arXiv subjects

Keping Qiu

Publications and source records attributed to Keping Qiu.

At least 19 recordsLinked to original sources

arXiv2026

Turbulence Cascade in Cygnus X Revealed by Multi-point VDF Method

Turbulence plays a crucial role in regulating star formation activities within molecular clouds, yet few methods can directly reveal its properties and underlying processes. We use molecular line data from the Nobeyama 45m Cygnus X CO Survey to study the turbulence properties and their relationships with star-forming activities and/or other non-thermal motions. In this work, we apply the multi-point velocity dispersion function (VDF), rather than direct linewidth measurements, to investigate the non-thermal properties of molecular cloud motions. We filter out the large-scale ordered structure and isolate a relatively small-scale turbulence component. Through the Friends In Velocity (FIVe) algorithm, we identify 10 substructures of the clouds and derive the turbulent properties of each cloud using the VDF method. We find that both the cloud-complex regions and the 10 velocity substructures exhibit turbulence correlation lengths of $\sim 2$--5 pc. This plateau scale suggests a parsec-scale turbulence correlation or driving scale in Cygnus X. Below this scale, the rising VDFs trace the velocity scaling of the turbulent cascade, whereas larger-scale VDF variations likely reflect cloud-scale motions. The comparison between cloud complexes and substructures further suggests that, in observational data, the VDF may constrain the turbulence correlation scale more robustly than the turbulence velocity dispersion.

astro-ph.GA↗

arXiv2026

A Unified Magnetohydrodynamic Scaling Relation for the Multiphase Interstellar Medium

The interplay of magnetic fields, turbulence, and gravity governs the structural evolution of the interstellar medium (ISM) and the initial conditions of star formation, yet observational gaps have long enforced a broken power-law description of the magnetic field--density relation. Here we assemble a unified dataset spanning ten orders of magnitude in density ($10^{-26}$--$10^{-16}\,\mathrm{g\,cm^{-3}}$) by combining pulsar and Zeeman observations. The unified data are consistent with a continuous magnetic-field evolution organised by the Alfv\'en Mach number $\mathcal{M}_{\rm A}=\sqrt{E_K/E_B}$. Within this interpretation, the low-density gas is magnetically dominated ($\mathcal{M}_{\rm A}<1$), whereas the high-density gas becomes kinetically dominated ($\mathcal{M}_{\rm A}>1$) as gravity increasingly contributes to the kinetic-energy budget, with magnetic tension continuing to influence the collapse geometry. Within the Gradual Transition interpretation, the empirical break density traces the vicinity of the trans-Alfv\'enic equipartition point, $\mathcal{M}_{\rm A}=1$. This Gradual Transition model makes three predictions tested here. Its exponent and background field are fixed in advance by turbulent physics and recovered by the fits ($\beta\approx0.15$--$0.21$ against a predicted $0.147$; $B_c\approx2.0\,\mu$G). A dense-gas fit, extrapolated blindly across four decades, passes through the diffuse pulsar data. And, under the adopted scale mappings, the implied magnetic-energy spectrum approaches a $k^{-5/3}$-like scaling on large scales and departs from this extrapolation on small scales, where gravitational compression amplifies the field. The broken power law can therefore be viewed as a piecewise approximation to the continuous magnetic equation of state, with its fitted transition density potentially retaining a physical connection to the onset of gravity-driven motions.

