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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Using Dense Array Waveform Correlations to Build a Velocity Model with Stochastic Variability

In an ongoing effort to improve 3D seismic-wave propagation modeling for frequencies up to 10 Hz, we used cross correlations between vertical-component waveforms from an underground chemical explosion to estimate the statistical properties of small-scale velocity heterogeneities. The waveforms were recorded by a dense 2D seismic array deployed during the Source Physics Experiments for event number 5 (SPE-5) in a series of six underground chemical explosions, conducted at the Nevada National Security Site. The array consisted of 996 geophones with a 50–100 m grid spacing, deployed at the SPE site at the north end of the Yucca Flat basin. The SPE were conducted to investigate the generation and propagation of seismic and acoustic waves from underground explosions. Comparisons of decay rates of waveform cross correlations as function of interstation distance, computed for observed and synthetic seismograms from the SPE-5 chemical explosion, were used to constrain statistical properties of correlated stochastic velocity perturbations representing small-scale heterogeneities added to a geology-based velocity model of the Yucca Flat basin. Using comparisons between recorded and simulated waveform cross correlations, we were able to recover sets of statistical properties of small-scale velocity perturbations in the velocity model that produce the best-fit between the recorded and simulated ground motion. The stochastic velocity fluctuations in the velocity model that produced the smallest misfits have a horizontal correlation distance of between 400 and 800 m, a vertical correlation distance between 100 and 200 m, and a standard deviation of 10% from the nominal model velocity in the alluvium basin layers. They also have a horizontal correlation distance of 1000 m, a vertical correlation distance of 250 m, and a standard deviation of 6% in the underlying and consolidated sedimentary layers, up to a depth of 4 km. Comparisons between observed and simulated wavefields were used to assess the proposed small-scale heterogeneity enhancements to the Yucca Flat basin model. We found that adding a depth-resolved stochastic variability to the geology-based velocity model improves the overall performance of ground-motion simulations of an SPE-5 explosion in the modeled frequency range up to 10 Hz. The results may be applicable to other similar basins.

58 GEOSCIENCES↗
DOE OSTI2023

On the Origins of Extreme Velocity Stars as Revealed by Large-scale Galactic Surveys

We assemble a large sample of 12,784 high-velocity stars with total velocity V GSR ≥ 300 km s -1 , selected from RAVE DR5, SDSS DR12, LAMOST DR8, APOGEE DR16, GALAH DR2, and Gaia EDR3. In this sample, 52 are marginally hypervelocity star (HVS) candidates that have VGSR exceeding their local escape velocities within 2σ confidence levels, 40 of which are discovered for the first time. All of the candidates are metal-poor, late-type halo stars, which are significantly different from the previously identified HVSs, which are largely massive early-type stars, discovered by extreme radial velocity. This finding suggests that our newly identified HVS candidates are ejected by different mechanisms from the previous population. To investigate their origins, for 547 extreme velocity stars with V GSR ≥ 0.8V esc , we reconstruct their backward-integrated trajectories in the Galactic potential. According to the orbital analysis, no candidates are found to be definitely ejected from the Galactic-center (GC), while eight metal-poor extreme velocity stars are found to have a closest distance to the GC within 1 kpc. Intriguingly, 15 extreme velocity stars (including 2 HVS candidates) are found to have experienced close encounters with the Sagittarius dSph, suggesting that they originated from this dSph. This hypothesis is supported by an analysis of the [α/Fe]–[Fe/H] diagram. From a preliminary analysis of all of the 547 extreme velocity stars, we propose a general picture–star ejection from Galactic subsystems such as dwarf galaxies and globular clusters can be an important channel to produce extreme velocity stars or even HVSs, particularly the metal-poor late-type halo population.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

