Non-axisymmetric Instabilities Research Articles

Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Accretion disks are highly unstable to magnetic instabilities driven by shear flow, where classically, the axisymmetric, weak-field magnetorotational instability (MRI) has received much attention through local WKB approximations. In contrast, discrete nonaxisymmetric counterparts require a more involved analysis through a full global approach to deal with the influence of the nearby magnetohydrodynamic (MHD) continua. Recently, rigorous MHD spectroscopy identified a new type of ultralocalized, nonaxisymmetric instability in global disks with super-Alfvénic flow. These super-Alfvénic rotational instabilities (SARIs) fill vast unstable regions in the complex eigenfrequency plane with (near eigen)modes that corotate at the local Doppler velocity and are radially localized between Alfvénic resonances. Unlike discrete modes, they are utterly insensitive to the radial disk boundaries. In this work, we independently confirm the existence of these unprecedented modes using our novel spectral MHD code Legolas, reproducing and extending our earlier study with detailed eigenspectra and eigenfunctions. We calculate the growth rates of SARIs and MRI in a variety of disk equilibria, highlighting the impact of field strength and orientation, and find correspondence with analytical predictions for thin, weakly magnetized disks. We show that nonaxisymmetric modes can significantly extend instability regimes at high mode numbers, with maximal growth rates comparable to those of the MRI. Furthermore, we explicitly show a region filled with quasi-modes whose eigenfunctions are extremely localized in all directions. These modes must be ubiquitous in accretion disks, and play a role in local shearing box simulations. Finally, we revisit recent dispersion relations in the appendix, highlighting their relation to our global framework.

Floquet-based analysis on three-dimensional non-axisymmetric instabilities in oscillatory-driven Taylor–Couette flows and their low-frequency asymptotic behavior using Wentzel–Kramers–Brillouin method

This paper revisits the linear stability analysis of oscillatory-driven flows between two oscillating cylinders against non-axisymmetric disturbances. This study is motivated by the lack of a sufficiently reliable theoretical analysis giving insight into the experimentally observed spiral-like non-axisymmetric patterns when the cylinders are counter-oscillating. A new generalized time-dependent algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional Navier–Stokes equations around the purely azimuthal basic state. Numerical evaluation of the critical eigenvalues combining both Floquet theory and spectral method reveals the existence of frequency ranges where this basic state becomes unstable against three-dimensional non-axisymmetric disturbances before it does so for two-dimensional axisymmetric ones. Indeed, as the oscillation frequency of the cylinders increases, the azimuthal wave number of the critical eigensolution is found to change from 0 to 2 to 1 and then back to 0. The primary bifurcation exchange between two instability modes with different azimuthal wave numbers occurs via different types of codimension-2 bifurcation points giving rise to discontinuities in the critical axial wave number where reversing and non-reversing non-axisymmetric Taylor vortex flows are identified. In addition, by extending our numerical calculations to the co-oscillating case, we show that the axisymmetric disturbances are the most unstable confirming thus existing experimental findings. Furthermore, a Wentzel–Kramers–Brillouin (WKB) analysis is performed to shed light on the asymptotic behavior of these time-dependent flows in the low-frequency limit when the cylinders are slowly oscillating.

Effect of stellar rotation on the development of post-shock instabilities during core-collapse supernovae

Context. The growth of hydrodynamical instabilities is key to triggering a core-collapse supernova explosion during the phase of stalled accretion shock, immediately after the birth of a proto-neutron star (PNS). Stellar rotation is known to affect the standing accretion shock instability (SASI) even for small rotation rates, but its effect on the onset of neutrino-driven convection is still poorly known. Aims. We assess the effect of stellar rotation on SASI when neutrino heating is taken into account as well as the effect of rotation on neutrino-driven convection. The interplay of rotation with these two instabilities affects the frequency of the mode m = 2, which can be detected with gravitational waves at the onset of a supernova explosion. Methods. We used a linear stability analysis to study the dynamics of the accreting gas in the equatorial plane between the surface of the PNS and the stationary shock. We explored rotation effects on the relative strength of SASI and convection by considering a large range of specific angular momenta and neutrino luminosities. Results. The nature of the dominant non-axisymmetric instability developing in the equatorial post-shock region depends on both the convection parameter, χ, and the rotation rate. Equatorial convective modes with χ ≳ 5 are hampered by differential rotation. At smaller χ, however, mixed SASI-convective modes with a large angular scale, m = 1, 2, 3, can take advantage of rotation and become dominant for relatively low rotation rates, at which centrifugal effects are small. For rotation rates exceeding ∼30% of the Keplerian rotation at the PNS surface, a new instability regime is characterised by a frequency that, when measured in units of the post-shock velocity and radius, vsh/rsh, is nearly independent of the convection parameter, χ. A strong prograde m = 2 spiral dominates over a large parameter range and is favorable to the production of gravitational waves. In this regime, a simple linear relation exists between the oscillation frequency of the dominant mode and the specific angular momentum of the accreted gas. Conclusions. Three different regimes of post-shock instabilities can be distinguished depending on the rotation rate. For low rotation rates (less than 10% of the Keplerian rotation at the PNS surface), differential rotation has a linear destabilising effect on SASI and a quadratic stabilising or destabilising effect on the purely convective equatorial modes depending on their azimuthal wavenumber. Intermediate rotation rates (10% to 30% of the Keplerian rotation) lead to the emergence of mixed SASI-convection-rotation modes that involve large angular scales. Finally, strong rotation erases the influence of the buoyancy and heating rate on the instability. This independence allows for a reduction in the parameter space, which can be helpful for gravitational wave analysis.

