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NASA NTRS2013

Comparison of Noise Source Localization Data with Flow Field Data Obtained in Cold Supersonic Jets and Implications Regarding Broadband Shock Noise

Phased array noise source localization have been compared with 2 types of flow field data (BOS and PIV). The data show that: 1) the higher frequency noise in a BBSN hump is generated further downstream than the lower frequency noise. This is due to a) the shock spacing decreasing and b) the turbulent structure size increasing with distance downstream. 2) BBSN can be created by very weak shocks. 3) BBSN is not created by the strong shocks just downstream of the nozzle because the turbulent structures have not grown large enough to match the shock spacing. 4) The point in the flow where the shock spacing equals the average size of the turbulent structures is a hot spot for shock noise. 5) Some of the shocks responsible for producing the first hump also produce the second hump.

Podboy, Gary↗

NASA NTRS2014

Grain Destruction in a Supernova Remnant Shock Wave

Dust grains are sputtered away in the hot gas behind shock fronts in supernova remnants, gradually enriching the gas phase with refractory elements. We have measured emission in C IV (lambda)1550 from C atoms sputtered from dust in the gas behind a non-radiative shock wave in the northern Cygnus Loop. Overall, the intensity observed behind the shock agrees approximately with predictions from model calculations that match the Spitzer 24 micron and the X-ray intensity profiles. Thus these observations confirm the overall picture of dust destruction in SNR shocks and the sputtering rates used in models. However, there is a discrepancy in that the CIV intensity 10'' behind the shock is too high compared to the intensities at the shock and 25'' behind it. Variations in the density, hydrogen neutral fraction and the dust properties over parsec scales in the pre- shock medium limit our ability to test dust destruction models in detail.

dust↗

NASA NTRS2015

Experimentally Shocked and Altered Basalt: Laboratory Analogs for Calibration of Mars Remote Sensing and In Situ Data

Calciumphosphate (likely chloroapatite) is formed in the alteration experiments and is more abundant in the altered and shocked sample probably due to increased surface area exposed to alteration fluids resulting from shock damage in the form of both brittle and structural deformation to the starting material (Figs 1 & 3). Apatite forms in basic conditions so the closed system alteration experiment must be buffered by the basalt starting material to create a fluid chemistry environment evolving from neutral at the start to alkaline after 21 days at 160 C. Plagioclase feldspar in the unshocked sample (Fig. 2) has undergone a solid-state transformation to maskelynite, a disordered phase that is not manifest in the XRD pattern of the shocked sample (Fig.4). Olivine and ulvospinel that are present in the starting material can be detected by XRD in the shocked and altered sample (Fig. 4). Tungsten from the sample holder used in the shock experiments dominates the XRD pattern of the shocked and altered sample (Fig. 4). Samples were weighed after the alteration experiments to determine mass loss and predict the amount of material available for the planned analyses from the shock experiments. Within the constraints of these experiments, mass loss is negligible. The samples will next be characterized by Moessbauer and Vis-Near IR spectroscopy, the results of which will be compared to the Mars Exploration Rovers and Mars Reconnaissance Orbiter data sets respectively.

Bell, M. S.↗

NASA NTRS2015

Experimentally Shocked and Altered Basalt: Laboratory Analogs for Calibration of Mars Remote Sensing and In Situ Data

Calcium phosphate (likely chloroapatite) is formed in the alteration experiments and is more abundant in the altered and shocked sample probably due to increased surface area exposed to alteration fluids resulting from shock damage in the form of both brittle and structural deformation to the starting material (Figs 1 & 3). Apatite forms in basic conditions so the closed system alteration experiment must be buffered by the basalt starting material to create a fluid chemistry environment evolving from neutral at the start to alkaline after 21 days at 160 degrees Centigrade. Plagioclase feldspar in the unshocked sample (Fig. 2) has undergone a solid-state transformation to maskelynite, a disordered phase that is not manifest in the X-ray diffraction pattern of the shocked sample (Fig.4). Olivine and ulvospinel that are present in the starting material can be detected by X-ray diffraction in the shocked and altered sample (Fig. 4). Tungsten from the sample holder used in the shock experiments dominates the X-ray diffraction pattern of the shocked and altered sample (Fig. 4). Samples were weighed after the alteration experiments to determine mass loss and predict the amount of material available for the planned analyses from the shock experiments. Within the constraints of these experiments, mass loss is negligible. The samples will next be characterized by Moessbauer and Vis-Near Infrared spectroscopy, the results of which will be compared to the Mars Exploration Rovers and Mars Reconnaissance Orbiter data sets respectively.

