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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Study of $\langle {p}_{\text{T}}\rangle$ and its higher moments, and extraction of the speed of sound in Pb-Pb collisions with ALICE

Ultrarelativistic heavy-ion collisions produce a state of hot and dense strongly interacting QCD matter called quark-gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultracentral collisions is mostly constant, while its total entropy can vary significantly due to quantum fluctuations, leading to variations in the temperature of the system. Exploiting this unique feature of ultracentral collisions allows for the interpretation of the correlation of the mean transverse momentum ($\langle$p T $\rangle$) of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound, c s . This speed is related to the rate at which compression waves travel in the QGP and is determined by fitting the relative increase in $\langle$p T $\rangle$ with respect to the relative change in the average charged-particle density ($\langle$dN ch /dη$\rangle$) measured at mid-rapidity. This study reports the event-average $\langle$p T $\rangle$ of charged particles as well as the variance, skewness, and kurtosis of the event-by-event transverse momentum per charged particle ([p T ]) distribution in ultracentral Pb-Pb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are used to select ultracentral collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used to perform the measurement, the influence of biases and their potential effects on the rise of the mean transverse momentum is tested. The measured c$^{2}_{s}$ is found to strongly depend on the exploited centrality estimator and ranges between 0.1146±0.0028 (stat.)±0.0065 (syst.) and 0.4374±0.0006 (stat.)±0.0184 (syst.) in natural units. The self-normalized variance shows a steep decrease towards ultracentral collisions, while the self-normalized skewness variables show a maximum, followed by a fast decrease. These non-Gaussian features are understood in terms of the vanishing of the impact-parameter fluctuations contributing to the event-to-event [p T ] distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

The depth of the solar convection zone

The transition of the temperature gradient between being subadiabatic and adiabatic at the base of the solar convection zone gives rise to a clear signature in the sound speed. Helioseismic measurements of the sound speed therefore permit a determination of the location of the base of the convection zone. Two techniques were tested by applying them to artifical data, obtained by adding simulated noise to frequencies computed from two different solar models. The determinations appear to be relatively insensitive to uncertainties of the physics of the solar interior. From an analysis of observed frequencies of solar oscillation it is concluded that the depth of the solar convection zone is (0.287 + or - 0.003) solar radii.

Christensen-Dalsgaard, J.↗
NASA NTRS1988

Cosmic-ray hydrodynamics at relativistic shocks

A test particle description of first-order Fermi acceleration of cosmic rays at plane-parallel relativistic shocks is presented in which the pitch angle distribution is obtained explicitly and used to determine the pressure anisotropy or variable Eddington factor as a function of position. The Eddington factor is in turn used to find the hydrodynamical cosmic-ray sound speed, taking the anisotropy into account. For upstream flows speeds above c/sq rt 3, it is shown that the cosmic-ray sound speed exceeds the shock speed in a region just upstream of the shock and decreases montonically with distance further upstream, reaching the value c/sq rt 3 far from the shock. Thus, the shock succeeds in maintaining an anisotropy in the cosmic-ray distribution which is sufficient to keep the flow subsonic with respect to the cosmic-ray sound speed both downstream and in a finite region upstream. The astrophysical implications of these findings are discussed.

Kirk, J. G.↗
NASA NTRS1977

Aerodynamic sound in a relaxing medium

A theory of aerodynamic sound propagation, when inhomogeneities characterized by a relaxation process are present in both the source and propagation region, is formulated. The details of the relaxation process need not be specified at the outset, although the relaxation process is characterized by a relaxation time and by an equilibrium and a frozen sound speed in a propagation region which is otherwise in equilibrium. Propagation is described in terms of a D'Alembertian characterized by the frozen sound speed relaxing toward one characterized by the equilibrium sound speed, while the source is interpreted in terms of a frozen Lighthill stress tensor relaxing toward the equilibrium stress tensor. An appropriate Green's function for the three-dimensional relaxing wave propagation operator is used to construct an exact integral for the aerodynamic sound. The sound generated far from the source is then estimated in terms of the aerodynamic sound source.

Liu, J. T. C.↗
NASA NTRS2022

Appendix to: Methodology for Creating Thermodynamic Tables for Application to Computation of Speed of Sound by the Global Reference Atmospheric Model (GRAM) Suite: Validation Testing

The primary report to which this document appends provides the background, methodology, and outputs for the development of constituent-specific tables of specific heats as functions of temperature and pressure. These tables are used by the GRAM Suite to compute speed of sound by a process detailed in the primary report. The current document details verification and validation testing that was performed on the contents and implementation of the output tables.

Speed of Sound↗
NASA NTRS2005

Sub-Microsecond Temperature Measurement in Liquid Water Using Laser Induced Thermal Acoustics

Using laser-induced thermal acoustics, we demonstrate non-intrusive and remote sound speed and temperature measurements over the range 10 - 45 C in liquid water. Averaged accuracy of sound speed and temperature measurements (10 s) are 0.64 m/s and 0.45 C respectively. Single-shot precisions based on one standard deviation of 100 or greater samples range from 1 m/s to 16.5 m/s and 0.3 C to 9.5 C for sound speed and temperature measurements respectively. The time resolution of each single-shot measurement was 300 nsec.

