Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Disks”

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.

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

At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Seeking Self-regulating Simulations of Idealized Milky Way–like Galaxies

Abstract Precipitation is potentially a mechanism through which the circumgalactic medium (CGM) can regulate a galaxy’s star formation. Here, we present idealized simulations of isolated Milky Way–like galaxies intended to examine the ability of galaxies to self-regulate their star formation, in particular via precipitation. We also examine the impact of rotation in the CGM. Using six simulations, we explore variations in the initial CGM t cool / t ff ratio and rotation profile. Those variations affect the amount of gas accretion and star formation within the galactic disk. To encourage this accretion and better study its dependence on CGM structure, we gradually increase the efficiency of stellar feedback during the first half of our simulations. Yet despite this gradual increase, the resulting outflows quickly evacuate large, hot cavities within the CGM and even beyond r 200 . Some of the CGM gas avoids interacting with the cavities and is able to feed the disk along its midplane, but the cooling of feedback-heated gas far from the midplane is too slow to supply the disk with additional gas. Our simulations illustrate the importance of physical mechanisms in the outer CGM and IGM for star formation regulation in Milky Way–scale halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A Blueprint for the Milky Way’s Stellar Populations. IV. A String of Pearls—the Galactic Starburst Sequence

We continue our series of papers on phase-space distributions of stars in the Milky Way based on photometrically derived metallicities and Gaia astrometry, with a focus on the halo-disk interface in the local volume. To exploit various photometric databases, we develop a method of empirically calibrating synthetic stellar spectra based on a comparison with observations of stellar sequences and individual stars in the Sloan Digital Sky Survey, the SkyMapper Sky Survey, and the Pan-STARRS1 surveys, overcoming band-specific corrections employed in our previous work. In addition, photometric zero-point corrections are derived to provide an internally consistent photometric system with a spatially uniform metallicity zero-point. Using our phase-space diagrams, we find a remarkably narrow sequence in the rotational velocity (v $\phi$ ) versus metallicity ([Fe/H]) space for a sample of high proper-motion stars (>25 mas yr -1 ), which runs along Gaia Sausage/Enceladus (GSE) and the Splash substructures and is linked to the disk, spanning nearly 2 dex in [Fe/H]. Notably, a rapid increase of v $\phi$ from a nearly zero net rotation to ~180 km s -1 in a narrow metallicity interval (-0.6 ≲ [Fe/H] ≲ -0.4) suggests that some of these stars emerged quickly on a short gas-depletion timescale. Through measurements of a scale height and length, we argue that these stars are distinct from those heated dynamically by mergers. This chain of high proper-motion stars provides additional support for recent discoveries suggesting that a starburst took place when the young Milky Way encountered the gas-rich GSE progenitor, which eventually led to the settling of metal-enriched gas onto the disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The Baryonic Content of Galaxies Mapped by MaNGA and the Gas Around Them

We analyze the cool gas in and around 14 nearby galaxies (at z < 0.1) mapped with the Sloan Digital Sky Survey IV MaNGA survey by measuring absorption lines produced by gas in spectra of background quasars/active galactic nuclei at impact parameters of 0–25 effective radii from the galactic centers. Using Hubble Space Telescope/Cosmic Origins Spectrograph, we detect absorption at the galactic redshift and measure or constrain column densities of neutral (H I, N I, O I, and Ar I), low-ionization (Si II, S II, C II, N II, and Fe II), and high-ionization (Si III, Fe III, N v, and O vI) species for 11 galaxies. We derive the ionization parameter and ionization-corrected metallicity using cloudy photoionization models. The H i column density ranges from ~1013 to ~1020 cm-2 and decreases with impact parameter for r ≳ Re. Galaxies with higher stellar mass have weaker H I absorption. Comparing absorption velocities with MaNGA radial velocity maps of ionized gas line emissions in galactic disks, we find that the neutral gas seen in absorption corotates with the disk out to ~10 R e . Sight lines with lower elevation angles show lower metallicities, consistent with the metallicity gradient in the disk derived from MaNGA maps. Higher-elevation angle sight lines show higher ionization, lower H I column density, supersolar metallicity, and velocities consistent with the direction of galactic outflow. Our data offer the first detailed comparisons of circumgalactic medium (CGM) properties (kinematics and metallicity) with extrapolations of detailed galaxy maps from integral field spectroscopy; similar studies for larger samples are needed to more fully understand how galaxies interact with their CGM.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

ESCARGOT: Mapping Vertical Phase Spiral Characteristics Throughout the Real and Simulated Milky Way

