Blazars as Probes for Fundamental Physics

Abstract

Blazars are a class of active galactic nuclei characterized by having one of their relativistic jets oriented close to our line of sight. Their broad emission spectrum makes them exceptional laboratories for probing fundamental physics. In this review, we explore the potential impact on blazar observations of three scenarios beyond the standard paradigm: (i) the hadron beam model, (ii) the interaction of photons with axion-like particles (ALPs), and (iii) Lorentz invariance violation. We focus on the very-high-energy spectral features these scenarios induce in the blazars Markarian 501 and 1ES 0229+200, making them ideal targets for testing such effects. Additionally, we examine ALP-induced effects on the polarization of UV-X-ray and high-energy photons from the blazar OJ 287. The unique signatures produced by these models are accessible to current and upcoming instruments—such as the ASTRI Mini Array, CTAO, LHAASO, IXPE, COSI, and AMEGO—offering new opportunities to probe and constrain fundamental physics through blazar observations.

1. Introduction

The search for new particles, interactions, and extensions of the Standard Model (SM) of particle physics is one of the most important and exciting frontiers in both physics and astrophysics, with the ultimate goal of understanding the fundamental laws that govern our Universe. Examples include dark matter and dark energy, which are believed to constitute the largest part of our Universe, but whose nature and behavior remain unknown, and their detection is still elusive. The astrophysical environment, with its extremely high energies unattainable in laboratory experiments, provides a unique opportunity to explore new physics. In particular, blazars—a type of active galactic nuclei (AGNs)—represent one of the best astrophysical sources for this purpose, as they can emit photons with energies E detectable even above $10\mathrm{TeV}$.

Specifically, radio-loud AGN are extragalactic, accreting supermassive black holes (SMBHs), whose main feature is the presence of two collimated relativistic jets emitted in opposite directions. The different AGN phenomenology is fundamentally defined by the viewing angle under which the AGN is seen from Earth [1]. In particular, AGN with jets oriented close to our line of sight are classified as blazars, whereas those with misaligned jets are referred to as radio galaxies. Blazars are further divided into two subclasses: (i) flat spectrum radio quasars (FSRQs) and (ii) BL Lacertae objects (BL Lacs). FSRQs are characterized by strong optical emission lines, attributed to photoionized gas clouds surrounding the central SMBH. They are also highly powerful sources thought to be powered by an efficient accretion disc. Moreover, very-high-energy (VHE) photons in FSRQs experience strong absorption due to interactions with photons from the broad-line region (BLR) and the dusty torus via the $\gamma \gamma \to e^{+}{e}^{-}$ process [2]. In contrast, BL Lacs are less powerful, do not exhibit prominent emission lines, likely due to a radiatively inefficient accretion flow that fails to ionize the gas surrounding the SMBH efficiently [3,4], and do not show strong absorption regions for VHE photons. As a consequence, their spectra can typically extend beyond $10\mathrm{TeV}$, making BL Lacs particularly suitable for probing fundamental physics at VHE.

The emission from blazars (both FSRQs and BL Lacs) spans a broad energy range, extending from VHE down to radio wavelengths. In particular, the spectral energy distribution (SED) of blazars—both FSRQs and BL Lacs—exhibits two distinctive broad humps: the first, located in the IR-UV band, originates from synchrotron emission by relativistic electrons in the jet, while the second appears at gamma-ray energies. The physical origin of the high-energy hump remains under discussion. In leptonic scenarios [5,6,7], this component arises from inverse Compton scattering, where the same population of relativistic electrons responsible for the synchrotron emission upscatters either the synchrotron photons themselves or external photons originating from the accretion disc or surrounding gas clouds. Alternatively, hadronic models account for the high-energy emission through synchrotron radiation from ultra-relativistic protons or via photohadronic interactions, such as photomeson production [8,9,10]. For our purposes, it is important to specify the behavior of the magnetic field $B_{\mathrm{jet}}$ and the electron number density $n_{e,\mathrm{jet}}$ along the jet. Assuming that photons are emitted and propagate along the y-direction, the relevant component of $B_{\mathrm{jet}}$ is its toroidal part [11,12,13], expressed as $B_{\mathrm{jet}}\left(y\right)=B_{\mathrm{jet},0}(y_{\mathrm{em}}/y)$, where $B_{\mathrm{jet},0}$ denotes the field strength at the emission distance $y_{\mathrm{em}}$ from the central SMBH. Owing to the expected conical geometry of the jet, the electron number density is modeled as $n_{e,\mathrm{jet}}\left(y\right)=n_{e,\mathrm{jet},0}{(y_{\mathrm{em}}/y)}^2$, with $n_{e,\mathrm{jet},0}$ representing the value of $n_{e,\mathrm{jet}}$ at $y=y_{\mathrm{em}}$. The value of $n_{e,\mathrm{jet},0}$ is inferred from Synchrotron Self-Compton (SSC) diagnostics applied to blazar spectra, yielding $n_{e,\mathrm{jet},0}=5\times {10}^4{\mathrm{cm}}^{-3}$ [14]. Two additional BL Lac parameters are crucial for our analysis: (i) the bulk Lorentz factor $\Gamma$, which characterizes the relativistic motion of the jet, and (ii) the initial degree of linear polarization of photons ${\Pi }_{L,0}$. The values of $y_{\mathrm{em}}$, $B_{\mathrm{jet},0}$, $\Gamma$, and ${\Pi }_{L,0}$ depend on the specific source under consideration and on the emission model—leptonic or hadronic. The particular values used in our analysis are presented in the dedicated sections below. As a general rule, hadronic models typically require larger values of $y_{\mathrm{em}}$, $B_{\mathrm{jet},0}$, and ${\Pi }_{L,0}$ compared to leptonic models, while $\Gamma$ tends to be smaller.

