-annihilation, meaning that they have the largest column densities, and thus place the strongest limits on σ0. For mDM = 10 keV, the limits range from ∼ O(10−33) cm2 (n = 1) to ∼ O(10−36) cm2 6Note that the bound on µ depends on E0, the chosen reference energy for σ0. In spite of this, all results shown in figures 3 do not depend on this choice. – 12 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 (n = −2), while for mDM = 1 TeV, the limits are weakened to ∼ O(10−25) cm2 (n = 1) to ∼ O(10−28) cm2 (n = −2). For benchmarks BM1 and BM1′ described above, the limits depend linearly on mDM. However, this is no longer the case when allowing for DM self-annihilation, as the saturation density depends on the DM mass, see the right panel of figure 2 and the discussion below eq. (3.2). This means that ΣDM becomes a function not only of ρDM(r) and Rem, but also of mDM, with lower values of DM mass associated to a larger suppression of the column density. Such behavior is evident in figure 4 where, for large DM mass, the bounds in benchmarks BM2(′) and BM3(′), shown in dotted and dashed lines, tend to coincide with those for benchmarks BM1(′), while for small DM mass they are much weaker. In particular, for mDM = 1 keV, the constraints on σ0 in benchmarks BM3(′) are roughly two orders of magnitude weaker than those for BM1(′). Finally, we address the bounds on σ0 for the models in consideration [49–51]. As commented in section 3, one can estimate Rem in each case. The model by Wang et al. [50] have the largest Rem, such that their emission region is practically outside the DM spike. In contrast, the flux by Yang et al. [51] has the smallest Rem, that is, it is generated deep within the spike. It is then to be expected that the column density of the former will be the smallest, and the latter will be largest. As an example, for BM1 we have ΣDM = (16.07, 261, 5.80, 1318.7) × 1028 GeV/cm2 for IceCube, Xue et al. [49], Wang et al. [50] and Yang et al. [51] fluxes, accordingly. The value of Rem is also connected to the sensitivity to changes in the DM density profile. As shown in figure 2, the density profile can change by the modification of γsp, or by the presence of DM self-annihilation, with this last feature depending on mDM and ⟨σv⟩ann. Furthermore, alterations due to self-annihilation are stronger for r < Rsp, that is, the spike is more sensitive to them than the NFW profile. Thus, the fluxes from Xue et al. [49] and Yang et al. [51] should be most affected by changes in γsp, ⟨σv⟩ann and mDM, while those by Wang et al. [50] should not be affected by γsp, and would be marginally sensitive to the other two parameters (apart from the explicit mDM dependence expected from eq. (4.11)). These considerations imply that even though the attenuation parameter µ could be less constrained in a specific model compared to another one, a large column density could turn this into a stronger limit in terms of σ0. This is shown in figure 5, where we plot bounds on σ0 as a function of the DM mass. As before, we show results for a cross-section proportional to (Eν/E0)n, for n = 1, 0, −1, −2. The figure shows a shaded region for each flux, indicating a range of bounds, obtained by comparing the tightest and loosest bounds, from BM1 and BM3′, respectively. Let us focus on results for mDM = 1 TeV (the right hand side of all panels). Here, the DM density profile is least affected by self-annihilation, so the uncertainty in the bound for each model is the lowest. Consistent with our expectations, for this DM mass, the bound from Wang et al. [50] have a very small uncertainty, followed by that from IceCube, and finally the ones from Xue et al. [49] and Yang et al. [51], where the uncertainty is relatively large, mainly due the variation in γsp. In contrast, for mDM = 10 keV (the left hand side of all panels) we have that even the NFW profile at r > Rsp is affected by the variation in ⟨σv⟩ann, leading to a large uncertainty for the bounds from all models. Still, the limits from Yang et al. [51] always have the largest uncertainty over the whole DM mass range we have considered. – 13 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 = 100 TeV0 E ν E∝ σ (a) 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 const∝ σ (b) 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 = 100 TeV0 E ν 1/E∝ σ (c) 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ IceCube Fig 3 Xue et al. 2021 Fig 2 Wang et al. 2022 Fig 6 Yang et al. 2025 = 100 TeV0 E ν 2 1/E∝ σ (d) Figure 5. Range of bounds between BM1 and BM3’ for each flux mode with a cross section σνDM ∝ En ν for a) n = 1, b) n = 0, c) n = −1 and d) n = −2. For n = 1, figure 5(a), the constraints placed