The presence of dark matter (DM) in galaxies and clusters of galaxies is well established by astrophysical and cosmological observations [1]. However, its particle nature remains unknown [2]. A variety of experiments have aimed to detect DM particles via their scatterings off nuclei and/or electrons at Earth-based detectors, setting strong upper limits on the interaction strength of DM particles with masses in the GeV scale but leaving the sub-GeV region of the parameter space yet largely unconstrained [3–7]. Historically, DM fermions with sub-GeV masses were disfavored by the cosmological bound [8,9]. However, large parameter space still remains unexplored in more complicated but well-motivated scenarios [10–12].

Different approaches have been proposed to extend the sensitivity reach of direct detection experiments for sub-GeV DM. Some of these consider a boosted component of DM particles reaching Earth, via gravitational effects or via scatterings with protons, electrons, or neutrinos in different astrophysical environments (e.g., Refs. [13–29]).

Active galactic nuclei (AGN) are promising sources of high-energy protons and electrons. While the dominant acceleration mechanism of these cosmic rays (CRs) is still under debate, modeling of multimessenger data has placed important constraints on not only energetics of CR production, but also the emission region of the observed neutrinos that can be produced via either inelastic pp collisions or pγ interactions [30–32]. For example, observations of high-energy neutrinos and gamma rays from NGC 1068 [33,34] suggest that the neutrino production occurs in the vicinity of the supermassive black hole (SMBH) at Rem≲(30–100)RS (where RS is the Schwarzschild radius), which is consistent with theoretical models [35–39], and the required proton luminosity is at least ∼10% of the intrinsic x-ray luminosity [40,41]. Another neutrino source candidate, TXS 0506+056 [42–46], is known to be a jet-loud AGN, the observed spectral energy distribution in photons is mostly explained by synchrotron and inverse-Compton emission from CR electrons [45,47–51], and the proton luminosity required by IceCube observations may even exceed the Eddington luminosity [47,48].

In this work, we propose CRs produced in AGN as a new, unique probe of DM-proton and DM-electron scatterings through their multimessenger observations. Given that emission regions of neutrinos and gamma rays are constrained to be near the SMBHs, CRs also need to traverse the DM spike around the central SMBH. If such additional cooling beyond the Standard Model (BSM) was too strong, CR energy losses are modified so that the required CR luminosity would be larger, and the neutrino and photon spectra could even be incompatible with the observations. Our work is different from previous studies on AGN probes of the DM scatterings with protons and electrons, which focused either on the boosted flux of DM particles from the source at Earth [22,52,53] or on the spectral distortions in the gamma-ray flux induced by CR scatterings off DM particles [54–59]. Instead, we focus on the impact of the DM-proton and DM-electron scatterings on the neutrino and photon fluxes or the CR power, considering for the first time the cooling of protons and electrons in the inner regions of the AGN, where a DM spike is likely to be formed (see Fig. 1).

The adiabatic growth of black holes may form a spike of DM particles in their vicinity [60–63]. An initial DM profile of the form ρ(r)=ρ0(r/r0)-γ evolves into ρsp(r)=ρRgγ(r)(Rspr)γsp,(1)where Rsp=αγr0(MBH/(ρ0r03))13-γ is the size of the spike, with numerical values αγ provided in Ref. [62]. The cuspiness of the spike is given by γsp=9-2γ4-γ. Furthermore, gγ(r)≈(1-4RSr), while ρR is a normalization factor, chosen to match the density profile outside of the spike, ρR=ρ0 (Rsp/r0)-γ. This density profile vanishes at 4RS, which is, however, a conservative approximation [64,65].

We consider that the initial DM distribution follows an Navarro-Frenk-White (NFW) profile [66,67], with γ=1, resulting in a spike with γsp=7/3 and αγ=0.122. The masses of the central SMBHs of the two AGN considered in this work are given in Table I. For the scale radius of both galaxies, we take r0=10  kpc. Finally, the normalization ρ0 is determined by the uncertainty on the SMBH mass [55,68], also provided in Table I. We have checked that these criteria yield masses of the DM halo compatible with those expected from universal relations between SMBH and galactic bulge masses [69,70]. We use Eq. (8) of Ref. [69].

If the DM particles self-annihilate, the maximal DM density in the inner regions of the spike is saturated to ρsat=mDM/(⟨σv⟩tBH), where ⟨σv⟩ is the velocity averaged DM self-annihilation cross section and tBH is the SMBH age. For TXS 0506+056 (NGC 1068), we take the value tBH=109 (1010) yr [52,71]. Furthermore, the DM spike extends to a maximal radius Rsp, beyond which the DM distribution follows the initial NFW profile. The DM density profile therefore reads [62,68,72] ρ(r)={0r≤4RS,ρsp(r)ρsatρsp(r)+ρsat4RS≤r≤Rsp,ρ0(rr0)-γ(1+rr0)-(3-γ)r≥Rsp.(2)The DM profiles in TXS 0506+056 and NGC 1068 are shown in the left panel in Fig. 2 for two values of ⟨σv⟩/mDM allowed for sub-GeV DM [73–75]. We find that the DM density is extremely high in the region where high-energy particles are produced.