Three dimensional magnetorotational core-collapse supernova explosions of a 39 solar mass progenitor star

ABSTRACT We perform three-dimensional simulations of magnetorotational supernovae using a $39\, {\rm M}_{\odot }$ progenitor star with two different initial magnetic field strengths of 1010 and 1012 G in the core. Both models rapidly undergo shock revival, and their explosion energies asymptote within a few hundred milliseconds to values of ≳2 × 1051 erg after conservatively correcting for the binding energy of the envelope. Magnetically collimated, non-relativistic jets form in both models, though the jets are subject to non-axisymmetric instabilities. The jets do not appear crucial for driving the explosion, as they only emerge once the shock has already expanded considerably. Our simulations predict moderate neutron star kicks of about 150 km s−1, no spin-kick alignment, and rapid early spin-down that would result in birth periods of about 20 ms, too slow to power an energetic gamma-ray burst jet. More than $0.2\, {\rm M}_\odot$ of iron-group material is ejected, but we estimate that the mass of ejected 56Ni will be considerably smaller as the bulk of this material is neutron-rich. Explosive burning does not contribute appreciable amounts of 56Ni because the burned material originates from the slightly neutron-rich silicon shell. The iron-group ejecta also showed no pronounced bipolar geometry by the end of the simulations. The models thus do not immediately fit the characteristics of observed hypernovae, but may be representative of other transients with moderately high explosion energies. The gravitational-wave emission reaches high frequencies of up to 2000 Hz and amplitudes of over 100 cm. The gravitational-wave emission is detectable out to distances of ∼4 Mpc in the planned Cosmic Explorer detector.

Numerical simulations of MHD jets from Keplerian accretion disks

Context. The most successful scenario for the origin of astrophysical jets requires a large-scale magnetic field anchored in a rotating object (black hole or star) and/or its surrounding accretion disk. Platform jet simulations, where the mass load onto the magnetic field is not computed by solving the vertical equilibrium of the disk but is imposed as a boundary condition, are very useful for probing the jet acceleration and collimation mechanisms. The drawback of such simulations is the very large parameter space: despite many previous attempts, it is very difficult to determine the generic results that can be derived from them. Aims. We wish to establish a firm link between jet simulations and analytical studies of magnetically driven steady-state jets from Keplerian accretion disks. In particular, the latter have predicted the existence of recollimation shocks – due to the dominant hoop stress –, which have so far never been observed in platform simulations. Methods. We performed a set of axisymmetric magnetohydrodynamics (MHD) simulations of nonrelativistic jets using the PLUTO code. The simulations are designed to reproduce the boundary conditions generally expected in analytical studies. We vary two parameters: the magnetic flux radial exponent α and the jet mass load κ. In order to reach the huge unprecedented spatial scales implied by the analytical solutions, we used a new method allowing us to boost the temporal evolution. Results. We confirm the existence of standing recollimation shocks at large distances. As in self-similar studies, their altitude evolves with the mass load κ. The shocks are weak and correspond to oblique shocks in a moderately high, fast magnetosonic flow. The jet emitted from the disk is focused toward the inner axial spine, which is the outflow connected to the central object. The presence of this spine is shown to have a strong influence on jet asymptotics. We also argue that steady-state solutions with α ≥ 1 are numerically out of range. Conclusions. Internal recollimation shocks may produce observable features such as standing knots of enhanced emission and a decrease in the flow rotation rate. However, more realistic simulations (e.g. fully three-dimensional) must be carried out in order to investigate nonaxisymmetric instabilities and with ejection only from a finite zone in the disk, so as to to verify whether these MHD recollimation shocks and their properties are maintained.

