Characterizing Power Spectra of Density Fluctuations in GRMHD Simulations of Black Hole Accretion Using Taylor's Frozen-in Hypothesis

TL;DR

This paper develops a framework to quantify intrinsic density fluctuations in GRMHD black hole accretion flows by mapping temporal power spectra to spatial spectra using Taylor's frozen-in hypothesis. Using KORAL simulations for MAD and SANE regimes across a range of spins, it distinguishes the appropriate velocity proxy—bulk flow in SANE and Alfvén speed in MAD—to derive $P(k)$ from $P(\omega)$ and fits a Beuermann profile to characterize the spectra. The results reveal broken power-law behavior with a break frequency $k_{\mathrm{br}}$ that declines with radius, with MAD flows showing stronger radial trends and distinct spin- and retrograde/prograde-dependent patterns in slopes $\alpha_1$ and $\alpha_2$. These findings provide a scale-dependent view of intrinsic accretion flow variability that can inform interpretation of EHT data, though linking to observables will require incorporating radiative transfer and relativistic effects.

Abstract

We characterize the spatial power spectrum of density fluctuations in magnetohydrodynamic flows in a suite of high-resolution, long-time-span general relativistic magnetohydrodynamic (GRMHD) simulations. Extracting the local spatial power spectrum in curved spacetime directly from GRMHD simulations can be challenging for several conceptual and mechanical reasons, including choices of the reference frame, the non-uniform co-ordinate grid of the outputs and limited resolution. Taylor's frozen-in hypothesis describes a mapping between the temporal and spatial power spectrum of turbulence, which we apply to density fluctuations. We explore the validity of the assumptions underlying Taylor's hypothesis and evaluate its applicability in extracting spatial power spectra of density fluctuations of black hole accretion flows. Using outputs from the GRMHD code KORAL, we explore models with strong and ordered magnetic fields (MAD, Magnetically Arrested Disks) as well as weak and disordered magnetic fields (SANE, Standard and Normal Evolution). We explore the effects of black hole spin on the power spectra and characterize their spectral properties as a function of distance from the black hole. The observed power spectra follow a broken power law with two slopes separated by a break frequency. Our analysis shows a decrease in break frequency with increasing radius, with distinct trends between SANE and MAD flows. We also observe the first slope to be steeper for SANE flows and some notable distinctions between prograde and retrograde spins.

Figures (7)

• Figure 1: Comparison between Alfvén wave velocity and bulk accretion flow velocity in the coordinate normal or stationary frame of reference for SANE (top row) and MAD (bottom row) flows with black hole spins ranging from $-0.9$ to $0.9$. Both quantities are averaged azimuthally, within the disk-region defined by polar angles $\theta$ between $45^{\circ}$ and $135^{\circ}$, and within radial bins of width $0.5\ M$. The quantities are also time-averaged over 2000 snapshots, spanning over 20,000 $GM/c^3$. In all SANE flows, the bulk velocity exceeds that of the Alfvén wave. The opposite is true in the case of MAD, except for the non-spinning model, for which both velocities are comparable.
• Figure 2: Azimuthally- and disk-averaged temporal power spectra of number density fluctuations for a non-spinning SANE flow. We show simulations with low cadence ($\Delta T = 10 \ GM/c^3$, solid) and high cadence ($\Delta T = 0.5 \ GM/c^3$, dotted). Each curve corresponds to the average one-dimensional temporal power spectrum ($\omega$-spectrum) of number density fluctuations within a range of radii from the black hole. Colors denote the radial ranges in units of $GM/c^2$.
• Figure 3: Azimuthally- and disk-averaged spatial power spectra of number density fluctuations for a non-spinning SANE flow. (left) Each temporal power spectrum from Figure \ref{['fig:temp_comp_SANEa9']} is mapped to its corresponding spatial spectrum following equation \ref{['eq:MAP']}. (right) Normalized spectra with lower frequency data points of the higher resolution $0.5 \ GM/c^3$ simulations prioritized, i.e., for frequencies where the two simulations overlap, we keep data points from the higher-cadence simulation.
• Figure 4: Azimuthal ($\phi$) power spectra of number density fluctuations averaged over time and within the disk region for a SANE simulation with black hole spin $a = 0.9$(dotted). We compare the $\phi$ spectra to those from Taylor’s hypothesis (solid) for the low-cadence ($10\ GM/c^3$, left) and high cadence ($0.5\ GM/c^3$, right) SANE simulation.
• Figure 5: Azimuthally- and disk-averaged spatial power spectra of number density fluctuations from MAD and SANE simulations for different black hole spins. The spectra are normalized and we prioritize lower frequency data points of the higher resolution $0.5 \ GM/c^3$ simulations as shown in Figure \ref{['fig:spat_comp_SANEa9']}.