Alderfer, David W.↗
NASA NTRS1992

Adaptive wall technology for three-dimensional models at high subsonic speeds and aerofoil testing through the speed of sound

Adaptive wall research at the University of Southampton has been directed towards the development of testing techniques for use in nonporous test sections where two flexible walls are profiled in single curvature. This paper highlights the recent advances that have been made in the testing of 2D airfoils through the speed of sound and the testing of 3D models at high subsonic speeds. Techniques have been developed to accommodate the variety of flow regimes encountered in near sonic airfoil tests. The experimental evidence to date suggests that the new techniques coupled with established procedures allow airfoil data, free from top and bottom wall interference, to be gathered from adaptive flexible walled test sections throughout the entire subsonic, transonic and supersonic speed ranges. Techniques applicable to the testing of 3D models have evolved primarily from experience gained by testing sidewall mounted half-wings. Emphasis has been placed upon models with planforms similar to those of current transport wings. Techniques for high subsonic speeds have now been developed to the point where the residual levels of interference are low.

Lewis, M. C.↗
DOE OSTI2026

Creation of Speed-of-Sound Inject Data for Technical Nuclear Forensics

Technical Nuclear Forensics (TNF) exercises simulate a detonation of a nuclear device within the United States, usually in a city. Speed-of-sound (SOS) phenomenology are the atmospheric overpressure and ground shock mechanical motions that are observed at over-pressure (air-blast and infrasound) and seismic sensors, respectively (Figure 1). Amplitudes of SOS data are related to the explosive yield (Kinney and Graham, 1985; Koper et al., 2002; Bonner et al., 2013ab; Ford et al., 2014, 2021; Templeton et al., 2018; Schnurr et al., 2020). Within the country, the United States Prompt Diagnostics System (USPDS) includes a network of geophysical sensors to capture such SOS signals. During the TNF exercise, the event data will be analyzed by the players who know nothing about the technical details of the source (e.g. location, yield, explosive). Specifically, they will use the Integrated Yield Determination Tool (IYDT) to estimate the yield and height-of-burst or depth-of-burial (HOB/DOB). The IYDT allows the user to measure features on the overpressure and seismic channels, evaluate the consistency of features and jointly estimate yield and HOB/DOB. For these exercises, SOS data are simulated for the location, emplacement and yield of the device and signals are propagated to the observing stations. This document describes the steps undertaken in the simulation, validation, preparation and verification of SOS signals for TNF exercises.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1987

Support of the eight-foot high-temperature tunnel modifications project

An ultrasonic level sensor was developed to measure the liquid level in a storage vessel under high pressures, namely up to 6000 psi. The sensor is described. A prototype sensor was installed in the cooling-water storage vessel of the Eight-Foot High-Temperature Tunnel. Plans are being made to install the readout instrument in the control room, so that tunnel operators can monitor the water level during the course of a tunnel run. It was discovered that the sensor will operate at cryogenic temperatures. Consequently, a sensor will be installed in the modified Eight-Foot High-Temperature Tunnel to measure the sound speed of liquid oxygen (LOX) as it is transferred from a storage vessel to the tunnel combustor at pressure of about 3000 psi. The sound speed is known to be a reliable indicator of contamination of LOX by pressurized gaseous nitrogen, which will be used to effect the transfer. Subjecting the sensor to a temperature cycle from room temperature to liquid nitrogen temperature and back again several times revealed no deterioration in sensor performance. The method using this sensor is superior to the original method, which was to bleed samples of LOX from the storage vessel to an independent chamber for measurement of the sound speed.

Hodges, Donald Y.↗
NASA NTRS1994

Prospects for Jovian seismological observations following the impact of comet Shoemaker-Levy 9

The impact of each fragment of comet SL-9 will produce a downward-propagating pressure wave which will travel at the sound speed through the jovian interior. Since the sound speed increases with depth, most of the energy in the pressure pulse will be strongly refracted and return to the surface, as recently computed by Marley (1994). This wave may in principle be observable as it propagates into the stratosphere, using sufficiently sensitive thermal infrared imaging. If so, it will provide a unique opportunity to constrain models of the jovian interior. This paper extends Marley's calculations to include the effect of the limited spatial resolution which will be characteristic of real observations. The wave pattern on the disk will consist of closely spaced regions of alternating temperature increases and decreases. Spatial averaging will significantly reduce the observed amplitude for resolutions attainable using earth-based telescopes, but the waves should remain above the detection limit.