assuming the flux from Yang et al. [51] are potentially the strongest, for all values of mDM. The weakest bounds, in turn, always come from the IceCube flux, for mDM ≳ 100 MeV. For lower masses, the maximum uncertainty in this case reaches somewhat over two orders of magnitude, also overlapping the bounds from Xue et al. [49] and Yang et al. [51]. Furthermore, we find in this case that the range of bounds from Xue et al. [49] and Wang et al. [50] are always fully contained within the range from Yang et al. [51]. Overall, the constraints placed for mDM = 10 keV range from O(10−36) to O(10−31) cm2, while those for mDM = 1 TeV go from O(10−28) to about O(10−25) cm2. For n = 0, figure 5(b), the strongest constraint is potentially placed by Yang et al. [51] over the whole mass range. However, the uncertainty is so large, that it encompasses the range of bounds placed by Wang et al. [50], the range by Xue et al. [49], and most of that by the IceCube flux. The latter also always potentially places the weakest bound. Overall, for mDM = 10 keV, the bounds span from O(10−36) to O(10−32) cm2. For mDM = 1 TeV, the limits reach as low as O(10−28) and as high as O(10−26) cm2. For n = −1, figure 5(c), and n = −2, figure 5(c), the model by Yang et al. [51] always potentially provides the most stringent constraints. The second strongest constraints are given by the model of Xue et al. [49], though its large uncertainty also leads it to potentially – 14 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 giving the weakest constraints of all the models. The range from the latter model fully encompasses those from IceCube and Wang et al. [50], except for a small, narrow region above ∼ 300 GeV for n = −2 where Wang et al. [50] gives much weaker bounds. It is also interesting to note that for n = −1 the range of constraints from Wang et al. [50] is also fully contained within the range from IceCube. Overall, for n = −1 and mDM = 1 keV, the constraints go from O(10−37) to O(10−32) cm2. For the same n but mDM = 1 TeV, the bounds span O(10−29) to O(10−27) cm2. For n = −2, we find that for mDM = 10 keV we have limits going from below O(10−37) up to O(10−33) cm2. Furthermore, for mDM = 1 TeV, the bounds range from O(10−29) to O(10−27) cm2. To summarize, we find that the bounds on σ0 depends very strongly on the neutrino emission model, the DM mass mDM, the DM self-annihilation cross section ⟨σv⟩ann, and the energy scaling n of the neutrino-DM cross-section. Without any further information on any of these inputs, the bound can vary from O(10−37) to O(10−25) cm2. However, this situation will greatly improve once the DM mass is measured, reducing the overall uncertainty to within 2–5 orders of magnitude. As commented earlier, it is important to take into account that the flux from Wang et al. [50] already have a low number of events when σνDM = 0. Thus, one could expect bounds on σ0 coming from this model to be particularly strong. Nevertheless, for a fixed mDM, the constraints on σ0 from IceCube, Xue et al. [49] and Yang et al. [51] are usually within the ballpark of those from Wang et al. [50], and can be even stronger, regardless of them having a large number of events in the σνDM = 0 scenario. This suggests that the number of events when σνDM = 0 is not necessarily the most important factor in the placement of the limits, but rather the interplay between the spectrum of the flux and the scaling n of σνDM, as shown when commenting the limits on µ. Another interesting fact we have shown is the uncertainty on the bound on σ0 depends crucially on the column density, and thus on the assumed value of Rem. Moreover, models with a large Rem have a very low sensitivity to particularities in the spike profile, and thus are likely to have low uncertainties. 4.1 Comparison with previous limits As commented in the Introduction, neutrino-DM interactions have previously been examined in similar contexts, that is, astrophysical emission of neutrinos from SMBH, and their attenuation by the DM spike. The most restrictive constraints of this kind come from IceCube neutrino detections associated with NGC 1068 (an AGN, Eν = 1.5–15 TeV [40]), the AT2019dsg event (from a TDE, Eν ∼ 270 TeV [41]), and the IC-170922A event (from blazar TXS 0506+056, Eν ∼ 290 TeV [38, 39]). It is thus desirable to compare these bounds with those derived in this work. To this end, in figure 6 we presents our limits on the cross-section σνDM as a function of the neutrino energy Eν , for mDM = 1 GeV, obtained using the fluxes from IceCube [29], Xue et al. [49], Wang et al. [50] and Yang et al. [51]. These constraints are the strongest we have derived for each model, assuming the BM1 benchmark, that