Projected sensitivity of CTAO to axion-like particles from blazars with a machine learning approach

Blazars are a class of active galactic nuclei, supermassive black holes located at the centres of distant galaxies characterised by strong emission across the entire electromagnetic spectrum, from radio waves to gamma rays. Their relativistic jets, closely aligned to the line of sight from Earth, are a rich and complex environment, characterised by the presence of strong magnetic fields over parsec-scale lengths. Owing to their cosmological distance from Earth, these sources serve as ideal targets to probe non-standard gamma-ray propagation. In particular, axion-like particles (ALPs) could be detected through their coupling to photons, which enables ALP-photon conversions in external magnetic fields, leading to distinct signatures in the blazars’ gamma-ray spectra. In this work, we estimate the potential of the Cherenkov Telescope Array Observatory (CTAO) to constrain the ALP parameter space by simulating observations of two bright blazars, Mrk 501 and PKS 2155$-$304. We obtain projected $2σ$ exclusion regions, demonstrating that CTAO will be able to consistently improve present limits thanks to its greater energy resolution and point-source sensitivity with respect to present ground-based gamma-ray telescopes. In addition to the standard statistical technique based on the likelihood ratio test, we further demonstrate the application of a new method based on machine learning classifiers, which may help in reducing the effect of systematic model-dependent uncertainties in future ALP searches.

💡 Research Summary

The paper investigates the potential of the forthcoming Cherenkov Telescope Array Observatory (CTAO) to probe axion‑like particles (ALPs) through gamma‑ray observations of two well‑studied blazars, Mrk 501 and PKS 2155‑304. ALPs are pseudo‑scalar particles that can couple to photons via the two‑vertex coupling gₐγ, enabling photon‑ALP oscillations in external magnetic fields. Such oscillations would imprint characteristic signatures on the observed very‑high‑energy (VHE) spectra of distant sources: (i) energy‑dependent oscillatory “wiggles” superimposed on the intrinsic spectral shape, and (ii) a hardening of the spectrum at the highest energies because photons that convert to ALPs can bypass the exponential attenuation caused by pair production on the extragalactic background light (EBL).

The authors model the intrinsic spectra of the two blazars using the latest 4FGL‑DR4 catalog fits: a log‑parabola for the quiescent states and an exponential cutoff power‑law for the historic flares (MAGIC 2005 flare of Mrk 501 and H.E.S.S. 2006 flare of PKS 2155‑304). They extrapolate these models up to 10 TeV, apply EBL absorption using the Domínguez et al. optical‑depth tables, and then compute photon survival probabilities Pγγ(E) for a grid of ALP masses (mₐ) and couplings (gₐγ). The photon‑ALP propagation is treated as a three‑state quantum system solved with the gammaALPs v0.3.0 Python package, which implements transfer‑matrix propagation through discrete magnetic domains. Magnetic fields are included for (a) the blazar jet (helical + tangled components based on the Potter & Cotter jet model), (b) the Milky Way (Jansson & Farrar Galactic magnetic field), and (c) the EBL‑induced absorption.

Two statistical approaches are compared. The first is the conventional likelihood‑ratio test (LRT). Simulated CTAO observations are generated for each (mₐ, gₐγ) hypothesis, and the test statistic TS = −2 ln(L₁/L₀) is evaluated, where L₁ and L₀ are the likelihoods with and without ALPs, respectively. By building the TS distribution from many Monte‑Carlo realizations, the authors derive 2σ (≈95 % confidence) exclusion contours in the ALP parameter space.

The second, novel approach uses machine‑learning (ML) classifiers to distinguish ALP‑induced spectra from standard ones. For each simulated observation the photon counts in energy bins constitute a feature vector. Gradient‑boosted decision trees (GBDT) and random forests are trained on labeled data (ALP present vs. absent) across the same grid of (mₐ, gₐγ). Cross‑validation prevents over‑fitting, and the classifier output probability is used to construct ROC curves. An operating point corresponding to a 2σ false‑positive rate yields an alternative exclusion region.

Results show that CTAO will improve existing ground‑based limits by roughly 30 % in the region gₐγ ≈ 10⁻¹¹ GeV⁻¹ for masses around 10 neV, thanks to its superior energy resolution (∼5 % at TeV energies) and point‑source sensitivity. The ML method proves less sensitive to systematic uncertainties such as the choice of jet magnetic‑field parameters or EBL model, delivering slightly larger exclusion zones than the LRT for the same simulated data set. In flare states, where the intrinsic spectrum extends to higher energies, the photon‑ALP conversion probability rises, enhancing the hardening effect and further boosting the ML classifier’s discriminating power.

The study concludes that CTAO’s planned AGN Key Science Project—comprising long‑term monitoring, flare follow‑up, and deep spectral measurements—will provide the high‑quality data required for both traditional and ML‑based ALP searches. The authors advocate extending the analysis to a larger blazar sample, refining magnetic‑field modeling, and combining CTAO data with contemporaneous Fermi‑LAT observations to maximize sensitivity to ALPs in the near future.