Repulsive Self-interaction Research Articles

Interpreting Mass and Radius Measurements of Neutron Stars with Dark Matter Halos

The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate. Depending on the DM model, these DM admixed NSs (DANSs) could have significantly different properties than pure baryonic NSs, accessible through X-ray observations of rotation-powered pulsars. We adopt the two-fluid formalism in general relativity to numerically simulate stable configurations of DANSs, assuming a fermionic equation of state (EOS) for the DM with repulsive self-interaction. The distribution of DM in the DANS as a halo affects the path of X-rays emitted from hot spots on the visible baryonic surface, causing notable changes in the pulse profile observed by telescopes such as NICER, compared to pure baryonic NSs. We explore how various DM models affect the DM mass distribution, leading to different types of dark halos. We quantify the deviation in observed X-ray flux from stars with each of these halos. We identify the pitfalls in interpreting mass and radius measurements of NSs inferred from electromagnetic radiation and constraining the baryonic matter EOS if these dark halos exist.

Quantum vortex phases of charged pion condensates induced by rotation in a magnetic field

Using the relativistic complex scalar field model with a repulsive self-interaction, we discuss the ground state structure of charged pion condensation under the coexistence of parallel rotation and magnetic field. Our previous study found that the density distribution profile of the condensates is a supergiant quantum vortex phase and change with rotational speed and coupling constant. In this work, we further discover vortex lattice structures in the condensates under conditions of small rotation and strong coupling constant. This mechanism can be thought of as electrical superconductivity: Vortex lattices are created to better adapt to changes in rotation and interaction. Furthermore, large rotation and weak coupling constant are more likely to cause the vortex lattices to be destroyed and form a giant quantum vortex similar to a doughnut. We expect this phenomenon can be observed in the relativistic noncentral heavy ion collisions with large rotation and strong magnetic field. Published by the American Physical Society 2024

Kinetic relaxation and nucleation of Bose stars in self-interacting wave dark matter

We revisit kinetic relaxation and soliton/boson star nucleation in fuzzy scalar dark matter featuring short-ranged self-interactions Hint=−λ|ψ|4/2m2, alongside gravitational self-interactions. We map out the full curve of nucleation timescale for both repulsive (λ<0) and attractive (λ>0) short-ranged self-interaction strength and in doing so reveal two new points. Firstly, besides the two usual terms, ∝G2 and ∝λ2, in the total relaxation rate Γrelax, there is an additional cross term ∝Gλ arising due to interference between gravitational and short-ranged self-interaction scattering amplitudes. This yields a critical repulsive interaction strength λcr≃−2πGm2/v02, at which the relaxation rate is smallest and serves as the transition point between typical net attractive self-interaction (λ≳λcr) and net repulsive self-interaction (−λ≳−λcr). Secondly, while in the net attractive regime, nucleation timescale is similar to inverse relaxation timescale τnuc∼Γrelax−1; in the net repulsive regime, nucleation occurs at a delayed time τnuc∼(λ/λcr)Γrelax−1. We confirm our analytical understanding by performing 3D field simulations with varying average mass density ρ¯, box size L and grid size N. Published by the American Physical Society 2024

The MUSE-Faint survey

Aims. We use the stellar line-of-sight velocities of Antlia B (Ant B), a faint dwarf galaxy in the NGC 3109 association, to derive constraints on the fundamental properties of scalar field dark matter (SFDM), which was originally proposed to solve the small-scale problems faced by cold dark matter models. Methods. We used the first spectroscopic observations of Ant B, a distant (d ∼ 1.35 Mpc) faint dwarf (MV = −9.7, M⋆ ∼ 8 × 105 M⊙), from MUSE-Faint, a survey of ultra-faint dwarfs conducted using the Multi Unit Spectroscopic Explorer. By measuring the line-of-sight velocities of stars in the 1′×1′ field of view, we identified 127 stars as members of Ant B, which enabled us to model its dark matter density profile with the Jeans modelling code GRAVSPHERE. We implemented a model for SFDM into GRAVSPHERE and used this to place constraints on the self-coupling strength of this model. Results. We find a virial mass of M200 ≈ 1.66−0.92+2.51 × 109 M⊙ and a concentration parameter of c200 ≈ 17.38−4.20+6.06 for Ant B. These results are consistent with the mass-concentration relations in the literature. We constrain the characteristic length scale of the repulsive self-interaction RTF of the SFDM model to RTF ≲ 180 pc (68% confidence level), which translates to a self-coupling strength of g/m2c4 ≲ 5.2 × 10−20 eV−1 cm3. The constraint on the characteristic length scale of the repulsive self-interaction is inconsistent with the value required to match observations of the cores of dwarf galaxies in the Local Group, suggesting that the cored density profiles of those galaxies are not caused by SFDM.

