Small Spins Research Articles

Inferring Small Neutron Star Spins with Neutron Star–Black Hole Mergers

The precise measurement of neutron star (NS) spins can provide important insight into the formation and evolution of compact binaries containing NSs. While traditional methods of NS spin measurement rely on pulsar observations, gravitational-wave detections offer a complementary avenue. However, determining component spins with gravitational waves is hindered by the small dimensionless spins of the NSs and the degeneracy in the mass and spin parameters. This degeneracy can be addressed by the inclusion of higher-order modes in the waveform, which are important for systems with unequal masses. This study shows the suitability of NS–black hole mergers, which are naturally mass-asymmetric, for precise NS spin measurements. We explore the effects of the black hole masses and spins, higher-mode content, inclination angles, and detector sensitivity on the measurement of NS spin. We find that networks with next-generation observatories like the Cosmic Explorer and the Einstein Telescope can distinguish NS dimensionless spin of 0.04 (0.1) from zero at 1σ confidence for events within ∼350 (∼1000) Mpc. Networks with A+ and A♯ detectors achieve similar distinction within ∼30 (∼70) Mpc and ∼50 (∼110) Mpc, respectively.

Binary Black Hole Spins: Model Selection with GWTC-3

The origin of the spins of stellar-mass black holes is still controversial, and angular momentum transport inside massive stars is one of the main sources of uncertainty. Here, we apply hierarchical Bayesian inference to derive constraints on spin models from the 59 most confident binary black hole merger events in the third gravitational-wave transient catalogue (GWTC-3). We consider up to five parameters: chirp mass, mass ratio, redshift, effective spin, and precessing spin. For the model selection, we use a set of binary population synthesis simulations spanning drastically different assumptions for black hole spins and natal kicks. In particular, our spin models range from the maximal to minimal efficiency of angular momentum transport in stars. We find that if we include the precessing spin parameter into our analysis, models predicting only vanishingly small spins are in tension with GWTC-3 data. On the other hand, models in which most spins are vanishingly small but that also include a subpopulation of tidally spun-up black holes are a good match to the data. Our results show that the precessing spin parameter has a crucial impact on model selection.

Double dome structure of the Bose–Einstein condensation in diluted S = 3/2 quantum magnets

Bose–Einstein condensation (BEC) in quantum magnets, where bosonic spin excitations condense into ordered ground states, is a realization of BEC in a thermodynamic limit. Although previous magnetic BEC studies have focused on magnets with small spins of S ≤ 1, larger spin systems potentially possess richer physics because of the multiple excitations on a single site level. Here, we show the evolution of the magnetic phase diagram of S = 3/2 quantum magnet Ba2CoGe2O7 when the averaged interaction J is controlled by a dilution of magnetic sites. By partial substitution of Co with nonmagnetic Zn, the magnetic order dome transforms into a double dome structure, which can be explained by three kinds of magnetic BECs with distinct excitations. Furthermore, we show the importance of the randomness effects induced by the quenched disorder: we discuss the relevance of geometrical percolation and Bose/Mott glass physics near the BEC quantum critical point.

Superfluid transport in quantum spin chains

Spin superfluids enable long-distance spin transport through classical ferromagnets by developing topologically stable magnetic textures. For small spins at low dimensions, however, the topological protection suffers from strong quantum fluctuations. We study the remanence of spin superfluidity inherited from the classical magnet by considering the two-terminal spin transport through a finite spin-1/2 magnetic chain with planar exchange. By fermionizing the system, we recast the spin-transport problem in terms of quasiparticle transmission through a superconducting region. We show that the topological underpinnings of a semiclassical spin superfluid relate to the topological superconductivity in the fermionic representation. In particular, we find an efficient spin transmission through the magnetic region of a characteristic resonant length, which can be related to the properties of the boundary Majorana zero modes.

Numerical evaluation of spin foam amplitudes beyond simplices

We present the first numerical calculation of the 4D Euclidean spin foam vertex amplitude for vertices with hypercubic combinatorics. Concretely, we compute the amplitude for coherent boundary data peaked on cuboid and frustum shapes. We present the numerical algorithms to explicitly compute the vertex amplitude and compare the results in different cases to the semiclassical approximation of the amplitude. Overall we find good qualitative agreement of the amplitudes and evidence of convergence of the asymptotic formula to the full amplitude already at fairly small spins, yet also differences in the frequency of oscillations and a phase shift absent in the 4-simplex case. However, due to rapidly growing numerical costs, we cannot reach sufficiently high spins to prove agreement of both amplitudes. Lastly, this setup allows us to explore nonuniform vertex amplitudes, where some representations are small while others are large; we find indications that scenarios might exist in which the semiclassical amplitude is a valid approximation even if some spins remain small. This suggests that the transition of the quantum to the semiclassical regime (for a single vertex amplitude) is intricate.

