Full-polarization millimeter wavelength variability of Sagittarius A* during the 2018 EHT campaign

1. Problem and Scientific Context

Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, serves as a unique laboratory for studying accretion dynamics and plasma physics near the event horizon. While previous studies (including the 2017 Event Horizon Telescope campaign) have characterized Sgr A*'s variability, significant gaps remain regarding:

• Polarization Variability: How linear and circular polarization behave on short timescales compared to total intensity.
• Flare Mechanisms: The physical connection between high-energy (X-ray) flares and millimeter-wave emission. Specifically, whether millimeter flares are delayed due to cooling/expansion or simultaneous due to continuous energy injection.
• Model Constraints: The discrepancy between observed low variability in total intensity and the high variability often predicted by General Relativistic Magnetohydrodynamic (GRMHD) simulations.

This study addresses these issues by analyzing high-cadence, full-polarization light curves from the Atacama Large Millimeter/submillimeter Array (ALMA) during the April 2018 EHT campaign, with a specific focus on an X-ray flare detected by Chandra on April 24, 2018.

2. Methodology

The authors employed a rigorous multi-step approach to data processing and analysis:

• Data Acquisition: ALMA observations were conducted in phased-array mode on April 21, 22, 24, and 25, 2018, covering four spectral windows (213–229 GHz).
• Specialized Calibration (Intra-field): Standard ALMA calibration (QA2) assumes a constant flux source, which fails for the intrinsically variable Sgr A*. The authors implemented a custom algorithm to separate the compact, variable core (Sgr A*) from the extended, stable "minispiral" component. This involved:
  1. Generating a CLEAN image of the source.
  2. Subtracting the core to isolate the minispiral.
  3. Fitting a two-component visibility model to derive time-varying gain corrections.
  4. Transferring variability corrections to the core light curves.
• Time-Series Analysis:
  • Cross-Correlation: Used the Locally Normalized Discrete Correlation Function (LNDCF) to measure inter-band delays between spectral windows.
  • Structure Function (SF) & Power Spectral Density (PSD): Analyzed the SF to determine characteristic variability timescales and calculate PSD slopes ($\alpha_{PSD}$) to characterize the noise type (e.g., red noise).
  • Polarimetric Loop Analysis: Applied differential geometry techniques to the $Q-U$ plane to quantify the rotation speed and handedness (clockwise vs. counter-clockwise) of polarization loops.
• Comparative Analysis: Results were compared against historical data (2005–2019), the 2017 EHT campaign, and a library of 9,720 synthetic GRMHD light curves (including 1-temperature and 2-temperature plasma models).

3. Key Contributions

• Novel Calibration Pipeline: The development and application of an intra-field calibration method that successfully recovers the intrinsic variability of Sgr A* while correcting for the contamination of the extended minispiral, enabling high-fidelity full-polarization light curves.
• Simultaneous Multi-wavelength Flare Analysis: A detailed investigation of the April 24, 2018, event where an X-ray flare coincided with a millimeter peak, challenging standard delayed-emission models.
• Polarization Stability vs. Intensity Volatility: The demonstration that while total intensity is relatively stable, polarization exhibits significantly higher variability and coherent structural evolution.

4. Key Results

Variability Characteristics

• Total Intensity (Stokes I): Exhibits low variability with a modulation index ($\sigma/\mu$) of < 10%.
• Polarized Intensity (P): Shows significantly higher variability, with modulation indices of ~30% (linear) and ~50% (circular).
• Timescales:
  • Total intensity shows variable timescales ranging from ~20 minutes to 1.5 hours.
  • Polarized intensity displays a stable intra-day timescale of ~30 minutes, suggesting a coherent emission region for polarization distinct from the total flux.
• Power Spectral Density: Both Stokes I and P exhibit red-noise behavior. The PSD slopes range between -2 and -3 (specifically $\approx -2.4$ for Stokes I and $\approx -2.6$ for Polarized Intensity), consistent with turbulent accretion flows.

The April 24, 2018 Flare

• Simultaneity: Unlike the 2017 flare (where millimeter emission lagged X-rays by hours), the 2018 event showed near-simultaneous peaks in X-ray and millimeter bands (within a 5-minute window).
• Polarization Delay: A statistically significant inter-band delay was detected in polarized intensity, with the lower frequency band (B1) lagging the higher frequency band (B4) by $21 \pm 13$ seconds. No such delay was found in total intensity.
• Q-U Loop Evolution: The flare day exhibited the strongest clockwise coherence in the $Q-U$ polarization loops, suggesting a dominant, organized polarized hotspot during the event.

Comparison with GRMHD Models

• Variability Mismatch: The observed low variability in total intensity ($M_3 \approx 0.03-0.05$) is significantly lower than predictions from standard single-temperature (1T) GRMHD models, which tend to overproduce variability.
• 2T Models: Models incorporating two-temperature (2T) plasma physics (separate ion and electron temperatures) and radiative cooling better reproduce the observed low variability levels.

5. Significance and Conclusions

• Physical Mechanism of Flares: The simultaneity of the X-ray and millimeter peaks, combined with the inter-band polarization delay, challenges the standard "cooling/expanding blob" model. Instead, the authors favor a scenario of continuous energy injection in an optically thin region where electron cooling and re-acceleration occur concurrently.
• Accretion Flow Geometry: The persistent clockwise rotation of $Q-U$ loops (observed in both 2017 and 2018) implies a coherent, large-scale magnetic field structure in the accretion flow that remains stable over year-long timescales ($\sim 1.6 \times 10^6$ gravitational timescales).
• Plasma Physics: The results support the necessity of non-ideal plasma physics (collisionless effects, 2T treatments) in modeling Sgr A*. The data suggests that the magnetic field near the event horizon is organized rather than purely turbulent.
• Future Impact: These high-fidelity light curves provide critical constraints for refining theoretical models of accretion and plasma behavior, serving as a benchmark for future EHT imaging campaigns and multi-messenger observations of supermassive black holes.