BASS. XXVI. DR2 Host Galaxy Stellar Velocity Dispersions

We present new central stellar velocity dispersions for 484 Sy 1.9 and Sy 2 from the second data release of the Swift/BAT AGN Spectroscopic Survey (BASS DR2). This constitutes the largest study of velocity dispersion measurements in X-ray-selected obscured active galactic nuclei (AGN) with 956 independent measurements of the Ca II H and K λ3969, 3934 and Mg I λ5175 region (3880–5550 Å) and the calcium triplet region (8350–8730 Å) from 642 spectra mainly from VLT/X-Shooter or Palomar/DoubleSpec. Our sample spans velocity dispersions of 40–360 km s 1 , corresponding to 4–5 orders of magnitude in black hole mass (M BH = 10 5.5-9.6 M ⊙ ), bolometric luminosity (L bol ~ 10 42–46 erg s -1 ), and Eddington ratio (L/L Edd ~ 10 -5 to 2). For 281 AGN, our data and analysis provide the first published central velocity dispersions, including six AGN with low-mass black holes (M BH = 10 5.5-6.5 M ⊙ ), discovered thanks to high spectral resolution observations (σ inst ~ 25 km s -1 ). The survey represents a significant advance with a nearly complete census of velocity dispersions of hard X-ray–selected obscured AGN with measurements for 99% of nearby AGN (z < 0.1) outside the Galactic plane (|b| > 10°). The BASS AGN have much higher velocity dispersions than the more numerous optically selected narrow-line AGN (i.e., ~150 versus ~100 km s -1 ) but are not biased toward the highest velocity dispersions of massive ellipticals (i.e., >250 km s -1 ). Despite sufficient spectral resolution to resolve the velocity dispersions associated with the bulges of small black holes (~10 4–5 M ⊙ ), we do not find a significant population of super-Eddington AGN. Using estimates of the black hole sphere of influence from velocity dispersion, direct stellar and gas black hole mass measurements could be obtained with existing facilities for more than ~100 BASS AGN.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Sound velocity and compressibility of melts along the hedenbergite (CaFeSi2O6)-diopside (CaMgSi2O6) join at high pressure : Implications for stability and seismic signature of Fe-rich melts in the mantle

Iron-rich silicate melts play an important role in the magmatic history of the Earth and the 16 Moon. However, their elastic properties at high pressures, especially the sound velocity, are poorly 17 understood. Here we determined the ultrasonic sound velocity for the first time of a hedenbergite 18 (Hd, CaFeSi2O6) melt and a melt mixture of 50 mol% hedenbergite + 50 mol% diopside (Hd50Di50) 19 at high pressure and temperature conditions up to 6 GPa and 2329 K, using high-pressure ultrasonic 20 technique combined with synchrotron radiation in a multi-anvil apparatus. Our results show that 21 Fe can significantly reduce the sound velocity while increase the density of silicate melts. 22 Comparing the Di, Hd, and Hd50Di50 melts, we find that the sound velocity does not mix linearly 23 2 for melts in the Hd-Di join, whereas the density for Hd-Di melts at high pressures can be well-24 described by linear mixing. Combined with melt geometry and melt compaction models, we 25 applied our results to study the stability and seismic signature of Fe-rich silicate melts in the Earth’s 26 upper mantle. For the low-velocity zone (LVZ) in mantle asthenosphere, although the degree of 27 seismic velocity reduction can be explained by the presence of a small amount of partial melt 28 distributed in film/band geometry along grain boundaries, Fe-rich melts formed at this depth are 29 unlikely to be gravitationally stable, but may be dynamically unextractable if the melt supply is 30 continuous. For the low-velocity layer (LVL) above the mantle transition zone, the presence of Fe-31 rich melts (with FeO>~10 wt%) distributed in textural equilibrium with the ambient mantle is a 32 plausible explanation.

diopside↗
DOE OSTI2023

Computer-controlled finishing via dynamically constraint position-velocity-time scheduler