In this review, we investigate the effects of new physics and of alternative astrophysical mechanisms on both blazar spectra and polarization. The most relevant energy bands for polarization studies are the UV-X-ray and high-energy (HE) ranges, while for spectral analyses we focus on the VHE regime. However, at VHE, another important effect must be taken into account: photons emitted at cosmological distances can interact with the IR-optical-UV radiation of the extragalactic background light (EBL; see, e.g., [15,16,17,18]) and be absorbed via the $\gamma \gamma \to e^{+}{e}^{-}$ process. In this review, we examine the effects of three scenarios on blazar spectra at VHE: (i) the hadron beam model as an alternative emission mechanism (see, e.g., [19,20,21]), and two new physics scenarios, (ii) the interaction of photons with axion-like particles (ALPs; see, e.g., [22,23]), and (iii) Lorentz invariance violation (LIV; see, e.g., [24,25]). Each of these scenarios can reduce EBL absorption and generate distinctive, potentially detectable features in the observable spectra. While all three can, therefore, lead to a photon excess at VHE, the photon–ALP scenario predicts unique spectral signatures that, if detected or excluded, can help distinguish it from the other models. Furthermore, we investigate how the photon–ALP interaction affects the polarization of blazar photons in the UV-X-ray and HE bands. The observational signatures discussed in this review are within the reach of current and upcoming instruments—both for spectral observations, such as ASTRI Mini Array [26], CTAO [27], GAMMA-400 [28], HAWC [29], HERD [30], LHAASO [31], and TAIGA-HiSCORE [32]; and for polarimetric studies, including IXPE [33] (already operational), eXTP [34], XL-Calibur [35], NGXP [36], and XPP [37] in the X-ray band, as well as COSI [38], e-ASTROGAM [39,40], and AMEGO [41] at higher energies—making the proposed scenarios testable in the near future.

This review is structured as follows. In Section 2, we present the hadron beam scenario. Section 3 outlines the main properties and implications of the photon–ALP interaction, while Section 4 discusses Lorentz invariance violation (LIV) and its consequences. In Section 5, we analyze the impact of the three scenarios on blazar spectra, and in Section 6, we examine the effects of the photon–ALP interaction on blazar polarization. Section 7 is devoted to the discussion of the results, and we summarize our conclusions in Section 8.

Throughout this review, we employ the natural Lorentz–Heaviside (rationalized) units with $\hslash =c=k_B=1$.

2. Hadron Beam

As discussed in the introduction, a possible explanation for the higher energy hump in blazar spectra is given by standard hadronic models, where gamma-ray photons are generated by proton-synchrotron emission or photomeson production. In the so-called hadron beam scenario, a collimated beam of ultra-relativistic hadrons accelerated in the jet is expected to escape and then to interact with extragalactic background photons producing electromagnetic cascades [19,20,21]. As secondary photons produced in the cascades are emitted closer to the Earth, they suffer a smaller EBL absorption resulting in a hardening of the observed blazar spectra.

However, strong crossed magnetic fields like those present in clusters and filaments can deflect the primary hadrons emitted by the source for energies $E\lesssim {10}^{19}\mathrm{eV}$ [21]. Even the extragalactic magnetic field $B_{\mathrm{ext}}$ may deflect the produced cascade depending on its strength and morphology. Unfortunately, the knowledge of the $B_{\mathrm{ext}}$ properties is still very poor, but even assuming a coherence length ${\lambda }_{\mathrm{coh}}=\mathcal{O}\left(1\right)\mathrm{Mpc}$ and $B_{\mathrm{ext}}\gtrsim {10}^{-15}\mathrm{G}$—not far above the lower observational bound [42,43,44,45]—the resulting deflection of the cosmic ray-induced cascade becomes large enough to make the hadron beam scenario inefficient at generating a TeV photon excess [46]. In fact, a sufficiently strong $B_{\mathrm{ext}}$ tends to isotropize the distribution of cosmic rays, thereby increasing the required cosmic ray luminosity to generate a significant flux of secondary photons. Moreover, the time delays introduced by the cascade process make the resulting radiation poorly compatible with sources exhibiting rapid variability [21]. This is the reason why we apply the hadron beam scenario to 1ES 0229+200 (see Section 5.2) but not to Markarian 501, which exhibits a high variability.

The main consequence of the hadron beam scenario on blazars is a spectral hardening observable at energies up to (20–30) TeV [47]. This effect becomes increasingly pronounced with the source distance: for nearby sources (redshift $z\lesssim 0.3$), a hard spectral tail is expected above ∼10 TeV, whereas for more distant ones, the tail shifts to lower energies due to enhanced EBL attenuation (see, e.g., [21]).