Impact of rotation on the multimessenger signatures of a hadron-quark phase transition in core-collapse supernovae

We study the impact of rotation on the multimessenger signals of core-collapse supernovae (CCSNe) with the occurrence of a first-order hadron-quark phase transition (HQPT). We simulate CCSNe with the \texttt{FLASH} code starting from a 20~$M_\odot$ progenitor with different rotation rates, and using the RDF equation of state from \textit{Bastian} 2021 that prescribes the HQPT. Rotation is found to delay the onset of the HQPT and the resulting dynamical collapse of the protocompact star (PCS) due to the centrifugal support. All models with the HQPT experience a second bounce shock which leads to a successful explosion. The oblate PCS as deformed by rotation gives rise to strong gravitational-wave (GW) emission around the second bounce with a peak amplitude larger by a factor of $\sim10$ than that around the first bounce. The breakout of the second bounce shock at the neutrinosphere produces a $\bar{\nu}_e$-rich neutrino burst with a luminosity of serveral 10$^{53}$~erg~s$^{-1}$. In rapidly rotating models the PCS pulsation following the second bounce generates oscillations in the neutrino signal after the burst. In the fastest rotating model with the HQPT, a clear correlation is found between the oscillations in the GW and neutrino signals immediately after the second bounce. In addition, the HQPT-induced collapse leads to a jump in the ratio of rotational kinetic energy to gravitational energy ($\beta$) of the PCS, for which persistent GW emission may arise due to secular nonaxisymmetric instabilities.

“Super-kilonovae” from Massive Collapsars as Signatures of Black Hole Birth in the Pair-instability Mass Gap

The core collapse of rapidly rotating massive ∼ 10M ⊙ stars (“collapsars”), and the resulting formation of hyperaccreting black holes, comprise a leading model for the central engines of long-duration gamma-ray bursts (GRBs) and promising sources of r-process nucleosynthesis. Here, we explore the signatures of collapsars from progenitors with helium cores ≳ 130M ⊙ above the pair-instability mass gap. While the rapid collapse to a black hole likely precludes prompt explosions in these systems, we demonstrate that disk outflows can generate a large quantity (up to ≳ 50M ⊙) of ejecta, comprised of ≳ 5–10M ⊙ in r-process elements and ∼ 0.1–1M ⊙ of 56Ni, expanding at velocities ∼0.1 c. Radioactive heating of the disk wind ejecta powers an optical/IR transient, with a characteristic luminosity ∼ 1042 erg s−1 and a spectral peak in the near-IR (due to the high optical/UV opacities of lanthanide elements), similar to kilonovae from neutron star mergers, but with longer durations ≳1 month. These “super-kilonovae” (superKNe) herald the birth of massive black holes ≳ 60M ⊙, which—as a result of disk wind mass loss—can populate the pair-instability mass gap “from above,” and could potentially create the binary components of GW190521. SuperKNe could be discovered via wide-field surveys, such as those planned with the Roman Space Telescope, or via late-time IR follow-up observations of extremely energetic GRBs. Multiband gravitational waves of ∼ 0.1–50 Hz from nonaxisymmetric instabilities in self-gravitating massive collapsar disks are potentially detectable by proposed observatories out to hundreds of Mpc; in contrast to the “chirp” from binary mergers, the collapsar gravitational-wave signal decreases in frequency as the disk radius grows (“sad trombone”).

Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability

The standard magnetorotational instability (SMRI) is a promising mechanism for turbulence and rapid accretion in astrophysical disks. It is a magnetohydrodynamic (MHD) instability that destabilizes otherwise hydrodynamically stable disk flow. Due to its microscopic nature at astronomical distances and stringent requirements in laboratory experiments, SMRI has remained unconfirmed since its proposal, despite its astrophysical importance. Here we report a nonaxisymmetric MHD instability in a modified Taylor-Couette experiment. To search for SMRI, a uniform magnetic field is imposed along the rotation axis of a swirling liquid-metal flow. The instability initially grows exponentially, becoming prominent only for sufficient flow shear and moderate magnetic field. These conditions for instability are qualitatively consistent with SMRI, but at magnetic Reynolds numbers below the predictions of linear analyses with periodic axial boundaries. Three-dimensional numerical simulations, however, reproduce the observed instability, indicating that it grows linearly from the primary axisymmetric flow modified by the applied magnetic field.

