# How Spatially Resolved Polarimetry Informs Black Hole Accretion Flow Models

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Simulating Black Hole Accretion Flows

^{3}), improved spatial resolution (decreasing from about 20 μas to ∼10–15 μas), and time-resolved images of the dynamical activity in both M87* and Sgr A* over hundreds-to-thousands of gravitational timescales. This will result in movies of both the accretion disks and relativistic jets near SMBHs. In this article, we discuss what physical information each of these maps carry.

## 2. Total Intensity and Spectral Index

## 3. Linear Polarization

## 4. Rotation Measure

## 5. Circular Polarization

## 6. Scattering

## 7. Studying Polarimetry with Interferometry

## 8. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | |

2 | ${\mathsf{\Theta}}_{e}$ is the temperature normalized by the electron rest mass energy, ${\mathsf{\Theta}}_{e}={k}_{B}T/{m}_{e}{c}^{2}$, where ${k}_{B}$ is the Boltzmann constant, T is the temperature in Kelvin, ${m}_{e}$ is the electron rest mass, and c is the speed of light. |

3 | These distributions are characterized by a thermal core with the addition of a high energy power-law tail, with slope $p=\kappa -1$. |

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**Figure 1.**A single GRMHD snapshot ray-traced and scaled to Sgr A* properties, with three decades in dynamic range shown. In the leftmost panel, ticks representing the linear polarization have lengths scaled proportionally to the total linearly polarized intensity. To date, total intensity maps have been produced for both Sgr A* and M87*, a linear polarization map has been produced for M87*, and the remaining observables have yet to be generated for either source. In the era of ngEHT, we will have access to each of these observables with improved dynamic range and time-domain information, which will greatly inform models of the black hole accretion flow. Note that finite spatial resolution and other data corruptions have not been taken into account.

**Figure 2.**Intensity and spectral index map of a MAD model of Sgr A* adapted from Figure 4 of [41]. The top left panel plots total intensity in log scale averaged between 214 and 228 GHz, the top center panel plots the spectral index across this bandwidth calculated by ray tracing the image at two different frequencies, and the top right panel plots an analytic prediction of the spectral index in each pixel obtained by combining the three quantities in the bottom panel: electron temperature, optical depth, and magnetic field strength, each computed by performing an emissivity-weighted average long each geodesic. The excellent agreement between the true spectral index map and the analytic prediction illustrates the power of spectral index maps to jointly constrain these plasma quantities.

**Figure 3.**Polarization pattern of a ring of emission around a Schwarzschild black hole threaded with magnetic fields of different geometries: toroidal, radial, and vertical adapted from Figure 3 of [8]. The toroidal and radial magnetic field cases clearly illustrate the fact that synchrotron emission is polarized perpendicular to the magnetic field projected onto the sky. The orientation of the ticks in the vertical field case encodes the direction of the fluid’s motion [8], chosen here to be clockwise on the sky. These maps were computed using the analytic ring model of Narayan et al. [51]. Here, the color map encodes the total intensity, and unlike in Figure 1, the linear polarization ticks do not scale with the polarized intensity.

**Figure 4.**Rotation measure map of a MAD simulation of M87* adapted from Figure 13 of Ricarte et al. [44]. Both positive and negative RM regions are simultaneously present, reflecting flips in the line-of-sight magnetic field direction due to turbulence in the accretion flow. The motion of these structures produces a time variable spatially unresolved RM, written at the bottom of each panel.

**Figure 5.**Maps of circular polarization encode properties of the geometry of the magnetic field, both its line-of-sight direction and twist. A cartoon of a generic helical field geometry is depicted on the left. On the right, we plot the circular polarization of a MAD model of M87* at two inclinations. Both are reproduced from Ricarte et al. [37]. The top row depicts a 5${}^{\circ}$ viewing angle, and the bottom row depicts a 90${}^{\circ}$ viewing angle. The first column shows the time averaged circularly polarized image, the second column shows the same at a single snapshot, and the third column shows fractional circular polarization. For face-on viewing angles, the photon ring exhibits an interesting sign flip due to Faraday conversion and the sourcing of photons from the opposite side of the disk. For edge-on viewing angles, circular polarization exhibits a “four quadrants” pattern that reflects the line-of-sight magnetic field direction.

**Figure 6.**GRMHD model of Sgr A* at 230 GHz before (

**left**) and after (

**right**) including the effects of interstellar scattering. This simulation is a MAD with ${a}_{\u2022}=0.7$, ${R}_{\mathrm{high}}=20$, and $i={30}^{\circ}$. The background image shows total intensity with respect to the image peak, while the ticks show the polarization magnitude and direction, colored by fractional polarization, while scattering severely affects the image, key polarimetric measures are nearly immune to scattering. For example, the unresolved fractional polarization is 10.5% before scattering and is 10.6% after scattering. Likewise, the ${\beta}_{2}$ mode in polarization [55] has $|{\beta}_{2}|=0.40$ and $arg\left({\beta}_{2}\right)=52.{1}^{\circ}$ before scattering, and $|{\beta}_{2}|=0.37$ and $arg\left({\beta}_{2}\right)=51.{0}^{\circ}$ after scattering.

**Figure 7.**Interferometric properties of the GRMHD model shown in Figure 6. Solid lines show the normalized intensity $\left|\tilde{I}\left(\mathbf{u}\right)/\tilde{I}\left(\mathbf{0}\right)\right|$ before (blue) and after (red) scattering, and the dashed lines show the interferometric fractional polarization magnitude $\left|\stackrel{\u02d8}{m}\left(\mathbf{u}\right)\right|$. For these curves, baselines are oriented along the East–West direction: $\mathbf{u}=(u,0)$. Over the full range of baseline lengths accessible from the ground, the fractional polarization is largely immune to scattering, while diffractive scattering causes a substantial reduction in the flux on long baselines.

**Figure 8.**Two GRMHD models imaged at 228 GHz and corresponding maps of linear polarization in visibility space. The top row corresponds to a MAD model of M87* with ${a}_{\u2022}=0.9$ and ${R}_{\mathrm{high}}=1$, while the bottom row corresponds to a SANE model with ${a}_{\u2022}=-0.3$ and ${R}_{\mathrm{high}}=40$. Due to a much larger Faraday depth, written at the bottom of the images, the SANE model exhibits a much more disordered linear polarization pattern. In the ordered model, measures of the linear polarization rise dramatically with radius in the Fourier domain, while the disordered model is characterized by blobs with a coherence length corresponding to the size of the image.

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## Share and Cite

**MDPI and ACS Style**

Ricarte, A.; Johnson, M.D.; Kovalev, Y.Y.; Palumbo, D.C.M.; Emami, R. How Spatially Resolved Polarimetry Informs Black Hole Accretion Flow Models. *Galaxies* **2023**, *11*, 5.
https://doi.org/10.3390/galaxies11010005

**AMA Style**

Ricarte A, Johnson MD, Kovalev YY, Palumbo DCM, Emami R. How Spatially Resolved Polarimetry Informs Black Hole Accretion Flow Models. *Galaxies*. 2023; 11(1):5.
https://doi.org/10.3390/galaxies11010005

**Chicago/Turabian Style**

Ricarte, Angelo, Michael D. Johnson, Yuri Y. Kovalev, Daniel C. M. Palumbo, and Razieh Emami. 2023. "How Spatially Resolved Polarimetry Informs Black Hole Accretion Flow Models" *Galaxies* 11, no. 1: 5.
https://doi.org/10.3390/galaxies11010005