In a Computer Numerical Controlled (CNC) finishing process, the target material removal from an optical surface is guided by the convolution between the influence function of a machine tool and its dwell time at certain points over the surface. To reduce dynamics stressing and increase machining efficiency, the dwell time must be converted to varying velocities, which are the actual inputs to the machine tool controller. Conventionally, the conversion assumed constant acceleration and relied on linear motion interpolation, which caused discontinuities in velocities. This unsmooth motion affects the material removal distribution, and, thus, the accuracy of the finished surface shape. Many modern CNC machines support the smoother, cubic-polynomial interpolated Position-Velocity-Time (PVT) motion mode; however, the conventional scheduler may fail to provide suitable velocities for the PVT. Here in this study answers this challenge by proposing a novel PVT-based velocity scheduler that achieves smooth motion while considering CNC dynamic limits. Firstly, the principle of the PVT is explained, and the PVT-based velocity scheduler is formulated. Secondly, a quadratic programming is used to optimize the velocities by imposing the CNC dynamic constraints and the C 1 continuities (zeroth and first derivatives are continuous) simultaneously. Thirdly, the smoothness and accuracy of the scheduled velocities are studied on different kinds of tool paths via simulation. Finally, a sub-0.3 nm level surface finishing experiment using ion beam figuring is demonstrated to verify the feasibility of the proposed method. The PVT-based scheduler and simulator code is open-sourced.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Primary Velocity and Orbital Phase Effects on Planetary Detectability from Small Epoch Number Data Sets

Cross-correlation analyses of high-resolution spectroscopic data have recently shown great success in directly detecting planetary signals and enabling the characterization of their atmospheres. One such technique aims to observe a system at multiple epochs and combine the measured planetary radial velocities from each epoch into a measurement of the planetary Keplerian orbital velocity K {sub p}, constituting a direct detection of the planetary signal. Recent work has shown that in few-epoch (∼5) data sets, unintended structure can arise at a high level, obscuring the planetary detection. In this work, we look to simulations to examine whether there are ways to reduce this structured noise in few-epoch data sets by careful planning of observations. The choice of observation date allows observers to select the primary (stellar) velocity through a set systemic velocity and chosen barycentric velocity and the planetary orbital phase so we focus on the effects of these two parameters. We find that epochs taken when the primary velocity is near zero and the stellar lines remain relatively fixed to the telluric rest-frame greatly reduce the level of structured noise and allow for much stronger planetary detections, on average more than twice the significance of detections made with epochs using randomly selected primary velocities. Following these results, we recommend that observers looking to build up high-resolution multi-epoch data sets target nights when their system has a near-zero primary velocity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

The 3D Kinematics of the Orion Nebula Cluster: NIRSPEC-AO Radial Velocities of the Core Population

The kinematics and dynamics of stellar and substellar populations within young, still-forming clusters provide valuable information for constraining theories of formation mechanisms. Using Keck II NIRSPEC+AO data, we have measured radial velocities for 56 low-mass sources within 4' of the core of the Orion Nebula Cluster (ONC). We also remeasure radial velocities for 172 sources observed with SDSS/APOGEE. These data are combined with proper motions measured using HST ACS/WFPC2/WFC3IR and Keck II NIRC2, creating a sample of 135 sources with all three velocity components. The velocities measured are consistent with a normal distribution in all three components. We measure intrinsic velocity dispersions of (${\sigma }_{{v}_{\alpha }}$, ${\sigma }_{{v}_{\delta }}$, ${\sigma }_{{v}_{r}}$) = (1.64 ± 0.12, 2.03 ± 0.13, ${2.56}_{-0.17}^{+0.16}$) km s –1 . Our computed intrinsic velocity dispersion profiles are consistent with the dynamical equilibrium models from Da Rio et al. (2014) in the tangential direction but not in the line-of-sight direction, possibly indicating that the core of the ONC is not yet virialized, and may require a nonspherical potential to explain the observed velocity dispersion profiles. We also observe a slight elongation along the north–south direction following the filament, which has been well studied in previous literature, and an elongation in the line-of-sight to tangential velocity direction. These 3D kinematics will help in the development of realistic models of the formation and early evolution of massive clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