Bursting on a vortex tube with initial axial core-size perturbations

Axisymmetric rectilinear vortex tubes develop twist waves if their core size varies along the centerline. These twist waves propagate, and when two opposite-signed twist waves meet their interaction leads to vortex bursting. We perform numerical simulations of vortex tubes with a range of initial core-size perturbation amplitudes, and provide a detailed analysis of the bursting dynamics. Our results explain the main mechanisms driving and subsequently arresting the bursting process; quantify the accelerated energy dissipation due to bursting; and show that bursting is susceptible to non-axisymmetric instabilities that further accelerate the decay of the vortex tube.

Self-interactions can stabilize excited boson stars

We study the time evolution of spherical, excited (i.e. nodeful) boson star (BS) models. We consider a model including quartic self-interactions, controlled by a coupling Λ. Performing non-linear simulations of the Einstein-(complex)–Klein–Gordon system, using as initial data equilibrium BSs solutions of that system, we assess the impact of Λ in the stability properties of the BSs. In the absence of self-interactions (Λ = 0), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a non-excited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about t ∼ 104). The stabilization of the excited states for large enough self-interactions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning BSs.

Fracture patterns in viscoplastic gravity currents

Constant-flux gravity currents of viscoplastic fluid remain axisymmetric when extruded onto a dry horizontal plane. However, if the plane is coated with a shallow layer of water, the current suffers a dramatic non-axisymmetric instability in which localized $v$ -shaped cuts appear in the outer edge where the viscoplastic fluid is in contact with water. These ‘fractures’ lengthen and guide the subsequent radial outflow, leading to distinctive flower-like patterns. This pattern formation process is illustrated for two viscoplastic materials, an aqueous suspension of Carbopol, and a mixture of water and joint compound (a kaolin-based, commercially available product). The fracturing spreads over the entire upper surface of the current when deeper water baths are used, complicating the extrusion patterns. The instability can be removed entirely when the ambient water layer is replaced by an immiscible liquid of comparable viscosity, indicating that the presence of water at the surface is key to the pattern formation process. We conjecture that the underlying mechanism is the fracture under tension of the viscoplastic material, exacerbated by the ambient water.

Driving Galactic Outflows with Magnetic Fields at Low and High Redshift

Abstract Although galactic outflows play a key role in our understanding of the evolution of galaxies, the exact mechanism by which galactic outflows are driven is still far from being understood and, therefore, our understanding of associated feedback mechanisms that control the evolution of galaxies is still plagued by many enigmas. In this work, we present a simple toy model that can provide insight on how non-axisymmetric instabilities in galaxies (bars, spiral arms, warps) can lead to local exponential magnetic field growth by radial flows beyond the equipartition value by at least two orders of magnitude on a timescale of a few 100 Myr. Our predictions show that the process can lead to galactic outflows in barred spiral galaxies with a mass-loading factor η ≈ 0.1, in agreement with our numerical simulations. Moreover, our outflow mechanism could contribute to an understanding of the large fraction of barred spiral galaxies that show signs of galactic outflows in the chang-es survey. Extending our model shows the importance of such processes in high-redshift galaxies by assuming equipartition between magnetic energy and turbulent energy. Simple estimates for the star formation rate in our model together with cross correlated masses from the star-forming main sequence at redshifts z ∼ 2 allow us to estimate the outflow rate and mass-loading factors by non-axisymmetric instabilities and a subsequent radial inflow dynamo, giving mass-loading factors of η ≈ 0.1 for galaxies in the range of M ⋆ = 109–1012 M ⊙, in good agreement with recent results of sinfoni and kmos 3D.

Transient quasi-periodic oscillations at γ-rays in the TeV blazar PKS 1510-089

ABSTRACT We present periodicity search analyses on the γ-ray light curve of the TeV blazar PKS 1510-089 observed by the Fermi Large Area Telescope. We report the detection of two transient quasi-periodic oscillations: A 3.6-d QPO during the outburst in 2009 that lasted five cycles (MJD 54906–54923); and a periodicity of 92 d spanning over 650 d from 2018 to 2020 (MJD 58200–58850), which lasted for seven cycles. We employed the Lomb–Scargle periodogram, Weighted Wavelet Z-transform, redfit, and the Monte Carlo light-curve simulation techniques to find any periodicity and the corresponding significance. The 3.6-d QPO was detected at a moderate significance of ∼3.5σ, while the detection significance of the 92-d QPO was ∼7.0σ. We explore a few physical models for such transient QPOs including a binary black hole system, precession of the jet, a non-axisymmetric instability rotating around the central black hole near the innermost stable circular orbit, the presence of quasi-equidistant magnetic islands inside the jet, and a geometric model involving a plasma blob moving helically inside a curved jet.

