Delayed Radio Flares in Neutrino-associated Blazars: The Case of TXS 0506+056

The gist: The delayed radio flare in TXS 0506+056 is likely produced by downstream dissipation and beaming evolution rather than being a direct radiative echo of the neutrino-production region becoming transparent.

Introduction and Motivation

High-energy astrophysical neutrinos probe hadronic processes in relativistic jets, but the location and properties of their production sites remain uncertain The first association between a high-energy neutrino and an active galaxy came with IceCube170922A, detected in September 2017 during a bright γ-ray flare from the blazar TXS 0506+056 VLBI observations revealed rapid expansion of the compact radio core after the neutrino detection In TXS 0506+056, the IceCube-170922A neutrino arrived during a major γ-ray flare, while RATAN-600 monitoring shows that the associated GHz radio outburst started rising around the same epoch but peaked only around ∼2020, implying a γ–radio delay of 2–3 years This points to a dynamical connection to the 2017 event, but not a one-to-one radiative connection between the neutrino-emitting region and the delayed GHz outburst

Modeling Scenarios for Radio Evolution

The study investigates three scenarios for the subsequent evolution of the emitting region to explain the 2020 radio outburst

1. Scenario A: expansion of the initial pair population This scenario was excluded because SSA-driven expanding blob models cannot reproduce the timing and evolution of the radio-flare

2. Scenario B: continuous injection with escape While this scenario can sustain radio-emitting electrons at later times, it shows two discrepancies with the observed radio data: first, nearsimultaneity of peaks across GHz bands is difficult to reproduce in a flare driven by ν’ssa second, the observed radio decline in all bands at ∼ 2021 is faster than the model prediction

3. Scenario C: Optically thin re-dissipation and blob deceleration This scenario successfully describes the radio evolution by invoking a renewed particle energization episode in the optically thin regime, triggered when the disturbance reaches parsec scales

Key Findings from Scenario C

In Scenario C, the delayed radio flare is produced by a renewed particle acceleration episode downstream after the source has become optically thin at GHz frequencies The modeling of this scenario yielded posterior median values of Vexp = 0.28c, t′reacc = 172.93R′0/c, ml = −0.68, and mb = 0.56 The rapid post-peak decay requires a decrease of the Doppler factor once the emitting region has reached the large sizes implied by the delayed radio outburst, consistent with a decelerating and/or velocity-stratified jet

Physical Interpretation

The delayed GHz emission primarily traces downstream dissipation and beaming evolution of the propagating disturbance The near-simultaneity of the RATAN-600 peaks across 1.2–22 GHz is against a flare driven by the slow passage of the SSA turnover through the observing bands, instead motivating an expansion phase long enough for the turnover to drop below the GHz regime, followed by renewed dissipation at parsec scales The role of the propagating disturbance is instead to provide a causal link to a downstream dissipation site where the delayed radio-flare is produced This implies that radio-flares appearing years after a neutrino alert may trace downstream dissipation and Doppler factor evolution, rather than direct radio unveiling of the neutrino zone

Conclusion

Within a one-zone time-dependent framework, the delayed radio-flare in TXS 0506+056 is unlikely to be a direct radiative echo of the neutrino-production region becoming transparent Instead, the delayed GHz emission primarily traces downstream dissipation and beaming evolution of the propagating disturbance Because the radio emission is dominated by leptonic synchrotron emission and is largely insensitive to the proton population relevant for neutrino production, a delayed radioflare is not necessarily linked to the proton distribution characteristics, but rather a diagnostic of how and where the jet reprocesses energy at parsec scales This informs future modeling of neutrino–blazar associations by indicating that radio-flares appearing years after a neutrino alert may trace downstream dissipation and Dopplerfactor evolution, rather than direct radio unveiling of the neutrino zone The paper also motivates long-term radio monitoring (months–years) and high-resolution VLBI followup after neutrino alerts to capture delayed flares and associated structural changes

How it works

The analysis begins by modeling the 2017 flaring state of TXS 0506+056 using parameters from the LMBB2b model The code used, LeHaMoC, is a time-dependent leptohadronic code that evolves the SED and candidate neutrino emission during the 2017 flare The subsequent evolution is modeled by considering an expanding spherical blob where the magnetic field decays as a power-law with radius, B′(R′) ∝ R′−mb Scenario C involves constructing the post-flare particle distribution by injecting the flare-state broken powerlaw pairs into a stationary zone and evolving it until a steady-state distribution is reached at t′ = 10 R′0/c