3. Axion-like Particles

ALPs are hypothetical particles, but they are well motivated within theories that extend the SM of particle physics, such as String Theory (e.g., [48,49]), and are currently among the best candidates for dark matter [50,51,52,53]. They constitute a generalization of the axion [54,55,56,57], the pseudo-Goldstone boson associated with the spontaneous breaking of the global Peccei–Quinn symmetry $\mathrm{U}{\left(1\right)}_{\mathrm{PQ}}$ introduced to solve the strong CP problem in quantum chromodynamics in a natural way. While the original axions interact with fermions and gluons and possess a strict relation between their mass and their coupling with photons, ALPs primarily interact with photons (but other interactions are still possible) and the ALP mass $m_a$ and the photon–ALP coupling $g_{a\gamma \gamma }$ are independent quantities. ALPs, denoted by a, are, therefore, very light, neutral, spin-zero pseudoscalar bosons, whose interaction with photons is described by the Lagrangian

$${\mathcal{L}}_{\mathrm{ALP}}={\displaystyle \frac{1}{2}}{\partial }^{\mu }a{\partial }_{\mu }a-{\displaystyle \frac{1}{2}}{m}_a^2{a}^2+g_{a\gamma \gamma }a\mathbf{E}·\mathbf{B},$$

(1)

where E and B represent the electric and magnetic components of the electromagnetic tensor. Two other effects must be considered: (i) QED vacuum polarization [58,59,60] and (ii) photon dispersion on the CMB [61]. Several studies have obtained bounds on the ALP parameter space $(m_a,g_{a\gamma \gamma })$ [62,63,64,65,66,67,68,69,70,71,72,73], among which the most reliable constraints appear: $g_{a\gamma \gamma }<0.66\times {10}^{-10}{\mathrm{GeV}}^{-1}$ for $m_a<0.02\mathrm{eV}$ as established by the CAST Collaboration [62]; $g_{a\gamma \gamma }<6.3\times {10}^{-13}{\mathrm{GeV}}^{-1}$ for $m_a<{10}^{-12}\mathrm{eV}$, derived from X-ray observations of H1821+643 [70]; and $g_{a\gamma \gamma }<5.4\times {10}^{-12}{\mathrm{GeV}}^{-1}$ for $m_a<3\times {10}^{-7}\mathrm{eV}$, obtained from polarimetric studies of magnetic white dwarfs [73].

Interpreting E in Equation (1) as the electric field of a propagating photon and B as an external magnetic field, the photon–ALP interaction produces two important effects [74,75]: (i) photon–ALP oscillations, (ii) modification of the photon polarization state. In particular, ALPs have a high impact in astrophysics both on source spectra [76,77,78,79,80,81,82,83,84,85,86] and on photon polarization [87,88,89,90,91,92,93,94,95,96,97]. Currently, three independent hints point to the existence of ALPs [80,85,86], the most recent and compelling being the observation of GRB 221009A above $10\mathrm{TeV}$, which challenges conventional physics and can be interpreted in terms of photon–ALP interaction [86].

The evaluation of the photon survival probability in the presence of photon–ALP interaction $P_{\gamma \to \gamma }^{\mathrm{ALP}}$ can be found, for instance, in the review [22]. The astrophysical spectra modified by the photon–ALP interaction are then simply given by the emitted ones multiplied by $P_{\gamma \to \gamma }^{\mathrm{ALP}}$. In particular, the photon–ALP interaction modifies the Universe transparency by partially reducing the EBL absorption: when photons oscillate into ALPs, the latter do not interact with EBL photons, thereby increasing the photon effective mean free path [79]. As a result, a photon excess is expected in blazar spectra at the energies where the EBL absorption starts to become significant [84]. Furthermore, ALP-induced spectral irregularities are also expected [84]. Instead, a detailed evaluation of the degree of linear polarization ${\Pi }_L$ and of the polarization angle $\chi$ in the presence of photon–ALP interaction is presented, for example, in the review [23]. The photon–ALP interaction produces a variation of the initial degree of linear polarization ${\Pi }_{L,0}$ and energy-dependent features in the final ${\Pi }_L$ and $\chi$ [95]. As the photon–ALP interaction is independent of the specific source state, we can study ALP-induced effects on spectra and polarization of BL Lacs in both steady and flaring states. In the following, therefore, we evaluate the ALP-induced modifications to the spectra of both Markarian 501 and 1ES 0229+200 (see Section 5.1 and Section 5.2) and to the polarization of OJ 287 (see Section 6).

4. Lorentz Invariance Violation

Achieving a unified theory of all fundamental interactions at the quantum level requires the quantization of gravity. Since gravity is a theory of dynamical spacetime, it produces its own fluctuations and the spacetime assumes a foam-like structure with a continuously changing metric and topology [98,99,100,101]. Studies have shown that such a spacetime foam behaves analogously to a quantum thermal bath, resulting in loss of coherence [102,103]. This dynamical vacuum affects the particle propagation, giving rise to a LIV at a scale $E_{\mathrm{LIV}}$ close to the Planck mass $M_P\equiv {(\hslash c/G)}^{1/2}\simeq 1.22\times {10}^{19}\mathrm{GeV}$. LIV exhibits a rich phenomenology, leading to modifications of standard physical interactions and permitting processes that are otherwise forbidden within conventional physics, such as the vacuum Cherenkov effect, photon decay, photon splitting, and changes in the threshold of reactions [104].

