Orbital Polarimetric Tomography of a Flare Near the Sagittarius A* Supermassive Black Hole

TL;DR

This work introduces orbital polarimetric tomography, a method to reconstruct a 3D, time-evolving flare in orbit around Sgr A$^*$ from single-view polarimetric light curves by marrying neural radiance fields with general relativistic ray tracing. By fitting ALMA 230 GHz linear polarization data with a forward model that encodes Kerr spacetime, Keplerian-like orbital dynamics, and optically thin synchrotron emission, the authors recover a 3D flare structure located at about $11$–$13~M$ from the black hole and constrain the observer’s inclination to be low ($\theta_{\rm o} < 18^\circ$) with a clockwise orbital motion. The approach demonstrates stability under physically motivated model choices and offers insights consistent with GRAVITY and EHT constraints, while highlighting sensitivity to magnetic-field configuration, orbital velocity, and background disk noise. This 3D tomographic framework enables probing the spatial origin and dynamics of flares near event horizons and can be extended to multi-frequency, spatially resolved data to refine black-hole spin, disk structure, and magnetic-field configurations. Overall, orbital polarimetric tomography provides a powerful, data-driven avenue to image and interpret near-horizon accretion phenomena in Sgr A$^*$ and similar systems.

Abstract

The interaction between the supermassive black hole at the center of the Milky Way, Sagittarius A*, and its accretion disk occasionally produces high-energy flares seen in X-ray, infrared, and radio. One proposed mechanism that produces flares is the formation of compact, bright regions that appear within the accretion disk and close to the event horizon. Understanding these flares provides a window into accretion processes. Although sophisticated simulations predict the formation of these flares, their structure has yet to be recovered by observations. Here we show the first three-dimensional (3D) reconstruction of an emission flare recovered from ALMA light curves observed on April 11, 2017. Our recovery shows compact, bright regions at a distance of roughly six times the event horizon. Moreover, it suggests a clockwise rotation in a low-inclination orbital plane, consistent with prior studies by GRAVITY and EHT. To recover this emission structure, we solve an ill-posed tomography problem by integrating a neural 3D representation with a gravitational model for black holes. Although the recovery is subject to, and sometimes sensitive to, the model assumptions, under physically motivated choices, our results are stable, and our approach is successful on simulated data.

Figures (16)

• Figure 1: A 3D recovery of a Sgr A$^*$ flare observed by ALMA on April 11, 2017. [Left panel] The validation-$\chi^2$, a robust data-fitting metric (see Methods section), indicates a preference of low inclination angles, $\theta_{\rm o} < 18^\circ$, with a local minimum around $\theta_{\rm o} = 12^\circ$ (red curve). For each inclination, the 3D recovery is run with five random initialization producing a spread that indicates recovery stability. The blue curve indicates that the analysis is largely insensitive to the black hole spin. [Right panels] A recovered 3D volume visualized from two view angles in intrinsic (flat space) coordinates (the event horizon illustrated for size comparison). The recovery shows two emission regions (blue arrows) at radii of $11 - 13~{\rm M}$ ($\sim 6$ times the Schwarzschild radius).
• Figure 1: Illustration of the simultaneous estimation of 3D emission and inclination angle from polarimetric lightcurve data. The light curves ($I_I, I_Q, I_U$) depend on the unknown inclination angle ($\theta_{\rm o}$) which gives rise to a different image-plane and subsequently model fit. From left to right: 1. An emission bright spot with azimuthal velocity ${\bf u}$ orbits a black hole on the equatorial plane. The vertical magnetic field ${\bf B}$ induces polarized synchrotron radiation. 2. Geodesic curves are computed for every pixel at each inclination angle. 3. Integrating emission along geodesics to generate a Stokes image plane over time. 4. Summing over image pixels gives the model prediction per inclination angle.
• Figure 2: ALMA light curves and a model fit over the a period of $\sim100$ minutes. [Top] The 229 GHz light curves were observed on 2017 April 11 (MJD 57854) as part of the EHT Sgr A$^*$ campaign. The red-shaded region corresponds to a time of period $\sim 100$ minutes in which polarimetric (Q-U) loops are apparent, directly after an X-ray flare was observed (gray-shaded region). The rotation of the polarization angle at a period similar to a Keplerian orbital period suggests the signal is coming from a bright compact structure in orbit around Sgr A$^*$wielgus2022orbital. [Bottom] A data-fit is preformed on the intrinsic LP curves (centered and de-rotated). The model light curves are produced through ray tracing the estimated 3D volume at a fiducial inclination angle of $\theta_{\rm o}=12^\circ$. The resulting model light curves accurately describe the data including the small looping feature highlighted by the blue arrow.
• Figure 2: Synthetic simulations of three emission structures: Simple Hotspot, Flux Tube, Double Source. Observations are generated at two inclination angles: $\theta_{\rm o}^{\rm lo}=12^\circ$, $\theta_{\rm o}^{\rm hi}=64^\circ$. This figure illustrates the gravitationally lensed LP images: $p_Q, p_U$ at three times within a period mimicking the radio-loops observed by ALMA: 9.35 -- 11 UTC (April 11, 2017). Images are computed at ${\rm FOV}=40M$ ($\sim 200 \mu {\rm as}$ for Sgr A$^*$) discretized into $64{\times}64$ pixels. To reduce aliasing effects, each pixel is computed as an average of 10 randomly sampled sub-pixel rays. All models share the same dimensions and orbit highlighted in blue for the Simple Hotspot. Note the secondary images formed by gravitational lensing, evident in the Simple Hotspot and Flux Tube models (the bottom half of the image plane at 9.50 UTC)
• Figure 3: An overview of the orbital tomography framework based on light curve observations. 1. An orbital model propagates an initial (canonical) emission volume ($e_0$) in time. 2. Ray tracing: we compute General Relativistic (GR) ray paths according to the black hole parameters and numerically integrate the 3D emissivities to synthesize image plane frames. 3. Each frame is summed to produce a single light curve data point which downstream is compared to the observations. 4. A neural representation of the underlying 3D volume. Each component is extensively discussed in the Methods section.