Multiwavelength variability of the high-energy neutrino candidate PKS 0735+178 over three decades

Technical Summary: Multiwavelength Variability of the High-Energy Neutrino Candidate PKS 0735+178 over Three Decades

Problem Statement
PKS 0735+178 is a classical BL Lac object associated with the high-energy neutrino event IC211208A (171 TeV). While the source is known for extreme multiwavelength variability and a relativistic jet viewed at small angles, the physical connection between emission regions at different frequencies, the nature of its long-term quasi-periodic behavior, and the specific mechanisms driving the activity surrounding the neutrino event remain poorly understood. Previous studies have focused primarily on short-term spectral properties or isolated flares, lacking a unified analysis of the source's temporal evolution over a multi-decade baseline to constrain jet geometry and disturbance propagation.

Methodology
The authors present a comprehensive analysis of $\sim$30 years (1995–2026) of multiwavelength data, integrating:

• Radio Data: Quasi-simultaneous observations at 1–22 GHz from the RATAN-600 telescope and 230 GHz data from the Submillimeter Array (SMA).
• Optical Data: R-band photometry from the Zeiss-1000, AS-500/2, KAIT, ZTF, and CRTS telescopes.
• Gamma-Ray Data: Fermi-LAT light curves (1.5–300 GeV) constructed using adaptive binning to resolve fine structures during flaring states.
• VLBI Constraints: Core-shift measurements at 15 and 43 GHz using MOJAVE and VLBA-BU-BLAZAR data to derive jet kinematics and physical parameters.

The analysis employed several statistical and physical modeling techniques:

1. Cross-Correlation: Discrete Correlation Functions (DCF) were used to measure time lags between bands.
2. Spectral Analysis: Radio spectra were grouped into three major flaring episodes to track spectral index evolution ($\alpha$).
3. Quasi-Periodicity Search: The Weighted Wavelet Z-transform (WWZ) and Generalized Lomb-Scargle (GLS) periodograms were applied to detect characteristic time-scales, with significance assessed against red-noise backgrounds via Monte Carlo simulations.
4. Physical Modeling:
   • Shock Propagation: Time delays were fitted to a power-law dependence ($\Delta t \propto \nu^{-1/k_r}$) to test an opacity-stratified jet model.
   • Jet Precession: A Bayesian optimization model (UltraNest) was used to fit light curves to a precession scenario, testing if geometric effects could explain the long-term modulation.
   • VLBI Core Shift: Used to estimate the jet viewing angle, apparent speed, magnetic field strength, and magnetic flux relative to the Magnetically Arrested Disk (MAD) limit.

Key Results

• Frequency-Dependent Time Delays: Light curves across radio, optical, and $\gamma$-ray bands are correlated, but radio emission lags behind higher frequencies. Delays increase systematically toward lower frequencies, reaching $\sim$1200 days at 1–2 GHz relative to $\gamma$-rays. This follows a power law with $k_r = 1.96 \pm 0.24$, consistent with an opacity-stratified jet where disturbances propagate downstream.
• Neutrino Event Flares: Short, bright flares in the optical and $\gamma$-ray bands occurred within days of the IC211208A event. A robust 12-day lag was detected between the optical and $\gamma$-ray peaks (optical leading), suggesting non-co-spatial emission regions or contributions from processes like external Compton scattering. The third major radio flare (2019–2026) exhibits inverted or flat spectra at low frequencies, indicating a compact, optically thick emission region with enhanced particle acceleration.
• Quasi-Periodic Variability: A characteristic variability time-scale of $\sim$10–11 years is robustly detected ($\ge 3\sigma$) in radio and millimeter bands (5–230 GHz). This modulation is coherent across these bands but is not strictly periodic. In contrast, optical and $\gamma$-ray data show weaker, shorter-period signals ($\sim$5–9 years) that are time-localized and less coherent.
• Jet Geometry and Physics:
  • VLBI core-shift measurements yield a jet viewing angle of $\theta \approx 3.6^\circ$ and an apparent speed $\beta_{app} \approx 0.8c$, consistent with time-delay derived propagation speeds.
  • The magnetic field at 1 pc is estimated at $\sim$0.36 G. The ratio of magnetic flux to the MAD limit suggests the accretion disk is not in a MAD state at current luminosity levels.
• Precession Model Limitations: While a jet precession model can reproduce the general shape of the light curves, the derived parameters (viewing angle $\sim$27.4°) contradict VLBI constraints ($\theta \sim 1^\circ-3^\circ$). This indicates that precession alone cannot explain the observed variability.

Significance and Claims
The paper claims that the variability of PKS 0735+178 is governed by two distinct physical processes operating on different timescales:

1. Long-term Modulation: A slow variation in energy release at the jet base drives a quasi-periodic ($\sim$11 yr) modulation, likely linked to the accretion flow or jet base dynamics, which regulates the rate of disturbance injection.
2. Short-term Flares: Individual flares, including the one associated with the neutrino event, arise from shocks propagating downstream through an opacity-stratified jet. The frequency-dependent delays and spectral evolution are naturally explained by the shock crossing synchrotron photospheres at different distances.

The study provides the first reliable measurement of the 12-day lag between optical and $\gamma$-ray emissions in this source, challenging simple one-zone synchrotron self-Compton scenarios. Furthermore, the consistency between independent constraints from VLBI core-shifts and radio time delays strongly supports a unified scenario of shock propagation in a stratified flow. The temporal clustering of the neutrino event with the multiwavelength flare reinforces the connection between PKS 0735+178 and high-energy neutrino production, likely occurring in the inner, optically thick regions of the jet.