In particular, LIV alters the standard photon dispersion relation by introducing additional energy-dependent terms of the form $E^{n+2}/E_{\mathrm{LIV}}^n$, with E representing the photon energy and n the order of the term (see, e.g., [24]). Considering the leading-order correction with $n=1$, the dispersion relation for photons becomes

$$E^2-p^2=\pm {\displaystyle \frac{E^3}{E_{\mathrm{LIV}}}},$$

(2)

with p denoting the photon momentum. The sign on the right-hand side of Equation (2) defines the so-called superluminal $(+)$ or subluminal $(-)$ case. While the superluminal case induces photon decay at TeV energies testable for galactic sources [105], we are interested here in the subluminal one, which produces a modification in the threshold of the process $\gamma \gamma \to e^{+}{e}^{-}$. Equation (2) shows that the LIV effects become increasingly significant with rising photon energy. As a consequence, the EBL absorption turns out to be strongly reduced for $E\gtrsim \mathcal{O}\left(10\right)\mathrm{TeV}$ depending on the value assumed by $E_{\mathrm{LIV}}$, which produces an observable hardening and detectable signatures in the blazar spectra [25]. While many bounds on $E_{\mathrm{LIV}}$ exist in the literature (see, e.g., [106,107,108,109,110,111]), the recent detection of a photon from GRB 221009A with energy up to $300\mathrm{TeV}$—incompatible with standard physics—has been interpreted as a potential signature of LIV [112].

The photon survival probability in the presence of LIV, denoted as $P_{\gamma \to \gamma }^{\mathrm{LIV}}$, is evaluated, for example, in [25]. The corresponding modification of the astrophysical spectra due to LIV effects is then obtained simply by multiplying the emitted spectrum by $P_{\gamma \to \gamma }^{\mathrm{LIV}}$. In particular, the LIV scenario induces a strong spectral hardening for $E\gtrsim \mathcal{O}\left(10\right)\mathrm{TeV}$: therefore, the best candidates to test these features are high-frequency peaked BL Lacs (HBLs) and extreme HBLs (EHBLs), as they can be observable up to few TeV [25,113]. Since the LIV effects are independent of the particular properties or state of the considered BL Lac, we can apply the LIV scenario to both steady- and flaring-state BL Lacs. Therefore, we discuss the LIV impact on the spectra of both Markarian 501 and 1ES 0229+200 (see Section 5.1 and Section 5.2).

5. Spectral Analysis

Following the approach presented in [114], we now examine the effects on blazar spectra at VHE of the three scenarios introduced above: (i) the hadron beam model, (ii) photon–ALP interaction, and (iii) LIV. We highlight both their similarities and distinctive features that may help distinguish between them. For this purpose, we focus on two particularly promising BL Lacs: Markarian 501 and 1ES 0229+200. As benchmark values, we adopt $m_a={10}^{-10}\mathrm{eV}$ and $g_{a\gamma \gamma }={10}^{-11}{\mathrm{GeV}}^{-1}$ for the ALP scenario, and $E_{\mathrm{LIV}}={10}^{20}\mathrm{GeV}$ for the LIV case. For the EBL, we employ the model described in [17]. Throughout this section, E denotes the photon energy as measured on Earth.

5.1. Markarian 501

Markarian 501 is a bright high-frequency peaked BL Lac (HBL) located at a redshift $z=0.034$. Its active states, whose most impressive example is represented by the HEGRA observations reaching energies above $10\mathrm{TeV}$ with a hard spectrum [115], are considered extremely promising for the study of possible new physics signals [25]. Due to the high variability of Markarian 501, the hadron beam scenario is not applicable to this source, so that, as reported in Figure 1, we consider only the effects induced by the photon–ALP interaction and by LIV. Concerning the emission mechanism, we assume a leptonic model with $y_{\mathrm{em}}=3\times {10}^{16}\mathrm{cm}$, $B_{\mathrm{jet},0}=0.5\mathrm{G}$, and $\Gamma =15$ [82]. Moreover, to describe the intrinsic spectrum, we adopt an exponentially truncated power law with energy index ${\alpha }_1=1$ and cutoff energy $E_{\mathrm{cut}}=20\mathrm{TeV}$ (for more details see [114]).

As discussed in [114], Figure 1 shows that the photon–ALP interaction produces two effects: (i) observable spectral irregularities at lower energies ($E\lesssim 5\mathrm{TeV}$); (ii) a photon excess with respect to conventional physics for energies above ∼10 TeV (see also [84,114]). Instead, LIV leads to a spectral hardening above approximately ∼20 TeV (see also [114]), which is similar to the effect produced by the photon–ALP interaction. However, unlike the ALP scenario, LIV additionally predicts a distinctive minimum in the spectrum near $40\mathrm{TeV}$, followed by a peak around $100\mathrm{TeV}$.

A photon excess above ∼10 TeV is unexpected within conventional physics due to EBL absorption; therefore, it could indicate new physics, potentially due to ALPs or LIV, although such a signal alone would not distinguish between the two scenarios. However, the possible detection of spectral irregularities would incontrovertibly indicate the ALP scenario, as such a feature is not predicted by LIV. All the ALP- and LIV-induced signatures reported in Figure 1 are expected to be observable by CTAO for a $50\mathrm{h}$ exposure [27,114].