Neutrinos and photons from AGN can be explained by emission from high-energy protons and electrons through purely SM mechanisms. Energy-loss mechanisms include scatterings with other SM particles in the plasma or synchrotron radiation as well as adiabatic losses. In addition, there are escape losses due to advection or diffusion via magnetic fields. The presence of DM coupling to protons and electrons in the vicinity of SMBHs would introduce additional scattering timescales, leading to the suppression of the observed neutrino and gamma-ray fluxes in certain energy ranges, if the BSM cooling timescales of CRs were shorter than the standard cooling timescales. For example, at mDM∼10-3  GeV, the currently allowed maximum DM-proton cross section stems from CR-boosted DM at the Super-Kamiokande experiment [76], with a value of σDM-p∼10-35  cm2. As discussed in the previous section, the average density of asymmetric DM particles in the coronal region of NGC 1068 is ⟨ρDM⟩∼5×1018  GeV/cm3. Thus, if the corresponding cross section for CR protons is comparable to σDM-p (although this is not the case, in general), the BSM cooling timescale for the currently allowed values in the literature is τDM-p∼1/(⟨nDM⟩σDM-pc)∼7×103  s, which is well below the proton cooling time inferred by observations of NGC 1068. This simple estimate clearly suggests that CRs in AGN can provide a powerful probe of these interactions.

More quantitatively, the BSM cooling timescale due to elastic DM scattering off CRs is given by [59] τDM-iel=[-1E(dEdt)DM-i]-1,(3)with (dEdt)DM-i=-⟨ρDM⟩mDM∫0TDMmaxdTDMTDMdσDM-CRidTDM,(4)where ⟨ρDM⟩ is the average density of DM particles in the region of CR production. See Table I for the specific values that we use for NGC 1068 and TXS 0506+056. Also, dσDM-CRi/dTDM is the differential elastic DM-proton or DM-electron cross section, and TDMmax is the maximal allowed value for TDM in a collision with a particle i with kinetic energy T=E-mi, which is TDMmax=2T2+4miTmDM[(1+mimDM)2+2TmDM]-1.(5)We consider fermionic DM which elastically interacts with protons and electrons via a heavy scalar mediator. The differential cross section reads [77] dσDM-CRidTDM=σDM-iTDMmaxFi2(q2)16μDM-i2s(q2+4mi2)(q2+4mDM2),(6)where σDM-i is the DM-proton or DM-electron cross section at the zero center-of-mass momentum, μDM-i is the reduced mass, s is the square of center-of-mass energy, and q2=2mDMTDM is the momentum transfer of the process. The quantity Fi is either the proton form factor [78] or equal to 1 for electrons.

In the right panel in Fig. 2, the solid lines represent the total standard energy-loss timescales as a function of energy for protons in NGC 1068 [40] and for electrons in TXS 0506+056 [79]. CR protons in NGC 1068 are almost depleted, and the dominant cooling mechanisms at increasing energies are inelastic pp interactions, Bethe-Heitler pair production, and pγ interactions [35]. CR protons do not cool efficiently in TXS 0506+056, and the fate is governed by a dynamical timescale of ∼105  s in the SMBH frame [79]. For electrons in TXS 0506+056, the dominant cooling mechanisms are inverse Compton scattering and synchrotron radiation. The breaks in the solid lines of the plots reflect the energies at which the transition of dominant processes occurs.

For comparison, we also show BSM cooling timescales due to elastic DM scatterings with protons and electrons. The dot-dashed line corresponds to values of the DM mass and cross section that would induce a contribution smaller than the proton and electron energy losses due to the SM processes. On the other hand, the dashed line shows values of the parameters that would induce larger energy losses than in the SM at relevant energies. It is important to point out that inelastic DM-proton scatterings are expected to dominate over the elastic channel at energies E≳mp2/2mDM. For simplicity, we restrict our analysis to the elastic channel.