An Assessment of Global Positioning System Velocity Uncertainty in California

We analyze data from 580 continuous global positioning system (GPS) stations in California to quantify differences in published velocity estimates from five analysis centers. Horizontal and vertical rates for individual stations can differ up to 5 mm/yr, with systematic differences in some areas comparable to deformation rates. Published velocity uncertainties vary between analysis centers and are systematically underreported in the horizontal relative to empirical uncertainties calculated from the scatter of analysis center velocities. In the vertical, published velocity uncertainties are both over and underreported and vary more widely between centers. An interpolated ensemble vertical velocity field shows high-subsidence regions in the Central Valley and Salton Trough have the largest empirical uncertainties, while station density has a modest impact on uncertainties. Applications that rely on subcentimeter GPS accuracy should consider the possibility that formal errors published with velocity rate estimates understate true velocity uncertainties in both the horizontal and vertical.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Stochastic modal velocity field in rough-wall turbulence

Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers in a range of Reynolds numbers extending from the wind tunnel to field conditions. Each profile consists in a sequence of steps, defined by the modal velocities and representing uniform momentum zones (UMZs), separated by velocity jumps representing the internal shear layers. Height-dependent UMZ is described by a minimal set of attributes: thickness, mid-height elevation, and streamwise (modal) and vertical velocities. These are informed by experimental observations and reproducing the statistical behaviour of rough-wall turbulence and attached eddy scaling, consistent with the corresponding experimental datasets. Sets of independently generated profiles are reorganized in the streamwise direction to form a spatially consistent modal velocity field, starting from any randomly selected profile. The operation allows one to stretch or compress the velocity field in space, increases the size of the domain and adjusts the size of the largest emerging structures to the Reynolds number of the simulated flow. By imposing the autocorrelation function of the modal velocity field to be anchored on the experimental measurements, we obtain a physically based spatial resolution, which is employed in the computation of the velocity spectrum, and second-order structure functions. The results reproduce the Kolmogorov inertial range extending from the UMZ and their attached-eddy vertical organization to the very-large-scale motions (VLSMs) introduced with the reordering process. The dynamic role of VLSM is confirmed in the –u'w' co-spectra and in their vertical derivative, representing a scale-dependent pressure gradient contribution.

42 ENGINEERING↗
DOE OSTI2023

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz–tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

A three-point velocity estimation method for two-dimensional coarse-grained imaging data

Time delay and velocity estimation methods have been widely studied subjects in the context of signal processing, with applications in many different fields of physics. The velocity of waves or coherent fluctuation structures is commonly estimated as the distance between two measurement points divided by the time lag that maximizes the cross correlation function between the measured signals, but this is demonstrated to result in erroneous estimates for two spatial dimensions. We present an improved method to accurately estimate both components of the velocity vector, relying on three non-aligned measurement points. We introduce a stochastic process describing the fluctuations as a superposition of uncorrelated pulses moving in two dimensions. Using this model, we show that the three-point velocity estimation method, using time delays calculated through cross correlations, yields the exact velocity components when all pulses have the same velocity. The two- and three-point methods are tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results reveal the superiority of the three-point technique. Finally, we demonstrate the applicability of the velocity estimation on gas puff imaging data of strongly intermittent plasma fluctuations due to the radial motion of coherent, blob-like structures at the boundary of the Alcator C-Mod tokamak.

Materials Science↗
DOE OSTI2023

Joint velocity and density reconstruction of the Universe with nonlinear differentiable forward modeling

Reconstructing the initial conditions of the Universe from late-time observations has the potential to optimally extract cosmological information. Due to the high dimensionality of the parameter space, a differentiable forward model is needed for convergence, and recent advances have made it possible to perform reconstruction with nonlinear models based on galaxy (or halo) positions. In addition to positions, future surveys will provide measurements of galaxies' peculiar velocities through the kinematic Sunyaev-Zel'dovich effect (kSZ), type Ia supernovae, the fundamental plane relation, and the Tully-Fisher relation. Here we develop the formalism for including halo velocities, in addition to halo positions, to enhance the reconstruction of the initial conditions. We show that using velocity information can significantly improve the reconstruction accuracy compared to using only the halo density field. Here we study this improvement as a function of shot noise, velocity measurement noise, and angle to the line of sight. We also show how halo velocity data can be used to improve the reconstruction of the final nonlinear matter overdensity and velocity fields. We have built our pipeline into the differentiable Particle-Mesh FlowPM package, paving the way to perform field-level cosmological inference with joint velocity and density reconstruction. This is especially useful given the increased ability to measure peculiar velocities in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Regional seismic velocity changes following the 2019 M w 7.1 Ridgecrest, California earthquake from autocorrelations and P / S converted waves

