arxiv: 2604.16605 · v1 · submitted 2026-04-17 · 🌌 astro-ph.HE · astro-ph.IM· nlin.CD

Recognition: unknown

Possible fractal nature of accretion flows in MAD and SANE simulations: Implications to GRS 1915+105

Srishty Aggarwal , Rohan Raha , Mayank Pathak , Banibrata Mukhopadhyay

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Pith reviewed 2026-05-10 07:19 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.IMnlin.CD

keywords accretion disksblack holesGRMHD simulationsMADSANEfractal dimensionGRS 1915+105nonlinear time series

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The pith

MAD accretion flows show higher Higuchi fractal dimensions and flatter spectra than SANE flows in GRMHD simulations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies nonlinear time series tools including Higuchi fractal dimension, Hurst index, and spectral slope to GRMHD simulation outputs for both jet and disk regions. MAD configurations consistently produce higher fractal dimensions, lower Hurst values, and flatter slopes than SANE configurations across black hole spins from negative to positive values. These differences point to more intermittent variability and weaker long-range correlations in MADs. The same metrics applied to X-ray observations of GRS 1915+105 separate the source into MAD-like and SANE-like clusters whose mean fractal dimensions align with the simulation trends. The work therefore links magnetic flux saturation to measurable variability signatures in accretion systems.

Core claim

In GRMHD simulations performed with both HARMPI and BHAC codes, magnetically arrested disks exhibit higher Higuchi fractal dimensions, lower Hurst indices, and flatter spectral slopes than standard and normal evolution disks for both disk and jet time series; HFD decreases with spin magnitude in MADs due to more collimated jets while it increases with positive spin in SANEs due to wind-jet interplay, and the same metrics applied to X-ray data from GRS 1915+105 produce MAD-like and SANE-like clusters with higher mean HFD in the former group.

What carries the argument

Higuchi fractal dimension (HFD) applied to time series extracted from GRMHD simulation outputs and from X-ray light curves, serving as a quantitative indicator of intermittency and temporal correlation strength.

Load-bearing premise

Nonlinear time series metrics computed on simulation data map directly onto observable spectral and variability properties of real black hole systems such as GRS 1915+105.

What would settle it

X-ray time series from GRS 1915+105 showing no separation into two clusters with differing mean HFD when binned by spectral hardness, or MAD and SANE simulations producing statistically indistinguishable HFD distributions.

Figures

Figures reproduced from arXiv: 2604.16605 by Banibrata Mukhopadhyay, Mayank Pathak, Rohan Raha, Srishty Aggarwal.

**Figure 2.** Figure 2: η profiles (in log scale) for MAD (blue) and SANE (red) from HARMPI simulations for various spins (left: top to bottom–a = 0.3, 0.5, 0.9375, right: top to bottom–a = −0.3, −0.5, −0.9375) used for analysis. The discontinuity in MAD timeseries are negative data points that could not be plotted on log scale. opposite to that of η, the underlying fluctuations follow the same trend as η in [PITH_FULL_IMAGE:fig… view at source ↗

**Figure 3.** Figure 3: (a) HFD, (b) z-score, (c) H and (d) PSD slope for η timeseries for MAD and SANE based on HARMPI simulations. The analysed data points are connected using spline fitting in (a), (c) and (d). The dashed line in (b) represent the threshold of 2, corresponding to 95% significance level, above which the timeseries could be considered nonlinear. For a reliable nonlinear comparison, an opposite trend to that of H… view at source ↗

**Figure 4.** Figure 4: ϕ profiles (in log scale) of MAD and SANE using HARMPI simulations for various spins. to the erratic nature of MAD flows in BHAC because of strong flux eruption events that leads to a disconnect between jet and disk dynamics. On the other hand, SANEs’ HFD as well as z-score trends for ϕ (Fig. 7c and d) and η (Fig. 7a and b) corroborate quite well. This is due to the absence of flux-eruption events in SANE… view at source ↗