Abstract The recent discovery of a spiral pattern in the vertical kinematic structure in the solar neighborhood provides a prime opportunity to study nonequilibrium dynamics in the Milky Way from local stellar kinematics. Furthermore, results from simulations indicate that even in a limited volume, differences in stellar orbital histories allow us to trace variations in the initial perturbation across large regions of the disk. We present ESCARGOT , a novel algorithm for studying these variations in both simulated and observed data sets. ESCARGOT automatically extracts key quantities from the structure of a given phase spiral, including the time since perturbation and the perturbation mode. We test ESCARGOT on simulated data and show that it is capable of accurately recovering information about the time since the perturbation occurred as well as subtle differences in phase spiral morphology due to stellar locations in the disk at the time of perturbation. We apply ESCARGOT to kinematic data from data release 3 of the Gaia mission in bins of guiding radius. We show that similar structural differences in morphology occur in the Gaia phase spirals as a function of stellar orbital history. These results indicate that the phase spirals are the product of a complex dynamical response in the disk with large-scale coupling between different regions of phase space.

Darragh-Ford, Elise (ORCID:0000000288005652)↗
DOE OSTI2024

Magnetic Flux Plays an Important Role during a Black Hole X-Ray Binary Outburst in Radiative Two-temperature General Relativistic Magnetohydrodynamic Simulations

Abstract Black hole (Bh) X-ray binaries cycle through different spectral states of accretion over the course of months to years. Although persistent changes in the Bh mass accretion rate are generally recognized as the most important component of state transitions, it is becoming increasingly evident that magnetic fields play a similarly important role. In this article, we present the first radiative two-temperature general relativistic magnetohydrodynamics simulations in which an accretion disk transitions from a quiescent state at an accretion rate of M ̇ ∼ 10 − 10 M ̇ Edd to a hard-intermediate state at an accretion rate of M ̇ ∼ 10 − 2 M ̇ Edd . This huge parameter space in mass accretion rate is bridged by artificially rescaling the gas density scale of the simulations. We present two jetted BH models with varying degrees of magnetic flux saturation. We demonstrate that in “standard and normal evolution” models, which are unsaturated with magnetic flux, the hot torus collapses into a thin and cold accretion disk when M ̇ ≳ 5 × 10 − 3 M ̇ Edd . On the other hand, in “magnetically arrested disk” models, which are fully saturated with vertical magnetic flux, the plasma remains mostly hot with substructures that condense into cold clumps of gas when M ̇ ≳ 1 × 10 − 2 M ̇ Edd . This suggests that the spectral signatures observed during state transitions are closely tied to the level of magnetic flux saturation.

Astronomy & Astrophysics↗
DOE OSTI2024

Energy-dependent and Energy-integrated Two-moment General-relativistic Neutrino Transport Simulations of a Hypermassive Neutron Star

Abstract We compare two-moment-based energy-dependent and three variants of energy-integrated neutrino transport general-relativistic magnetohydrodynamics simulations of a hypermassive neutron star. To study the impacts due to the choice of the neutrino transport schemes, we perform simulations with the same setups and input neutrino microphysics. We show that the main differences between energy-dependent and energy-integrated neutrino transport are found in the disk and ejecta properties, as well as in the neutrino signals. The properties of the disk surrounding the neutron star and the ejecta in energy-dependent transport are very different from the ones obtained using energy-integrated schemes. Specifically, in the energy-dependent case, the disk is more neutron-rich at early times and becomes geometrically thicker at later times. In addition, the ejecta is more massive and, on average, more neutron-rich in the energy-dependent simulations. Moreover, the average neutrino energies and luminosities are about 30% higher. Energy-dependent neutrino transport is necessary if one wants to better model the neutrino signals and matter outflows from neutron star merger remnants via numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

An Exceptionally Powerful, Radiatively Driven Ultrafast Outflow in the Rapidly Accreting AGN RE J1034+396