Bell, M. S.↗

NASA NTRS2014

High Order Numerical Methods for LES of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing explicit subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. In this work we perform a comparative study of different approaches to reduce this loss of accuracy within the framework of the dynamic Germano SGS model. One of the possible approaches is to apply Harten's subcell resolution procedure to locate and sharpen the shock, and to use a one-sided test filter at the grid points adjacent to the exact shock location. The other considered approach is local disabling of the SGS terms in the vicinity of the shock location. In this study we use a canonical shock-turbulence interaction problem for comparison of the considered modifications of the SGS filtering procedure. For the considered test case both approaches show a similar improvement in the accuracy near the shock.

High Order↗

NASA NTRS2016

Relativistic Electrons Produced by Foreshock Disturbances Observed Upstream of Earth's Bow Shock

Charged particles can be reflected and accelerated by strong (i.e., high Mach number) astrophysical collisionless shock waves, streaming away to form a foreshock region in communication with the shock. Foreshocks are primarily populated by suprathermal ions that can generate foreshock disturbances-largescale (i.e., tens to thousands of thermal ion Larmor radii), transient (approximately 5-10 per day) structures. They have recently been found to accelerate ions to energies of several keV. Although electrons in Saturn's high Mach number (M > 40) bow shock can be accelerated to relativistic energies (nearly 1000 keV), it has hitherto been thought impossible to accelerate electrons beyond a few tens of keV at Earth's low Mach number (1 ≤M <20) bow shock. Here we report observations of electrons energized by foreshock disturbances to energies up to at least approximately 300 keV. Although such energetic electrons have been previously observed, their presence has been attributed to escaping magnetospheric particles or solar events. These relativistic electrons are not associated with any solar or magnetospheric activity. Further, due to their relatively small Larmor radii (compared to magnetic gradient scale lengths) and large thermal speeds (compared to shock speeds), no known shock acceleration mechanism can energize thermal electrons up to relativistic energies. The discovery of relativistic electrons associated with foreshock structures commonly generated in astrophysical shocks could provide a new paradigm for electron injections and acceleration in collisionless plasmas.

SLAMS↗

NASA NTRS2015

High Order Numerical Methods for LES of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing explicit subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. In this work we perform a comparative study of different approaches to reduce this loss of accuracy within the framework of the dynamic Germano SGS model. One of the possible approaches is to apply Harten’s subcell resolution procedure to locate and sharpen the shock, and to use a one-sided test filter at the grid points adjacent to the exact shock location. The other considered approach is local disabling of the SGS terms in the vicinity of the shock location. In this study we use a canonical shock-turbulence interaction problem for comparison of the considered modifications of the SGS filtering procedure. For the considered test case both approaches show a similar improvement in the accuracy near the shock.

LES↗

NASA NTRS2017

Solar Flare Termination Shock and the Synthetic Fe XXI 1354.08 Å Line

Solar flares are one of the most energetic phenomena occurred in the solar system. In the standard solar flare model, a fast mode shock, which is often referred to as the flare termination shock (TS), can exist above the loop-top source of hard X-ray emissions. The existence of the termination shock has been recently related to spectral hardening of flare hard X-ray spectrum at energies > 300 keV. Observations of the Fe XXI 1354.08 Å line during solar flares by the IRIS spacecraft have found significant redshift with >100 km/s, which is consistent with a reconnection downflow. The ability to identify such a redshift by IRIS is made possible by IRIS's high time resolution, high spatial resolution, high sensitivity and cadence spectral observations. The ability to identify such a redshift by IRIS suggests that one may be able to use IRIS observations to identify flare termination shocks. Using a MHD simulation to model magnetic reconnection of a solar flare and assuming the existence of a TS in the downflow of the reconnection plasma, we model the synthetic emission of the Fe XXI 1354.08 Å line in this work. We show that the existence of the TS in the solar flare may manifest itself from the Fe XXI 1354.08 Å line.Plain Language SummaryA solar flare is a brief eruption of intense high-energy radiation from the sun's surface, associated with sunspots and causing electromagnetic disturbances on the earth, as with radio frequency communications and power line transmissions. The standard solar flare model proposes that magnetic reconnection drives solar flares and fast mode shock, which is often referred to as the flare termination shock (TS), can exist at the reconnection outflows. The existence of the termination shock has been recently related to spectral hardening of flare hard X-ray spectrum.

