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Critical problems of energy frontier Muon Colliders: optics, magnets and radiation

This White Paper brings together our previous studies on a Muon Collider (MC) and presents a design concept of the 6 TeV MC optics, the superconducting (SC) magnets, and a preliminary analysis of the protection system to reduce magnet radiation loads as well as particle backgrounds in the detector. The SC magnets and detector protection considerations impose strict limitations on the lattice choice, hence the design of the collider optics, magnets and Machine Detector Interface (MDI) are closely intertwined. As a first approximation we use the Interaction Region (IR) design with beta-star=3 mm, whereas for the arcs we re-scale the arc cell design of the 3 TeV MC. Traditional cos-theta coil geometry and Nb3Sn superconductor were used to provide field maps for the analysis and optimization of the arc lattice and IR design, as well as for studies of beam dynamics and magnet protection against radiation. The stress management in the coil will be needed to avoid large degradation or even damage of the brittle SC coils. In the assumed IR designs, the dipoles close to the Interaction Point (IP) and tungsten masks in each IR (to protect magnets) help reducing background particle fluxes in the detector by a substantial factor. The tungsten nozzles in the 6 to 600 cm region from the IP, assisted by the detector solenoid field, trap most of the decay electrons created close to the IP as well as most of the incoherent electron-positron pairs generated in the IP. With sophisticated tungsten, iron, concrete and borated polyethylene shielding in the MDI region, the total reduction of background loads by more than three orders of magnitude can be achieved.

43 PARTICLE ACCELERATORS↗

THE WISE LIGHT CURVES OF POLARS

We have extracted the WISE (Wide-field Infrared Survey Explorer) single-exposure data for a sample of 72 polars, which are highly magnetic cataclysmic variables (CVs). We combine these data with both published and unpublished optical and infrared data to explore the origins of the large amplitude variations seen in these systems. In nearly every case, we find evidence for cyclotron emission in the WISE bandpasses. We find that the derived magnetic field strengths for some polars are either too high, or cyclotron emission from lower field components, located spatially coincident to the main accreting poles, must be occurring. We have also estimated field strengths for a number of polars where no such values exist. In addition, contrary to expectations, we find that emission from the fundamental cyclotron harmonic (n = 1) appears to be nearly always present when the magnetic field is of the appropriate strength that it falls within a WISE bandpass. We find that the light curves for RBS 490, an ultrashort-period (46 minutes) CV, suggest that it is a polar. Modeling its spectrum indicates that its donor star is much hotter than expected. Nearly all of the detected polars show 11.5 μm (“W3 band”) excesses. The general lack of variability seen in the W3 bandpass light curves for higher-field polars demonstrates that these excesses are probably not due to cyclotron emission. There is circumstantial evidence that these excesses can be attributed to bremsstrahlung emission from their accretion streams. Reduction of the Spitzer 24 μm image of V1500 Cyg shows that it appears to be located at the center of a small nebula.

79 ASTRONOMY AND ASTROPHYSICS↗

FAR-ULTRAVIOLET SPECTROSCOPY OF THE NOVA-LIKE VARIABLE KQ MONOCEROTIS: A NEW SW SEXTANTIS STAR?

New optical spectra obtained with the SMARTS 1.5 m telescope and archival International Ultraviolet Explorer (IUE) far-ultraviolet (FUV) spectra of the nova-like variable KQ Mon are discussed. The optical spectra reveal Balmer lines in absorption as well as He I absorption superposed on a blue continuum. The 2011 optical spectrum is similar to the KPNO 2.1 m IIDS spectrum we obtained 33 years earlier except that the Balmer and He I absorption is stronger in 2011. Far-ultraviolet IUE spectra reveal deep absorption lines due to C II, Si III, Si IV, C IV, and He II, but no P Cygni profiles indicative of wind outflow. We present the results of the first synthetic spectral analysis of the IUE archival spectra of KQ Mon with realistic optically thick, steady-state, viscous accretion-disk models with vertical structure and high-gravity photosphere models. We find that the photosphere of the white dwarf (WD) contributes very little FUV flux to the spectrum and is overwhelmed by the accretion light of a steady disk. Disk models corresponding to a WD mass of {approx}0.6 M {sub Sun }, with an accretion rate of order 10{sup -9} M {sub Sun} yr{sup -1} and disk inclinations between 60 Degree-Sign and 75 Degree-Sign , yield distances from the normalization in the range of 144-165 pc. KQ Mon is discussed with respect to other nova-like variables. Its spectroscopic similarity to the FUV spectra of three definite SW Sex stars suggests that it is likely a member of the SW Sex class and lends support to the possibility that the WD is magnetic.