astro-ph.GA↗

arXiv2026

ALOHA IRDCs Molecular Line Follow-up: I. Gas properties and kinematics

Infrared Dark Clouds are ideal sites for investigating the initial conditions of massive star and cluster formation. The A Lei Of the Habitat and Assembly of Infrared Dark Clouds (ALOHA IRDCs), a James Clerk Maxwell Telescope (JCMT) Large Program, has mapped nearby IRDCs with SCUBA-2. Complementary molecular line observations are needed to characterise the physical, kinematic, and chemical properties of the dense gas. We aim to determine the thermal, kinematic, and chemical properties of clumps identified in the ALOHA IRDCs, and to assess their evolutionary status and level of star-forming activity. We performed single-pointing K-band and W-band observations towards 56 ALOHA IRDCs clumps using the Effelsberg 100-m and Yebes 40-m telescopes, respectively. We derived NH3 kinetic temperatures using the hyperfine group ratio (HFGR) method and identified infall and shock signatures from HCO+, H13CO+, SiO, and HNCO profiles. Water masers and NH2D emission were used as complementary tracers of chemical evolution and star formation. The clumps exhibit kinetic temperatures of 15-29 K. We detect NH2D emission towards 18 sources, with NH2D centroid velocities consistent with NH3, indicating both species trace the same dense gas component. More than half of the clumps display blue-asymmetric HCO+ profiles, identifying them as infall candidates. Water masers are detected in 22 sources, with prominent velocity ranges and variability. Broad SiO emission (>~20 km/s) indicates strong shocks, while narrower extents (<~6km/s) likely trace large-scale interactions or low-velocity shocks. The widespread infall signatures, shock tracers, masers, and NH2D emission suggest that relatively quiescent, chemically young material can coexist with dynamically active gas affected by early protostellar feedback, providing insight into the coupled physical and chemical evolution of massive IRDC clumps.

astro-ph.GA↗

arXiv2026

ALMA observations of Magnetic Fields in the Massive Star-forming Region IRAS 18360-0537

Assessing the significance of magnetic fields in high-mass star formation remains one of the most challenging topics in astrophysics. In this study, we present full polarization observations obtained from the Atacama Large Millimeter/Submillimeter Array (ALMA) of the high-mass star-forming region IRAS18360-0537. The polarized dust emission at 1.3 mm reveals a clear hourglass-shaped morphology of the magnetic field. Interestingly, the magnetic field orientation is nearly perpendicular to both the outflow and core rotation axes, while it aligns with the elongation of the core. This orientation poses challenges for interpretation, particularly in light of the strong magnetic field strength estimated using the Davis-Chandrasekhar-Fermi method. Several scenarios provide insights into the underlying reasons for this magnetic field morphology. A clear velocity gradient seen in high-density tracing of molecular spectral lines indicates that the core is fast-rotating. The curved outskirts of the magnetic fields coincide with the outflow cavity, suggesting a possible influence from the outflow. The accretion flows along the core's elongation are also notable. Our study shows that the morphology of the magnetic field is probably highly influenced by the gas bulk motions.

astro-ph.GA↗

arXiv2026

Projection Is All You Need: Interpreting Polarization Measurements in the Orion Clouds with Sub-Alfv\'enic MHD Simulations

Dust polarization observations are widely used to diagnose the relative importance of magnetic fields and turbulence in star forming molecular clouds, often through summary statistics such as the mean polarization direction $\mu$ and dispersion $\sigma$. Recent multi-scale polarization observations of the Orion Integral-Shaped Filament (ISF) reveal substantial diversity in polarization morphology among its dense cores, raising questions about the underlying Alfv\'enic nature of the cloud. In this work, we develop a statistical framework to compare polarization-based summary statistics from observations with those derived from projected three dimensional MHD simulations, explicitly accounting for projection effects. Using globally sub-Alfv\'enic simulations that naturally produce slightly super-Alfv\'enic dense cores, we show that modest deviations of core-scale magnetic fields from the parent cloud field, when combined with projection, can generate a wide range of plane-of-sky polarization dispersions. Applying hypothesis testing, we find that the observed $(\mu, \sigma)$ values in the Orion ISF are statistically consistent with sub-Alfv\'enic cloud models over a broad range of viewing angles. This broad degeneracy implies that $\mu$ and $\sigma$ alone cannot provide precise information about the three-dimensional magnetic-field distribution, and hence the Alfv\'en Mach number, of an individual cloud. While the observations can provide evidence against certain projection geometries, we demonstrate that polarization statistics based solely on $(\mu, \sigma)$ are insufficient to provide evidence against sub-Alfv\'enic cloud models. Our results highlight the necessity of explicitly incorporating projection effects when interpreting polarization observations of molecular clouds.

astro-ph.GA↗

arXiv2026

Measuring Magnetic Field Strengths in Galactic Star-forming Regions via the Zeeman Effect with the SKA

