SEARCH · Engineering Papers

Results for “box relaxation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

35 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRS2012

Challenges of Sustaining the International Space Station through 2020 and Beyond: Including Epistemic Uncertainty in Reassessing Confidence Targets

This paper introduces an analytical approach, Probability and Confidence Trade-space (PACT), which can be used to assess uncertainty in International Space Station (ISS) hardware sparing necessary to extend the life of the vehicle. There are several key areas under consideration in this research. We investigate what sparing confidence targets may be reasonable to ensure vehicle survivability and for completion of science on the ISS. The results of the analysis will provide a methodological basis for reassessing vehicle subsystem confidence targets. An ongoing annual analysis currently compares the probability of existing spares exceeding the total expected unit demand of the Orbital Replacement Unit (ORU) in functional hierarchies approximating the vehicle subsystems. In cases where the functional hierarchies availability does not meet subsystem confidence targets, the current sparing analysis further identifies which ORUs may require additional spares to extend the life of the ISS. The resulting probability is dependent upon hardware reliability estimates. However, the ISS hardware fleet carries considerable epistemic uncertainty (uncertainty in the knowledge of the true hardware failure rate), which does not currently factor into the annual sparing analysis. The existing confidence targets may be conservative. This paper will also discuss how confidence targets may be relaxed based on the inclusion of epistemic uncertainty for each ORU. The paper will conclude with strengths and limitations for implementing the analytical approach in sustaining the ISS through end of life, 2020 and beyond.

Anderson, Leif↗

DOE OSTI2023

Glutamine-rich regions of the disordered CREB transactivation domain mediate dynamic intra- and intermolecular interactions

The cyclic AMP response element (CRE) binding protein (CREB) is a transcription factor that contains a 280-residue N-terminal transactivation domain and a basic leucine zipper that mediates interaction with DNA. The transactivation domain comprises three subdomains, the glutamine-rich domains Q1 and Q2 and the kinase inducible activation domain (KID). NMR chemical shifts show that the isolated subdomains are intrinsically disordered but have a propensity to populate local elements of secondary structure. The Q1 and Q2 domains exhibit a propensity for formation of short β-hairpin motifs that function as binding sites for glutamine-rich sequences. These motifs mediate intramolecular interactions between the CREB Q1 and Q2 domains as well as intermolecular interactions with the glutamine-rich Q1 domain of the TATA-box binding protein associated factor 4 (TAF4) subunit of transcription factor IID (TFIID). Using small-angle X-ray scattering, NMR, and single-molecule Förster resonance energy transfer, we show that the Q1, Q2, and KID regions remain dynamically disordered in a full-length CREB transactivation domain (CREB TAD ) construct. The CREB TAD polypeptide chain is largely extended although some compaction is evident in the KID and Q2 domains. Paramagnetic relaxation enhancement reveals transient long-range contacts both within and between the Q1 and Q2 domains while the intervening KID domain is largely devoid of intramolecular interactions. Phosphorylation results in expansion of the KID domain, presumably making it more accessible for binding the CBP/p300 transcriptional coactivators. In conclusion, our study reveals the complex nature of the interactions within the intrinsically disordered transactivation domain of CREB and provides molecular-level insights into dynamic and transient interactions mediated by the glutamine-rich domains.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2012

Challenges of Sustaining the International Space Station Through 2020 and Beyond: Reassessing Confidence Targets for System Availability

The International Space Station (ISS) was originally designed to operate until 2015 with a plan for deorbiting the ISS in 2016. Currently, the international partnership has agreed to extend the operations until 2020 and discussions are underway to extend the life even further to 2028. Each partner is responsible for the sustaining engineering, sparing, and maintenance of their own segments. National Aeronautics and Space Administration's (NASA's) challenge is to purchase the needed number of spares to maintain the functional availability of the ISS systems necessary for the United States On-Orbit Segment s contribution. This presentation introduces an analytical approach to assessing uncertainty in ISS hardware necessary to extend the life of the vehicle. Some key areas for consideration are: establishing what confidence targets are required to ensure science can be continuously carried out on the ISS, defining what confidence targets are reasonable to ensure vehicle survivability, considering what is required to determine if the confidence targets are too high, and whether sufficient number of spares are purchased. The results of the analysis will provide a methodological basis for reassessing vehicle subsystem confidence targets. This analysis compares the probability of existing spares exceeding the total expected unit demand of the Orbital Replacement Unit (ORU) in functional hierarchies approximating the vehicle subsystems. In cases where the functional hierarchies' availability does not meet subsystem confidence targets, the analysis will further identify which ORUs may require additional spares to extend the life of the ISS. The resulting probability is dependent upon hardware reliability estimates. However, the ISS hardware fleet carries considerable epistemic uncertainty which must be factored into the development and execution of sparing risk postures. In addition, it is also recognized that uncertainty in the assessment is due to disconnects between modeled functions and actual subsystem operations. Perhaps most importantly, it is acknowledged that conservative confidence targets per subsystem are currently accepted. This presentation will also discuss how subsystem confidence targets may be relaxed based on calculating the level of uncertainty for each corresponding ORU-function. The presentation will conclude with the various strengths and limitations for implementing the analytical approach in sustaining the ISS through end of life; 2020 and beyond.