Deming, Drake↗
NASA NTRS1976

Properties of low-aspect-ratio pointed wings at speeds below and above the speed of sound

Low aspect ratio wings having pointed planforms are treated on the assumption that the flow potentials in planes at right angles of the long axis of the airfoils are similar to the corresponding two dimensional potentials. For the limiting case of small angles of attack and low aspect ratios the theory brings out the following significant properties: (1) the lift of a slender pointed airfoil moving in the direction of its long axis depends on the increase in width of the sections in a downstream direction; (2) spanwise loading of such an airfoil is independent of planform and approaches the distribution giving a minimum induced drag; and (3) lift distribution of a pointed airfoil traveling point-foremost is relatively unaffected by the compressibility of the air below or above the speed of sound.

Jones, R. T.↗
NASA NTRS1946

Properties of low-aspect-ratio pointed wings at speeds below and above the speed of sound

Low-aspect-ratio wings having pointed plan forms are treated on the assumption that the flow potentials in planes at right angles to the long axis of the airfoils are similar to the corresponding two-dimensional potentials. For the limiting case of small angles of attack and low aspect ratios the theory brings out the following significant properties: (1) The lift of a slender, pointed airfoil moving in the direction of its long axis depends on the increase in width of the sections in a downstream direction. Sections behind the section of maximum width develop no lift. (2) The spanwise loading of such an airfoil is independent of the plan form and approaches the distribution giving a minimum induced drag. (3) The lift distribution of a pointed airfoil travelling point-foremost is relatively unaffected by the compressibility of the air below or above the speed of sound. A best of a triangular airfoil at a Mach number of 1.75 verified the theoretical values of lift and center of pressure.

WINGS, DELTA↗
NASA NTRS1996

Tomographic Imaging of the Suns Interior

A new method is presented of determining the three-dimensional sound-speed structure and flow velocities in the solar convection zone by inversion of the acoustic travel-time data recently obtained by Duvall and coworkers. The initial inversion results reveal large-scale subsurface structures and flows related to the active regions, and are important for understanding the physics of solar activity and large-scale convection. The results provide evidence of a zonal structure below the surface in the low-latitude area of the magnetic activity. Strong converging downflows, up to 1.2 km/s, and a substantial excess of the sound speed are found beneath growing active regions. In a decaying active region, there is evidence for the lower than average sound speed and for upwelling of plasma.

Kosovichev, A. G.↗
NASA NTRS1992

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗
NASA NTRS2001

Our Sun IV: The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismic frequency observations provide an extremely accurate window into the solar interior; frequencies from the Michaelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft, enable the adiabatic sound speed and adiabatic index to be inferred with an accuracy of a few parts in 10(exp 4) and the density with an accuracy of a few parts in 10(exp 3). This has become a Serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of the sources of uncertainties in the standard solar models. We found that the largest effect on the interior structure arises from the observational uncertainties in the photospheric abundances of the elements, which affect the sound speed profile at the level of 3 parts in 10(exp 3). The estimated 4% uncertainty in the OPAL opacities could lead to effects of 1 part in 10(exp 3); the approximately 5%, uncertainty in the basic pp nuclear reaction rate would have a similar effect, as would uncertainties of approximately 15% in the diffusion constants for the gravitational settling of helium. The approximately 50% uncertainties in diffusion constants for the heavier elements would have nearly as large an effect. Different observational methods for determining the solar radius yield results differing by as much as 7 parts in 10(exp 4); we found that this leads to uncertainties of a few parts in 10(exp 3) in the sound speed int the solar convective envelope, but has negligible effect on the interior. Our reference standard solar model yielded a convective envelope position of 0.7135 solar radius, in excellent agreement with the observed value of 0.713 +/- 0.001 solar radius and was significantly affected only by Z/X, the pp rate, and the uncertainties in helium diffusion constants. Our reference model also yielded envelope helium abundance of 0.2424, in good agreement with the approximate range of 0.24 to 0.25 inferred from helioseismic observations; only extreme Z/X values yielded envelope helium abundance outside this range. We found that other current uncertainties, namely, in the solar age and luminosity, in nuclear rates other than the pp reaction, in the low-temperature molecular opacities, and in the low-density equation of state, have no significant effect on the quantities that can be inferred from helioseismic observations. The predicted pre-main-sequence lithium depletion is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by approximately 30% for the Cl-27 experiment and by approximately 3% for Ga-71 experiments, while the B-8 neutrino flux is uncertain by approximately 30%.

Boothroyd, Arnold I.↗
NASA NTRS1976

Wave propagation along a magnetic tube

Motivated by the filamentary structure of solar magnetic fields, this paper considers the propagation of quasi-longitudinal waves along a slender magnetic tube in pressure equilibrium with the ambient medium. The velocity of such waves is expressed in terms of the Alven speed and the sound speed inside the tube. The divergence of a vertical magnetic tube in a stratified atmosphere introduces a critical frequency below which propagation is impossible.

Defouw, R. J.↗
NASA NTRS1993

Time dependent simulation of cosmic-ray shocks including Alfven transport

Time evolution of plane, cosmic-ray modified shocks was simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven wave energy transport equations. Nonlinear feedback from the cosmic-rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the time scale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic-rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.

Jones, T. W.↗