79 ASTRONOMY AND ASTROPHYSICS↗

EVIDENCE FOR CLUSTER TO CLUSTER VARIATIONS IN LOW-MASS STELLAR ROTATIONAL EVOLUTION

The concordance model for angular momentum evolution postulates that star-forming regions and clusters are an evolutionary sequence that can be modeled with assumptions about protostar–disk coupling, angular momentum loss from magnetized winds that saturates in a mass-dependent fashion at high rotation rates, and core-envelope decoupling for solar analogs. We test this approach by combining established data with the large h Per data set from the MONITOR project and new low-mass Pleiades data. We confirm prior results that young low-mass stars can be used to test star–disk coupling and angular momentum loss independent of the treatment of internal angular momentum transport. For slow rotators, we confirm the need for star–disk interactions to evolve the ONC to older systems, using h Per (age 13 Myr) as our natural post-disk case. There is no evidence for extremely long-lived disks as an alternative to core-envelope decoupling. However, our wind models cannot evolve rapid rotators from h Per to older systems consistently, and we find that this result is robust with respect to the choice of angular momentum loss prescription. We outline two possible solutions: either there is cosmic variance in the distribution of stellar rotation rates in different clusters or there are substantially enhanced torques in low-mass rapid rotators. We favor the former explanation and discuss observational tests that could be used to distinguish them. If the distribution of initial conditions depends on environment, models that test parameters by assuming a universal underlying distribution of initial conditions will need to be re-evaluated.

79 ASTRONOMY AND ASTROPHYSICS↗

NGC 7538 IRS. 1. Interaction of a polarized dust spiral and a molecular outflow

We present dust polarization and CO molecular line images of NGC 7538 IRS 1. We combined data from the Submillimeter Array, the Combined Array for Research in Millimeter-wave Astronomy, and the James Clerk Maxwell Telescope to make images with ∼2.''5 resolution at 230 and 345 GHz. The images show a remarkable spiral pattern in both the dust polarization and molecular outflow. These data dramatically illustrate the interplay between a high infall rate onto IRS 1 and a powerful outflow disrupting the dense, clumpy medium surrounding the star. The images of the dust polarization and the CO outflow presented here provide observational evidence for the exchange of energy and angular momentum between the infall and the outflow. The spiral dust pattern, which rotates through over 180° from IRS 1, may be a clumpy filament wound up by conservation of angular momentum in the infalling material. The redshifted CO emission ridge traces the dust spiral closely through the MM dust cores, several of which may contain protostars. We propose that the CO maps the boundary layer where the outflow is ablating gas from the dense gas in the spiral.

79 ASTRONOMY AND ASTROPHYSICS↗

Electromagnetic radiation accompanying gravitational waves from black hole binaries

The transition of powerful gravitational waves, created by the coalescence of massive black hole binaries, into electromagnetic radiation in external magnetic fields is considered. In contrast to the previous calculations of the similar effect we study the realistic case of the gravitational radiation frequency below the plasma frequency of the surrounding medium. The gravitational waves propagating in the plasma constantly create electromagnetic radiation dragging it with them, despite the low frequency. The plasma heating by the unattenuated electromagnetic wave may be significant in hot rarefied plasma with strong magnetic field and can lead to a noticeable burst of electromagnetic radiation with higher frequency. The graviton-to-photon conversion effect in plasma is discussed in the context of possible electromagnetic counterparts of GW150914 and GW170104.

