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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Origin of spin–orbit misalignments: the microblazar V4641 Sgr

ABSTRACT Of the known microquasars, V4641 Sgr boasts the most severe lower limit (>52°) on the misalignment angle between the relativistic jet axis and the binary orbital angular momentum. Assuming the jet and black hole spin axes coincide, we attempt to explain the origin of this extreme spin–orbit misalignment with a natal kick model, whereby an aligned binary system becomes misaligned by a supernova kick imparted to the newborn black hole. The model inputs are the kick velocity distribution, which we measure customized to V4641 Sgr, and the immediate pre/post-supernova binary system parameters. Using a grid of binary stellar evolution models, we determine post-supernova configurations that evolve to become consistent with V4641 Sgr today and obtain the corresponding pre-supernova configurations by using standard prescriptions for common envelope evolution. Using each of these potential progenitor system parameter sets as inputs, we find that a natal kick struggles to explain the origin of the V4641 Sgr spin–orbit misalignment. Consequently, we conclude that evolutionary pathways involving a standard common envelope phase followed by a supernova kick are highly unlikely for V4641 Sgr. An alternative interpretation is that the jet axis does not reliably trace the black hole spin axis. Our results raise concerns about compact object merger statistics gleaned from binary population synthesis models, which rely on unverified prescriptions for common envelope evolution and natal kicks. We also challenge the spin–orbit alignment assumption routinely invoked to measure black hole spin magnitudes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The ‘Giraffe’: discovery of a stripped red giant in an interacting binary with an ∼2 M ⊙ lower giant

We report the discovery of a stripped giant + lower giant Algol-type binary, 2M04123153+6738486 (2M0412), identified during a search for non-interacting compact object – star binaries. 2M0412 is an evolved ( T eff, giant ≃ 4000 K), luminous ( L giant ≃ 150 L ⊙ ) red giant in a circular P = 81.2 d binary. 2M0412 is a known variable star previously classified as a semiregular variable. The cross-correlation functions of follow-up Keck/HIRES and LBT/Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) spectra show an radial velocity variable second component with implied mass ratio q = M giant / M comp ≃ 0.20 ± 0.01. The All-Sky Automated Survey for SuperNovae (ASAS-SN), Asteroid Terrestrial-impact Last Alert System (ATLAS), Transiting Exoplanet Survey Telescope ( TESS ), and Zwicky Transient Facility (ZTF) light curves show that the giant is a Roche lobe filling ellipsoidal variable with an inclination of 49.4 ± 0.3°, and a giant mass of M giant = 0.38 ± 0.01 M ⊙ for a distance of ≃ 3.7 kpc. The mass of the giant indicates that its envelope has been partially stripped. The giant companion on the lower red giant branch has a mass of M comp = 1.91 ± 0.03 M ⊙ with T eff, comp ≃ 5000 K, L comp ≃ 60 L ⊙ , and R comp ≃ 11 R ⊙ . The lower giant contributes ${\sim }35{{\ \rm per\ cent}}$ of the flux in the V band. We also identify an orbital phase dependent, broad $\rm H\,\alpha$ emission line which could indicate ongoing accretion from the stripped red giant on to the companion.

(stars:) binaries: spectroscopic↗
DOE OSTI2022

Kicks and induced spins of neutron stars at birth

ABSTRACT Using simulations of non-rotating supernova progenitors, we explore the kicks imparted to and the spins induced in the compact objects birthed in core collapse. We find that the recoil due to neutrino emissions can be a factor affecting core recoil, comparable to and at times larger than the corresponding kick due to matter recoil. This result would necessitate a revision of the general model of the origin of pulsar proper motions. In addition, we find that the sign of the net neutrino momentum can be opposite to the sign of the corresponding matter recoil. As a result, at times the pulsar recoil and ejecta can be in the same direction. Moreover, our results suggest that the duration of the dipole in the neutrino emissions can be shorter than the duration of the radiation of the neutron-star binding energy. This allows a larger dipole asymmetry to arise, but for a shorter time, resulting in kicks in the observed pulsar range. Furthermore, we find that the spin induced by the aspherical accretion of matter can leave the residues of collapse with spin periods comparable to those inferred for radio pulsars and that there seems to be a slight anticorrelation between the direction of the induced spin and the net kick direction. This could explain such a correlation among observed radio pulsars. Finally, we find that the kicks imparted to black holes are due to the neutrino recoil alone, resulting in birth kicks ≤100 km s−1 most of the time.