Magnetic fields thread the interstellar medium from the largest to the smallest scales and play an important role in molecular cloud evolution and star formation. Quantifying this requires measurements of the field strengths, and the most direct way to measure them is via the Zeeman effect in spectral lines. The effect is subtle for the typical field strengths expected from theory, from a few $\mu$G in diffuse molecular clouds to a few 10s of mG in dense star-forming regions, and detections are scarce. Existing measurements of magnetic field strength suggest dense clouds and cores are marginally supercritical (cannot prevent collapse, but can inhibit it), but may be biased due to small sample sizes. Zeeman effect measurements tracing different scales and densities within molecular clouds can reveal the variation of field strengths, providing critical measurements to address the question of whether star formation is primarily regulated by magnetic fields or turbulence on different scales. Observations with SKA precursors such MeerKAT and FAST are beginning to increase the number of Zeeman effect detections in nearby star-forming regions. The SKA will extend their reach to many regions within our Galaxy that are best representative of where most stars form, while zooming in on the densest star-forming regions, providing a statistical basis for the role of magnetic fields in molecular cloud evolution and star formation. We present predictions and plans for Zeeman effect observations with the SKA telescopes, demonstrating the significant advances they will provide for studies of magnetic fields in molecular clouds.

astro-ph.GA↗

arXiv2026

BISTRO Survey: Gravity-Dominated and Magnetically Regulated Star Formation in M17 SW

We present high-resolution magnetic field maps of the M17 SW molecular cloud using JCMT 850 $\mu$m dust polarization at a scale of 14$''$. The magnetic field exhibits a distinct arc-like structure that encircles three dense clumps (C1, C2, and C3). By combining polarization data with ammonia line observations, the plane-of-sky magnetic field strength, measured using the Skalidis-Tassis method to minimize angle dispersion errors, ranges from 0.1 to 2.4 mG (mean: 0.54 mG). Energy budget analysis reveals a hierarchy dominated by gravity ($e_G \approx 10^{-7.8}$ erg cm$^{-3}$), which exceeds both magnetic ($e_B \approx 10^{-8.3}$ erg cm$^{-3}$) and turbulent ($e_k \approx 10^{-8.7}$ erg cm$^{-3}$) energies. Since all three energy densities lie within one order of magnitude, gravitational dominance acts primarily as the global driver, while the system remains in a state of near-equipartition. Structurally, the northeastern boundary shows magnetic field lines perpendicular to the shock front, consistent with compression from the adjacent HII region. Within the cloud, magnetic field lines generally align with gravity to assist collapse, but turn perpendicular to gravity within curved accretion bridges. This configuration provides support against radial collapse while guiding gas flow. Kinematic evidence suggests that these channels transport material from Clump C3 onto the massive Clump C2. Star formation in M17 SW is globally driven by gravity but locally regulated by the magnetic field structure.

astro-ph.GA↗

arXiv2026

Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems

Complex physical systems, from supersonic turbulence to the macroscopic structure of the universe, are governed by continuous multiscale dynamics. While modern machine learning architectures excel at mapping the high-dimensional observables of these systems, it remains unclear whether they internalize the governing physical laws or merely interpolate discrete statistical correlations. Standard Explainable AI (XAI) architectures, particularly perturbation-based and gradient-saliency methods, rely on pixel-wise perturbations, which generate unphysical artifacts and push inputs off the valid empirical distribution. To resolve this, we introduce a diagnostic framework driven by Constrained Diffusion Decomposition (CDD), a diffusion-based multiscale data decomposition algorithm that enables physically constrained data generation and model evaluation via scale-aware modifications. Applying this framework to a Denoising Diffusion Probabilistic Model (DDPM), we execute deterministic interventions directly within the continuous, CDD-based scale space. We demonstrate that under moderate physical perturbations, the unconstrained generative model exhibits localized structural freezing and non-linear instability rather than continuous PDE-like responses. The network fails to maintain cross-scale continuity, causing the generative trajectory to diverge when pushed into unseen physical states. By synthesizing a continuum of physically coherent states, this scale-informed methodology establishes a controlled test ground to evaluate algorithmic vulnerabilities, providing the rigorous physical constraints necessary for future architectures to respect the multiscale causality of the natural universe.

cs.LG↗

arXiv2026

The dominance of turbulence over magnetism in the formation of massive star cluster seeds