79 ASTRONOMY AND ASTROPHYSICS↗

POST-OUTBURST RADIO OBSERVATIONS OF THE HIGH MAGNETIC FIELD PULSAR PSR J1119-6127

We have carried out high-frequency radio observations of the high magnetic field pulsar PSR J1119-6127 following its recent X-ray outburst. While initial observations showed no evidence of significant radio emission, subsequent observations detected pulsed emission across a large frequency band. In this Letter, we report on the initial disappearance of the pulsed emission and its prompt reactivation and dramatic evolution over several months of observation. The periodic pulse profile at S -band (2.3 GHz) after reactivation exhibits a multi-component emission structure, while the simultaneous X -band (8.4 GHz) profile shows a single emission peak. Single pulses were also detected at S -band near the main emission peaks. We present measurements of the spectral index across a wide frequency bandwidth, which captures the underlying changes in the radio emission profile of the neutron star. The high-frequency radio detection, unusual emission profile, and observed variability suggest similarities with magnetars, which may independently link the high-energy outbursts to magnetar-like behavior.

79 ASTRONOMY AND ASTROPHYSICS↗

Representing massive gravitons, as a way to quantify early universe magnetic field contributions to space-time, created by non linear electrodynamics

We review a relationship between cosmological vacuum energy and massive gravitons as given by Garattini and also the nonlinear electrodynamics of Camara et.al (2004) for a non singular universe and NLED. . In evaluating the Garattini result, we find that having the scale factor close to zero due to a given magnetic field value in, an early universe magnetic field affects how we would interpret Garattini’s linkage of the ‘cosmological constant’ value and non zero graviton mass.. We close as to how these initial conditions affect the issue of an early universe initial pressure and its experimental similarities and differences with results by Corda and Questa as to negative pressure at the surface of a star. Note, that in theDupays et.al. article , the star in question is rapidly spinning, which is not. assumed in the Camara et.al article , for an early universe. Also, Corda and Questa do not assume a spinning star. We conclude with a comparison between the Lagrangian Dupays and other authors bring up for non linear electrodynamics which is for rapidly spinning neutron stars , and a linkage between the Goldstone theorem and NLED. Our conclusion is for generalizing results seen in the Dupays neutron star Lagrangian with conditions which may confirm C. A. Escobar and L. F. Urrutia’s work on the Goldstone theorem and non linear electrodynamics, for some future projects we have in mind. If the universe does not spin, then we will stick with the density analogy given by adapting density as proportional to one over the fourth power of the minimum value of the scale factor as computed by adaptation of the Camara et.al.(2004) theory for non spinning universes. What may happen is that the Camara (2004) density and Quintessential density are both simultaneously satisfied, which would put additional restrictions on the magnetic field, which is one of our considerations, regardless if a universe spins, akin to spinning neutron stars. The spinning universe though may allow for easier reconciliation of the ‘Goldstone’ behavior of gravity and NLED though.

79 ASTRONOMY AND ASTROPHYSICS↗

3D Radiation Nonideal Magnetohydrodynamical Simulations of the Inner Rim in Protoplanetary Disks

Many planets orbit within 1 au of their stars, raising questions about their origins. Particularly puzzling are the planets found near the silicate sublimation front. We investigate conditions near the front in the protostellar disk around a young intermediate-mass star, using the first global 3D radiation nonideal MHD simulations in this context. We treat the starlight heating; the silicate grains’ sublimation and deposition at the local, time-varying temperature and density; temperature-dependent ohmic dissipation; and various initial magnetic fields. The results show magnetorotational turbulence around the sublimation front at 0.5 au. The disk interior to 0.8 au is turbulent, with velocities exceeding 10% of the sound speed. Beyond 0.8 au is the dead zone, cooler than 1000 K and with turbulence orders of magnitude weaker. A local pressure maximum just inside the dead zone concentrates solid particles, favoring their growth. Over many orbits, a vortex develops at the dead zone’s inner edge, increasing the disk’s thickness locally by around 10%. We synthetically observe the results using Monte Carlo transfer calculations, finding that the sublimation front is near-infrared bright. The models with net vertical magnetic fields develop extended, magnetically supported atmospheres that reprocess extra starlight, raising the near-infrared flux 20%. The vortex throws a nonaxisymmetric shadow on the outer disk. At wavelengths >2 μm, the flux varies several percent on monthly timescales. The variations are more regular when the vortex is present. The vortex is directly visible as an arc at ultraviolet through near-infrared wavelengths, given sub-au spatial resolution.