5.2. 1ES 0229+200

1ES 0229+200 is the archetype of extreme high-frequency peaked BL Lacs (EHBLs), with a hard spectrum observed beyond $10\mathrm{TeV}$ [116], despite its relatively high redshift $z=0.1396$, where the EBL absorption at TeV energies is strong (see, e.g., [17]). Moreover, EHBLs show an untypical low variability with respect to other BL Lacs [117], which allows us to apply to 1ES 0229+200 not only the photon–ALP interaction and LIV models but also the hadron beam scenario, as shown in Figure 2.

As the EHBL behavior is not yet completely understood, we consider both a leptonic emission model with $y_{\mathrm{em}}=3\times {10}^{16}\mathrm{cm}$, $B_{\mathrm{jet},0}=2\mathrm{mG}$, and $\Gamma =50$ [118] and a hadronic one with $y_{\mathrm{em}}=3\times {10}^{16}\mathrm{cm}$, $B_{\mathrm{jet},0}=0.5\mathrm{G}$, and $\Gamma =15$ [119] in the left and right panels of Figure 2, respectively. Furthermore, we adopt two different descriptions of the intrinsic spectrum: (i) an exponentially truncated power law with energy index ${\alpha }_1=0.4$ and cutoff energy $E_{\mathrm{cut}}=15\mathrm{TeV}$ in the upper panels of Figure 2; (ii) a broken power law with different parameters for the photon–ALP conversion model and the LIV scenario in the lower panels of Figure 2, by taking energy indices ${\alpha }_1^{\mathrm{ALP}}=0.6$ and ${\alpha }_1^{\mathrm{LIV}}=0.4$, high-energy indices ${\alpha }_2^{\mathrm{ALP}}=2.2$ and ${\alpha }_2^{\mathrm{LIV}}=2$, and break energy $E_b^{\mathrm{ALP}}=E_b^{\mathrm{LIV}}=10\mathrm{TeV}$.

Figure 2 shows that the hadron beam scenario remains unaffected by both the emission mechanism (leptonic or hadronic) and the assumed intrinsic spectrum. In contrast, the LIV case is sensitive to the choice of the intrinsic spectral model, while the photon–ALP interaction scenario depends on both the intrinsic spectrum and the emission mechanism. Therefore, in all the panels of Figure 2, the hadron beam scenario yields a hard tail above ∼10 TeV extending smoothly beyond $100\mathrm{TeV}$, as reported in [114]. Furthermore, the photon–ALP interaction scenario generates two effects: (i) observable energy-dependent spectral irregularities at lower energies ($E\lesssim 5\mathrm{TeV}$); (ii) a photon excess above ∼10 TeV (see also [84,114]). While the presence of the spectral irregularities is independent of the intrinsic spectrum and of the emission mechanism, the photon excess above ∼10 TeV is more evident in the case of the hadronic model due to the higher value of $B_{\mathrm{jet},0}$, which is responsible for a more efficient photon–ALP conversion inside the jet. The broken power law intrinsic spectrum mildly increases the latter effect and only at the highest considered energies. The LIV scenario does not predict substantial effects around ∼10 TeV but produces a peculiar peak around ∼100 TeV, which is, however, detectable only in the case of an intrinsic broken power law spectrum when compared to the predicted CTAO sensitivity [27,114].

The possible detection of a harder spectra above ∼10 TeV with respect to standard expectations could be explained either by the hadron beam or by the photon–ALP interaction scenario provided that the emission is of hadronic origin. However, a definitive way to discriminate between these two possibilities lies in the potential observation of spectral irregularities, which are peculiar of the photon–ALP interaction scenario. On the other hand, a spectral feature observed near ∼100 TeV would point exclusively toward a LIV scenario, since only LIV predicts such a high-energy signature. The above-described features produced by the three considered scenarios are expected to be observable by CTAO for a $50\mathrm{h}$ exposure [27,114].

6. Polarization Analysis

As detailed in [95,97], we investigate the impact of the photon–ALP interaction on the polarization of photons from blazars in the UV-X-ray and HE bands, focusing specifically on OJ 287. This interaction affects both the final degree of linear polarization ${\Pi }_L$, and the polarization angle $\chi$. Since the exact configuration of the encountered magnetic fields—particularly their orientations—is uncertain and can strongly influence ${\Pi }_L$, we perform multiple simulations varying the magnetic field properties during the photon–ALP beam propagation. This produces a distribution of ${\Pi }_L$ values, from which we derive a probability density function $f_{\Pi }$, highlighting the most probable polarization outcomes and helping assess the robustness of our results.

It is important to note that real polarimeters have limited spatial resolution and cannot distinguish photons emitted from different regions across the jet transverse section, instead collecting all photons together. Although this could, in principle, dilute ALP-induced polarization signatures, the analyses in [95,97] demonstrate that this effect is negligible in realistic observational scenarios. To be conservative, we assume a photon–ALP beam propagation length of $1\mathrm{pc}$ inside the jet (see [95,97] for details on how the polarimeter limitations are incorporated). In this section, $E_0$ stands for the photon energy as observed from Earth.