SUMMARY We examine regional transient changes of seismic velocities generated by the 2019 Mw 7.1 Ridgecrest earthquake in California, using autocorrelations of moving time windows in continuous waveforms recorded at regional stations. We focus on traveltime differences in a prominent phase generated by an interface around 2 km depth, associated with transmitted Pp waves and converted Ps waves from the ongoing microseismicity. Synthetic tests demonstrate the feasibility of the method for monitoring seismic velocity changes. Taking advantage of the numerous aftershocks in the early period following the main shock, we obtain a temporal resolution of velocity changes up to 20 min in the early post-main-shock period. The results reveal regional coseismic velocity drops in the top 1–3 km with an average value of ∼2 per cent over distances up to 100 km from the Ridgecrest event. These average velocity drops are likely dominated by larger changes in the shallow materials and are followed by rapid recoveries on timescales of days. Around the north end of the Ridgecrest rupture and the nearby Coso geothermal region, the observed coseismic velocity drops are up to ∼8 per cent. The method allows monitoring temporal changes of seismic velocities with high temporal resolution, fast computation and precise spatial mapping of changes. The results suggest that significant temporal changes of seismic velocities of shallow materials are commonly generated on a regional scale by large events.

58 GEOSCIENCES↗
DOE OSTI2024

Graph-learning approach to combine multiresolution seismic velocity models

SUMMARY The resolution of velocity models obtained by tomography varies due to multiple factors and variables, such as the inversion approach, ray coverage, data quality, etc. Combining velocity models with different resolutions can enable more accurate ground motion simulations. Toward this goal, we present a novel methodology to fuse multiresolution seismic velocity maps with probabilistic graphical models (PGMs). The PGMs provide segmentation results, corresponding to various velocity intervals, in seismic velocity models with different resolutions. Further, by considering physical information (such as ray path density), we introduce physics-informed probabilistic graphical models (PIPGMs). These models provide data-driven relations between subdomains with low (LR) and high (HR) resolutions. Transferring (segmented) distribution information from the HR regions enhances the details in the LR regions by solving a maximum likelihood problem with prior knowledge from HR models. When updating areas bordering HR and LR regions, a patch-scanning policy is adopted to consider local patterns and avoid sharp boundaries. To evaluate the efficacy of the proposed PGM fusion method, we tested the fusion approach on both a synthetic checkerboard model and a fault zone structure imaged from the 2019 Ridgecrest, CA, earthquake sequence. The Ridgecrest fault zone image consists of a shallow (top 1 km) high-resolution shear-wave velocity model obtained from ambient noise tomography, which is embedded into the coarser Statewide California Earthquake Center Community Velocity Model version S4.26-M01. The model efficacy is underscored by the deviation between observed and calculated traveltimes along the boundaries between HR and LR regions, 38 per cent less than obtained by conventional Gaussian interpolation. The proposed PGM fusion method can merge any gridded multiresolution velocity model, a valuable tool for computational seismology and ground motion estimation.