79 ASTRONOMY AND ASTROPHYSICS↗

NEAR-INFRARED POLARIZATION SOURCE CATALOG OF THE NORTHEASTERN REGIONS OF THE LARGE MAGELLANIC CLOUD

We present a near-infrared band-merged photometric and polarimetric catalog for the 39′ × 69′ fields in the northeastern part of the Large Magellanic Cloud (LMC), which were observed using SIRPOL, an imaging polarimeter of the InfraRed Survey Facility. This catalog lists 1858 sources brighter than 14 mag in the H band with a polarization signal-to-noise ratio greater than three in the J, H, or K{sub s} bands. Based on the relationship between the extinction and the polarization degree, we argue that the polarization mostly arises from dichroic extinctions caused by local interstellar dust in the LMC. This catalog allows us to map polarization structures to examine the global geometry of the local magnetic field, and to show a statistical analysis of the polarization of each field to understand its polarization properties. In the selected fields with coherent polarization position angles, we estimate magnetic field strengths in the range of 3−25 μG using the Chandrasekhar–Fermi method. This implies the presence of large-scale magnetic fields on a scale of around 100 parsecs. When comparing mid- and far-infrared dust emission maps, we confirmed that the polarization patterns are well aligned with molecular clouds around the star-forming regions.

79 ASTRONOMY AND ASTROPHYSICS↗

HST imaging of fading AGN candidates. I. Host-galaxy properties and origin of the extended gas

We present narrow- and medium-band Hubble Space Telescope imaging, with additional supporting ground-based imaging, spectrophotometry, and Fabry–Perot interferometric data, for eight galaxies identified as hosting a fading active galactic nucleus (AGN). These are selected to have AGN-ionized gas projected >10 kpc from the nucleus and energy budgets with a significant shortfall of ionizing radiation between the requirement to ionize the distant gas and the AGN as observed directly, indicating fading of the AGN on ≈50,000 yr timescales. This paper focuses on the host-galaxy properties and origin of the gas. In every galaxy, we identify evidence of ongoing or past interactions, including tidal tails, shells, and warped or chaotic dust structures; a similarly selected sample of obscured AGNs with extended ionized clouds shares this high incidence of disturbed morphologies. Several systems show multiple dust lanes in different orientations, broadly fit by differentially precessing disks of accreted material viewed ∼1.5 Gyr after its initial arrival. The host systems are of early Hubble type; most show nearly pure de Vaucouleurs surface brightness profiles and Sérsic indices appropriate for classical bulges, with one S0 and one SB0 galaxy. The gas has a systematically lower metallicity than the nuclei; three systems have abundances uniformly well below solar, consistent with an origin in tidally disrupted low-luminosity galaxies, while some systems have more nearly solar abundances (accompanied by such signatures as multiple Doppler components), which may suggest redistribution of gas by outflows within the host galaxies themselves. These aspects are consistent with a tidal origin for the extended gas in most systems, although the ionized gas and stellar tidal features do not always match closely. Unlike extended emission regions around many radio-loud AGNs, these clouds are kinematically dominated by rotation, in some cases in warped disks. Outflows can play important kinematic roles only in localized regions near some of the AGNs. We find only a few sets of young star clusters potentially triggered by AGN outflows. In UGC 7342 and UGC 11185, multiple luminous star clusters are seen just within the projected ionization cones, potentially marking star formation triggered by outflows. As in the discovery example, Hanny’s Voorwerp/IC 2497, there are regions in these clouds where the lack of a strong correlation between Hα surface brightness and ionization parameter indicates that there is unresolved fine structure in the clouds. Together with thin coherent filaments spanning several kpc, persistence of these structures over their orbital lifetimes may require a role for magnetic confinement. Overall, we find that the sample of fading AGNs occur in interacting and merging systems, that the very extended ionized gas is composed of tidal debris rather than galactic winds, and that these host systems are bulge-dominated and show no strong evidence of triggered star formation in luminous clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparing Poynting flux dominated magnetic tower jets with kinetic-energy dominated jets