Kinetic Solution and Scaling of SSA Frequency

The kinetic equation for an expanding spherical blob with power-law injection Q′inj(γ, R′) = Q′0R′0R′mlγ−p H(R′−R'0) is solved using the method of characteristics to find the asymptotic behavior at large radii R' > R'0 The total number of electrons per unit γ behaves as N(γ, R′) ≃ C γ−p R′ 1−ml The comoving volume is V′ = (4π/3)R′3, leading to a differential number density of electrons ne(γ, R′) ≡ dne/dγ = N(γ, R′)/V′, with a radius-dependent normalization ke(R′) ∝ R′−(2+ml)

Scaling of the SSA Frequency

The SSA turnover frequency ν′ssa is defined by the condition that the optical depth across the source is of order unity, τν′ ≡ κδν' R' ∼ 1 By combining Eq. (C14) with Eq. (C15), it is found that ν′ssa ∝ R′−(1+ml+mb)2p+4 Substituting the scalings ke(R′)B′(R′) into this relation yields ν′ssa ∝ R'−[1+ml+mb]p+2

MCMC Fitting and Spectral Analysis

The model fitting uses Bayesian inference with the affine-invariant ensemble Markov Chain Monte Carlo (MCMC) sampler implemented in emcee to explore the posterior distribution of parameters like Vexp, ml, t′reacc, and mb The spectral shape during the outburst was investigated by fitting individual epochs with a smooth broken power-law model to obtain parameters such as the break frequency and slopes before and after the break The results show that the slope before the spectral break remains in the range 0 ≲ α1 ≲ 1, which is substantially softer than the optically thick SSA expectation of Fν ∝ ν5/2

Conclusion

The paper concludes that a direct adiabatic expansion of primary pairs related to the neutrino/γ-ray flare is excluded A more plausible interpretation is that the disturbance responsible for the 2017 neutrino/γ-ray flare exhibits redissipation of energy downstream, after the source has become optically thin at GHz frequencies Within a one-zone time-dependent framework, the delayed radio-flare in TXS 0506+056 is unlikely to be a direct radiative echo of the neutrino-production region becoming transparent Instead, the delayed GHz emission primarily traces downstream dissipation and beaming evolution of the propagating disturbance Because the radio emission is dominated by leptonic synchrotron emission and is largely insensitive to the proton population relevant for neutrino production, a delayed radioflare is not necessarily linked to the proton distribution characteristics, but rather a diagnostic of how and where the jet reprocesses energy at parsec scales This informs future modeling of neutrino–blazar associations by indicating that radio-flares appearing years after a neutrino alert may trace downstream dissipation and Dopplerfactor evolution, rather than direct radio unveiling of the neutrino zone The paper also motivates long-term radio monitoring (months–years) and high-resolution VLBI followup after neutrino alerts to capture delayed flares and associated structural changes

References

Aartsen, M. G., Ackermann, M., Adams, J., et al.

1. Improved physical modeling of jet evolution by incorporating downstream dissipation: The improved AI system can now test whether a downstream dissipation episode of particles in the optically thin regime, followed by jet deceleration successfully describes radio evolution, moving beyond simple expanding blob scenarios which were found to be insufficient.

2. Enhanced constraint on neutrino-blazar connection via dynamical diagnostics: The AI system can use multi-year radio monitoring to test whether the same compact region responsible for the 2017 neutrino/GeV γ-ray activity becomes transparent to radio emission through expansion and the consequent reduction of SSA, allowing it to distinguish between a direct radiative echo and effects tracing downstream dissipation and beaming evolution.

3. Refined parameter estimation for jet structure: The system can now constrain the physical parameters of the emitting region by fitting models to VLBI data, determining a radial expansion velocity Vexp using the formula in Eq. (B4) derived from core-size evolution, which yields specific constraints on jet geometry.

4. Improved spectral shape inference: The AI can perform Bayesian fitting of RATAN data with a smooth broken power-law model to derive posterior probability distributions for spectral parameters like the break frequency and slopes, finding that the slope before the spectral break remain in the range 0 ≲ α1 ≲ 1 (see top panel in the left column of Fig. 8) rather than simple SSA expectations.

5. Distinction between physical mechanisms: The system can differentiate between scenarios by evaluating whether observed radio features are explained by SSA-driven expanding blob models (which fail) versus a scenario invoking energy dissipation on parsec scales and jet deceleration, providing a physically motivated interpretation of the 2–3 yr delay.