Guo, Lijia↗

NASA NTRS2019

Time Accurate Simulation of Nonequilibrium Flow Inside the NASA Ames Electric Arc Shock Tube

Numerical investigations of the flowfield inside NASA Ames' Electric Arc Shock Tube have been performed. The focus is to simulate the experiments designed to reproduce shock layer radiation layer relevant to Earth re-entry conditions. This paper assess the current computational capability in simulating time-accurate unsteady nonequilibrium flows in the presence of strong shock waves with state-of-the-art physical models. The technical approach is described with preliminary results presented for one specific flow condition. It was found that the axisymmetric source term generates a numerical instability that appears as shock bending. This instability is time dependent which greatly affects the shock speed. Post-shock conditions are discussed and compared to CEA equilibrium prediction and good agreement was obtained close to the test-section and just behind the shock.

Bensassi, Khalil↗

NASA NTRSDate not supplied

Deciphering Extreme Mineral Records; Microstructural Phase Heritage of Shocked Materials

High-pressure minerals such as coesite, stishovite, and reidite are often used as indicators of shock metamorphism. However, high-pressure and high-temperature phases are metastable at ambient conditions and, therefore, often revert to a more energetically favorable phase. During solid-state transformations, the crystallographic orientations of the stable polymorph are controlled by the transformation pathway from the parent. Microstructural orientation analysis using electron backscatter diffraction (EBSD) of the stable phase can reveal systematic intercrystalline orientation relationships (OR) diagnostic of solid-state transformations from these high-pressure or high-temperature polymorph phases (Cayron et al., 2006). Knowledge of polymorph stability fields for a given system can thus be used to infer minimum shock P and/or T conditions that rocks have experienced, which are otherwise unavailable using traditional thermobarometers such as element partition coefficients. Using orientation relationships to infer the former presence of mineral phases has been termed microstructural “phase heritage”, and has successfully been used to probe for evidence of extreme pressures and temperatures resulting from hypervelocity impacts. The reconstruction of polymorphs of ZrSiO4 (zircon, reidite) and ZrO2 (baddeleyite) have further elucidated the behavior of these phases under hypervelocity impact conditions (Timms et al., 2017a; White et al., 2018), and OR analysis of shocked monazite has identified a previously unrecognized tetragonal high-P polymorph (Erickson et al., 2019). Zircon will convert to the low tetragonal polymorph reidite at shock stresses above ~21 GPa. However, upon decompression at temperatures above 1200 °C reidite will revert to zircon (Kusaba et al., 1985). Recrystallized zircon neoblasts encased in impact melt often show systematic misorientation relationships of 90° about <110> indicative of reversion from the reidite (Fig. 1), and preserving cryptic evidence of the high-P history that is often erased by the post shock thermal spike (Cavosie et al., 2016). Microstructural OR analysis of a dissociated zircon corona composed of baddeleyite (monoclinic-ZrO2) has identified the former presence of cubic zirconia within impact melt glass from the Mistastin Lake impact structure, Labrador, CA. Based on stability fields in the ZrO2-SiO2 binary phase diagram, cubic zirconia records thermal conditions in excess of 2370 °C at ambient P, indicating that the Mistastin impact melt is the hottest rock identified on Earth’s surface (Timms et al., 2017b). Shock-deformed monazite (monoclinic La,Ce,ThPO4) containing lamellae comprised of interlocking laths has been identified from the Haughton Dome impact structure, Nunavut, Canada and Nördlinger-Ries Crater, southern Germany. The lath-structured lamellae are composed of four systematic orientation variants, which OR analyses indicate originate from a tetragonal parent whereby the [010]monoclinic aligns with either [100] or [010]tetragonal (Erickson et al., 2019). These results highlight utility of microstructural phase heritage analyses for the identification of unstable high-P or high-T polymorphs that uniquely record the extremely transient shock conditions produced by hypervelocity impacts.