Scalar dark matter vortex stabilization with black holes

Galaxies and their dark-matter halos are commonly presupposed to spin. But it is an open question how this spin manifests in halos and soliton cores made of scalar dark matter (SDM, including fuzzy/wave/ultralight-axion dark matter). One way spin could manifest in a necessarily irrotational SDM velocity field is with a vortex. But recent results have cast doubt on this scenario, finding that vortices are generally unstable except with substantial repulsive self-interaction. In this paper, we introduce an alternative route to stability: in both (non-relativistic) analytic calculations and simulations, a black hole or other central mass at least as massive as a soliton can stabilize a vortex within it. This conclusion may also apply to AU-scale halos bound to the sun and stellar-mass-scale Bose stars.

Generation and Control of Shock Waves in Exciton-Polariton Condensates

We propose a scheme to generate and control supersonic shock waves in a non-resonantly incoherent pumped exciton-polariton condensate, and different types of shock waves can be generated. Under conditions of different initial step waves, the ranges of parameters about various shock waves are determined by the initial incidence function and the cross-interaction between the polariton condensate and the reservoir. In addition, shock waves are successfully found by regulating the incoherent pump. In the case of low condensation rate from polariton to condensate, these results are similar to the classical nonlinear Schrödinger equation, and the effect of saturated nonlinearity resulted from cross interaction is equivalent to the self-interaction between polariton condensates. At high condensation rates, profiles of shock waves become symmetrical due to the saturated nonlinearity. Compared to the previous studies in which the shock wave can only be found in the system with repulsive self-interaction (defocusing nonlinearity), we not only discuss the shock wave in the exciton-polariton condensate system with the repulsive self-interaction, but also find the shock wave in the condensates system with attractive self-interaction. Our proposal may provide a simple way to generate and control shock waves in non-resonantly pumped exciton-polariton systems.

Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive |φ|4 self-interaction

We derive an approximate analytical expression of the maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|\ensuremath{\varphi}{|}^{4}$ self-interaction. This expression interpolates between the general relativistic maximum mass of noninteracting bosons stars, the general relativistic maximum mass of bosons stars with a repulsive self-interaction in the Thomas-Fermi limit, and the Newtonian maximum mass of dilute axion stars with an attractive self-interaction [P. H. Chavanis, Phys. Rev. D 84, 043531 (2011)]. We obtain the general structure of our formula from simple considerations and determine the numerical coefficients in order to recover the exact asymptotic expressions of the maximum mass in particular limits. As a result, our formula should provide a relevant approximation of the maximum mass of relativistic boson stars for any value (positive and negative) of the self-interaction parameter. We discuss the evolution of the system above the maximum mass and consider application of our results to dark matter halos and inflaton clusters. We also make a short review of boson stars and Bose-Einstein condensate dark matter halos and point out analogies with models of extended elementary particles.

Tachyon condensation in a chromomagnetic background field and the groundstate of QCD

I consider the chromomagnetic vacuum in SU(2). The effective Lagrangian in one loop approximation is known to have a minimum below zero which results in a spontaneously generated magnetic field. However, this minimum is not stable; the effective action has an imaginary part. Over the past decades, there were many attempts to handle this situation which all were at some point unsatisfactory. I propose an idea for a new solution by assuming that the tachyonic mode, at low temperature, acquires a condensate and, as a result, undergoes a phase transition like in the Higgs model. I consider the approximation where all gluon modes are dropped except for the tachyonic one. For this mode, we have a O(2)-model with quartic self-interaction in two dimensions. I apply the CJT (2PI) formalism in Hartree approximation. As a result, at zero and low temperatures, a minimum of the effective action at a certain value of the condensate and of the background fields is observed and there is no imaginary part. Raising the temperature, this minimum becomes shallower and at a critical temperature, the perturbative state becomes that with lower effective potential; the symmetry is restored. The physical interpretation says that the unstable mode creates tachyons until these come into equilibrium with their repulsive self-interaction and form a condensate. The relation to the Mermin-Wagner theorem is discussed.