High-mass stars form in protoclusters, where gravo-magnetic processes shape collapsing clouds and clumps to be elongated preferentially perpendicular to magnetic (B) fields. Yet it remains unclear whether gravo-magnetic processes still govern the formation of smaller-scale condensations in massive-star-forming protoclusters, which are crucial for understanding the stellar initial mass function and multiplicity. Here we report the first statistical evidence that the condensation elongations are preferentially aligned with local B fields, based on high-resolution data from the largest dust polarization survey toward 30 massive star-forming regions with the Atacama Large Millimeter/submillimeter Array (ALMA). Our clustered massive star formation simulations reveal that this more parallel alignment is exclusively observed in models where initial turbulence dominates B fields. In contrast, models with initial B fields dominating turbulence distinctly exhibit a more perpendicular alignment. The comparison between observations and simulations suggests that turbulence could play a more important role than B fields in the formation of condensations in the context of clustered massive star formation, contradicting the prediction of classical magnetically regulated models. Moreover, we find a possibly turbulence-induced preferential misalignment between the B field and rotation axis of condensations, which may potentially reduce the magnetic braking efficiency and facilitate the formation of large protostellar disks. Our findings indicate that turbulence could be critical in determining the initial stellar properties.

astro-ph.GA↗

arXiv2026

A complete survey of filaments in Cygnus X

Filamentary structures are widely observed in molecular clouds, yet most filament observations are biased toward case studies and small samples; a uniform census within a single giant molecular cloud is still missing. We do a complete census of filaments in Cygnus X and quantify their links to dense cores, the magnetic field (B field), and HII regions. Using the updated getsf algorithm on the Cygnus X column-density map, we extracted 2633 filaments and 6551 cores. We built CMFs for cores on and off filaments, compared filament orientations with the Planck B field, measured radial column-density profiles near HII-region boundaries, and computed distances between young stellar objects and filament spines. Filaments have a typical width of 0.5 pc in Cygnus X at a resolution of 0.12 pc and host > 93% of high-mass cores (>= 20 Msun). The on-filament CMF shows a high-mass (> 10 Msun) slope of -2.30, while the off-filament CMF is steeper (-2.83). The onCMF peak mass is well below the Bonnor-Ebert mass, whereas the outCMF peak is comparable to it. At 5' resolution, filaments are mostly perpendicular to the B field except at the lowest column densities; the transition occurs near Av = 10 mag. Prominent filaments and high-mass cores preferred to be located around HII-region boundaries or at intersections of multiple HII regions; filament profiles are steeper on the side facing the HII region. Massive-core formation depends strongly on filaments, which may provide reservoirs that feed cores via accretion. The B field likely regulates filament formation, consistent with the type-O mode (converging flows along an oblique MHD shock) and an HII-driven bubble-filament paradigm for Cygnus X.

astro-ph.GA↗

arXiv2026

Magnetic threads and gravity: ALMA Observations of IRDC G14.225-0.506

During the star formation process, the interplay between gravity, turbulence, and B-fields is significant, with B-fields apparently serving a regulatory function. However, the extent to which B-fields are decisive relative to turbulence and gravity remains uncertain. This study aims to ascertain the role of B-fields in the fragmentation of molecular clouds. We examine the B-field observed with ALMA at core scales towards the infrared dark cloud G14.225-0.506, focusing on 3 regions with shared physical conditions, and juxtapose it with prior observations at the Hub-filament system scale. Our findings indicate a similar B-field strength and fragmentation level between the 2 hubs. However, distinct B-field morphologies are identified across the 3 regions where polarized emission is detected. In the region N, the large-scale B-field, which is perpendicular to the filamentary structure, persists at smaller scales in the southern half but becomes distorted near the more massive condensations in the northern half. Notably, these condensations exhibit signs of impending collapse, as evidenced by supercritical mass-to-flux values. In the region S, the B-field is considerably inhomogeneous among the detected condensations, and we do not observe a direct correlation between the field morphology and the condensation density. Lastly, in an isolated dust clump located within a southern filament of the northern hub, the B-field aligns parallel to the elongated emission, suggesting a transition in the field geometry. The B-field shows a clear evolution with spatial scales. We propose that the most massive condensations detected in the northern Hub are undergoing gravitational collapse, as revealed by the relative significance of the magnetic field and gravitational potential and mass-to-flux ratio. The distortion of the B-field could be a response to the flow of material due to the collapse.