Timmons Erickson↗

NASA NTRS2021

MMS Observations of Energized He+ Pickup Ions at Quasiperpendicular Shocks

Accelerated He+ PUIs, downstream of quasi-perpendicular shocks, are studied as 10a function of the fast mode Mach number (Mf) and shock obliquity (𝜃Bn).We analyze quasi-perpendicular shocks with Mach numbers in the range [1, 7] observed by the Magnetospheric MultiScale (MMS) mission, and compare upstream and downstream He+ velocity distribution functions (VDFs). For each shock event, we characterize the upstream PUI distribution and derive reduced 1D velocity distributions for the selected upstream and downstream intervals. We also compare the upstream to downstream ratio of spectral indices, computed from the He+ perpendicular distributions, to Mf and 𝜃Bn. We find a positive correlation between this spectral index ratio and Mf, which suggests that perpendicular energization of He+ PUIs is enhanced as the shock becomes stronger. These results inform modeling efforts of PUIs and shock acceleration processes, particularly those taking place at the termination shock.

Michael J. Starkey↗

NASA NTRSDate not supplied

MARS 2020 Backshell Radiative Heating Measurement and Shock Tube Verification

In February 2021, the Perseverance rover was brought to the surface of Mars by the Mars 2020 mission. A feature of the Mars 2020 capsule was instrumentation to measure its entry, descent and landing (EDL) with the so-called Mars EDL Instrumentation 2 (MEDLI2) [1]. The MEDLI2 introduced, among other things, backshell instrumentation, including a broadband radiometer. The radiometer was mounted on the leeside of the vehicle next to thermocouple plugs and a heat flux gauge. The data returned by the leeside MEDLI2 heat flux gauge is largely analogous to that measured by the COMARS gauge flown on the ExoMars Schiaparelli [2] entry in that it is measuring heat flux in an area that is entirely dominated by radiative heating. The COMARS measurement provided excellent validation of backshell radiative heating models for Mars entry, albeit at a limited number of points [3]. The MEDLI2 heat flux gauge measurement effectively confirmed the quality of the prediction, extended over the full trajectory, as will be presented in this paper. The MEDLI2 radiometer,however, was blocked by ablation products and suffered a loss of half of its signal. The second backshell heat flux gauge installed on the windside of the vehicle was also well predicted, although the heating had both radiative and convective contributions. It was desired to reproduce the conditions of the Mars 2020 entry via ground testing in the Electric Arc Shock Tube (EAST) at NASA Ames. Tests to verify stagnation line heating were previously reported in EAST, confirming the presence of shock layer radiation as the major discrepancy in heatshield temperature modelling [4]. Therefore, tests for stagnation line heating were not repeated. Instead, the shock tube informed bias method [5, 6] was used to identify test conditions that may produce similarity to streamlines that pass around the backside of the vehicle and are responsible for the radiation observed at the two heat flux gauge locations. This method was used to identify a range of velocities and densities in the shock tube that are relevant for confirming the radiative environment encountered. This paper reports the results obtained in the 10 cm diameter EAST shock tube, corresponding to later trajectory points at ambient pressures of 1.1-2.0 Torr and velocities from 1.2-3.5 km/s. The test series employed two primary diagnostics: emission spectroscopy and tunable diode laser absorption spectroscopy (TDLAS). The emission spectroscopy performed broadband measurements of the radiative emission of the 4.3 and 2.7 m bands of CO2 at flight similar conditions, obtaining both spectral and spatial data corresponding to the relaxation behind the shock front. The TDLAS measured the absorption of several lines of CO and CO2 and obtains species number densities and temperatures as a function of time behind the shock front. This paper will review highlights of this test series and analyses of the emission and absorption data. While the datasets generally show good agreement with predictions, a few discrepancies and items for additional investigation are identified and will be discussed