Formation of a supergiant quantum vortex in a relativistic Bose-Einstein condensate driven by rotation and a parallel magnetic field

Analysis based on the energy spectrum of noninteracting bosons shows that, under the circumstance of parallel rotation and magnetic field, charged bosons form a Bose-Einstein condensate because of the lift of the Landau level degeneracy by rotation [\textcolor{blue}{Y. Liu and I. Zahed, Phys. Rev. Lett. {\bf120}, 032001 (2018)}]. In this work, we study the interaction effect on the ground state of this Bose-Einstein condensate of charged bosons from the viewpoint of spontaneous symmetry breaking. We employ a minimal model for charged bosons with repulsive self-interaction. We find that the ground state of such a Bose-Einstein condensate is a supergiant quantum vortex, i.e., a quantized vortex with a large circulation. The size of the vortex is as large as the system size. The low-energy dispersion of the excitation spectra exhibits quadratic behavior, which is an anisotropic realization of the type-II Goldstone boson. Our study may give some implications to off-central relativistic heavy ion collisions, where large vorticity and magnetic fields can be generated.

Gravitational instability with a dark matter background: exploring the different scenarios

We study the Jeans-type gravitational instability for a self-gravitating medium composed of two species, baryonic (bright) and dark matter particles, using a hybrid quantum-classical fluid approach. Baryonic matter is treated classically, which is appropriate for most astrophysical environments, e.g., Bok globules, while dark matter is treated through a quantum hydrodynamic approach allowing for possible nonlinearities. These nonlinearities may arise in bosonic dark matter due to attractive or repulsive short-range self-interaction (attractive interaction being more relevant for axions) or from the Pauli exclusion principle for fermionic dark matter, e.g., massive neutrinos. This allows us to explore, in a very broad context, the impact of a dark matter background on the Jeans process for different scenarios discussed in the literature. We confront the established stability criterion with Bok globule stability observations and show that the model adequately accounts for the data with dark matter parameters close to those predicted independently from numerical simulations.

Orbits and adiabatic contraction in scalar-field dark matter halos: revisiting the cusp-core problem in dwarf galaxies

ABSTRACT Bose–Einstein-condensed dark matter, also called scalar field dark matter (SFDM), has become a popular alternative to cold dark matter (CDM), because it predicts galactic cores, in contrast to the cusps of CDM halos (‘cusp-core problem’). We continue the study of SFDM with a strong, repulsive self-interaction; the Thomas–Fermi (TF) regime of SFDM (SFDM-TF). In this model, structure formation is suppressed below a scale related to the TF radius RTF, which is close to the radius of central cores in these halos. We investigate for the first time the impact of baryons onto realistic galactic SFDM-TF halo profiles by studying the process of adiabatic contraction (AC) in such halos. In doing so, we first analyse the underlying quantum Hamilton–Jacobi framework appropriate for SFDM and calculate dark matter orbits, in order to verify the validity of the assumptions usually required for AC. Then, we calculate the impact of AC onto SFDM-TF halos of mass $\sim 10^{11}\, {\rm M}_{\odot }$, with various baryon fractions and core radii, RTF ∼ (0.1–4) kpc, and compare our results with observational velocity data of dwarf galaxies. We find that AC-modified SFDM-TF halos with kpc-size core radii reproduce the data well, suggesting stellar feedback may not be required. On the other hand, halos with sub-kpc core radii face the same issue than CDM, in that they are not in accordance with galaxy data in the central halo parts.