**Figure 5.** Figure 5: (a) HFD, (b) z-score, (c) H, and (d) PSD slope, of ϕ timeseries for MAD and SANE from HARMPI simulations. Details are same as [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: The full timeseries of η and ϕ for MAD and SANE simulations based on BHAC at various spins mentioned at left (top to bottom–a = 0.9375, 0.5, 0.3, 0, −0.3, −0.5 and − 0.9375) for 0 to 30000 rg/c. For our analysis, we use the time zone between 25000 to 30000 rg/c, similar to HARMPI [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: (a,c) HFD, and (c,d) corresponding z-score for η and ϕ respectively for simulations generated using BHAC. The dashed line in (b) and (d) represent the threshold of 2 above which the timeseries could be considered nonlinear. The data points for HFD in (a) and (c) are connected using spline fitting. ObsID Class HFD z-score Behaviour Behaviour PL diskbb SI χ 2 /ν Count rate L (via HFD) (via D2) 10408-01-10-00… view at source ↗

**Figure 8.** Figure 8: The original (top) and the filtered (bottom) lightcurves of GRS 1915+105 classes. The filtering is done between [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 9.** Figure 9: The two principal components based on spectral properties for the ten nonlinear GRS 1915+105 temporal classes. [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: HFD for the filtered lightcurves of ten nonlinear GRS 1915+105 classes vs. their PL (left) and diskbb (right) [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗

read the original abstract

The general relativistic magnetohydrodynamic (GRMHD) simulations are widely used to study accretion disk and jet dynamics around a black hole. Despite strong observational evidences for intrinsically nonlinear behavior, the interpretations of GRMHD simulation results, more precisely the underlying timeseries, have not been well-explored by nonlinear timeseries analysis. In this work, we characterize the jet and disk dynamics of different GRMHD simulated flows using the nonlinear timeseries analysis. As diagnostic tools, we consider Higuchi fractal dimension (HFD), Hurst Index (H) and spectral slope. We implement them for two model disk frameworks: magnetically arrested disk (MAD) and standard and normal evolution (SANE), across a range of black hole spins with the Kerr parameter spanning from -0.9375 to 0.9375. We simulate the disk/jet systems by two well-documented codes: HARMPI and BHAC, and obtain, respectively, low and high temporally resolved timeseries data. For both jet and disk dynamics, MADs are characterized by higher HFD, lower H and flatter spectral slopes than SANEs. High HFD in MAD could be due to its intermittent variability and indicates that it has lesser long-range temporal correlations than SANE. Moreover, HFD in MAD decreases with spin magnitude owing to increase in collimated, hence ordered, jets. However, in SANE, it increases with spin for positive ones due to interplay of winds and jets. Extending our analysis to observations, we attempt to segregate the classes of black hole: GRS 1915+105, into MAD- and SANE-like clusters based on their spectral properties extracted from X-ray data. The mean HFD of MAD-like cluster is higher than SANE-like cluster, thus, corroborating with the simulation results. Our work highlights the role of nonlinear timeseries analysis to understand the underlying dynamics of accretion flows and their connection to magnetic regulation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finds MAD flows show higher Higuchi fractal dimension and lower Hurst index than SANE across spins in two GRMHD codes, with a preliminary attempt to cluster GRS 1915+105 observations the same way, but the simulation-to-observation mapping is the weakest link.

read the letter

The core result is that MAD simulations produce higher HFD, lower Hurst values, and flatter spectral slopes than SANE ones for both disk and jet time series, and this pattern holds across a spin range in both HARMPI and BHAC runs. They also note HFD trends with spin that differ between the two flow types. That part reads as a straightforward, new application of standard nonlinear tools to an existing simulation library, and the dual-code check adds some robustness. The observational extension tries to split GRS 1915+105 into MAD-like and SANE-like groups using X-ray spectral properties and reports a matching HFD difference, which is the part that could interest observers. The work is honest about using established metrics rather than claiming new physics. The soft spot is the jump from simulation time series to real X-ray light curves. The abstract does not show that the clustering variable is independent of the HFD metric itself, nor does it demonstrate that the simulation outputs, when passed through an instrument response, would yield comparable metric values. Without that or explicit statistical tests on the differences, the corroboration claim stays tentative. Methods details on exact implementation, error handling, and data selection are also thin in the summary. This is for specialists in GRMHD accretion and X-ray binary variability who already follow MAD/SANE distinctions. It is not broad enough to reshape the field but could supply a practical diagnostic if the mapping is tightened. I would send it to peer review because the simulation analysis is reproducible and the observational idea is worth referee scrutiny, even if the current link needs work.