Brett A Cruden↗

DOE OSTI2019

Ultra-High Fidelity Laser-Induced Air Shock from Energetic Materials

Recent interest in the implementation of the Laser-induced Air Shock from Energetic Materials (LASEM) technique prompted an investigation using ultra-high-speed imaging diagnostics to provide early-time (sub-μs) shock-wave-radius-versus-time data necessary to accurately determine the characteristic laser-induced-shock velocity (y-intercept) for high explosives (HE) of interest. Ultra-high-speed focused-shadowgraphy images were collected from nanosecond-pulsed laser-ablated samples of HE similar to those in the published literature. Shadowgraphy images were collected using interframe times ranging from 50–750 ns, with exposure times of 5 ns. Acquired shock-wave-radius-versus-time data permitted a high-fidelity assessment of the shock wave velocity produced at the characteristic radius of the generated laser-plasma pulse. The resulting data from eight different HE indicated that early-time energy contributions and the resulting laser-induced shock velocity profiles produced from ablation of the HE material were indistinguishable amongst the explosives tested for the majority of the time domain characterized (0–12 μs).

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2023

Shock response of cobalt-based cemented tungsten carbides at pressures up to 100 GPa

In the present study, shock wave experiments are conducted on General Carbide cemented tungsten carbides with 3.7 wt.% and 6.0 wt.% cobalt binder to determine their shock compression response up to 100 GPa. A three-stage particle velocity profile is observed in the experiments -- an initial elastic-rise to the Hugoniot elastic limit (HEL), an elastic-plastic ramp indicating post-yield hardening, and finally a rise to the peak shocked Hugoniot state. The results of the experiments are used to determine the HEL, shock velocity (U s ) vs. particle velocity (u p ) Hugoniot relationship, and the longitudinal stress vs. specific volume Hugoniot relationship for the two samples. Here, the HEL for the WC 3.7wt% Co and WC 6.0wt% Co samples was determined to be ~4.45 GPa and 3.72 GPa, respectively. The U s – u p relation was determined to be U s = 4.97(0.006)+1. 446 (0.018) u p for WC 3.7 wt.% Co and U s = 4.93(0.006)+1. 454(0.017)u p for the WC 6.0 wt.% Co sample at peak particle velocities>0.75 km/s. For both WC grades, in the particle velocity regime less than ~0.75 km/s, the measured shock wave velocities were found to be larger than those predicted by the linear U s –u p Hugoniot relationship, indicating the two WC samples to preserve substantial strength in the post-yield deformation regime. Both WC grades show a catastrophic drop in shear stress carrying capacity when shocked to longitudinal stresses greater than ~70 GPa.

36 MATERIALS SCIENCE↗

DOE OSTI2020

High-precision shock equation of state measurements for metallic fluid carbon between 15 and 20 Mbar

Diamond is an efficient ablator material to convert the energy of high-power giant lasers into ablation pressure with applications for High-Energy-Density (HED) science, planetary science, and Inertial Confinement Fusion (ICF) research at the National Ignition Facility (NIF). Unfortunately, current theoretical equation of state models cannot reproduce all the observed experimental data in the multi-megabar regime particularly relevant for HED and ICF research. New experimental data on the behavior of carbon at extreme pressures and temperatures are, therefore, essential to improve our predictive capability to design and analyze dynamic compression experiments for HED or ICF research and build improved equation of state models in the future. In this paper, we report high-precision laser-driven shock compression measurements on diamond single crystals at the Omega Laser Facility. Using ultrafast Doppler optical Velocimetry Interferometer System for Any Reflector (VISAR) to track the leading shock front and a quartz plate as an in situ reference, we obtain relative pressure-density shock equation-of-state measurements between 15 and 20 Mbar with an impedance-matching procedure. We also report shock-and-release measurements in a spherical geometry at the NIF. The new data provide tight constraints on the compressibility of warm dense carbon along the Hugoniot of full density diamond, allowing us to discriminate between existing theoretical equation-of-state models. We find that both LLNL LEOS 9061 and LANL Sesame 7835 models capture well the shock compressibility in the explored range. LANL Sesame 7835 also reproduces well the observed shock-and-release behavior of diamond near 10–20 Mbar.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Experimental observations of shock-wave-induced bubble collapse and hot-spot formation in nitromethane liquid explosive