Lutomski, Michael G.↗

NASA NTRS2003

Evaluation of Neutral Body Posture on Shuttle Mission STS-57 (SPACEHAB-1)

Research has shown that the space environment induces physiological changes in the human body, such as fluid shifts in the upper body and chest cavity, spinal lengthening, muscular atrophy, space motion sickness, cardiopulmonary deconditioning, and bone mass loss, as well as some changes in visual perception. These require a period of adaptation and can substantially affect both crew member performance and posture. These physiological effects, when work activities are conducted, have been known to impact the body's center of gravity, reach, flexibility, and dexterity. All these aspects of posture must be considered to safely and efficiently design space systems and hardware. NASA has documented its microgravity body posture in the Man-Systems Integration Standards (MSIS); the space community uses the MSIS posture to design workstations and tools for space application. However, the microgravity body posture should be further investigated for several reasons, including small sample size in previous studies, possible imprecision, and lack of detail. JSC undertook this study to investigate human body posture exhibited under microgravity conditions. STS-57 crew members were instructed to assume a relaxed posture that was not oriented to any work area or task. Crew members were asked to don shorts and tank tops and to be blindfolded while data were recorded. Video data were acquired once during the mission from each of the six crew members. No one crew member exhibited the typical NBP called out in the MSIS; one composite posture is not adequate. A range of postures may be more constructive for design purposes. Future evaluations should define precise posture requirements for workstation, glove box, maintenance, foot-restraint, and handhold activities.

Mount, Frances E.↗

DOE OSTI2026

Scattering phase shift in quantum mechanics on quantum computers

Here, we investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in the work by Guo and Gasparian [Phys. Rev. D 108, 074504 (2023)] that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of postdata analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.

Guo, Peng [Dakota State Univ., Madison, SD (United↗

DOE OSTI2025

The hierarchical growth of bright central galaxies and intracluster light as traced by the magnitude gap

Using a sample of 2800 galaxy clusters identified in the Dark Energy Survey across the redshift range 0.20 < z < 0.60, we characterize the hierarchical assembly of bright central galaxies (BCGs) and the surrounding intracluster light (ICL). To quantify hierarchical formation we use the stellar mass–halo mass (SMHM) relation, comparing the halo mass, estimated via the mass–richness relation, to the stellar mass within the BCG + ICL system. Moreover, we incorporate the magnitude gap (M14), the difference in brightness between the BCG (measured within 30 kpc) and fourth brightest cluster member galaxy within 0.5 $R_{200,c}$, as a third parameter in this linear relation. The inclusion of M14, which traces BCG hierarchical growth, increases the slope and decreases the intrinsic scatter, highlighting that it is a latent variable within the BCG + ICL SMHM relation. Moreover, the correlation with M14 decreases at large radii. However, the stellar light within the BCG + ICL transition region (30 –80 kpc) most strongly correlates with halo mass and has a statistically significant correlation with M14. Since the transition region and M14 are independent measurements, the transition region may grow due to the BCG’s hierarchical formation. Additionally, as M14 and ICL result from hierarchical growth, we use a stacked sample and find that clusters with large M14 values are characterized by larger ICL and BCG + ICL fractions, which illustrates that the merger processes that build the BCG stellar mass also grow the ICL. Furthermore, this may suggest that M14 combined with the ICL fraction can identify dynamically relaxed clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