Black hole induced spins from hyperbolic encounters in dense clusters

The black holes that have been detected via gravitational waves (GW) can have either astrophysical or primordial origin. Some GW events show significant spin for one of the components and have been assumed to be astrophysical, since primordial black holes are generated with very low spins. However, it is worth studying if they can increase their spin throughout the evolution of the universe. Possible mechanisms that have already been explored are multiple black hole mergers and gas accretion. We propose here a new mechanism that can occur in dense clusters of black holes: the spin-up of primordial black holes when they are involved in close hyperbolic encounters. We explore this effect numerically with the Einstein Toolkit for different initial conditions, including variable mass ratios. For equal masses, there is a maximum spin that can be induced on the black holes, $\chi = a/m \leq 0.2$. We find however that for large mass ratios one can attain spins up to $\chi \simeq 0.8$, where the highest spin is induced on the most massive black hole. For small induced spins we provide simple analytical expressions that depend on the relative velocity and impact parameter.

State of the Field: Binary Black Hole Natal Kicks and Prospects for Isolated Field Formation after GWTC-2

Abstract Advanced LIGO and Advanced Virgo’s newly released GWTC-2 catalog of gravitational-wave detections offers unprecedented information about the spin magnitudes and orientations of merging binary black holes (BBHs). Notably, analysis of the BBH population suggests the presence of binaries whose component spins are significantly misaligned with respect to their orbital angular momenta. Significantly misaligned spins are typically predicted to be at odds with isolated field formation via standard common envelope (CE) evolution, and hence a “smoking gun” signature of dynamical binary formation inside dense stellar clusters. Here, we explore whether the LIGO/Virgo observation of spin–orbit misalignment indeed rules out the possibility that BBHs are formed entirely in the field via standard CE evolution. In particular, we seek to understand whether, by varying the natal kicks black holes receive upon formation, we can invoke the CE scenario to self-consistently explain both the observed spin distribution and merger rate of BBHs. We find that, if isolated black holes are born with small natal spins, then BBHs formed through CE require extreme natal kicks to match the observed BBH population, with a velocity dispersion σ = 9.7 − 5.9 + 26.7 × 10 2 km s − 1 and σ > 260 km s−1 at 99% credibility. To avoid the need for extreme kicks, we argue that it is necessary to assume that isolated black holes are born with nonvanishing natal spins, that one or more alternative channels contribute to the observed BBH population, and/or that other unforeseen mechanisms serve to yield large spin–orbit misalignment in the field.

The Relative Contribution to Heavy Metals Production from Binary Neutron Star Mergers and Neutron Star–Black Hole Mergers

Abstract The origin of the heavy elements in the universe is not fully determined. Neutron star–black hole (NSBH) and binary neutron star (BNS) mergers may both produce heavy elements via rapid neutron-capture (r-process). We use the recent detection of gravitational waves from NSBHs, improved measurements of the neutron star equation of state (EoS), and the most modern numerical simulations of ejected material from binary collisions to measure the relative contribution of NSBHs and BNSs to the production of heavy elements. As the amount of r-process ejecta depends on the mass and spin distribution of the compact objects, as well as on the EoS of the neutron stars, we consider various models for these quantities, informed by gravitational-wave and pulsar data. We find that in most scenarios, BNSs have produced more r-process elements than NSBHs over the past 2.5 billion years. If black holes have preferentially small spins, BNSs can produce at least twice the amount of r-process elements than NSBHs. If black hole spins are small and there is a dearth of low-mass (<5M ⊙) black holes within NSBH binaries, BNSs can account for the near totality of the r-process elements from binaries. For NSBH to produce a large fraction of r-process elements, black holes in NSBHs must have small masses and large aligned spins, which is disfavored by current data.