Astronomy & Astrophysics↗
DOE OSTI2022

Gamma-ray observations of MAXI J1820+070 during the 2018 outburst

ABSTRACT MAXI J1820+070 is a low-mass X-ray binary with a black hole (BH) as a compact object. This binary underwent an exceptionally bright X-ray outburst from 2018 March to October, showing evidence of a non-thermal particle population through its radio emission during this whole period. The combined results of 59.5 h of observations of the MAXI J1820+070 outburst with the H.E.S.S., MAGIC and VERITAS experiments at energies above 200 GeV are presented, together with Fermi-LAT data between 0.1 and 500 GeV, and multiwavelength observations from radio to X-rays. Gamma-ray emission is not detected from MAXI J1820+070, but the obtained upper limits and the multiwavelength data allow us to put meaningful constraints on the source properties under reasonable assumptions regarding the non-thermal particle population and the jet synchrotron spectrum. In particular, it is possible to show that, if a high-energy (HE) gamma-ray emitting region is present during the hard state of the source, its predicted flux should be at most a factor of 20 below the obtained Fermi-LAT upper limits, and closer to them for magnetic fields significantly below equipartition. During the state transitions, under the plausible assumption that electrons are accelerated up to ∼500 GeV, the multiwavelength data and the gamma-ray upper limits lead consistently to the conclusion that a potential HE and very-HE gamma-ray emitting region should be located at a distance from the BH ranging between 1011 and 1013 cm. Similar outbursts from low-mass X-ray binaries might be detectable in the near future with upcoming instruments such as CTA.

Astronomy & Astrophysics↗
DOE OSTI2023

Dynamics of a relativistic jet through magnetized media

The merger of two neutron stars (NSs) produces the emission of gravitational waves, the formation of a compact object surrounded by a dense and magnetized environment. If the binary undergoes delayed collapse a collimated and relativistic jet, which will eventually produce a short gamma-ray burst (SGRB), may be launched. The interaction of the jet with the environment has been shown to play a major role in shaping the structure of the outflow that eventually powers the gamma-ray emission. In this paper, we present a set of 2.5D RMHD simulations that follow the evolution of a relativistic non-magnetized jet through a medium with different magnetization levels, as produced after the merger of two NSs. We find that the predominant consequence of a magnetized ambient medium is that of suppressing instabilities within the jet and preventing the formation of a series of collimation shocks. One implication of this is that internal shocks lose efficiency, causing bursts with low-luminosity prompt emission. On the other hand, the jet-head velocity and the induced magnetization within the jet are fairly independent of the magnetization of the ambient medium. Future numerical studies with a larger domain are necessary to obtain light curves and spectra in order to better understand the role of magnetized media.

(magnetohydrodynamics) MHD↗
DOE OSTI2023

Tree-based solvers for adaptive mesh refinement code $\scriptsize{FLASH}$ – IV. An X-ray radiation scheme to couple discrete and diffuse X-ray emission sources to the thermochemistry of the interstellar medium

X-ray radiation, in particular radiation between 0.1 and 10 keV, is evident from both point-like sources, such as compact objects and T-Tauri young stellar objects, and extended emission from hot, cooling gas, such as in supernova remnants. The X-ray radiation is absorbed by nearby gas, providing a source of both heating and ionization. While protoplanetary chemistry models now often include X-ray emission from the central young stellar object, simulations of star-forming regions have yet to include X-ray emission coupled to the chemo-dynamical evolution of the gas. We present an extension of the $\scriptsize{TREERAY}$ reverse ray trace algorithm implemented in the flash magnetohydrodynamic code which enables the inclusion of X-ray radiation from 0.1 keV < E γ < 100 keV, dubbed $\scriptsize{XRAYTHESPOT}$. $\scriptsize{XRAYTHESPOT}$ allows for the use of an arbitrary number of bins, minimum and maximum energies, and both temperature-independent and temperature-dependent user-defined cross-sections, along with the ability to include both point and extended diffuse emission and is coupled to the thermochemical evolution. We demonstrate the method with several multibin benchmarks testing the radiation transfer solution and coupling to the thermochemistry. Finally, we show two example star formation science cases for this module: X-ray emission from protostellar accretion irradiating an accretion disc and simulations of molecular clouds with active chemistry, radiation pressure, and protostellar radiation feedback from infrared to X-ray radiation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Benchmark of the Fe xvv 𝓡 ratio in photoionized plasma during eclipse of Centaurus X-3 with XRISM/Resolve