Magnetic towers represent one of two fundamental forms of MHD out flows. Driven by magnetic pressure gradients, these flows have been less well studied than magneto-centrifugally launched jets even though magnetic towers may well be as common. We present new results exploring the behavior and evolution of magnetic tower outflows and demonstrate their connection with pulsed power experimental studies and purely hydrodynamic jets which might represent the asymptotic propagation regimes of magneto-centrifugally launched jets. High-resolution AMR MHD simulations (using the AstroBEAR code) provide insights into the underlying physics of magnetic towers and help us constrain models of their propagation. Our simulations have been designed to explore the effects of thermal energy losses and rotation on both towerflows and their hydro counterparts. We find these parameters have significant effects on the stability of magnetic towers, but mild effects on the stability of hydro jets. Current-driven perturbations in the Poynting Flux Dominated (PDF) towers are shown to be amplified in both the cooling and rotating cases. Our studies of the long term evolution of the towers show that the formation of weakly magnetized central jets within the tower are broken up by these instabilities becoming a series of collimated clumps which magnetization properties vary over time. In addition to discussing these results in light of laboratory experiments, we address their relevance to astrophysical observations of young star jets and outflow from highly evolved solar type stars.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Late-time near-infrared observations of SN 2005df

We present late-time near-infrared (NIR) spectral evolution, at 200–400 days, for the Type Ia supernova SN 2005df. The spectra show numerous strong emission features of [Co ii], [Co iii], and [Fe ii] throughout the 0.8–1.8 μm region. As the spectrum ages, the cobalt features fade as would be expected from the decay of {sup 56}Co to {sup 56}Fe. We show that the strong and isolated [Fe ii] emission line at 1.644 μm provides a unique tool to analyze NIR spectra of SNe Ia. Normalization of spectra to this line allows the separation of features produced by stable versus unstable isotopes of iron group elements. We develop a new method of determining the initial central density, ρ{sub c}, and the magnetic field, B, of the white dwarf (WD) using the width of the 1.644 μm line. The line width (LW) is sensitive because of electron capture in the early stages of burning, which increases as a function of density. The sensitivity of the LW to B increases with time, and the effects of the magnetic field shift toward later times with decreasing ρ{sub c}. Through comparison with spherical models, the initial central density for SN 2005df is measured as ρ{sub c}=0.9(±0.2)×10{sup 9} g cm{sup −3}, which corresponds to a WD close to the Chandrasekhar mass, with M{sub WD}=1.31(±0.03) M{sub ⊙} and systematic error less than 0.04 M{sub ⊙}. This error estimate is based on spherical models. We discuss the potential uncertainties due to multi-dimensional effects, mixing, and rotation. The latter two effects would increase the estimate of the WD mass. Within M{sub Ch} explosions, however, the central density found for SN 2005df is very low for a H-accretor, possibly suggesting a helium star companion or a tidally disrupted WD companion. As an alternative, we suggest mixing of the central region. We find some support for high initial magnetic fields of strength 10{sup 6} G for SN 2005df, however, 0 G cannot be ruled out because of noise in the spectra combined with low ρ{sub c}. We discuss our findings in the context of mixing by Rayleigh–Taylor instabilities during deflagration burning and a wide variety of explosion scenarios. Observations strongly support a very limited amount of mixing during a deflagration phase and high central densities characteristic of a M{sub Ch} WD.

79 ASTRONOMY AND ASTROPHYSICS↗

What physics determines the peak of the IMF? Insights from the structure of cores in radiation-magnetohydrodynamic simulations

As star-forming clouds collapse, the gas within them fragments to ever-smaller masses. Naively one might expect this process to continue down to the smallest mass that is able to radiate away its binding energy on a dynamical time-scale, the opacity limit for fragmentation, at ~0.01M⊙. However, the observed peak of the initial mass function (IMF) lies a factor of 20-30 higher in mass, suggesting that some other mechanism halts fragmentation before the opacity limit is reached. Here, we analyse radiation-magnetohydrodynamic simulations of star cluster formation in typical Milky Way environments in order to determine what physical process limits fragmentation in them. We examine the regions in the vicinity of stars that form in the simulations to determine the amounts of mass that are prevented from fragmenting by thermal and magnetic pressure. We show that, on small scales, thermal pressure enhanced by stellar radiation heating is the dominant mechanism limiting the ability of the gas to further fragment. In the brown dwarf mass regime, ~0.01M⊙, the typical object that forms in the simulations is surrounded by gas whose mass is several times its own that is unable to escape or fragment, and instead is likely to accrete. This mechanism explains why ~0.01M⊙ objects are rare: unless an outside agent intervenes (e.g. a shock strips away the gas around them), they will grow by accreting the warmed gas around them. In contrast, by the time stars grow to masses of ~0.2M⊙, the mass of heated gas is only tens of percent of the central star mass, too small to alter its final mass by a large factor. This naturally explains why the IMF peak is at ~0.2M⊙.