Spins of primordial black holes formed in different cosmological scenarios

Primordial black holes (PBHs) could account for all or part of dark matter, as well as for some LIGO events. We discuss the spins of primordial black holes produced in different cosmological scenarios, with the emphasis on recently discovered possibilities. PBHs produced as a horizon-size collapse of density perturbations are known to have very small spins. In contrast, PBHs resulting from assembly of matterlike objects (particles, Q-balls, oscillons, etc.) can have large or small spins depending on their formation history and the efficiency of radiative cooling. We show that scalar radiation can remove the angular momentum very efficiently, leading to slowly rotating PBHs in those scenarios for which the radiative cooling is important. Gravitational waves astronomy offers an opportunity to determine the spins of black holes, opening a new window on the early Universe if, indeed, some black holes have primordial origin.

Path integral renormalization in loop quantum cosmology

A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient was an SU(1, 1) group and Lie algebra structure of the physical observables as well as the use of Perelomov coherent states for SU(1, 1). It was shown that the coarse graining operation is completely captured by changing group representations. Based on this result, it was subsequently shown that one can extract an explicit renormalisation group flow of the loop quantum cosmology Hamiltonian operator in a simple model with dust-clock. In this paper, we continue this line of investigation and derive a coherent state path integral formulation of this quantum theory and extract an explicit expression for the renormalisation-scale dependent classical Hamiltonian entering the path integral for a coarse grained description at that scale. We find corrections to the non-renormalised Hamiltonian that are qualitatively similar to those previously investigated via canonical quantisation. In particular, they are again most sensitive to small quantum numbers, showing that the large quantum number (spin) description captured by so called "effective equations" in loop quantum cosmology does not reproduce the physics of many small quantum numbers (spins). Our results have direct impact on path integral quantisation in loop quantum gravity, showing that the usually taken large spin limit should be expected not to capture (without renormalisation, as mostly done) the physics of many small spins that is usually assumed to be present in physically reasonable quantum states.

The Fascinating World of Low-Dimensional Quantum Spin Systems: Ab Initio Modeling.

In recent times, ab initio density functional theory has emerged as a powerful tool for making the connection between models and materials. Insulating transition metal oxides with a small spin forms a fascinating class of strongly correlated systems that exhibit spin-gap states, spin–charge separation, quantum criticality, superconductivity, etc. The coupling between spin, charge, and orbital degrees of freedom makes the chemical insights equally important to the strong correlation effects. In this review, we establish the usefulness of ab initio tools within the framework of the N-th order muffin orbital (NMTO)-downfolding technique in the identification of a spin model of insulating oxides with small spins. The applicability of the method has been demonstrated by drawing on examples from a large number of cases from the cuprate, vanadate, and nickelate families. The method was found to be efficient in terms of the characterization of underlying spin models that account for the measured magnetic data and provide predictions for future experiments.

Bayesian analysis of the spin distribution of LIGO/Virgo black holes

Gravitational wave detection from binary black hole (BBH) inspirals has become routine thanks to the LIGO/Virgo interferometers. The nature of these back holes remains uncertain. We study here the spin distributions of LIGO/Virgo black holes from the first catalogue GWTC-1 and the first four published BBH events from run O3. We compute the Bayes evidence for several independent priors: flat, isotropic, spin-aligned and anti-aligned. We find strong evidence for low spins in all of the cases, and significant evidence for small isotropic spins versus any other distribution. When considered as a homogeneous population of black holes, these results give support to the idea that LIGO/Virgo BBH are primordial.

Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes. II. Spins and Incoming Objects

Abstract The masses, rates, and spins of merging stellar mass binary black holes (BBHs) detected by aLIGO and Virgo provide challenges to traditional BBH formation and merger scenarios. An active galactic nucleus (AGN) disk provides a promising additional merger channel because of the powerful influence of the gas that drives orbital evolution, makes encounters dissipative, and leads to migration. Previous work showed that stellar mass black holes (sBHs) in an AGN disk migrate to regions of the disk, known as migration traps, where positive and negative gas torques cancel out, leading to frequent BBH formation. Here we build on that work by simulating the evolution of additional sBHs that enter the inner disk by either migration or inclination reduction. We also examine whether the BBHs formed in our models have retrograde or prograde orbits around their centers of mass with respect to the disk, determining the orientation of the spin of the merged BBHs relative to the disk. Orbiters entering the inner disk form BBHs with sBHs on resonant orbits near the migration trap. When these sBHs reach ≳80 M ☉, they form BBHs with sBHs in the migration trap, which reach ∼1000 M ☉ over 10 Myr. We find 68% of the BBHs in our simulation orbit in the retrograde direction, which implies that BBHs in our merger channel will have small dimensionless aligned spins, χ eff. Overall, our models produce BBHs that resemble both the majority of BBH mergers detected thus far (0.66–120 Gpc−3 yr−1) and two recent unusual detections, GW190412 (∼0.3 Gpc−3 yr−1) and GW190521 (∼0.1 Gpc−3 yr−1).