The $\mathcal {R}$ ratio is a useful diagnostic of the X-ray emitting astrophysical plasmas and is defined as the intensity ratio of the forbidden over the inter-combination lines in the K$\alpha$ line complex of He-like ions. The value is altered by excitation processes (electron impact or UV photoexcitation) from the metastable upper level of the forbidden line, thereby constraining the electron density or UV field intensity. The diagnostic has been applied mostly in electron density constraints in collisionally ionized plasmas using low-Z elements, as was originally proposed for the Sun (Gabriel & Jordan, 1969a, MNRAS, 145, 241), but it can also be used in photoionized plasmas. To make use of this diagnostic, we need to know its value in the limit of no excitation of metastables ($\mathcal {R}_{0}$), which depends on the element, how the plasmas are formed, how the lines are propagated, and the spectral resolution affecting line blending principally with satellite lines from Li-like ions. We benchmark $\mathcal {R}_0$ for photoionized plasmas by comparing calculations using radiative transfer codes and observation data taken with the Resolve X-ray microcalorimeter onboard XRISM. We use the Fe xxv He$\alpha$ line complex of the photo-ionized plasma in Centaurus X-3 observed during eclipse, in which the plasma is expected to be in the limit of no metastable excitation. The measured $\mathcal {R} = 0.65 \pm 0.08$ is consistent with the value calculated using xstar for the plasma parameters derived from other line ratios of the spectrum. We conclude that the $\mathcal {R}$ ratio diagnostic can be used for high-Z elements such as Fe in photoionized plasmas, which has wide applications in plasmas around compact objects at various scales.

X-rays: binaries↗
DOE OSTI2025

Neutron stars with exceptionally light QCD axions

We present a comprehensive study of axion condensed neutron stars that arise in models of an exceptionally light axion that couples to quantum chromodynamics (QCD). These axions solve the strong-charge-parity (𝐶⁢𝑃) problem, but have a mass-squared lighter than that due to QCD by a factor of 𝜖 < 1. Inside dense matter, the axion potential is altered, and much of the matter in neutron stars resides in the axion condensed phase where the strong-𝐶⁢𝑃 parameter 𝜃 = 𝜋 and 𝐶⁢𝑃 remains a good symmetry. In these regions, masses and interactions of nucleons are modified, in turn changing the equation of state (EOS), structure, and phenomenology of the neutron stars. We take the first steps toward the study of the EOS of neutron star matter at 𝜃 = 𝜋 within chiral effective field theory and use relativistic mean field theory to deduce the resulting changes to nuclear matter and the neutron star low-density EOS. We derive constraints on the exceptionally light axion parameter space based on observations of the thermal relaxation of accreting neutron stars, isolated neutron star cooling, and pulsar glitches, excluding the region up to 5 ×10 −7 ≲ 𝜖 ≲ 0.2 for 𝑚 𝑎 ≳ 2 × 10 −9 eV. We comment on potential changes to the neutron star mass-radius relationship, and discuss the possibility of novel, nuclear-density compact objects with 𝜃 = 𝜋 that are stabilized not by gravity but by the axion potential.