Transient radial spray from electrified viscous jets

An applied radial electric field can influence the instability and breakup behavior of a liquid jet. Particularly, when the electric field is sufficiently strong, a multi-cone-jet structure can be formed: a number of Taylor cones arise transiently at the equator of the most deformed droplet in the jet; from the tip of each cone, a fine secondary jet is emitted, which quickly breaks up into micrometer-sized progeny droplets. This tip streaming phenomenon is experimentally investigated for finitely conducting, viscous liquid jets in the present work. Different regimes are distinguished in the Be (the electric Bond number)-We (the Weber number) plane and also in the Be-We-Oh (the Ohnesorge number) space. The results show that both viscosity and inertia have a suppression effect on the formation of a multi-cone-jet structure. Moreover, the number of secondary jets can be greatly reduced by increasing viscosity or inertia. Increasing electrical conductivity leads to intense spray of secondary jets. In addition, some interesting phenomena like the coalescence of secondary jets and the coexistence of axisymmetric and non-axisymmetric instability are observed.

Instability of coaxial viscoelastic jets under a radial electric field

In this paper we investigate temporal linear instability and absolute/convective instability of coaxial viscoelastic jets in the presence of a radial electric field. With a leaky dielectric model to describe the finite conductivity of the outer liquid, both axisymmetric instability and nonaxisymmetric instability are studied and compared to determine the predominant mode in the jet instability. For relatively small wavenumbers, the electric field suppresses the axisymmetric instability, while it enhances axisymmetric instability for relatively large wavenumbers. As the electric field increases, the instability mode tends to be a short wave. The elasticity of the inner and outer liquid is found to contribute to the coaxial jet instability, and the increase of the inner-liquid elasticity is discovered to allow the para-sinuous mode to predominate over the helical mode. Furthermore, the spatiotemporal instability analysis indicates that under weaker electric fields the axisymmetric mode is convectively unstable, but becomes absolutely unstable when the electric field is relatively strong, when the outer liquid has a certain degree of elasticity. While the nonaxisymmetric mode is found to be always absolutely unstable. A boundary line between absolute and convective instability is given on the parameter space of the Deborah number (relative relaxation time) of the outer liquid and the electrical Euler number. Our results in temporal and spatiotemporal instability analysis can be useful for understanding the origin of the different modes and desired mode control in coaxial electrospinning.

Amplification and generation of turbulence during self-gravitating collapse

Context. The formation of astrophysical structures, such as stars, compact objects, and also galaxies, entail an enhancement of densities by many orders of magnitude, which occurs through gravitational collapse. Aims. The role played by turbulence during this process is important. Turbulence generates density fluctuations, exerts a support against gravity, and possibly delivers angular momentum. How exactly turbulence behaves and is amplified during the collapse remains a matter of investigation and is the aim of the present paper. Methods. We carried out spherical averaging of the fluid equations, leading to 1D fluid equations that describe the evolution of mean quantities in particular the mean radial velocity as well as the mean radial and transverse turbulent velocities. These equations differ from the ones usually employed in the literature. We then performed a series of 3D numerical simulations of collapsing clouds for a wide range of thermal and turbulent supports with two polytropic equations of state, P ∝ ρΓ, with Γ = 1 and 1.25. For each 3D simulation, we performed a series of 1D simulations using the spherically averaged equations and the same initial conditions. Results. By performing a detailed comparison between 3D and 1D simulations, we can analyse the observed behaviours in great detail. Altogether, we find that the two approaches agree remarkably well, demonstrating the validity of the inferred equations; although, when turbulence is initially strong, major deviations from spherical geometry certainly preclude quantitative comparisons. The detailed comparisons lead us to an estimate of the turbulent dissipation parameter, which, when the turbulence is initially low, is found to be in good agreement with previous estimates of non self-gravitating supersonic turbulence. When turbulence is initially dynamically significant, larger values of the dissipation appear necessary for the 1D simulations to match the 3D ones. We find that the behaviour of turbulence depends on the cloud thermal support. If it is high, initial turbulence is amplified, as proposed earlier in the literature. However, if thermal support is low, turbulence is also generated by the development of local non-axisymmetric gravitational instabilities reaching values several times larger and in equipartition with gravitational energy. Conclusions. The inferred 1D equations offer an easy way to estimate the level reached by turbulence during gravitational collapse. Depending on the cloud thermal support, turbulence is either amplified or locally generated.