The OFP-6M transport jet

This report presents a preliminary design of a commercial jet transport that meets the criteria of the Request For Proposal presented by the American Institute of Aeronautics and Astronauts (AIAA). The proposal requires an innovative design of a low cost domestic commercial transport that will reduce operating costs for airline companies while still meeting present and future requirements of the Federal Aviation Regulations for this type of aircraft. Specifications for the design include a mixed class, 153 passenger aircraft, traveling a range of 3000 nm. The intent of the project is to identify factors that reduce cost and to design within the limits of these constraints. The project includes techniques or options that incorporate new technologies but do not override practicality, alternative design approaches, and a comparison between the new design and current aircraft in its class. The OFP-6M is an alternative design approach to the conventional commercial transport jet and is geared towards customer satisfaction through efficiency and reliability. The goals of the OFP-6M transport design are to provide original, sensible, and practical solutions by combining essential preliminary design factors with growing technology. The design focus of the OFP-6M reduces costs by simplifying systems where significant weight or maintenance savings can be achieved, and by integrating advanced technology for improved performance. Key aspects of the OFP-6M design are efficient use of materials like composites, and efficient advanced ducted high bypass turbofan engines. The high bypass engines lower fuel consumption and aid in reducing costs and meeting future noise emission restrictions. Composites are used for most structural components, including flooring and wing box. Although composites are an emerging technology and presently, a high maintenance material, they can be cost effective and an alternative to aluminum structures when correct manufacturing and design strategies are applied. Since, composites are lighter and require less manufacturing of complex parts, they can significantly reduce structural weight. Because of the large 17 ft. diameter, sophisticated aerodynamic considerations were implemented to significantly lower the drag. Supercritical airfoils were chosen with simple control surface design which allows for less maintenance and manufacturing costs. The interior configuration accommodates either all passenger, dual and single class flights or complete cargo. Also, a relaxed conventional stability is integrated with a stability augmentation system. As a result of these design implementations, the OFP-6M bottom line direct operating costs, compare favorably with the Boeing 737 and 757, at 3.49 cents per available seat mile and costs are expected to reduce when improved manufacturing and maintenance methods are implemented.

Alexander, Kelly↗

NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗

DOE OSTI2025

Constraining the phase shift of relativistic species in DESI BAOs

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $\beta _{\phi }$ and apply it to the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $\beta _{\phi }$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $\beta _{\phi }$ for the different tracers, and additionally a combined fit to $\beta _{\phi }$ resulting in $\beta _{\phi } = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using Planck we find $\beta _{\phi } = 2.7^{+0.60}_{-0.67}$ suggesting $\beta _{\phi } > 0$ at 4.3$\sigma$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm {eff}}$ or could be a upwards statistical fluctuation in the measured $\beta _{\phi }$; this result relaxes in models with additional freedom beyond Lambda-cold dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2003

Studies of Elementary Reactions of Chemical Importance in the Atmospheres of Planets

The paper discusses the following: 1. F + Cl2 Kinetics. Absolute rate constant for the reaction F(P-2) with Cl2 has been measured using the discharge flow kinetics technique coupled to mass spectrometric detection at T = 180 - 360 K and 1 Torr He nominal pressure. 2. Vapor pressure system. The main effort on the vapor pressure system involved the design and construction of an insulated enclosure ("Bakeout Box") to improve the uniformity of heating during the bakeout process. 3. Sunphotometer System. This period saw the completion of the two-channel sunphotometer, its calibration, and two field deployments. 4. Vibrational-to-translation (V-T) transfer rates for light hydrocarbons at low temperatures are important parameters in thermal-structure models of the upper atmospheres of the outer planets and their satellites. However, the required data are either simply not available or do not extend to the low temperatures found in those systems. Because methane is such an important constituent in outer planet atmospheres, we have initiated a program to measure the temperature dependence of (V-T) rates for its relaxation by appropriate collision partners. 5. The central focus of this research has been the vapor phase nucleation and growth of metals/refractory species into small particles and the aggregation of these primary particles into larger structures. These topics are part of the broader goal of understanding the conditions under which interstellar dust grains condense from stellar outflows and how these small dust grains coagulate into larger bodies such as planetesimals or planets.

Nesbitt, Fred L.↗

NASA NTRS2016

Heating and Acceleration of Solar Wind Ions by Turbulent Wave Spectrum in Inhomogeneous Expanding Plasma

Near the Sun (< 10Rs) the acceleration, heating, and propagation of the solar wind are likely affected by the background inhomogeneities of the magnetized plasma. The heating and the acceleration of the solar wind ions by turbulent wave spectrum in inhomogeneous plasma is studied using a 2.5D hybrid model. The hybrid model describes the kinetics of the ions, while the electrons are modeled as massless neutralizing fluid in an expanding box approach. Turbulent magnetic fluctuations dominated by power-law frequency spectra, which are evident from in-situ as well as remote sensing measurements, are used in our models. The effects of background density inhomogeneity across the magnetic field on the resonant ion heating are studied. The effect of super- Alfvenic ion drift on the ion heating is investigated. It is found that the turbulent wave spectrum of initially parallel propagating waves cascades to oblique modes, and leads to enhanced resonant ion heating due to the inhomogeneity. The acceleration of the solar wind ions is achieved by the parametric instability of large amplitude waves in the spectrum, and is also affected by the inhomogeneity. The results of the study provide the ion temperature anisotropy and drift velocity temporal evolution due to relaxation of the instability. The non-Maxwellian velocity distribution functions (VDFs) of the ions are modeled in the inhomogeneous solar wind plasma in the acceleration region close to the Sun.