axions↗
DOE OSTI2025

Assessing the impact of uniform rotation on the structure of neutron stars

Driven by recent laboratory experiments and astronomical observations, significant advances have deepened our understanding of neutron-star physics. NICER's Pulse Profile Modeling has refined our knowledge of neutron star masses and radii, while gravitational-wave detections have revealed key insights into the structure of neutron stars. Particularly relevant is the extraction of the tidal deformability by the LIGO-Virgo collaboration and the most recent determination of stellar radii by NICER, both suggesting a relatively soft equation of state (EOS) at intermediate densities. Additionally, measurements from the PREX collaboration and from pulsar timing suggest instead that the EOS is stiff in the vicinity of saturation density and at the highest densities accessible to date. But how stiff can the EOS be at these very high densities? Recent events featuring compact objects near the “lower mass gap” have raised questions about the existence of very massive neutron stars. Motivated by this finding and in light of new refinements to theoretical models, we explore the possibility that these massive objects may indeed be rapidly rotating neutron stars. Here, we explore how rotation affects both the maximum neutron star mass and their associated radii, and discuss the implications they may have on the equation of state.

Equations of state of nuclear matter↗
DOE OSTI2020

Direct astrophysical tests of chiral effective field theory at supranuclear densities

Recent observations of neutron stars with gravitational waves and X-ray timing provide unprecedented access to the equation of state (EoS) of cold dense matter at densities difficult to realize in terrestrial experiments. At the same time, predictions for the EoS equipped with reliable uncertainty estimates from chiral effective field theory ( x EFT) allow us to bound our theoretical ignorance. In this work, we analyze astrophysical data using a nonparametric representation of the neutron-star EoS conditioned on x EFT to directly constrain the underlying physical properties of the compact objects without introducing modeling systematics. We discuss how the data alone constrain the EoS at high densities when we condition on x EFT at low densities. Here, we also demonstrate how to exploit astrophysical data to directly test the predictions of x EFT for the EoS up to twice nuclear saturation density, in order to estimate the density at which these predictions might break down. We nd that the existence of massive pulsars, gravitational waves from GW170817, and NICER observations of PSR J0030+0451 favor x EFT predictions for the EoS up to nuclear saturation density over a more agnostic analysis by as much as a factor of 7 for the quantum Monte Carlo (QMC) calculations used in this work. While x EFT predictions using QMC are fully consistent with gravitational-wave data up to twice nuclear saturation density, NICER observations suggest that the EoS stiffens relative to these predictions at or slightly above nuclear saturation density. Additionally, for these QMC calculations, we marginalize over the uncertainty in the density at which x EFT begins to break down, constraining the radius of a 1.4M $\bigodot$ neutron star to R 1.4 = $11.40^{+1.38}_{–1.04}$ ($12.54^{+0.71}_{–0.63}$) km and the pressure at twice nuclear saturation density to p(2n sat ) = $14.2^{+18.1}_{–8.4}$ ($28.7^{+15.3}_{–15.0}$) MeV=fm 3 with massive pulsar and gravitational-wave (and NICER) data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Limiting masses and radii of neutron stars and their implications

We combine the equation of state of dense matter up to twice nuclear saturation density 𝑛 sat obtained using chiral effective field theory (𝜒⁢EFT) and recent observations of neutron stars to gain insights about the high-density matter encountered in their cores. A key element in our study is the recent Bayesian analysis of correlated EFT truncation errors based on order-by-order calculations up to next-to-next-to-next-to-leading order in the 𝜒⁢EFT expansion. We refine the bounds on the maximum mass imposed by causality at high densities and provide stringent limits on the maximum and minimum radii of ∼1.4M ⊙ and ∼2.0M ⊙ stars. Including 𝜒⁢EFT predictions from 𝑛sat to 2𝑛 sat reduces the permitted ranges of the radius of a ~1.4M ⊙ star, 𝑅 1.4 , by ∼3.5km. If observations indicate 𝑅 1.4 < 11.2km, then our study implies that either the squared speed of sound 𝑐$^{2}_{𝑠}$ > 1/2 for densities above 2𝑛 sat or that 𝜒⁢EFT breaks down below 2𝑛 sat . Here, we also comment on the nature of the secondary compact object in GW190814 with mass ≃ 2.6M ⊙ and discuss the implications of massive neutron stars > 2.1⁢M ⊙ ⁡(2.6M ⊙ ) in future radio and gravitational-wave searches. Some form of strongly interacting matter with 𝑐$^{2}_{𝑠}$ > 0.35⁢(0.55) must be realized in the cores of such massive neutron stars. In the absence of phase transitions below 2𝑛 sat , the small tidal deformability inferred from GW170817 lends support for the relatively small pressure predicted by 𝜒⁢EFT for the baryon density 𝑛 B in the range 1–2𝑛 sat . Together they imply that the rapid stiffening required to support a high maximum mass should occur only when 𝑛 B ≳ 1.5–1.8 𝑛 sat .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Radius and equation of state constraints from massive neutron stars and GW190814