astro-ph.GA↗

arXiv2026

The Column Density Probability Density Function of Cygnus-X

The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by HI and Young Stellar Objects (YSO) data. We find that the N-PDFs of Cygnus-X and four sub-regions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.

astro-ph.GA↗

arXiv2026

Unveiling Fiber Networks and Core Formation in the DR21 South Filament

We present high-resolution ($\sim$1000 AU) 3 mm observations with the NOrthern Extended Millimeter Array toward the DR21 South Filament, aiming to reveal its internal fragmentation and search for deeply embedded star-forming activities. Both the continuum and molecular line emissions align well with the filament axis traced by the low-resolution ($\sim$18$^{\prime\prime}$) column density map. The 3 mm continuum, CS (2$-$1), and HCO$^+$ (1$-$0) emissions reveal continuous and diffuse structures with measured FWHM widths of 0.054, 0.029, and 0.030 pc, respectively. In contrast, the H$^{13}$CO$^+$ (1$-$0) emission appears more clumpy and localized. The non-thermal motion in the filament is predominantly subsonic to transonic. We detect 13 dense cores in NH$_2$D (1$_{11}-1_{01}$), three of which coincide with continuum peaks; virial analysis suggests most are gravitationally bound. Using a friend-of-friend algorithm, we identify 32, 34, and 22 velocity-coherent fibers from the CS, HCO$^+$, and H$^{13}$CO$^+$ data, respectively. Compared to fibers traced by CS and HCO$^+$, H$^{13}$CO$^+$ fibers are more frequently associated with NH$_2$D cold cores and exhibit higher average mass-per-unit-length values. Differences among CS, HCO$^+$, and H$^{13}$CO$^+$ emissions likely arise from variations in effective critical densities. These results are consistent with a hierarchical structure, in which the 3.6-pc DR21SF contains velocity-coherent fibers and gravitationally bound dense cores.

astro-ph.GA↗

arXiv2025

Scientific Objectives of the Xue-shan-mu-chang 15-meter Submillimeter Telescope

Submillimeter astronomy is poised to revolutionize our understanding of the Universe by revealing cosmic phenomena hidden from optical and near-infrared observations, particularly those associated with interstellar dust, molecular gas, and star formation. The Xue-shan-mu-chang 15-meter submillimeter telescope (XSMT-15m), to be constructed at a premier high-altitude site (4813 m) in Qinghai, China, marks a major milestone for Chinese astronomy, establishing the China mainland's first independently developed, world-class submillimeter facility. Equipped with state-of-the-art instruments, XSMT-15m will address a diverse range of frontier scientific questions spanning extragalactic astronomy, Galactic structure, time-domain astrophysics, and astrochemistry. In synergy with current and forthcoming observatories, XSMT-15m will illuminate the formation and evolution of galaxies, unravel the physical and chemical processes shaping the interstellar medium, and explore transient phenomena in the submillimeter regime. These capabilities will advance our understanding across extragalactic astronomy, Galactic ecology, astrochemistry, and time-domain astrophysics, inaugurating a new era for submillimeter research in China and the northern hemisphere.

astro-ph.GA↗

arXiv2025

Detection of a septuple stellar system in formation via disk fragmentation

Stellar multiple systems play a pivotal role in cluster dynamics and stellar evolution, leading to intense astronomical phenomena like X-ray binaries, gamma-ray bursts, Type Ia supernova, and stellar mergers, which are prime sources of gravitational waves. However, their origin remains poorly understood. Here we report the discovery of a septuple protostellar system embedded in a Keplerian disk within the high-mass star-forming region NGC\,6334IN, with close separations of 181-461 AU. The stability analysis reveals that the disk surrounding the septuple system is dynamically unstable, indicating that the septuple system formed via disk fragmentation. Previous studies have typically found only 2--3 members forming via disk fragmentation in both low- and high-mass star-forming regions. Our findings provide compelling observational evidence that the fragmentation of a gravitationally unstable disk is a viable mechanism for the formation of extreme high-order multiplicity, confirming what was previously only a theoretical concept. The results shed new light on the formation of extreme high-order multiplicity in cluster environments.