Cosmological structure formation in scalar field dark matter with repulsive self-interaction: the incredible shrinking Jeans mass

ABSTRACT Scalar field dark matter (SFDM) comprised of ultralight (≳ 10−22 eV) bosons is an alternative to standard, collisionless cold dark matter (CDM) that is CDM-like on large scales but inhibits small-scale structure formation. As a Bose–Einstein condensate, its free-field (‘fuzzy’) limit (FDM) suppresses structure below the de Broglie wavelength, λdeB, creating virialized haloes with central cores of radius ∼ λdeB, surrounded by CDM-like envelopes, and a halo mass function (HMF) with a sharp cut-off on small scales. With a strong enough repulsive self-interaction (SI), structure is inhibited, instead, below the Thomas–Fermi (TF) radius, RTF (the size of an SI-pressure-supported (n = 1)-polytrope), when RTF > λdeB. Previously, we developed tools to describe SFDM dynamics on scales above λdeB and showed that SFDM-TF haloes formed by Jeans-unstable collapse from non-cosmological initial conditions have RTF-sized cores, surrounded by CDM-like envelopes. Revisiting SFDM-TF in the cosmological context, we simulate halo formation by cosmological infall and collapse, and derive its transfer function from linear perturbation theory to produce cosmological initial conditions and predict statistical measures of structure formation, such as the HMF. Since FDM and SFDM-TF transfer functions both have small-scale cut-offs, we can align them to let observational constraints on FDM proxy for SFDM-TF, finding FDM with particle masses 1 ≲ m/(10−22 eV/c2) ≲ 30 corresponds to SFDM-TF with 10 ≳ RTF/(1 pc) ≳ 1, favouring subgalactic (sub-kpc) core size. The SFDM-TF HMF cuts off gradually, however, leaving more small-mass haloes: Its Jeans mass shrinks so fast that scales filtered early can still recover and grow!

Phases of the Bose–Einstein Condensate Dark Matter Model with Both Two- and Three-Particle Interactions

In this paper, we further elaborate on the Bose–Einstein condensate (BEC) dark matter model extended in our previous work [Phys. Rev. D 2020, 102, 083510] by the inclusion of sixth-order (or three-particle) repulsive self-interaction term. Herein, our goal is to complete the picture through adding to the model the fourth-order repulsive self-interaction. The results of our analysis confirm the following: while in the previous work the two-phase structure and the possibility of first-order phase transition was established, here we demonstrate that with the two self-interactions involved, the nontrivial phase structure of the enriched model remains intact. For this to hold, we study the conditions which the parameters of the model, including the interaction parameters, should satisfy. As a by-product and in order to provide some illustration, we obtain the rotation curves and the (bipartite) entanglement entropy for the case of a particular dwarf galaxy.

Core-envelope haloes in scalar field dark matter with repulsive self-interaction: fluid dynamics beyond the de Broglie wavelength

ABSTRACT Scalar field dark matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless cold dark matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger–Poisson equations. In the free-field (‘fuzzy’) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have ‘solitonic’ cores of radius ∼λdeB, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length-scale, λSI, with λSI > λdeB – called the Thomas–Fermi (TF) regime. FDM dynamics differ from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-λdeB limit, however, we can model all three by fluid conservation equations for a compressible, γ = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, PSI ∝ ρ2. We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of RTF, the radius of an SI-pressure-supported (n = 1)-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the [‘too-big-to-fail’ + ‘cusp–core’]-test if RTF ≳ 1 kpc.

Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the mass-radius relation of Bose-Einstein condensate dark matter halos [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive self-interaction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum mass of Bose-Einstein condensate dark matter halos with an attractive self-interaction. We use the mass-radius relation of dark matter halos and the observational evidence of a ``minimum halo'' (with typical radius $R\sim 1\, {\rm kpc}$ and typical mass $M\sim 10^8\, M_{\odot}$) to constrain the mass $m$ and the scattering length $a_s$ of the dark matter particle.

Core fragmentation in simplest superfluid dark matter scenario

We study the structure of galactic halos within a scalar dark matter model, endowed with a repulsive quartic self-interaction, capable of undergoing the superfluid phase transition in high-density regions. We demonstrate that the thermalized cores are prone to fragmentation into superfluid droplets due to the Jeans instability. Furthermore, since cores of astrophysical size may be generated only when most of the particles comprising the halo reside in a highly degenerate phase-space, the well-known bound on the dark matter self-interaction cross section inferred from the collision of clusters needs to be revised, accounting for the enhancement of the interaction rate due to degeneracy. As a result, generation of kpc-size superfluid solitons, within the parameter subspace consistent with the Bullet Cluster bound, requires dark matter particles to be ultra-light.