Motivated by the unknown nature of the 2.50–2.67M⊙ compact object in the binary merger event GW190814, we study the maximum neutron star mass based on constraints from low-energy nuclear physics, neutron star tidal deformabilities from GW170817, and simultaneous mass-radius measurements of PSR J0030+045 from NICER. Our prior distribution is based on a combination of nuclear modeling valid in the vicinity of normal nuclear densities together with the assumption of a maximally stiff equation of state at high densities, a choice that enables us to probe the connection between observed heavy neutron stars and the transition density at which conventional nuclear physics models must break down. Here we demonstrate that a modification of the highly uncertain suprasaturation density equation of state beyond 2.64 times normal nuclear density is required in order for chiral effective field theory models to be consistent with current neutron star observations and the existence of 2.6M⊙ neutron stars. We also show that the existence of very massive neutron stars strongly impacts the radii of ≈ 2.0M⊙ neutron stars (but not necessarily the radii of 1.4 M⊙ neutron stars), which further motivates future NICER radius measurements of PSR J1614 – 2230 and PSR J0740+6620.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions

Weak interaction charged current transition strengths from highly excited nuclear states are fundamental ingredients for accurate modeling of compact object composition and dynamics, but are difficult to obtain either from experiment or theory. For lack of alternatives, calculations have often fallen back upon a generalized Brink-Axel hypothesis, that is, assuming the strength function (transition probability) is independent of the initial nuclear state but depends only upon the transition energy and the weak interaction properties of the parent nucleus ground state. Here we present numerical evidence for a modified “local” Brink-Axel hypothesis for Gamow-Teller transitions for pf-shell nuclei relevant to astrophysical applications. Specifically, while the original Brink-Axel hypothesis does not hold globally, strength functions from initial states nearby in energy are similar within statistical fluctuations. This agrees with previous work on strength function moments. Using this modified hypothesis, we can tackle strength functions at previously intractable initial energies, using semiconverged initial states at arbitrary excitation energy. Our work provides a well-founded method for computing accurate thermal weak transition rates for medium-mass nuclei at temperatures occurring in stellar cores near collapse. We finish by comparing results to previous calculations of astrophysical rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Chiral effective field theory calculation of neutrino reactions in warm neutron-rich matter

Neutrino scattering and absorption rates of relevance to supernovae and neutron star mergers are obtained from nuclear matter dynamical structure functions that encode many-body effects from nuclear mean fields and correlations. In this study, we employ nuclear interactions from chiral effective field theory to calculate the density, spin, isospin, and spin-isospin response functions of warm β-equilibrium nuclear matter. We include corrections to the single-particle energies in the mean field approximation as well as vertex corrections resummed in the random phase approximation (RPA), including both direct and exchange diagrams. We find that correlations included through the RPA redistribute the strength of the response to higher energy for neutrino absorption and lower energy for antineutrino absorption. This tends to suppress the absorption rate of electron neutrinos across all relevant energy scales. In contrast, the inclusion of RPA correlations enhances the electron antineutrino absorption rate at low energy and suppresses the rate at high energy. These effects are especially important at high-density and in the vicinity of the neutrino decoupling region. Implications for heavy element nucleosynthesis, electromagnetic signatures of compact object mergers, supernova dynamics, and neutrino detection from galactic supernovae are discussed briefly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Updated constraints on asteroid-mass primordial black holes as dark matter