astro-ph.GA↗

arXiv2025

Impact of gravity on changing magnetic field orientations in a sample of massive protostellar clusters observed with ALMA

The magnetic field is integral to our understanding of the formation and dynamical evolution of molecular clouds and star formation within. We present a polarimetric survey of 17 massive protostellar cluster forming clumps, covered in 34 pointings in the 230-GHz window using the Atacama Large Millimeter/submillimeter Array (ALMA). The two array configurations, C43-1 and C43-4, probe linearly polarized dust emission, hence the plane-of-the-sky orientation of magnetic fields, at resolutions of 1\arcsec\ and 0\arcsec.4 that correspond to approximately 0.01pc core and $10^3$ au envelope scales, respectively. The relative orientations (ROs) of the magnetic field probed at two spatial scales are analyzed for the entire protostellar cluster sample and for a subset of objects in NGC 6334. We found a bimodal distribution of ROs with peaks at 0\deg\ (parallel) and 90\deg (orthogonal) for the entire sample combined as well as for NGC 6334. We investigate the physical origin of this bimodal distribution through a projected Rayleigh statistic (PRS) analysis in relation to column densities and local gravity in NGC 6334. We found an excess of parallel magnetic fields at column densities $> 10^{23}$ \cmm. The underlying cause of the RO distribution of the magnetic field is gravitational collapse at higher gas densities, which drags and reorients the magnetic field as shown in the alignment between the magnetic field and the direction of gravitational forces. The distribution of ROs observed here is consistent with the evolution of relative orientations of an initially sub-Alv\'enic cloud that becomes magnetically super-critical and super-Alv\'enic as the cloud collapses to form stars.

astro-ph.GA↗

arXiv2025

Parallel Alignments between Magnetic Fields and Dense Structures in the Central Molecular Zone

The recent Far-Infrared Polarimetric Large-Area Central Molecular Zone Exploration (FIREPLACE) survey with SOFIA has mapped plane-of-the-sky magnetic field orientations within the Central Molecular Zone (CMZ) of the Milky Way. Applying the Histogram of Relative Orientation (HRO) analysis to the FIREPLACE data, we find that the relative orientation between magnetic fields and column density structures is random in low-density regions (2x10^22 10^23 cm^{-2}). This trend is in contrast with that of the nearby molecular clouds, where the relative orientation transitions from parallel to perpendicular with increasing column densities. However, the relative orientation varies between individual CMZ clouds. Comparisons with MHD simulations specific to the CMZ conditions suggest that the observed parallel alignment is intrinsic rather than artifacts caused by the projection effect. The origin of this parallel configuration may arise from the fact that most dense structures in the CMZ are not self-gravitating, as they are in super-virial states, except for the mini-starburst region Sgr B2. These findings are consistent with the low star formation efficiency observed in the CMZ compared to that in the Galactic disk.

astro-ph.GA↗

arXiv2025

Equation vs. AI: Predict Density and Measure Width of molecular clouds by Multiscale Decomposition

Interstellar medium widely exists in the universe at multi-scales. In this study, we introduce the {\it Multi-scale Decomposition Reconstruction} method, an equation-based model designed to derive width maps of interstellar medium structures and predict their volume density distribution in the plane of the sky from input column density data. This approach applies the {\it Constrained Diffusion Algorithm}, based on a simple yet common physical picture: as molecular clouds evolve to form stars, the density of interstellar medium increases while their scale decreases. Extensive testing on simulations confirms that this method accurately predicts volume density with minimal error. Notably, the equation-based model performs comparably or even more accurately than the AI-based DDPM model(Denoising Diffusion Probabilistic Models), which relies on numerous parameters and high computational resources. Unlike the "black-box" nature of AI, our equation-based model offers full transparency, making it easier to interpret, debug, and validate. Their simplicity, interpretability, and computational efficiency make them indispensable not only for understanding complex astrophysical phenomena but also for complementing and enhancing AI-based methods.

astro-ph.GA↗