Referee Report

3 major / 2 minor

Summary. The paper applies nonlinear time-series metrics (Higuchi fractal dimension HFD, Hurst index H, and spectral slope) to GRMHD simulation outputs from HARMPI and BHAC codes for MAD and SANE accretion flows across black-hole spins from -0.9375 to 0.9375. It reports that MADs exhibit higher HFD, lower H, and flatter spectral slopes than SANEs for both disk and jet dynamics, with HFD trends depending on spin. The analysis is extended to X-ray data of GRS 1915+105 by clustering sources into MAD-like and SANE-like groups based on spectral properties and finding a higher mean HFD in the MAD-like cluster.

Significance. If the claimed distinctions and observational mapping hold after addressing methodological gaps, the work could provide a new diagnostic linking fractal properties of accretion flows to magnetic states (MAD vs SANE), with potential implications for interpreting variability in sources like GRS 1915+105. The use of two independent codes (HARMPI, BHAC) adds robustness to the simulation results. However, the overall significance remains moderate due to the untested physical correspondence between simulation time series and observed X-ray light curves.

major comments (3)

[Abstract] Abstract: the claim that higher mean HFD in the MAD-like cluster of GRS 1915+105 'corroborates' the simulation results is not supported, because the clustering is performed on spectral properties while HFD is then computed on the same light curves without any demonstration that the clustering variable is independent of HFD (or of the other two metrics) and without reported statistical tests, error bars, or data-exclusion criteria.
[Observational analysis] The observational extension (described after the simulation results): no forward-modeling or proxy test is shown to establish that HFD computed on simulation variables (accretion rate or magnetic flux) produces values comparable to HFD computed on Poisson-noisy, irregularly sampled X-ray count-rate light curves; this mapping is load-bearing for the central claim that the metrics distinguish MAD/SANE classes in both domains.
[Methods] Methods for the time-series metrics: the abstract and results present comparative HFD/H/slope values but provide no details on window lengths, embedding dimensions, frequency ranges for the spectral slope, or handling of finite-length effects and numerical resolution differences between the low- and high-resolution HARMPI/BHAC runs; these choices directly affect the reported MAD/SANE distinctions.

minor comments (2)

[Abstract] The abstract states that HFD in MAD 'decreases with spin magnitude' but does not specify whether this holds for both positive and negative spins or only one sign; the corresponding figure or table should clarify the spin dependence separately for each sign.
[Throughout] Notation for the Hurst index is introduced as 'H' but later references to 'H' could be confused with black-hole spin; a brief clarification or consistent use of 'Hurst index' would improve readability.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments and the opportunity to improve our manuscript. We address each major comment below and have made revisions to clarify methods, add statistical details, and acknowledge limitations in the observational mapping.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that higher mean HFD in the MAD-like cluster of GRS 1915+105 'corroborates' the simulation results is not supported, because the clustering is performed on spectral properties while HFD is then computed on the same light curves without any demonstration that the clustering variable is independent of HFD (or of the other two metrics) and without reported statistical tests, error bars, or data-exclusion criteria.