is γsp = 7/3 and no DM self-annihilation. On each panel of the figure, we present scenarios with n = 1, 0, −1, −2 in red, blue, green and purple, respectively. – 15 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 1−10 1 10 210 310 410 510 610 [TeV]νE 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m -D M νσ IceCube flux 2018 n=0 n=1 n=-1 n=-2 = 0.0227 pcBLR = RemR IC-170922A NGC 1068 AT2019dsg (a) 1−10 1 10 210 310 410 510 610 [TeV]νE 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m -D M νσ Flux from Xue et al. 2021 n=0 n=1 n=-1 n=-2 IC-170922A NGC 1068 AT2019dsg (b) 1−10 1 10 210 310 410 510 610 [TeV]νE 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m -D M νσ Flux from Wang et al. 2022 n=0 n=1 n=-1 n=-2 IC-170922A NGC 1068 AT2019dsg (c) 1−10 1 10 210 310 410 510 610 [TeV]νE 37−10 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m -D M νσ Flux from Yang et al. 2025 n=0 n=1 n=-1 n=-2 IC-170922A NGC 1068 AT2019dsg (d) Figure 6. Bounds on σνDM in function of neutrino energy Eν obtained using the neutrino flux given in a) IceCube [29], b) Xue et al. [49], c) Wang et al. [50] and d) Yang et al. [51]; with their respective Rem. The dark matter mass is assumed to be mDM = 1 GeV. The figure also includes the aforementioned previous limits obtained from high-energy neutrinos. We begin our comparison with the limit from AT2019dsg [41]. Being based on a single 270 TeV neutrino, and derived for n = 0, it is presented on every panel as a blue triangle at the corresponding Eν . By comparing this with our blue lines, we find the bound from AT2019dsg to be stronger than those obtained at this value of energy from the IceCube and Wang et al. [50] models, but weaker than Xue et al. [49] and Yang et al. [51]. In all cases excepting IceCube, the difference is by less than an order of magnitude. We now turn to the IC-170922A event, which again is based on a single 290 TeV neutrino. In this case, the bound for n = 1 is taken from [38], while that for n = 0 is extracted from [39]. Both are represented on each panel as red and blue triangles, respectively. We see that for the n = 0 case, the limit is weaker than that from AT2019dsg [41] by more than an order of magnitude, being also weaker than the bounds from all of our models. The constraint for n = 1 case is weaker than n = 0, but when compared with our limits, we see that for the corresponding energy it can be stronger than the bound derived from the IceCube flux, while being weaker than the rest. We finish this part of the discussion by comparing the constraints from active galaxy NGC 1068. This time, we have a continuous emission of neutrinos, with IceCube observing – 16 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 around 80 events with energies between 1–15 TeV. Constraints for n = 1 and n = 0 come from [40], presented as usual as red and blue triangles in all panels, respectively, placed at the reference energy E0 = 10 TeV used in [40]. Here, we see that both cases place stronger constraints than the IceCube flux and the three models considered. For n = 1, the models putting the closest constraint at the reference energy are those by Wang et al. [50] and Yang et al. [51], while for n = 0 we have Yang et al. [51] slightly over one order of magnitude above it. Interestingly, no other work has considered the n = −1 and n = −2 cases, which we consider particularly important. As we have mentioned before, most fluxes rely their prediction of Npred on the lowest energy part of the spectrum, which is very strongly affected by interactions going like (Eν/E0)−1 or (Eν/E0)−2. Beyond astrophysical sources, a model-independent signal of interactions between DM and neutrinos is their effect on the CMB angular power spectra and the late-time mat- ter power spectrum. For a constant cross section, ref. [73] derives a limit of σνDM < 2.2 × 10−30 cm2 (mDM/GeV) using data from the CMB, baryon acoustic oscillations and gravitational lensing. In addition, the study carried out in [74] recognized the Lyman-α forest as a good probe of neutrino-DM interactions, setting a constraint on the cross- section of O(10−33) cm2, assuming it to be constant in energy and taking mDM = 1 GeV. However, a refined analysis in [75] found a preference for non-zero DM-neutrino interac- tions7 so, to be conservative, we take this bound equal to their lower limit at 1σ, that is, σνDM < 3.6 × 10−32 cm2 (mDM/GeV). A recent analysis using the observational data of Milky-Way satellite galaxies from the Dark Energy Survey (DES) and PanSTARRS1 obtain a bound of σνDM < 10−32 cm2 (mDM/GeV) [78]. Even stronger bounds have been obtained from 21 cm cosmology, reaching σνDM < 4.4 × 10−33 cm2 (mDM/GeV) [79]. In addition to cosmological constraints, neutrino-DM interactions can be probed in direct detection experiments under the assumption that DM interacts with nucleons or leptons. High-energy neutrinos from stars [80], diffuse supernovae [81], or the supernova SN1987A [82] could boost DM particles, leading to an increased energy deposition from light DM candidates. Other methods to probe DM-neutrino interactions involve studying the attenuation of neutrino fluxes from supernovae, the Galactic Center, active galaxies, or tidal disruption events (TDEs). Figure 7, displays the most stringent limits for energy-independent cross-sections and compares them with the range of constrains derived in this work. We can see that the strongest limits come from cosmology and from the AGN NGC 1068. 5 Conclusions With the true nature of dark matter remaining ever more elusive, it is important to gather data from all possible sources of interactions. In this work, we have used the neutrino flux observed during the 2014–2015 neutrino outburst of TXS 0506+056 to constrain the neutrino-DM cross-section. The logic behind the bound is that of preventing attenuation, which means that, given a particular neutrino flux coming from a blazar surrounded by a DM profile, one can place constraints on the neutrino-DM cross-section by demanding their interactions not to diminish the flux below a specific threshold. 7Further support for a possible nonzero interaction was found in an analysis based on CMB data from the Atacama Cosmology Telescope [76, 77], consistent with the Lyman-α result in [75]. – 17 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 5−10 4−10 3−10 2−10 1−10 1 10 210 310 [GeV]DMm 35−10 33−10 31−10 29−10 27−10 25−10]2 [c m 0σ CMB+BAO α Lyman- AT2019dsg IC170922A NGC 1068 21 cm dSN Xenon1T dSN Super-K Stelar BDM SN1987A MW sat This work 0σ = σ Figure 7. Range of 90% C.L. bounds on DM-neutrino cross section obtained considering energy- independent cross section, with previous constrains for comparison: (blue) CMB, baryon acoustic oscillations and lensing [73]; (orange) Lyman-α preferred model [75]; (red) 21 cm cosmology [79]; (black) Milky-Way satellite galaxies [78]; boosted dark matter searches with (pink, brown) diffuse supernova neutrinos [81]; (gray) stellar neutrinos [80]; (teal) supernova SN1987A [82]; (purple) bound from IC-170922A [38, 39]; (green) tidal disrupted event AT2019dsg [41]; (cyan) active galaxy NGC 1068 [40]. An noteworthy difficulty found by most blazar models is to generate the high-energy neutrino flux while remaining consistent with X-ray and gamma-ray constraints. For our results, we took into account fluxes from three very different models giving a relatively large number of events at IceCube. We also considered the flux originally used by IceCube to fit their observed events. Then, by solving the cascade equation, we quantified the attenuation caused by both the DM spike and the DM halo, considering various energy-dependent cross-sections motivated by simplified models. To account for uncertainties in the DM spike parameters, we present our results as a range of bounds, obtained by comparing the most and least restrictive constraints. We find that the limits on the reference cross-section σ0 are highly sensitive to the assumed neutrino flux model, the DM particle mass mDM, the properties of the DM spike (such as its slope γsp and the DM self-annihilation cross-section ⟨σv⟩ann), and the energy scaling n of the neutrino-DM cross-section. The main results of this work can be found in figure 5, which shows the uncertainty bands as a function of mDM for each blazar model and for each assumed n for the cross-section. We find that for a fixed mDM, the uncertainty can span between ∼ 2 and ∼ 5 orders of magnitude, with the strongest bounds being around O(10−37) cm2 (O(10−29) cm2) for mDM = 10 keV (1 TeV), for the model of Yang et al. [51] and n = −2. Our results are compared with other constraints in figures 6 and 7. Although our limits are weaker than those derived from NGC 1068, they are comparable to, and in some cases more restrictive than, those obtained from TDEs and the IC-170922A event. Notably, no – 18 – J C A P 0 7 ( 2 0 2 5 ) 0 4 2 previous study has explored cross-sections with n = −1 or n = −2, cases that we introduce in this work, motivated by models involving light scalar mediators. Looking ahead, future data from Baikal-GVD and KM3NeT, together with continued IceCube observations, will enable the identification of more high-energy neutrino sources. This will further improve our understanding of neutrinos and their interactions with dark matter. 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