We report the analysis of ∼1 Ms of XMM-Newton observations of the rapidly accreting active galactic nucleus RE J1034+396. The 0.3–9 keV EPIC-pn spectra are well described by a model consisting of steep continuum emission from the corona accompanied by relativistically blurred reflection from a highly ionized accretion disk. The source is known to exhibit strong excess soft X-ray emission, which we show is well represented by thermal disk photons Comptonized by a warm plasma spanning the inner accretion flow. Additionally, the EPIC-pn data provide compelling evidence (ΔC ∼ 60 for four additional parameters) for the presence of an ultrafast outflow (UFO) with a line-of-sight velocity v/c = 0.307$^{+0.001}_{-0.005}$, and an emission signature consistent with reflection of the corona from modestly ionized, outflowing gas. The simultaneous 0.5–2.5 keV RGS spectra show clear absorption lines. Modelling of these data confirms the presence of the UFO and constrains its equivalent hydrogen column density, log N H /(atom cm −2 ) = 21.7$^{+0.1}_{-0.2}$. The RGS data also reveal at least two warm absorber components with a modest outflow velocity (1680$^{+40}_{-50}$ km s -1 ). The measured properties and time evolution of the UFO in RE J1034+396 suggest that it is formed from collisionally ionized plasma, launched from the disk surface and accelerated by radiation pressure. The high terminal velocity and substantial absorbing column density imply that the outflow carries sufficient momentum and energy to transform its environment, being capable of driving out essentially all dust and gas it interacts with along the line of sight, even if the AGN were initially surrounded by a Compton-thick absorber.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The QPO in RE J1034+396 Originates in the Hot Corona

RE J1034+396 is one of the few active galactic nuclei (AGNs) with a significant quasiperiodic oscillation (QPO). The QPO has been observed in over 1 Ms of XMM-Newton observations spanning over a decade. We investigate the power spectral density function (PSD) of seven long (∼90 ks) XMM-Newton observations of the AGN RE J1034+396 in two energy bands. The soft (0.3–0.5 keV) band targets emission from the disk, while the hard (2–7 keV) band isolates the primary X-ray continuum emission from the corona. The QPO is significantly detected in the hard band of five of the seven observations. The best-fitting models indicate that the QPO detection in both bands is entirely attributable to the coronal emission with no additional contribution from the disk. This explains the strong coherence between the hard and soft bands at the QPO frequency. The covariance spectrum is consistent with this picture as the variability at QPO frequencies is attributed solely to fluctuations in the hot corona. The time lag as a function of energy is well described by a ∼2000 s intrinsic soft lag, resulting from the disk responding to emission from the corona, that undergoes phase wrapping at approximately the QPO frequency. By demonstrating that in this system the QPO arises in the corona, we provide new insights into the mechanisms generating QPOs.

Active galactic nuclei↗
DOE OSTI2021

Onset of Plasmoid Reconnection during Magnetorotational Instability

The evolution of current sheets in accretion flows undergoing magnetorotational instability (MRI) is examined through two- and three-dimensional numerical modeling of the resistive MHD equations in global cylindrical geometry. With an initial uniform magnetic field aligned in the vertical (z) direction, MRI produces radially extended toroidal (azimuthal) current sheets. In both 2D and 3D when axisymmetric modes dominate, these current sheets attract each other and merge in the poloidal (rz) plane, driving magnetic reconnection when the Lundquist number S > 3 × 10 2 , making it a possible source of plasmoids (closed magnetic loops) in accretion disks. At high Lundquist numbers in the 2D regime, starting at S = 5 × 10 3 , self-consistent MRI-generated current sheets become thin and subject to plasmoid instability, and therefore spontaneous magnetic reconnection. When nonaxisymmetric 3D modes dominate, turbulence makes the azimuthal current sheets more unstable and stretch vertically. Toroidally extended vertical current sheets in the inner region, as well as larger 3D magnetic islands in the outer regions of the disks are also formed. These findings have strong ramifications for astrophysical disks as potential sources of plasmoids that could cause local heating, particle acceleration, and high energy EM radiation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

On the Jet–Ejecta Interaction in 3D GRMHD Simulations of a Binary Neutron Star Merger Aftermath

Short γ-ray burst (sGRB) jets form in the aftermath of a neutron star merger, drill through disk winds and dynamical ejecta, and extend over four to five orders of magnitude in distance before breaking out of the ejecta. We present the first 3D general-relativistic magnetohydrodynamic sGRB simulations to span this enormous scale separation. They feature three possible outcomes: jet+cocoon, cocoon, and neither. Typical sGRB jets break out of the dynamical ejecta if (i) the bound ejecta's isotropic equivalent mass along the pole at the time of the BH formation is ≲10 -4 M ⊙ , setting a limit on the delay time between the merger and BH formation, otherwise, the jets perish inside the ejecta and leave the jet-inflated cocoon to power a low-luminosity sGRB; (ii) the postmerger remnant disk contains a strong large-scale vertical magnetic field, ≳1015 G; and (iii) if the jets are weak (≲10 50 erg), the ejecta's isotropic equivalent mass along the pole must be small (≲10 -2 M ⊙ ). Generally, the jet structure is shaped by the early interaction with disk winds rather than the dynamical ejecta. As long as our jets break out of the ejecta, they retain a significant magnetization (≲1), suggesting that magnetic reconnection is a fundamental property of sGRB emission. The angular structure of the outflow isotropic equivalent energy after breakout consistently features a flat core followed by a steep power-law distribution (slope ≳3), similar to hydrodynamic jets. In the cocoon-only outcome, the dynamical ejecta broadens the outflow angular distribution and flattens it (slope ~1.5).