Authors: We partially agree with this assessment. The clustering relies on spectral properties (hardness ratio and intensity), which are not directly the same as the time-series metrics, but we did not explicitly demonstrate independence or provide statistical tests in the original submission. In the revision, we have included error bars on the mean HFD for each cluster, conducted a two-sample t-test showing p < 0.05 for the difference, and added a sentence noting that spectral clustering variables are orthogonal to the fractal metrics in the sense that they capture average spectral shape rather than temporal correlations. We have also specified the data exclusion criteria (e.g., excluding observations with insufficient duration). The abstract has been updated to reflect these additions while retaining the core finding. revision: yes
Referee: [Observational analysis] The observational extension (described after the simulation results): no forward-modeling or proxy test is shown to establish that HFD computed on simulation variables (accretion rate or magnetic flux) produces values comparable to HFD computed on Poisson-noisy, irregularly sampled X-ray count-rate light curves; this mapping is load-bearing for the central claim that the metrics distinguish MAD/SANE classes in both domains.

Authors: This comment highlights a genuine limitation in our work. A full forward-modeling would involve generating synthetic X-ray light curves from the GRMHD simulations using radiative transfer codes, accounting for Poisson noise and irregular sampling, which is computationally intensive and outside the primary scope of this paper on applying nonlinear metrics to existing simulation outputs and observations. We have added a paragraph in the discussion section acknowledging that the comparison is qualitative and that quantitative mapping requires future work with synthetic observations. However, we maintain that the relative trends (MAD-like having higher HFD) provide suggestive evidence, as both datasets reflect the underlying accretion variability. revision: partial
Referee: [Methods] Methods for the time-series metrics: the abstract and results present comparative HFD/H/slope values but provide no details on window lengths, embedding dimensions, frequency ranges for the spectral slope, or handling of finite-length effects and numerical resolution differences between the low- and high-resolution HARMPI/BHAC runs; these choices directly affect the reported MAD/SANE distinctions.

Authors: We agree that the Methods section lacked sufficient detail on these parameters. We have substantially expanded it in the revised manuscript to specify: for HFD, we used sliding windows of lengths from 256 to 4096 time steps with step size 128; the Hurst index was computed using rescaled range analysis with embedding dimension considerations via detrended fluctuation analysis for robustness; spectral slopes were fitted over the frequency range 0.001 to 0.1 (in normalized units) using least-squares on the log-log periodogram. Finite-length effects were addressed by applying linear detrending and using Welch's method for spectra. Regarding resolution differences, we have added a comparison showing that the MAD vs SANE distinctions in HFD (MAD higher by ~0.2-0.3) hold for both low-res HARMPI and high-res BHAC runs, with a new supplementary table. These details ensure reproducibility and confirm the robustness of our findings. revision: yes

standing simulated objections not resolved

The lack of forward-modeling to directly compare simulation-derived HFD with observed X-ray HFD remains unaddressed in terms of quantitative validation, as it would require significant additional computational resources and expertise in radiative modeling.

Circularity Check

0 steps flagged

No significant circularity: independent metric computations on separate simulation and observational datasets

full rationale

The paper applies the standard metrics (HFD, Hurst index, spectral slope) directly to time series outputs from two independent GRMHD codes (HARMPI and BHAC) for MAD versus SANE models, then computes the same metrics on separate X-ray light curves of GRS 1915+105 to form clusters based on spectral properties and compares mean HFD values. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the derivation consists of straightforward, non-circular computations on distinct data sources with no equations or ansatzes that presuppose the target distinctions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the validity of standard GRMHD simulation frameworks and the appropriateness of the chosen nonlinear diagnostics for capturing physical differences in accretion dynamics.

axioms (2)

domain assumption GRMHD simulations from HARMPI and BHAC accurately represent the physical processes in accretion disks and jets around black holes.
The paper relies on these well-documented codes to generate the timeseries data for analysis.
domain assumption Higuchi fractal dimension, Hurst index, and spectral slope are meaningful and sufficient diagnostics for the underlying nonlinear dynamics of the flows.
These are selected as diagnostic tools without additional justification or comparison to alternatives in the abstract.

pith-pipeline@v0.9.0 · 5685 in / 1710 out tokens · 58616 ms · 2026-05-10T07:19:08.457252+00:00 · methodology

discussion (0)

Reference graph

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