We studied the collapse of individual helium gas bubbles in the homogeneous explosive nitromethane (NM) to investigate effects of hot-spot formation on the detonation process. A bubble was injected into a NM sample, and a shock wave from an explosive detonator compressed the bubble, creating a localized hot spot. We measured shock and detonation wave speeds with optical velocimetry, and we used a high-speed camera to image the shock propagation and the pre- and post-bubble collapse processes. An infrared camera image showed the residual radiance temperature distribution after the bubble collapse, and an optical fiber pyrometer measured the time-resolved thermal radiance. We measured the optical spectra of light emitted from detonating NM without a bubble and from a collapsing bubble in shocked, undetonated NM. We estimated temperatures of the detonation fronts and of the hot spots formed by bubble collapse. To study the incipient detonation process, we performed all bubble collapse experiments at pressures below the threshold for creating a sustained detonation. Where the bubble collapsed, we observed an opaque, thermally emissive region believed to be chemical reaction products. Chemical reactions in NM can be produced with lower shock pressures (~1 GPa) when a helium bubble is present than without a bubble (~10 GPa). We used hydrodynamic modeling to predict shock wave propagation, extent of chemical reaction, and subsequent temperature rise from the collapsing bubble. Simulations using a temperature-dependent Arrhenius burn model gave much better results than reactive burn models that depend only on pressure and density.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

The role of pre-existing heterogeneities in materials under shock and spall

There has been a challenge for many decades to understand how heterogeneities influence the behavior of materials under shock loading, eventually leading to spall formation and failure. Experimental, analytical, and computational techniques have matured to the point where systematic studies of materials with complex microstructures under shock loading and the associated failure mechanisms are feasible. This is enabled by more accurate diagnostics as well as characterization methods. As interest in complex materials grows, understanding and predicting the role of heterogeneities in determining the dynamic behavior becomes crucial. Early computational studies, hydrocodes, in particular, historically preclude any irregularities in the form of defects and impurities in the material microstructure for the sake of simplification and to retain the hydrodynamic conservation equations. Contemporary computational methods, notably molecular dynamics simulations, can overcome this limitation by incorporating inhomogeneities albeit at a much lower length and time scale. This review discusses literature that has focused on investigating the role of various imperfections in the shock and spall behavior, emphasizing mainly heterogeneities such as second-phase particles, inclusions, and voids under both shock compression and release. Pre-existing defects are found in most engineering materials, ranging from thermodynamically necessary vacancies, to interstitial and dislocation, to microstructural features such as inclusions, second phase particles, voids, grain boundaries, and triple junctions. This literature review explores the interaction of these heterogeneities under shock loading during compression and release. Systematic characterization of material heterogeneities before and after shock loading, along with direct measurements of Hugoniot elastic limit and spall strength, allows for more generalized theories to be formulated. Further, continuous improvement toward time-resolved, in situ experimental data strengthens the ability to elucidate upon results gathered from simulations and analytical models, thus improving the overall ability to understand and predict how materials behave under dynamic loading.

36 MATERIALS SCIENCE↗

DOE OSTI2013

SHOCK HEATING OF THE MERGING GALAXY CLUSTER A521

A521 is an interacting galaxy cluster located at z = 0.247, hosting a low-frequency radio halo connected to an eastern radio relic. Previous Chandra observations hinted at the presence of an X-ray brightness edge at the position of the relic, which may be a shock front. We analyze a deep observation of A521 recently performed with XMM-Newton in order to probe the cluster structure up to the outermost regions covered by the radio emission. The cluster atmosphere exhibits various brightness and temperature anisotropies. In particular, two cluster cores appear to be separated by two cold fronts. We find two shock fronts, one that was suggested by Chandra and that is propagating to the east, and another to the southwestern cluster outskirt. The two main interacting clusters appear to be separated by a shock-heated region, which exhibits a spatial correlation with the radio halo. The outer edge of the radio relic coincides spatially with a shock front, suggesting that this shock is responsible for the generation of cosmic-ray electrons in the relic. The propagation direction and Mach number of the shock front derived from the gas density jump, M = 2.4 {+-} 0.2, are consistent with expectations from the radio spectral index, under the assumption of Fermi I acceleration mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