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

Technical Summary: Search for Neutrino Emission from Blazar $\gamma$-Ray Flares Accounting for Possible Neutrino Time Delays

Problem Statement
While the IceCube neutrino observatory has established the existence of astrophysical high-energy neutrinos ($E_\nu \gtrsim 1$ TeV), the specific sources contributing to the diffuse flux remain largely unidentified, despite evidence linking specific events to blazars (e.g., TXS 0506+056) and active galaxies (e.g., NGC 1068). Previous searches for correlations between blazars and IceCube neutrinos typically assumed temporal coincidence between neutrino arrival and major electromagnetic (specifically $\gamma$-ray) flares. However, theoretical considerations suggest this coincidence may not hold. If neutrinos are produced via $p\gamma$ interactions, the timescales for proton acceleration ($t'_{acc}$) and proton energy losses ($t'_{p\gamma}$) in the jet frame can be orders of magnitude longer than those for electrons responsible for electromagnetic flares. Consequently, high-energy neutrinos ($\gtrsim 100$ TeV) may arrive months to years after the associated $\gamma$-ray flare peak. This paper addresses the lack of searches that account for such potential time lags.

Methodology
The authors performed a cross-matching analysis between high-energy neutrino alerts from the IceCat-1 public catalogue and two distinct blazar source samples, scanning for correlations over a wide range of jet-frame time delays ($t'_{delay}$).

1. Datasets:

   • Neutrinos: 348 alerts from the IceCat-1 catalogue ($E_\nu \gtrsim 100$ TeV), excluding those with coincident IceTop signals.
   • Source Lists:
     • H21+: A sample of 294 AGNs from the MOJAVE database (Homan et al. 2021) with known Doppler factors ($D$), redshifts ($z$), and Fermi-LAT light curves.
     • R24+: A sample of 295 blazars from the CGRaBS catalogue (Rodrigues et al. 2024b) with Doppler factors derived from spectral-energy distribution modeling, also cross-matched with Fermi-LAT light curves.
   • Light Curves: Monthly-binned photon flux light curves from the Fermi-LAT Light Curve Repository (LCR).

2. Statistical Framework:

   • Spatial Association: Neutrinos were associated with blazars if the source fell within an enlarged angular uncertainty region (incorporating a systematic uncertainty $\Delta = 0.78^\circ$).
   • Weighting Scheme: For each alert, a weight $w_\nu(t'_{delay})$ was calculated based on the signalness of the alert, a penalty factor for large angular uncertainties, and a temporal factor $G_{\nu a}$.
   • Temporal Factor: The temporal factor linked the neutrino arrival time ($t_\nu$) to the global maximum of the blazar's $\gamma$-ray light curve prior to the arrival ($t^{\gamma \max}_a$). The factor assigned maximum weight if the time difference matched the anticipated observer-frame delay ($t_{delay} = t'_{delay}(1+z)/D$) within a bin size, applying a Gaussian penalty for deviations.
   • Test Statistic (TS): The global TS was defined as the sum of individual weights over all alerts.
   • Significance Testing: The TS for the real data was compared against a distribution of TS values generated from 49,999 mock datasets where neutrino right ascensions and arrival times were randomized. Pre-trial $p$-values were calculated and subsequently corrected for trials (scanning over $t'_{delay}$).

Key Contributions

• Novel Search Strategy: This work represents the first attempt to search for associations between IceCube neutrinos and blazar $\gamma$-ray flares specifically accounting for a universal jet-frame time delay ($t'_{delay}$) caused by slow proton acceleration or energy losses.
• Dual Source Samples: The study utilizes two independent blazar catalogues with different methods for determining Doppler factors (brightness temperature arguments vs. SED modeling) to test the robustness of potential correlations against uncertainties in jet kinematics.
• Systematic Delay Scanning: The analysis scans $t'_{delay}$ from 1 month to $\sim 3.5 \times 10^4$ days, covering the theoretical range where neutrino production might lag behind electromagnetic emission.

Results

• Statistical Significance: The search yielded no statistically significant evidence of a correlation between IceCat-1 neutrinos and the AGNs in either the H21+ or R24+ source lists.
  • For the H21+ list, the minimum pre-trial $p$-value was 0.037 (at $t'_{delay} \approx 7.7 \times 10^3$ d).
  • For the R24+ list, the minimum pre-trial $p$-value was 0.026 (at $t'_{delay} \approx 1.9 \times 10^3$ d).
  • After trial correction, these minima correspond to post-trial $p$-values of 0.14 (1.06$\sigma$) and 0.11 (1.21$\sigma$) respectively, consistent with the null hypothesis.
• Top Candidates: The most significant associations were driven by the alert IC120523B (linked to the 2010 flare of 3C 454.3) and IC150926A (linked to a flare of 3C 279). While these specific events showed temporal alignment with anticipated delays, they were insufficient to establish a global correlation across the dataset.
• Discrepancy in Doppler Factors: The optimal delay times differed significantly between the two source lists (a factor of 4), largely driven by discrepancies in the estimated Doppler factors for 3C 454.3 and 3C 279 between the H21 and R24 methodologies.

Significance and Claims
The authors modestly conclude that their results do not support a significant correlation between IceCat-1 neutrinos and the specific blazar populations studied, even when accounting for time delays. They suggest several non-mutually exclusive reasons for these null results:

1. Inefficiency: Blazars may be inefficient sources of $\sim 100$ TeV neutrinos, contributing only a small fraction ($\sim 0.5\%$) to the IceCube flux.
2. Energy Scale: If blazars are efficient neutrino sources, the peak of their emission may lie at much higher energies ($\gtrsim 10$ PeV), beyond the primary sensitivity of the current IceCube alert sample.
3. Model Assumptions: The assumption of a universal jet-frame time delay ($t'_{delay}$) may be invalid due to source-to-source variations in acceleration mechanisms and magnetic fields.
4. Decoupling: Proton acceleration and energy dissipation may be spatially or temporally decoupled from electron processes, meaning neutrino production is not causally linked to the observed $\gamma$-ray flares.

The paper posits that future improvements in sensitivity will likely require larger datasets (e.g., the upcoming IceCat-2 and CAZ catalogues) and the inclusion of radio light curves, which are known to lag $\gamma$-ray flares and may better correlate with neutrino production timescales.