79 ASTRONOMY AND ASTROPHYSICS↗

FARGO3D: A NEW GPU-ORIENTED MHD CODE

We present the FARGO3D code, recently publicly released. It is a magnetohydrodynamics code developed with special emphasis on the physics of protoplanetary disks and planet–disk interactions, and parallelized with MPI. The hydrodynamics algorithms are based on finite-difference upwind, dimensionally split methods. The magnetohydrodynamics algorithms consist of the constrained transport method to preserve the divergence-free property of the magnetic field to machine accuracy, coupled to a method of characteristics for the evaluation of electromotive forces and Lorentz forces. Orbital advection is implemented, and an N-body solver is included to simulate planets or stars interacting with the gas. We present our implementation in detail and present a number of widely known tests for comparison purposes. One strength of FARGO3D is that it can run on either graphical processing units (GPUs) or central processing units (CPUs), achieving large speed-up with respect to CPU cores. We describe our implementation choices, which allow a user with no prior knowledge of GPU programming to develop new routines for CPUs, and have them translated automatically for GPUs.

79 ASTRONOMY AND ASTROPHYSICS↗

FARADAY ROTATION DISTRIBUTIONS FROM STELLAR MAGNETISM IN WIND-BLOWN BUBBLES

Faraday rotation is a valuable tool for detecting magnetic fields. Here, the technique is considered in relation to wind-blown bubbles. In the context of spherical winds with azimuthal or split monopole stellar magnetic field geometries, we derive maps of the distribution of position angle (P.A.) rotation of linearly polarized radiation across projected bubbles. We show that the morphology of maps for split monopole fields are distinct from those produced by the toroidal field topology; however, the toroidal case is the one most likely to be detectable because of its slower decline in field strength with distance from the star. We also consider the important case of a bubble with a spherical sub-volume that is field-free to approximate crudely a 'swept-up' wind interaction between a fast wind (or possibly a supernova ejecta shell) overtaking a slower magnetized wind from a prior state of stellar evolution. With an azimuthal field, the resultant P.A. map displays two arc-like features of opposite rotation measure, similar to observations of the supernova remnant G296.5+10.0. We illustrate how P.A. maps can be used to disentangle Faraday rotation contributions made by the interstellar medium versus the bubble. Although our models involve simplifying assumptions, their consideration leads to a number of general robust conclusions for use in the analysis of radio mapping data sets.

79 ASTRONOMY AND ASTROPHYSICS↗

AMBIPOLAR DIFFUSION HEATING IN TURBULENT SYSTEMS

The temperature of the gas in molecular clouds is a key determinant of the characteristic mass of star formation. Ambipolar diffusion (AD) is considered one of the most important heating mechanisms in weakly ionized molecular clouds. In this work, we study the AD heating rate using two-fluid turbulence simulations and compare it with the overall heating rate due to turbulent dissipation. We find that for observed molecular clouds, which typically have Alfven Mach numbers of {approx}1 and AD Reynolds numbers of {approx}20, about 70% of the total turbulent dissipation is in the form of AD heating. AD has an important effect on the length scale where energy is dissipated: when AD heating is strong, most of the energy in the cascade is removed by ion-neutral drift, with a comparatively small amount of energy making it down to small scales. We derive a relation for the AD heating rate that describes the results of our simulations to within a factor of two. Turbulent dissipation, including AD heating, is generally less important than cosmic-ray heating in molecular clouds, although there is substantial scatter in both.

79 ASTRONOMY AND ASTROPHYSICS↗

Topology, Magnetic Field, and Strongly Interacting Matter

Gauge theories with compact symmetry groups possess topologically nontrivial configurations of gauge field. This characteristic has dramatic implications for the vacuum structure of quantum chromodynamics (QCD) and for the behavior of QCD plasma, as well as for condensed matter systems with chiral quasi-particles. Here, I review the current status of this problem with an emphasis both on the interplay between chirality and a background magnetic field and on the observable manifestations of topology in heavy-ion collisions, Dirac semimetals, neutron stars, and the early Universe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