Angular momentum and the absence of vortices in the cores of fuzzy dark matter haloes

ABSTRACT Scalar field dark matter (SFDM), comprised of ultralight (≳ 10−22 eV) bosons, is distinguished from massive (≳GeV), collisionless cold dark matter (CDM) by its novel structure-formation dynamics as Bose–Einstein condensate (BEC) and quantum superfluid with wave-like properties, described by the Gross-Pitaevskii and Poisson (GPP) equations. In the free-field (‘fuzzy’) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength λdeB, but resembles CDM on larger scales. Virialized haloes have ‘solitonic’ cores of radius ∼λdeB that follow the ground-state attractor solution of GPP, surrounded by CDM-like envelopes. As superfluid, SFDM is irrotational (vorticity-free) but can be unstable to vortex formation. We previously showed this can happen in halo cores, from angular momentum arising during structure formation, when repulsive self-interaction (SI) is present to support them out to a second length scale λSI with λSI > λdeB (the Thomas–Fermi regime), but only if SI is strong enough. This suggested FDM cores ($ {\rm without}$ SI) would not form vortices. FDM simulations later found vortices, but only outside halo cores, consistent with our previous suggestion based upon TF-regime analysis. We extend that analysis now to FDM, to show explicitly that vortices should not arise in solitonic cores from angular momentum, modelling them as either Gaussian spheres, or ( n = 2)-polytropic, irrotational Riemann-S ellipsoids. We find that, for typical halo spin parameters, angular momentum per particle is below ℏ, the minimum required even for one singly-quantized vortex in the centre. Even for higher angular momentum, however, vortex formation is not energetically favoured.

Many-particle limit for a system of interaction equations driven by Newtonian potentials

We consider a one-dimensional discrete particle system of two species coupled through nonlocal interactions driven by the Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable existence theory in a finite-dimensional framework, we explore the behaviour of the particle system in case of collisions and analyse the behaviour of the solutions with initial data featuring particle clusters. Subsequently, we prove that the empirical measure associated to the particle system converges to the unique 2-Wasserstein gradient flow solution of a system of two partial differential equations with nonlocal interaction terms in a proper measure sense. The latter result uses uniform estimates of the \(L^m\)-norms of a piecewise constant reconstruction of the density using the particle trajectories.

Decay of boson stars with application to glueballs and other real scalars

One of the most interesting candidates for dark matter are massive real scalar particles. A well-motivated example is from a pure Yang-Mills hidden sector, which locks up into glueballs in the early universe. The lightest glueball states are scalar particles and can act as a form of bosonic dark matter. If self-interactions are repulsive this can potentially lead to very massive boson stars, where the inward gravitational force is balanced by the repulsive self-interaction. This can also arise from elementary real scalars with a regular potential. In the literature it has been claimed that this allows for astrophysically significant boson stars with high compactness, which could undergo binary mergers and generate detectable gravitational waves. Here we show that previous analyses did not take into proper account $3 \to 2$ and $4 \to 2$ quantum mechanical annihilation processes in the core of the star, while other work misinterpreted the classical $3 \to 1$ process. In this work, we compute the annihilation rates, finding that massive stars will rapidly decay from the $3 \to 2$ or $4 \to 2$ processes (while the $3 \to 1$ process is typically small). Using the Einstein-Klein-Gordon equations, we also estimate the binding energy of these stars, showing that even the densest stars do not have quite enough binding energy to prevent annihilations. For such boson stars to live for the current age of the universe and to be consistent with bounds on dark matter scattering in galaxies, we find the following upper bound on their mass for $O(1)$ self-interaction couplings: $M_*<10^{-18}M_{sun}$ when $3 \to 2$ processes are allowed and $M_*<10^{-11}M_{sun}$ when only $4 \to 2$ processes are allowed. We also estimate destabilization from parametric resonance which can considerably constrain the phase space further. Furthermore, such stars are required to have very small compactness to be long lived.

Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.