OJ 287

OJ 287 is a low-frequency peaked BL Lac (LBL) lying at redshift $z=0.3056$. Thanks to its strong emission in both the X-ray and HE bands, OJ 287 is considered a promising candidate for polarimetric observations across these energy ranges [120]. Regarding the emission mechanism we assume the typical values for the LBL parameters: $y_{\mathrm{em}}=3\times {10}^{16}\mathrm{cm}$, $B_{\mathrm{jet},0}=1\mathrm{G}$, and $\Gamma =10$ for the leptonic model and $y_{\mathrm{em}}={10}^{17}\mathrm{cm}$, $B_{\mathrm{jet},0}=20\mathrm{G}$, and $\Gamma =15$ [121] for the hadronic model. The profile of the initial degree of linear polarization ${\Pi }_{L,0}$ for both the leptonic and hadronic cases is derived in [120] and reported in Figure 3, Figure 4 and Figure 5 as a reference, where it is represented by the dashed gray line. We concentrate on two different energy bands: (i) UV-X-ray band in Figure 3, where we assume $g_{a\gamma \gamma }=0.5\times {10}^{-11}{\mathrm{GeV}}^{-1}$ and $m_a\lesssim {10}^{-14}\mathrm{eV}$; (ii) HE band, with the same parameter values in Figure 4, and $m_a={10}^{-10}\mathrm{eV}$ in Figure 5.

In particular, in the UV-X-ray band $(4\times {10}^{-2}-{10}^2)\mathrm{keV}$, we show $P_{\gamma \to \gamma }$, ${\Pi }_L$, and $\chi$ in the top subfigure of Figure 3 and the corresponding behavior of $f_{\Pi }$ for the benchmark energies: (i) $E_0=1\mathrm{keV}$ and (ii) $E_0=10\mathrm{keV}$ in the bottom subfigure of Figure 3. Results within the leptonic emission model are reported in the left panels of Figure 3, while those within the hadronic one in the right panels of Figure 3. We recall that in the present situation, we assume the ALP parameters: $g_{a\gamma \gamma }=0.5\times {10}^{-11}{\mathrm{GeV}}^{-1}$, $m_a\lesssim {10}^{-14}\mathrm{eV}$. As shown by the top subfigure of Figure 3, the photon–ALP beam propagates in the weak mixing regime in the UV-X-ray band since the plasma effect plays a non-negligible role compared to the photon–ALP mixing term particularly within the jet of OJ 287. As a consequence, $P_{\gamma \to \gamma }$, ${\Pi }_L$ and $\chi$ in the top subfigure of Figure 3 show an energy-dependent behavior for a few decades, as a result of the strong variation of $B_{\mathrm{jet}}$ and $n_{e,\mathrm{jet}}$ with the distance (for details see also [95,97]). The binned data in the top subfigure of Figure 3 concerning the final ${\Pi }_L$ show that not only is ${\Pi }_L$ strongly modified with respect to the initial ${\Pi }_{L,0}$ both in the leptonic and hadronic cases, but also that observatories such as IXPE [33], eXTP [34], XL-Calibur [35], NGXP [36], and XPP [37] may detect the polarization features induced by the photon–ALP interaction for $E_0\gtrsim 0.5\mathrm{keV}$. Furthermore, we can observe that in the hadronic model, the energy-dependent variation of ${\Pi }_L$ and $\chi$ is more pronounced than in the leptonic scenario, owing to the higher value of $B_{\mathrm{jet},0}$ and the larger spatial extent of the jet region.

The bottom subfigure of Figure 3 reports the behavior of $f_{\Pi }$, showing a broadening of the final ${\Pi }_L$ if compared to the initial ${\Pi }_{L,0}$. Around $E_0=1\mathrm{keV}$, the most probable final value of ${\Pi }_L$ remains quite consistent with the initial polarization degree ${\Pi }_{L,0}$, while around $E_0=10\mathrm{keV}$ and in the case of the leptonic model, the most probable outcome exceeds ${\Pi }_L\gtrsim 0.8$, which represents a value that is difficult to reconcile with predictions from conventional physics (see [97] for more details). Therefore, the latter case represents an interesting candidate for a case study to search for ALP-induced polarization features in blazars.

Instead, in the HE band $({10}^{-1}-5\times {10}^2)\mathrm{MeV}$, we start by considering the case $g_{a\gamma \gamma }=0.5\times {10}^{-11}{\mathrm{GeV}}^{-1}$, $m_a\lesssim {10}^{-14}\mathrm{eV}$. Correspondingly, the behavior of $P_{\gamma \to \gamma }$, ${\Pi }_L$ and $\chi$ is shown in the top subfigure of Figure 4 and the derived $f_{\Pi }$ for the benchmark energies: (i) $E_0=300\mathrm{keV}$ and (ii) $E_0=3\mathrm{MeV}$ in the bottom subfigure of Figure 4. The results obtained under the leptonic emission model are presented in the left panels of Figure 4, whereas those derived from the hadronic emission model are shown in the right panels. The top subfigure of Figure 4 shows that the photon–ALP beam propagates in the strong mixing regime throughout almost the entire considered energy band, as the photon–ALP mixing term dominates over all other effects producing a behavior of $P_{\gamma \to \gamma }$, ${\Pi }_L$, and $\chi$, which is energy independent for $E_0\gtrsim (0.5-1)\mathrm{MeV}$. We further observe that the final ${\Pi }_L$, is significantly altered compared to its initial value ${\Pi }_{L,0}$, but no appreciable differences emerge between the leptonic and hadronic emission models. The binned data in the top subfigure of Figure 4 exhibit reduced uncertainties with respect to those in the UV-X-ray band, primarily due to the fact that the photon–ALP system remains in the strong mixing regime across the relevant energy range. As a result, OJ 287 turns out to be a particularly promising observational target for future polarimetric missions, such as COSI [38], e-ASTROGAM [39,40], and AMEGO [41].