Geochemistry & Geophysics↗
DOE OSTI2022

Impact of bar resonances in the velocity–space distribution of the solar neighbourhood stars in a self-consistent N -body Galactic disc simulation

ABSTRACT The velocity–space distribution of the solar neighbourhood stars shows complex substructures. Most of the previous studies use static potentials to investigate their origins. Instead we use a self-consistent N-body model of the Milky Way, whose potential is asymmetric and evolves with time. In this paper, we quantitatively evaluate the similarities of the velocity–space distributions in the N-body model and that of the solar neighbourhood, using Kullback–Leibler divergence (KLD). The KLD analysis shows the time evolution and spatial variation of the velocity–space distribution. The KLD fluctuates with time, which indicates the velocity–space distribution at a fixed position is not always similar to that of the solar neighbourhood. Some positions show velocity–space distributions with small KLDs (high similarities) more frequently than others. One of them locates at $(R,\phi)=(8.2\,\,\rm{\mathrm{kpc}}, 30^\circ)$, where R and ϕ are the distance from the galactic centre and the angle with respect to the bar’s major axis, respectively. The detection frequency is higher in the inter-arm regions than in the arm regions. In the velocity maps with small KLDs, we identify the velocity–space substructures, which consist of particles trapped in bar resonances. The bar resonances have significant impact on the stellar velocity–space distribution even though the galactic potential is not static.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Can we observe the ion-neutral drift velocity in prestellar cores?

Given the low-ionization fraction of molecular clouds, ambipolar diffusion is thought to be an integral process in star formation. However, chemical and radiative-transfer effects, observational challenges, and the fact that the ion-neutral drift velocity is inherently very small render a definite detection of ambipolar diffusion extremely non-trivial. Here, we study the ion-neutral drift velocity in a suite of chemodynamical, non-ideal magnetohydrodynamic (MHD), two-dimensional axisymmetric simulations of prestellar cores where we alter the temperature, cosmic-ray ionization rate, visual extinction, mass-to-flux ratio, and chemical evolution. Subsequently, we perform a number of non-local thermodynamic equilibrium (non-LTE) radiative-transfer calculations considering various idealized and non-idealized scenarios in order to assess which factor (chemistry, radiative transfer, and/or observational difficulties) is the most challenging to overcome in our efforts to detect the ion-neutral drift velocity. We find that temperature has a significant effect in the amplitude of the drift velocity with the coldest modelled cores (T = 6 K) exhibiting drift velocities comparable to the sound speed. Against expectations, we find that in idealized scenarios (where two species are perfectly chemically co-evolving) the drift velocity ‘survives’ radiative-transfer effects and can in principle be observed. However, we find that observational challenges and chemical effects can significantly hinder our view of the ion-neutral drift velocity. Finally, we propose that HCN and HCNH + ⁠, being chemically co-evolving, could be used in future observational studies aiming to measure the ion-neutral drift velocity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗
DOE OSTI2021

The Foundation Supernova Survey: Photospheric Velocity Correlations in Type Ia Supernovae

The ejecta velocities of Type Ia supernovae (SNe Ia), as measured by the Si ii λ6355 line, have been shown to correlate with other supernova properties, including color and standardized luminosity. We investigate these results using the Foundation Supernova Survey, with a spectroscopic data release presented here, and photometry analyzed with the SALT2 light-curve fitter. We find that the Foundation data do not show significant evidence for an offset in color between SNe Ia with high and normal photospheric velocities, with Δc = 0.004 ± 0.015. Our SALT2 analysis does show evidence for redder high-velocity SNe Ia in other samples, including objects from the Carnegie Supernova Project, with a combined sample yielding Δc = 0.018 ± 0.008. When split on velocity, the Foundation SNe Ia also do not show a significant difference in Hubble diagram residual, ΔHR = 0.015 ± 0.049 mag. Intriguingly, we find that SN Ia ejecta velocity information may be gleaned from photometry, particularly in redder optical bands. For high-redshift SNe Ia, these rest-frame red wavelengths will be observed by the Nancy Grace Roman Space Telescope. Our results are in line with previous work that suggests SN Ia host-galaxy stellar mass is correlated with ejecta velocity: high-velocity SNe Ia are found nearly exclusively in high-stellar-mass hosts. However, host-galaxy properties alone do not explain velocity-dependent differences in supernova colors and luminosities across samples. Measuring and understanding the connection between intrinsic explosion properties and supernova environments, across cosmic time, will be important for precision cosmology with SNe Ia.

79 ASTRONOMY AND ASTROPHYSICS↗