Semiclassical behavior of spinfoam amplitude with small spins and entanglement entropy

Spinfoam amplitudes with small spins can have interesting semiclassical behavior and relate to semiclassical gravity and geometry in four dimensions. We study the generalized spinfoam model [spinfoams for all loop quantum gravity (LQG) [Kaminski et al., Spin-foams for all loop quantum gravity, Classical Quantum Gravity 27, 095006 (2010); Erratum, Classical Quantum Gravity 29, 049502(E) (2012), Ding et al., Generalized spinfoams, Phys. Rev. D 83, 124020 (2011)] with small spins $j$ but a large number of spin degrees of freedom (d.o.f.), and find that it relates to the simplicial Engle-Pereira-Rovelli-Livine-Freidel-Krasnov model with large spins and Regge calculus by coarse-graining spin d.o.f. $\mathrm{Small}\text{\ensuremath{-}}j$ generalized spinfoam amplitudes can be employed to define semiclassical states in the LQG kinematical Hilbert space. Each of these semiclassical states is determined by a four-dimensional Regge geometry. We compute the entanglement R\'enyi entropies of these semiclassical states. The entanglement entropy interestingly coarse grains spin d.o.f. in the generalized spinfoam model, and satisfies an analog of the thermodynamical first law. This result possibly relates to the quantum black hole thermodynamics in [Ghosh and Perez, Black Hole Entropy and Isolated Horizons Thermodynamics, Phys. Rev. Lett. 107, 241301 (2011); 108, 169901(E) (2012)].

Effect of spin on the inspiral of binary neutron stars

We perform long-term simulations of spinning binary neutron stars, with our highest dimensionless spin being $\chi \sim 0.32$. To assess the importance of spin during the inspiral we vary the spin, and also use two equations of state, one that consists of plain nuclear matter and produces compact stars (SLy), and a hybrid one that contains both nuclear and quark matter and leads to larger stars (ALF2). Using high resolution that has grid spacing $\Delta x\sim 98$ m on the finest refinement level, we find that the effects of spin in the phase evolution of a binary system can be larger than the one that comes from tidal forces. Our calculations demonstrate explicitly that although tidal effects are dominant for small spins ($\lesssim 0.1$), this is no longer true when the spins are larger, but still much smaller than the Keplerian limit.

Critical Phenomena in Coupled Magnetic Systems —Application to the Organic Antiferromagnet λ-(BETS)2FeCl4—

In this study, we construct a free-energy functional model for coupled magnetic systems that consist of free large spins and strongly interacting small spins, and apply it to the two-dimensional or...

Small body shapes and spins reveal a prevailing state of maximum topographic stability

Over the past thirty years, spacecraft missions, Earth-based radar experiments, and telescopic observations have revolutionized our knowledge of Main Belt asteroids, near-Earth asteroids, and comet nuclei. As a result of this effort, we now possess high resolution shape models and well-constrained spin rates, pole orientations, and basic surface properties for a few dozen such small bodies. Here we present the results of a geomorphological examination of 32 such small body shape models along with their associated spin properties, and show that small body shape, gravity, and spin combine to gradually drive the surface towards a condition of maximum topographic stability; that is, a state of low topographic variation, low slopes, and low surface erosion (mass-wasting) rates. Of the 32 bodies investigated, 15 (47%) reside within this ‘zone of maximum topographic stability’, and when asteroid lightcurve-derived rotation rate and body elongation estimates are included, 1941 (70%) of 2791 well-observed asteroids reside within this zone. This finding indicates that given a mobile surface layer and sufficient time, small body surfaces naturally tend to erode, and their spin states gradually evolve, towards a state of maximum topographic stability, which also corresponds to a state of lowest internal stress. This erosional effect is most prominent on bodies several kilometers and larger in diameter, where YORP induced spin-state changes are small.