Ofman, Leon↗

NASA NTRS2004

Nucleation in Synoptically Forced Cirrostratus

Formation and evolution of cirrostratus in response to weak, uniform and constant synoptic forcing is simulated using a one-dimensional numerical model with explicit microphysics, in which the particle size distribution in each grid box is fully resolved. A series of tests of the model response to nucleation modes (homogeneous-freezing-only/heterogeneous nucleation) and heterogeneous nucleation parameters are performed. In the case studied here, nucleation is first activated in the prescribed moist layer. A continuous cloud-top nucleation zone with a depth depending on the vertical humidity gradient and one of the nucleation parameters is developed afterward. For the heterogeneous nucleation cases, intermittent nucleation zones in the mid-upper portion of the cloud form where the relative humidity is on the rise, because existent ice crystals do not uptake excess water vapor efficiently, and ice nuclei (IN) are available. Vertical resolution as fine as 1 m is required for realistic simulation of the homogeneous-freezing-only scenario, while the model resolution requirement is more relaxed in the cases where heterogeneous nucleation dominates. Bulk microphysical and optical properties are evaluated and compared. Ice particle number flux divergence, which is due to the vertical gradient of the gravity-induced particle sedimentation, is constantly and rapidly changing the local ice number concentration, even in the nucleation zone. When the depth of the nucleation zone is shallow, particle number concentration decreases rapidly as ice particles grow and sediment away from the nucleation zone. When the depth of the nucleation zone is large, a region of high ice number concentration can be sustained. The depth of nucleation zone is an important parameter to be considered in parametric treatments of ice cloud generation.

Lin, R.-F.↗

NASA NTRS1994

Results From The First Interactive Scientific Expert System In Space

We describe recent work on automation and support of science experiments on the Space Shuttle. PI-in-a-Box, the first interactive expert system for scientific support, was flown onboard STS-58 in October 1993. It was designed to help astronauts perform better science in space by providing expert-level advice in real-time. The system provides help with 'technician' tasks such as data acquisition, data quality monitoring, and diagnostic, troubleshooting and repair. The system also performs 'expert' reasoning on the scientific model and experiment steps scheduling. It can make scheduling recommendations based on hardware status, time available, and agreement between predictions and flight data. The system was successfully deployed and used throughout the mission. Most of the 'technician' skills of the system were used with success. The scientific model study performed correctly, but we believe the results were not exploited by the astronauts because of Spacelab operational pressures. Also, portions of the system were designed around rigid schedule constraints that were essentially relaxed during the mission. This version was tailored to a specific vestibular experiment known as the 'rotating dome'. We are currently expanding our effort in various scientific (other life and microgravity sciences experiments) and technological directions (integrated telescience, astronaut science advisor, and autonomous control).

Groleau, Nicolas↗

NASA NTRS1994

Results from the First Interactive Scientific Expert System in Space

We describe recent work on automation and support of science experiments on the Space Shuttle. PI-in-a-Box, the first interactive expert system for scientific support, was flown onboard STS-58 in October 1993. It was designed to help astronauts perform better science in space by providing expert-level advice in real-time. The system provides help with "technician" tasks such as data acquisition, data quality monitoring, and diagnostic, troubleshooting and repair. The system also performs "expert" reasoning on the scientific model and experiment steps scheduling. It can make scheduling recommendations based on hardware status, time available, and agreement between predictions and flight data. The system was successfully deployed and used throughout the mission. Most of the "technician" skills of the system were used with success. The scientific model study performed correctly, but we believe the results were not exploited by the astronauts because of Spacelab operational pressures. Also, portions of the system were designed around rigid schedule constraints that were essentially relaxed during the mission. This version was tailored to a specific vestibular experiment known as the "rotating dome". We are currently expanding our effort in various scientific (other life and microgravity sciences experiments) and technological directions (integrated telescience, astronaut science advisor, and autonomous control).

Groleau, Nicolas↗

DOE OSTI2026

Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID↗

DOE OSTI2025

Constraining gas motion and non-thermal pressure beyond the core of the Abell 2029 galaxy cluster with XRISM

We report on a detailed spectroscopic study of the gas dynamics and hydrostatic mass bias of the galaxy cluster Abell 2029, utilizing high-resolution observations from XRISM Resolve. Abell 2029, known for its cool core and relaxed X-ray morphology, provides an excellent opportunity to investigate the influence of gas motions beyond the central region. Expanding upon prior studies that revealed low turbulence and bulk motions within the core, our analysis covers regions out to the scale radius $R_{2500}$ (670 kpc) based on three radial pointings extending from the cluster center toward the northern side. We obtain accurate measurements of bulk and turbulent velocities along the line of sight. The results indicate that non-thermal pressure accounts for no more than 2% of the total pressure at all radii, with a gradual decrease outward. The observed radial trend differs from many numerical simulations, which often predict an increase in non-thermal pressure fraction at larger radii. These findings suggest that deviations from hydrostatic equilibrium are small, leading to a hydrostatic mass bias of around 2% across the observed area.

X-rays: galaxies: clusters↗