Microlensing of stars places significant constraints on subplanetary-mass compact objects, including primordial black holes, as dark matter candidates. As the lens’ Einstein radius in the source plane becomes comparable to the size of the light source, however, source amplification is strongly suppressed, making it challenging to constrain lenses with a mass at or below 10 –10 solar masses, i.e., asteroid-mass objects. Current constraints, using Subaru Hyper Suprime Cam (HSC) observations of M31, assume a fixed source size of one solar radius. However, the actual stars in M31 bright enough to be used for microlensing are typically much larger. We correct the HSC constraints by constructing a source size distribution based on the M31 PHAT survey and on a synthetic stellar catalog and by correspondingly weighting the finite-size source effects. In this work, we find that the actual HSC constraints are weaker by up to almost 3 orders of magnitude in some cases, broadening the range of masses for which primordial black holes can be the totality of the cosmological dark matter by almost 1 order of magnitude.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Reconsidering astrophysical constraints on macroscopic dark matter

Macroscopic dark matter—“macros”—refers to a broad class of alternative candidates to particle dark matter with still unprobed regions of parameter space. These candidates would transfer energy primarily through elastic scattering with approximately their geometric cross section. For sufficiently large cross sections, the linear energy deposition could produce observable signals if a macro were to pass through compact objects such as white dwarfs or neutron stars in the form of thermonuclear runaway, leading to a type Ia supernova or superburst, respectively. Here, we update the constraints from white dwarfs. These are weaker than previously inferred in important respects because of more careful treatment of the passage of a macro through the white dwarf and greater conservatism regarding the size of the region that must be heated to initiate runaway. On the other hand, we place more stringent constraints on macros at a low cross section, using new data from the Montreal White Dwarf Database. New constraints are inferred from the low mass x-ray binary 4U 1820-30, in which more than a decade passed between successive superbursts. Updated microlensing constraints are also reported.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Estimates for disk and ejecta masses produced in compact binary mergers

There is irresistible observational evidence that binary systems of compact objects with at least one neutron star are progenitors of short gamma-ray bursts, as well as a production site for r -process elements, at least when some matter is ejected by the merger and an accretion disk is formed. Here, the recent observations of gravitational waves in conjunction with electromagnetic counterparts fuel the need for models predicting the outcome of a given merger and the properties of the associated matter outflows as a function of the initial parameters of the binary. In this manuscript, we provide updated fitting formulas that estimate the disk mass for double neutron star binaries and ejecta masses for black hole–neutron star and double neutron star binaries, fitted to the results of numerical simulations. Our proposed fitting formulas improve on existing models by aiming for analytical simplicity, by covering a larger region of parameter space, and by accounting for regions of parameter space not covered by numerical simulations but with physically manifest merger outcomes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Inference offers a metric to constrain dynamical models of neutrino flavor transformation

The multimessenger astrophysics of compact objects presents a vast range of environments where neutrino flavor transformation may occur and may be important for nucleosynthesis, dynamics, and a detected neutrino signal. Development of efficient techniques for surveying flavor evolution solution spaces in these diverse environments, which augment and complement existing sophisticated computational tools, could leverage progress in this field. To this end we continue our exploration of statistical data assimilation (SDA) to identify solutions to a small-scale model of neutrino flavor transformation. SDA is a machine learning formula wherein a dynamical model is assumed to generate any measured quantities. Specifically, we use an optimization formulation of SDA wherein a cost function is extremized via the variational method. Regions of state space in which the extremization identifies the global minimum of the cost function will correspond to parameter regimes in which a model solution can exist. Our example study seeks to infer the flavor transformation histories of two monoenergetic neutrino beams coherently interacting with each other and with a matter background. We require that the solution be consistent with measured neutrino flavor fluxes at the point of detection, and with constraints placed upon the flavor content at various locations along their trajectories, such as the point of emission, and the locations of the Mikheyev-Smirnov-Wolfenstein resonances. We show how the procedure efficiently identifies solution regimes and rules out regimes where solutions are infeasible. Overall, results in this work intimate the promise of this “variational annealing” methodology to efficiently probe an array of fundamental questions that traditional numerical simulation codes render difficult to access.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