Spin Wave Theory in Two-Dimensional Coupled Antiferromagnets

We apply spin wave theory to two-dimensional coupled antiferromagnets. In particular, we primarily examine a system that consists of small spins coupled by a strong exchange interaction J1, large spins coupled by a weak exchange interaction J2, and an anisotropic exchange interaction J12 between the small and large spins. This system is an effective model of the organic antiferromagnet λ-(BETS)2FeCl4 in its insulating phase, in which intriguing magnetic phenomena have been observed, where the small and large spins correspond to π electrons and 3d spins, respectively. BETS stands for bis(ethylenedithio)tetraselenafulvalene. We obtain the antiferromagnetic transition temperature TN and the sublattice magnetizations m(T) and M(T) of the small and large spins, respectively, as functions of the temperature T. When T increases, m(T) is constant with a slight decrease below TN, even where M(T) decreases significantly. When J1 ≫ J12 and J2 = 0, an analytical expression for TN is derived. The estimated value of TN...

The connection between mass, environment, and slow rotation in simulated galaxies

Recent observations from integral field spectroscopy (IFS) indicate that the fraction of galaxies that are slow rotators, $F_{\rm SR}$, depends primarily on stellar mass, with no significant dependence on environment. We investigate these trends and the formation paths of slow rotators (SRs) using the EAGLE and Hydrangea hydro-dynamical simulations. EAGLE consists of several cosmological boxes of volumes up to $(100\,\rm Mpc)^3$, while Hydrangea consists of $24$ cosmological simulations of galaxy clusters and their environment. Together they provide a statistically significant sample in the stellar mass range $10^{9.5}\,\rm M_{\odot}-10^{12.3}\,\rm M_{\odot}$, of $16,358$ galaxies. We construct IFS-like cubes and measure stellar spin parameters, $\lambda_{\rm R}$, and ellipticities, allowing us to classify galaxies into slow/fast rotators as in observations. The simulations display a primary dependence of $F_{\rm SR}$ on stellar mass, with a weak dependence on environment. At fixed stellar mass, satellite galaxies are more likely to be SRs than centrals. $F_{\rm SR}$ shows a dependence on halo mass at fixed stellar mass for central galaxies, while no such trend is seen for satellites. We find that $\approx 70$% of SRs at $z=0$ have experienced at least one merger with mass ratio $\ge 0.1$, with dry mergers being at least twice more common than wet mergers. Individual dry mergers tend to decrease $\lambda_{\rm R}$, while wet mergers mostly increase it. However, $30$% of SRs at $z=0$ have not experienced mergers, and those inhabit halos with median spins twice smaller than the halos hosting the rest of the SRs. Thus, although the formation paths of SRs can be varied, dry mergers and/or halos with small spins dominate.

Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation

Quantum magnetic phases near the magnetic saturation of triangular-lattice antiferromagnets with XXZ anisotropy have been attracting renewed interest since it has been suggested that a nontrivial coplanar phase, called the $\ensuremath{\pi}$-coplanar or $\mathrm{\ensuremath{\Psi}}$ phase, could be stabilized by quantum effects in a certain range of anisotropy parameter $J/{J}_{z}$ besides the well-known 0-coplanar (known also as $V)$ and umbrella phases. Recently, Sellmann et al. [Phys. Rev. B 91, 081104(R) (2015)] claimed that the $\ensuremath{\pi}$-coplanar phase is absent for $S=1/2$ from an exact-diagonalization analysis in the sector of the Hilbert space with only three down-spins (three magnons). We first reconsider and improve this analysis by taking into account several low-lying eigenvalues and the associated eigenstates as a function of $J/{J}_{z}$ and by sensibly increasing the system sizes (up to 1296 spins). A careful identification analysis shows that the lowest eigenstate is a chirally antisymmetric combination of finite-size umbrella states for $J/{J}_{z}\ensuremath{\gtrsim}2.218$ while it corresponds to a coplanar phase for $J/{J}_{z}\ensuremath{\lesssim}2.218$. However, we demonstrate that the distinction between 0-coplanar and $\ensuremath{\pi}$-coplanar phases in the latter region is fundamentally impossible from the symmetry-preserving finite-size calculations with fixed magnon number. Therefore, we also perform a cluster mean-field plus scaling analysis for small spins $S\ensuremath{\le}3/2$. The obtained results, together with the previous large-$S$ analysis, indicate that the $\ensuremath{\pi}$-coplanar phase exists for any $S$ except for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ and the existence range in $J/{J}_{z}$ is largest in the most quantum case of $S=1/2$.