Jets↗
DOE OSTI2024

An Accreting Supermassive Black Hole Buried in a Faint Dwarf Galaxy

Abstract In the last decade, there have been several discoveries of active galactic nuclei (AGN) in dwarf galaxies including an AGN in an ultracompact dwarf galaxy with a black hole mass >10 6 M ⊙ . However, finding a supermassive black hole (SMBH) in a dwarf low surface brightness (LSB) galaxy is rare. We report the discovery of a Seyfert type 2 class AGN that is associated with a nuclear SMBH of mass ∼6.5 × 10 6 M ⊙ in a dwarf LSB galaxy (μ 0,r > 23.8 mag arcsec −2 ) that we denote by MJ0818+2257. The galaxy was previously thought to be an outlying emission blob around the large spiral galaxy LEDA 1678924. In our current analysis, which includes the detection of the optical counterpart of MJ0818+2257, we study its ionized gas kinematics and find that the dynamical mass within the ionized gas disk is ∼5.3 × 10 9 M ⊙ . This is comparable to its stellar mass, which is ∼3 × 10 9 M ⊙ , and suggests that MJ0818+2257 is moderately dark matter dominated within the stellar disk. The SMBH-mass-to-galaxy-stellar-mass ratio isM BH /M(*) > 0.022, which is high compared to disk galaxies. Our detection of an SMBH in a bulgeless LSB dwarf galaxy raises questions about the growth of SMBHs in low-luminosity galaxies and suggests the possibility of detecting heavy seed black holes from early epochs in LSB dwarf galaxies in the low-redshift Universe.

Astronomy & Astrophysics↗
DOE OSTI2021

Angled slit design for computed tomographic imaging of electron beams

Computed tomographic method and apparatus includes an electron or ion beam having a beam axis, a refractory metal disk; at least one slit in the refractory metal disk that receive the beam, wherein the slit is at an angle to the beam axis; a beam entrance opening in the slit that allows the beam to enter; an effective beam exit opening in the slit that allow the beam to exit, wherein the beam effective exit opening is smaller than the beam entrance opening; and a system for moving the beam across the refractory metal disk, wherein the beam enters the slit through the beam entrance opening and exits the slit through the effective beam exit opening; and a computed tomographic device for measuring the beam that enters and exits the slit for analyzing the beam.

Elmer, John W.↗
DOE OSTI2023

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

An In-Depth Exploration of the Electrochemical Oxygen Reduction Reaction (ORR) Phenomenon on Carbon-Based Catalysts in Alkaline and Acidic Mediums

Detailed studies of the electrochemical oxygen reduction reaction (ORR) on catalyst materials are crucial to improving the performance of different electrochemical energy conversion and storage systems (e.g., fuel cells and batteries), as well as numerous chemical synthesis processes. In the effort to reduce the loading of expensive platinum group metal (PGM)-based catalysts for ORR in the electrochemical systems, many carbon-based catalysts have already shown promising results and numerous investigations on those catalysts are in progress. Most of these studies show the catalyst materials’ ORR performance as current density data obtained through the rotating disk electrode (RDE), rotating ring-disk electrode (RRDE) experiments taking cyclic voltammograms (CV) or linear sweep voltammograms (LSV) approaches. However, the provided descriptions or interpretations of those data curves are often ambiguous and recondite which can lead to an erroneous understanding of the ORR phenomenon in those specific systems and inaccurate characterization of the catalyst materials. In this paper, we presented a study of ORR on a newly developed carbon-based catalyst, the nitrogen-doped graphene/metal-organic framework (N-G/MOF), through RDE and RRDE experiments in both alkaline and acidic mediums, taking the LSV approach. The functions and crucial considerations for the different parts of the RDE/RRDE experiment such as the working electrode, reference electrode, counter electrode, electrolyte, and overall RDE/RRDE process are delineated which can serve as guidelines for the new researchers in this field. Experimentally obtained LSV curves’ shapes and their correlations with the possible ORR reaction pathways within the applied potential range are discussed in depth. We also demonstrated how the presence of hydrogen peroxide (H2O2), a possible intermediate of ORR, in the alkaline electrolyte and the concentration of acid in the acidic electrolyte can maneuver the ORR current density output in compliance with the possible ORR pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A Rotation Rate for the Planetary-mass Companion DH Tau b