For the purpose of constraining the interaction strength, we find for each mDM the largest DM-proton (electron) cross section yielding a timescale equal or larger to the cooling timescales determined with models at relevant energies. In particular, we use τDM-iel≥Cτicool.(7)The coefficient C is a model-dependent factor, and we use C=0.1 in this work. In other words, we find the maximum DM-proton (electron) cross section that would have an O(10) or less impact on the proton (electron) cooling timescale. This is reasonable and may be even conservative from the energetics requirement of neutrino-emitting AGN. For NGC 1068, the proton luminosity would be 1043  erg s-1≲Lp≲LX≲1044  erg s-1 [35,40], justifying C∼0.1–1. For TXS 0506+056, the proton luminosity in the single-zone model already violates the Eddington luminosity LEdd [47], so our choice is conservative. This is also reasonable for electrons because of Le∼8×1047  erg s-1∼20LEdd [79]. In principle, if the CR acceleration mechanism is understood, spectral modification due to BSM cooling may allow us to improve constraints and C∼1 is possible. For proton energies of interest, we use 10–300 TeV for NGC 1068 [33], which is required to match the IceCube data [40]. For protons in TXS 0506+056, we use 0.1–20 PeV [43], and for electrons we use 50 GeV–2 TeV, following Ref. [79].

Applying the condition of Eq. (7) for NGC 1068 and TXS 0506+056, we set constraints on the DM-proton and DM-electron cross sections via a heavy mediator (see Fig. 3). The solid lines correspond to scenario I, and the dashed lines correspond to scenario II (see Table I). We find that our constraints become stronger at lower DM masses, due to the fact that the number density of DM particles increases, and the cross section needed to induce energy losses becomes smaller. However, for protons the dependence of the constraint on the DM mass is more pronounced than for electrons, since the elastic DM-proton cross section decreases with reference to its maximum value for E≳mp2/2mDM.

For comparison, we show complementary constraints from other methods. The green region is excluded by DM direct detection experiments [88–94]. The cyan region is constrained by Milky Way satellite galaxy counts [95], and the gray region is constrained by big bang nucleosynthesis (constraints can be stronger by a factor as large as ∼3 depending on the details of the model) [96–99]. The orange region is constrained by CR-boosted DM at XENON1T [19], and the red regions are excluded when considering the blazar-boosted DM flux from TXS 0506+056 [22,52]. Finally, values above the brown line are constrained by CR-boosted DM at the Super-Kamiokande experiment [76]. Further, for DM-electron scatterings, we include constraints from the solar reflection [100], and the region of values where light thermal DM acquires its relic abundance via various mechanisms [12,87,101]. From Fig. 3, one sees that our constraints for light DM coupling to protons are stronger than complementary bounds for mDM≲10-3−10-2  GeV. Additional constraints from colliders may also apply; see, e.g., Ref. [102] for constraints on dark matter with masses above mDM≳0.1  GeV, assuming a mediator of mass mϕ∼1  GeV and a direct coupling to quarks. If the mediator were more massive, or if it couples to gluons, those constraints could be weaker.

For DM-electron scatterings, our constraints are stronger than direct detection bounds at masses below mDM≲5×10-3  GeV. In addition, for DM-electron interactions, AGN data allow one to probe the parameter space favored for DM models with mDM≲10-4  GeV. Effects of different assumptions on the DM distribution and constraints in a concrete model of DM-proton interactions are discussed in Supplemental Material [103].

Recent multimessenger measurements of AGN have indicated that high-energy particles, in particular, CR protons and secondary neutrinos, are produced in the vicinity of SMBHs. CR cooling could be significantly enhanced by BSM interactions with DM, thanks to a large DM density around the central SMBH. We demonstrated that neutrino-emitting AGN, NGC 1068 and TXS 0506+056, allow us to set strong constraints on sub-GeV DM coupled to protons and/or electrons. The new constraints on light DM coupling to protons are stronger than other complementary bounds for mDM≲10-3−10-2  GeV. For DM-electron scatterings, our constraints are stronger than direct detection bounds at masses below mDM≲5×10-3  GeV, which potentially allows us to probe the parameter space favored for thermal DM models with mDM≲10-4  GeV.

Remarkably, our method based on CR cooling is unique and different from previous AGN constraints from boosted DM [22] and those on neutrino-DM interactions [65,104–109], in that the results are largely insensitive to CR and neutrino spectra. Regarding uncertainties in CR cooling timescales, we stress that our constraints are robust and conservative for NGC 1068. This is because the neutrino production efficiency of CR protons has to be nearly maximal to explain the neutrino flux [40], and relaxing assumptions (e.g., with longer CR cooling timescales and/or softer CR spectra) will make the limits stronger. Future multimessenger observations and astrophysical modeling will allow us to better understand the sources and reduce uncertainties, and the resulting limits on the DM-proton and the DM-electron cross section will become more stringent and robust. Understanding acceleration mechanisms will also enable us to compare τDM--iel to the acceleration timescale for placing constraints.

Multimessenger observations of neutrino sources have been proposed to study DM interactions with photons [65] and neutrinos [65,104–111], as well as historically investigated annihilating or decaying signatures. Now there is accumulating evidence that AGN can accelerate CRs to TeV–PeV energies. We demonstrate that high-energy particle emission from AGN provides us with a powerful probe of DM scatterings with protons and electrons through CR interactions.