The behavior of $f_{\Pi }$ reported in the bottom subfigure of Figure 4 indicates that the most probable final value of ${\Pi }_L$ exceeds the initial ${\Pi }_{L,0}$ with a marked broadening. The energy range around $E_0=3\mathrm{MeV}$ emerges as particularly favorable for probing ALP-induced effects on photon polarization, as the most probable value of ${\Pi }_L$ reaches ${\Pi }_L\gtrsim 0.8$, which is significantly higher than standard physics expectations.

Still, in the HE band $({10}^{-1}-5\times {10}^2)\mathrm{MeV}$ but taking the ALP parameters $g_{a\gamma \gamma }=0.5\times {10}^{-11}{\mathrm{GeV}}^{-1}$, $m_a={10}^{-10}\mathrm{eV}$, we report the behavior of $P_{\gamma \to \gamma }$, ${\Pi }_L$ and $\chi$ in the top subfigure of Figure 5 and the associated $f_{\Pi }$ for the benchmark energies: (i) $E_0=300\mathrm{keV}$, (ii) $E_0=3\mathrm{MeV}$ in the bottom subfigure of Figure 5. The left panels of Figure 5 display the results obtained within the leptonic emission model, while the right panels report the findings within the hadronic one. As shown by the top subfigure of Figure 5, the photon–ALP system propagates in the weak mixing regime, as the effect of the higher ALP mass term ($m_a={10}^{-10}\mathrm{eV}$ with respect to the previously considered $m_a\lesssim {10}^{-14}\mathrm{eV}$) cannot be neglected in comparison with the photon–ALP mixing term. Consequently, $P_{\gamma \to \gamma }$, ${\Pi }_L$ and $\chi$ turn out to be energy dependent in all the examined band with a substantial modification of the final ${\Pi }_L$ with respect to the initial ${\Pi }_{L,0}$ especially in the leptonic case. As previously noted in the X-ray band for $g_{a\gamma \gamma }=0.5\times {10}^{-11}{\mathrm{GeV}}^{-1}$ and $m_a\lesssim {10}^{-14}\mathrm{eV}$, the extended energy range over which the photon–ALP system remains in the weak mixing regime arises from the significant spatial variation of $B_{\mathrm{jet}}$ and $n_{e,\mathrm{jet}}$ (see also [95,97] for further details). The binned data presented in the top subfigure of Figure 5 suggest that future polarimetric missions, such as COSI [38], e-ASTROGAM [39,40], and AMEGO [41], could be sensitive to ALP-induced modifications of ${\Pi }_L$ for $E_0\gtrsim 0.2\mathrm{MeV}$, under both leptonic and hadronic emission scenarios.

The bottom subfigure of Figure 5 reporting the behavior of $f_{\Pi }$ shows a broadening of the final ${\Pi }_L$ compared to the initial ${\Pi }_{L,0}$. The most probable value of the final ${\Pi }_L$ is significantly larger than the initial one ${\Pi }_{L,0}$ within the leptonic model, making it an interesting case study especially for $E_0\gtrsim 3\mathrm{MeV}$. Instead, within the hadronic model, the modification of ${\Pi }_L$ with respect to ${\Pi }_{L,0}$ is less marked, making it a less compelling object of investigation.

7. Discussion and Future Perspectives

In Section 5, we have demonstrated that blazar spectra at VHE can exhibit imprints of the three scenarios beyond the standard paradigm, discussed in this review (see [114] for further details): the hadron beam model, the photon–ALP interaction, and LIV. Our analysis has focused on two representative BL Lacs: Markarian 501 and 1ES 0229+200. In particular, when the hadron beam model is applicable—notably for steady sources such as 1ES 0229+200—both the hadron beam and the photon–ALP interaction scenarios predict a photon excess at energies $E\gtrsim 10\mathrm{TeV}$, where the EBL absorption is significant. However, only the photon–ALP interaction induces distinctive energy-dependent oscillatory features in the range $0.5\mathrm{TeV}\lesssim E\lesssim 5\mathrm{TeV}$. In contrast, the LIV scenario leads to a photon excess at much higher energies, around $100\mathrm{TeV}$. As a result, the three scenarios may be distinguishable based on the observed spectral features and energy band. We have also shown that, given a reasonable exposure time, CTAO [27] is expected to be able to detect the spectral signatures predicted by these scenarios, provided that they are realized in nature. For instance, a possible detection by CTAO [27] of photon excess around 100 TeV would strongly favor LIV. Conversely, an excess at $E\gtrsim 10\mathrm{TeV}$ could arise from either the hadron beam or the photon–ALP interaction scenario. However, the presence or absence of the mentioned spectral irregularities—likely resolvable with CTAO expected energy resolution [27]—would provide a way to discriminate between them. Additionally, the ASTRI Mini Array [26] may also detect significant deviations from standard predictions related to photon excesses, provided that the exposure time is sufficiently long. Other facilities, such as GAMMA-400 [28], HAWC [29], HERD [30], LHAASO [31], and TAIGA-HiSCORE [32], also have the potential to detect the effects of the three considered scenarios on blazar spectra, possibly providing evidence or placing new constraints on their properties.

