Search for neutrino emission from blazar $γ$-ray flares accounting for possible neutrino time delays

We report the results of the search for the high-energy neutrino emission associated with blazar flares, accounting for a possible lag of neutrinos with respect to the electromagnetic emission, either due to the slowness of the proton energy losses in $pγ$ collisions and/or proton acceleration. We perform two tests, cross-matching neutrinos with energies $E_ν \gtrsim 100$ TeV from the public catalogue of neutrino alerts IceCat-1 with active galactic nuclei from two source samples based on 1) the MOJAVE database and 2) the CGRaBS catalogue, and utilising Fermi-LAT light curves from the public light curve repository. We scan over a wide range of values of the jet-frame time delay $t^{\prime}{\mathrm{delay}}$ between the neutrino arrival and the time of the prior major $γ$-ray flare and find a pre-trial $\sim 2σ$ correlation at $t^{\prime}{\mathrm{delay}} \sim 10^{3}$ d, which is consistent ($p_{\mathrm{post-trial}} \sim 0.1$) with expectations under the null hypothesis after trial correction.

💡 Research Summary

This paper investigates whether high‑energy neutrinos detected by IceCube are temporally associated with major γ‑ray flares of blazars, allowing for a possible lag between the electromagnetic outburst and the neutrino arrival. The motivation stems from theoretical expectations that the production of ≳100 TeV neutrinos in blazar jets may be delayed relative to the γ‑ray flare because (i) protons require substantially longer acceleration times than electrons, and/or (ii) the proton‑photon (pγ) interaction timescale can be orders of magnitude longer than the electron cooling time that powers the flare. Consequently, a neutrino could be emitted months to years after the flare peak, depending on the jet Doppler factor D and redshift z (t_delay = t′_delay (1+z)/D).

The authors use the IceCat‑1 public catalogue of IceCube high‑energy alerts, selecting 348 neutrino events with estimated muon energies ≳100 TeV and removing those flagged as likely atmospheric background. For each event they retain the signalness, detection time, reconstructed direction and its uncertainty. To assess the significance of any spatial coincidence they generate 49 999 mock neutrino datasets by randomising right ascension and detection time while preserving declination and energy distributions, thereby preserving IceCube’s exposure pattern.

Two independent blazar samples are constructed. The first (H21+) consists of 294 radio‑bright AGN from the MOJAVE programme that have measured Doppler factors (from VLBI brightness‑temperature analyses), known redshifts (from 4LAC or NED), and monthly‑binned γ‑ray light curves from the Fermi‑LAT Light‑Curve Repository (LCR). The second (R24+) contains 295 blazars drawn from the CGRaBS catalogue for which Doppler factors were derived by Rodrigues et al. (2024) through broadband SED modelling, again with redshifts and LCR light curves. Both samples are dominated by flat‑spectrum radio quasars (FSRQs) and BL Lac objects.

The analysis proceeds in two steps. First, a spatial association is required: a neutrino is linked to a blazar if the angular separation between the neutrino’s best‑fit direction (including a systematic 0.78° term) and the blazar position is ≤ 1°. This criterion follows earlier work that found optimal correlation strength for radio‑bright blazars. Second, for each associated pair the authors identify the most prominent γ‑ray flare preceding the neutrino detection. The flare time is taken as the month of maximum photon flux in the LCR light curve. The time difference Δt_obs = t_ν – t_flare is then transformed to the jet frame using the measured D and z, yielding a candidate jet‑frame delay t′_delay.

A systematic scan over t′_delay from 10⁰ to 10⁴ days (logarithmic steps) is performed. For each trial delay the authors count how many neutrino–flare pairs satisfy Δt_obs ≈ t′_delay D/(1+z) within a tolerance set by the monthly bin width. The same counting is repeated on each of the 49 999 mock datasets, producing a distribution of expected random coincidences. The observed excess is quantified by a pre‑trial p‑value (the fraction of mocks with equal or larger counts) and then corrected for the number of delay trials.

The results show a modest excess at a jet‑frame delay of ∼10³ days. The pre‑trial significance corresponds to roughly 2σ (p_pre ≈ 0.03). After accounting for the ∼30 independent delay trials, the post‑trial p‑value rises to about 0.1, indicating that the signal is not statistically significant under conventional thresholds. Spatially, 12 neutrino–blazar pairs fall within the 1° window, slightly above the ∼9 pairs expected from random sky positions.

The authors discuss several implications. The ∼10³‑day lag is compatible with scenarios where proton acceleration dominates the delay, or where pγ interactions occur in external photon fields near the photopion threshold, both of which can produce year‑scale lags for typical Doppler factors (D∼20–30). However, uncertainties in D (often derived from VLBI brightness temperatures) and redshift propagate into large uncertainties on the inferred jet‑frame delay. Moreover, the analysis assumes a linear scaling between γ‑ray and neutrino fluxes (F_ν ∝ F_γ), which is justified for pγ processes with Doppler boosting p≈4–6, but alternative hadronic models could alter this relationship.

The study highlights the current limitations: the modest number of high‑energy neutrino alerts, the coarse monthly resolution of the γ‑ray light curves, and the systematic angular uncertainty of IceCube events. Future improvements—larger neutrino samples from IceCube‑Gen2 or KM3NeT, higher‑cadence γ‑ray monitoring (e.g., with CTA or next‑generation Fermi‑LAT analyses), and more precise Doppler factor measurements (e.g., from VLBI monitoring campaigns)—will enhance sensitivity to delayed neutrino emission.

In conclusion, this work presents the first systematic search for delayed high‑energy neutrino emission from blazar γ‑ray flares, finding an intriguing but statistically inconclusive hint of a ∼10³‑day jet‑frame lag. While the current data do not allow a definitive claim, the methodology establishes a framework for future multimessenger studies that incorporate physically motivated time delays, and it underscores the importance of coordinated electromagnetic and neutrino observations for unraveling the origins of the astrophysical neutrino flux.