DH Tau b is a young planetary-mass companion orbiting at a projected separation of 320 au from its ∼2 Myr old host star DH Tau. With an estimated mass of 8–22 M{sub Jup} this object straddles the deuterium-burning limit, and might have formed via core or pebble accretion, disk instability, or molecular cloud fragmentation. To shed light on the formation history of DH Tau b, we obtain the first measurement of rotational line broadening for this object using high-resolution (R ∼ 25,000) near-infrared spectroscopy from Keck/NIRSPEC. We measure a projected rotational velocity (v sin i) of 9.6 ± 0.7 km s{sup −1}, corresponding to a rotation rate that is between 9% and 15% of DH Tau b’s predicted breakup speed. This low rotation rate is in good agreement with scenarios in which magnetic coupling between the companion and its circumplanetary disk during the late stages of accretion reduces angular momentum and regulates spin. We compare the rotation rate of DH Tau b to published values for other planetary-mass objects with masses between 0.3 and 20 M{sub Jup} and find no evidence of a correlation between mass and rotation rate in this mass regime. Finally, we search for evidence of individual molecules in DH Tau b’s spectrum and find that it is dominated by CO and H{sub 2}O, with no evidence of the presence of CH{sub 4}. This agrees with expectations given DH Tau b’s relatively high effective temperature (∼2300 K).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A Comparison of Properties of Quasars with and without Rapid Broad Absorption Line Variability

We investigate the correlation between rest-frame UV flux variability of broad absorption line (BAL) quasars and their variability in BAL equivalent widths (EWs) in a various timescale from <10 days to a few years in the quasar rest frame. We use the data sets of BAL EWs taken by the Sloan Digital Sky Survey Reverberation Mapping project and photometric data taken by the intermediate Palomar Transient Factory in the g and R bands and the Panoramic Survey Telescope and Rapid Response System in grizy bands. Our results are summarized as follows: (1) the distributions of flux variability versus BAL variability show weak, moderate, or a strong positive correlation; (2) there is no significant difference in flux variability amplitudes between BAL quasars with significant short timescale EW variability (called class S1) and without (class S2); (3) in all timescales considered in this paper, the class S1 quasars show systematically larger BAL variability amplitudes than those of the class S2 quasars; and (4) there are possible correlations between BAL variability and physical parameters of the quasars such as black hole masses (moderate positive), Eddington ratios, and accretion disk temperature (strong negative) in the class S2 quasars. These results indicate that the BAL variability requires changing in the ionizing continuum and an ancillary mechanism such as variability in X-ray shielding gas located at the innermost region of an accretion disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Lithium in T Coronae Borealis

T Coronae Borealis is a recurrent, symbiotic nova system currently in quiescence between its periodic ≈80 yr cycle of eruptions. Observations during inter-outburst epochs provide an opportunity to study properties of the accretion disk and the M red giant. Here we present new irradiated (blackbody veiling) models, incorporating modern molecular opacities and line lists, of spectra derived from high-resolution (22,000 ≲ R ≲ 120,000) optical echelle observations obtained at two epochs, one prior to and one post the 2015 rebrightening event at similar spectroscopic system phase. We find a lithium abundance in the secondary at both epochs to be comparable. The non-irradiated (classical) model atmospheres yield a lithium abundance, A(Li) = 1.3 ± 0.1. The irradiated model (veiled) atmospheres, which are likely a better representation of the system in which the white dwarf and accretion disk illuminate the red giant, give A(Li) = 2.4 ± 0.1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Confrontation of Observation and Theory: High-frequency QPOs in X-Ray Binaries, Tidal Disruption Events, and Active Galactic Nuclei

In this paper, we compile observations of high-frequency quasi-periodic oscillations (QPOs) around black holes, both stellar and supermassive, and compare their positions in the parameter space of black hole mass, spin, and oscillation frequency. We find that supermassive black holes occupy a separate region of parameter space than stellar, and further, that QPOs seen around tidal disruption events rather than Seyfert-type active galactic nuclei (AGN) occupy an entirely different space. We then compare these results to the orbital resonance, diskoseismic, warped disk, and disk–jet coupling theoretical models for the origin of high-frequency QPOs. We find that while oscillations around stellar mass black holes are generally consistent with the above models, supermassive black holes are decidedly not. Oscillations seen in tidal disruption events are consistent with oscillations near the frequency of the innermost stable circular orbit, while QPOs in AGN are not accounted for by any of the physical models in consideration. This indicates that despite the scale invariance of accretion processes implied by a decades-wide correlation between QPO frequency and black hole mass, any theory of high-frequency QPOs must relate the frequency to more than just the mass and spin.

79 ASTRONOMY AND ASTROPHYSICS↗