Similarly, in Section 6, we have demonstrated that the polarization of photons emitted from blazars may carry distinctive signatures of the photon–ALP interaction, in both the UV-X-ray and HE bands (see [95,97] for more details). We have focused on the representative BL Lac OJ 287 and found that the photon–ALP interaction can significantly alter the final degree of linear polarization ${\Pi }_L$ with respect to the initial one ${\Pi }_{L,0}$. In particular, when ${\Pi }_L$ reaches very high values (e.g., ${\Pi }_L\gtrsim 0.8$), blazars become very promising candidates for detecting ALP-induced polarization effects. In such potential cases, even hadronic emission models struggle to explain the observations within the framework of standard physics [97]. A potential detection of ${\Pi }_L\gtrsim 0.8$ by observatories such as IXPE [33] in the X-ray band would therefore provide strong evidence in support of the ALP existence. Prospectively, future or already-approved missions like eXTP [34], XL-Calibur [35], NGXP [36], and XPP [37] in the UV-X-ray range, as well as COSI [38], e-ASTROGAM [39,40], and AMEGO [41] in the HE band, are expected to offer enhanced sensitivity. These instruments could either strengthen evidence for ALPs or further constrain their parameter space. On the contrary, lower ${\Pi }_L$ values remain compatible with standard physics under hadronic emission models. However, recent IXPE observations [122,123,124,125,126,127,128,129,130] challenge scenarios with initially high ${\Pi }_{L,0}$, and new theoretical models suggest that the turbulent structure of the jet magnetic field $B_{\mathrm{jet}}$ may naturally reduce ${\Pi }_{L,0}$ [131]. While the photon–ALP interaction can either increase or decrease the final polarization, LIV tends only to suppress ${\Pi }_L$ [132]. Additionally, LIV can induce an energy-dependent rotation of the linear polarization plane for photons from blazars—a vacuum birefringence effect—observable in both the optical-X-ray and HE bands [133,134,135]. Such signatures may be exploited to constrain or even detect LIV, especially with the next-generation polarimetric missions mentioned above.

In this review, we have adopted benchmark values for key BL Lac properties, such as $y_{\mathrm{em}}$ and $B_{\mathrm{jet},0}$. A full exploration of the BL Lac parameter space lies beyond our scope; however, as shown in [82], variations in $y_{\mathrm{em}}$ and $B_{\mathrm{jet},0}$ only mildly affect the photon–ALP interaction scenario. In particular, larger values of these parameters lead to stronger photon–ALP conversion in the jet, potentially resulting in tighter constraints on the ALP parameter space $(m_a,g_{a\gamma \gamma })$ from both spectral and polarization studies.

8. Conclusions

In this review, we have presented blazars as privileged astrophysical laboratories for probing alternative emission mechanisms and fundamental physics. In particular, we have explored the impact on blazars of three scenarios beyond the standard paradigm: (i) the hadron beam model, (ii) the photon–ALP interaction, and (iii) LIV.

We have analyzed how these scenarios affect blazar spectra, identifying Markarian 501 and 1ES 0229+200 as particularly promising sources. We have also shown that, although these scenarios may produce a similar photon excess at VHE, we can discriminate among them by searching for ALP-induced spectral irregularities (see also [114]). These investigations are timely, as current and upcoming facilities—such as ASTRI Mini Array [26], CTAO [27], GAMMA-400 [28], HAWC [29], HERD [30], LHAASO [31], and TAIGA-HiSCORE [32]—have the potential to detect deviations from standard predictions.

We have also examined the effects of the photon–ALP interaction on the polarization of photons from blazars, focusing in particular on the BL Lac OJ 287. The induced modifications to the final degree of linear polarization can be significant (see also [95,97]), and potentially detectable by missions such as IXPE [33], eXTP [34], XL-Calibur [35], NGXP [36], and XPP [37] in the X-ray band, as well as COSI [38], e-ASTROGAM [39,40], and AMEGO [41] in the HE range. In addition to blazars, galaxy clusters also represent very promising targets to investigate ALP-induced effects on photon polarization with the aforementioned observatories. Indeed, while their diffuse emission is expected to be entirely unpolarized in the X-ray and HE bands under standard physics, the photon–ALP interaction can induce a detectable level of polarization [95,96].

Both spectral and polarimetric studies have the potential to find hints at the above-mentioned three scenarios or to constrain their parameter space further. Therefore, a promising future lies ahead for fundamental physics, with blazars serving as natural laboratories to test scenarios beyond the standard paradigm. This approach may help us to drive theoretical research in a well-defined direction.