Imaging and polarization patterns of various thick disks around Kerr-MOG black holes

TL;DR

This work addresses testing modified gravity in the strong-field regime by examining horizon-scale imaging and polarization around Kerr–MOG black holes encircled by geometrically thick accretion flows. It combines two physically motivated disk models (RIAF and BAAF) with general relativistic radiative transfer to compute synchrotron emission and polarization across a range of spins $a$, MOG parameter $oldsymbol{\alpha}$, inclinations $ heta_o$, and observing frequencies, introducing diagnostics such as the net EVPA $oldsymbol{chi_{net}}$ and the second azimuthal Fourier mode angle $oldsymbol{etaup_2}$ to quantify near-horizon polarization features. The results show that both $oldsymbol{\alpha}$ and $a$ strongly shape near-horizon polarization and intensity patterns: increasing $oldsymbol{\alpha}$ enlarges the bright ring and horizon-like region, while higher $a$ induces frame-dragging–driven brightness asymmetries; the BAAF model yields a narrower bright ring and distinctive near-horizon polarization morphologies, with $oldsymbol{etaup_2}$ flips and convergence behavior tied to flow energy and spacetime parameters. The findings suggest that high-resolution polarimetric imaging, as pursued by the Event Horizon Telescope and successors, could provide a viable observational test of Kerr–MOG gravity, enabling constraints on the MOG parameter $oldsymbol{\alpha}$ through horizon-scale polarization signatures.

Abstract

We investigate the imaging and polarization properties of Kerr-MOG black holes surrounded by geometrically thick accretion flows. The MOG parameter $α$ introduces deviations from the Kerr metric, providing a means to test modified gravity in the strong field regime. Two representative accretion models are considered: the phenomenological radiatively inefficient accretion flow (RIAF) and the analytical ballistic approximation accretion flow (BAAF). Using general relativistic radiative transfer, we compute synchrotron emission and polarization maps under different spins, MOG parameters, inclinations, and observing frequencies. In both models, the photon ring and central dark region expand with increasing $α$, whereas frame dragging produces pronounced brightness asymmetry. The BAAF model predicts a narrower bright ring and distinct polarization morphology near the event horizon. By introducing the net polarization angle $χ_{\text{net}}$ and the second Fourier mode $\angleβ_2$, we quantify inclination- and frame-dragging-induced polarization features. Our results reveal that both $α$ and spin significantly influence the near-horizon polarization patterns, suggesting that high-resolution polarimetric imaging could serve as a promising probe of modified gravity in the strong field regime.

Figures (15)

• Figure 1: Intensity maps in the RIAF model with isotropic emission. The motion of the accretion flow corresponds to the infalling case. From left to right, the spin parameter takes the values $a = 0.1,~0.5,~0.9$; from top to bottom, the MOG parameter is set to $\alpha = 0.2,~0.4,~0.6,~0.8$. The observation is performed at a frequency of $345~\mathrm{GHz}$ and $\theta_o=30^\circ$.
• Figure 2: Intensity distribution for the Kerr-MOG black hole in the RIAF model with isotropic emission. The accretion flow follows the infalling motion. The observation is performed at a frequency of $345~\mathrm{GHz}$ and $\theta_o=30^\circ$. Left column: profiles for varying spin $a$ with $\alpha=0.2$. Right column: profiles for varying deformation $\alpha$ with $a=0.1$. Upper and lower panels correspond to horizontal ($X$-axis) and vertical ($Y$-axis) cuts, respectively.
• Figure 3: Intensity maps in the RIAF model with isotropic emission for different inclinations. The motion of the accretion flow corresponds to the infalling case. From left to right, $\theta_o = 1^\circ,~30^\circ,~60^\circ,~80^\circ$. The observation frequency is $345~\mathrm{GHz}$, with spin parameter $a = 0.1$ and MOG parameter $\alpha = 0.2$.
• Figure 4: Intensity maps in the RIAF with isotropic emission and infalling motion. The top row shows the images at observing frequencies of 85, 230, and 345 GHz (from left to right). The bottom row presents the horizontal (left) and vertical (right) intensity cuts for different frequencies. The inclination angle is fixed at $1^\circ$, with $a = 0.9$ and $\alpha = 0.6$.
• Figure 5: Intensity maps in the RIAF model with anisotropic emission. The motion of the accretion flow corresponds to the infalling case. From left to right, the spin parameter takes the values $a = 0.1,~0.5,~0.9$; from top to bottom, the MOG parameter is set to $\alpha = 0.2,~0.4,~0.6,~0.8$. The observation frequency is $345~\mathrm{GHz}$, and the inclination angle is $30^\circ$.