Insights into non-axisymmetric instabilities in three-dimensional rotating supernova models with neutrino and gravitational-wave signatures

ABSTRACT We present a detailed analysis to clarify what determines the growth of the low-T/|W| instability in the context of rapidly rotating core collapse of massive stars. To this end, we perform three-dimensional core-collapse supernova (CCSN) simulations of a 27 M⊙ star including several updates in the general relativistic correction to gravity, the multi-energy treatment of heavy-lepton neutrinos, and the nuclear equation of state. Non-axisymmetric deformations are analyzed from the point of view of the time evolution of the pattern frequency and the corotation radius. The corotation radius is found to coincide with the convective layer in the proto neutron star (PNS). We propose a new mechanism to account for the growth of the low-T/|W| instability in the CCSN environment. Near the convective boundary where a small Brunt–Väisälä frequency is expected, Rossby waves propagating in the azimuthal direction at mid latitude induce non-axisymmetric unstable modes in both hemispheres. They merge with each other and finally become the spiral arm in the equatorial plane. We also investigate how the growth of the low-T/|W| instability impacts the neutrino and gravitational-wave signatures.

Evolution of bare quark stars in full general relativity: Single star case

We introduce our approaches, in particular, the modifications of the primitive recovery procedure, to handle bare quark stars in numerical relativity simulations. Reliability and convergence of our implementation are demonstrated by evolving two triaxially rotating quark star models with different mass as well as a differentially rotating quark star model which has sufficiently large kinetic energy to be dynamically unstable. These simulations allow us to verify that our method is capable of resolving the evolution of the discontinuous surface of quark stars and possible mass ejection from them. The evolution of the triaxial deformation and the properties of the gravitational-wave emission from triaxially rotating quark stars are also studied, together with the mass ejection of the differentially rotating case. We find that supramassive quark stars are not likely to be ideal sources of a continuous gravitational wave as the star recovers axisymmetry much faster than models with smaller mass and gravitational-wave amplitude decays rapidly in a timescale of 10 ms, although the instantaneous amplitude from more massive models is larger. As with the differentially rotating case, our result confirms that quark stars could experience nonaxisymmetric instabilities similar to the neutron star case but with a quite small degree of differential rotation, which is expected according to previous initial-data studies.

Magnetic reconnection and thermal equilibration

When a magnetic field is forced to evolve on a time scale τev, as by footpoint motions driving the solar corona or non-axisymmetric instabilities in tokamaks, the magnetic field lines undergo large-scale changes in topology on a time scale approximately an order of magnitude longer than τev. But the physics that allows such changes operates on a time scale eight or more orders of magnitude slower. An analogous phenomenon occurs in air. Temperature equilibration occurs on a time scale approximately an order of magnitude longer than it takes air to cross a room, τev, although the physical mechanism that allows temperature equilibration is approximately four orders of magnitude slower than τev. The use of Lagrangian coordinates allows the fundamental equations to be solved and both phenomena explained. The theories of thermal equilibration and magnetic reconnection are developed in parallel to help readers obtain an understanding of the importance and implications of analyses using Lagrangian coordinates.

Stability of rotating scalar boson stars with nonlinear interactions

We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D, beginning with stationary boson star solutions. We show that the linear, non-axisymmetric instability found in mini boson stars with azimuthal number $m=1$ persists across the entire parameter space for these stars, though the timescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$ that is sufficiently far into the non-relativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar self-interactions. However, we do find regions of $m=1$ boson star parameter space where adding nonlinear interactions to the scalar potential quenches the non-axisymmetric instability, both on the non-relativistic, and the relativistic branches of solutions. We also consider select boson stars with $m=2$, finding instability in all cases. For the cases exhibiting instability, we follow the nonlinear development, finding a range of dynamics including fragmentation into multiple unbound non-rotating stars, and formation of binary black holes. Finally, we comment on the relationship between stability and criteria based on the rotating boson star's frequency in relation to that of a spherical boson star or the existence of a co-rotation point. The boson stars that we find not to exhibit instability when evolved for many dynamical times include rapidly rotating cases where the compactness is comparable to that of a black hole or neutron star.