arXiv subjects

Rainer Hollerbach

Publications and source records attributed to Rainer Hollerbach.

At least 19 recordsLinked to original sources

arXiv2026

Tidal dissipation in magnetised, rotating stars and planets: linear calculations exploring various magnetic field configurations

We study tidal flows in the convective envelopes of rotating, magnetised fluid bodies, such as low-mass stars and giant planets. In well-mixed convective regions, (magneto-)inertial waves are linearly excited by tidal forcing, and their dissipation can dominantly drive spin and orbital evolution in many close star-planet and binary star systems. We perform linear magnetohydrodynamic calculations of wavelike tides in spherical-shell geometry of a tidally-forced, rotating, incompressible, viscous and non-ideal magnetised fluid. Our calculations consider the widest range of magnetic field configurations to date (including both aligned and misaligned dipole fields, free-decay dipole and quadrupole fields, azimuthal "Malkus fields" and mixed poloidal-toroidal "Prendergast fields") to analyse the effects of magnetic fields on the wavelike response and dissipation. We find that the tidal response at a given frequency depends strongly on both magnetic field strength and geometry. Magnetic fields with strong poloidal components modify the flow more efficiently and introduce high-frequency Alfv\'enic resonances associated with weakly damped eigenmodes. When an enhanced (turbulent) viscosity is adopted, we find that viscous dissipation remains comparable to Ohmic dissipation for strong fields, in contrast to previous studies in which Ohmic dissipation was argued to dominate. We also explore the variation in magnetic effects as the shell thickness, magnetic Prandtl and Ekman numbers are varied. Finally, the frequency-averaged tidal power is found to be largely insensitive to the magnetic field in most cases, though significant deviations are found for free-decay fields. Our results have important implications for the tidal evolution of magnetised, rotating stars and planets.

astro-ph.EP↗

arXiv2025

Three-dimensional numerical simulations of neutron star cores in the two-fluid MHD approximation: simple configurations

Magnetic field evolution in neutron star cores is not fully understood. We describe the field evolution both for one barotropic fluid as well as two collisionally coupled barotropic fluids with different density profiles using the anelastic approximation and the Navier-Stokes equations to simulate the evolution in three dimensions. In the one-fluid case, a single fluid describes the motion of the charged particles. In the two-fluid model, the neutral fluid is coupled to the electrically conductive fluid by collisions, the latter being dragged by the magnetic field. In this model, both fluids have distinct density profiles. This forces them to move at slightly different velocities, resulting in a relative motion between the two barotropic fluids -- ambipolar diffusion. We develop a code based on Dedalus and study the evolution of simple poloidal dipolar and toroidal magnetic fields. Previous 2D studies found that poloidal magnetic fields evolve towards a stable Grad-Shafranov equilibrium. In our 3D simulations we find an instability of the two-fluid system similar to the one in the barotropic fluid system. After the instability saturates, a highly non-linear Lorentz force introduces small-scale fluid motion that leads to turbulence, development of a cascade and significant, non-axially symmetric changes in the magnetic field configuration. Fluid viscosity plays an essential role in regularizing the small-scale fluid motion, providing an energy drain.

astro-ph.HE↗

arXiv2025

Tidal dissipation and spin-orbit alignment due to the precessional instability in convection zones in rotating giant planets and stars

Tidal dissipation in star-planet systems occurs through various mechanisms, including the precessional instability. This is an instability of laminar flows (``Poincar\'{e} flows") forced by axial precession of a rotating, oblate, spin-orbit misaligned fluid planet or star, which excites inertial waves in convective regions if the dimensionless precession rate (``Poincar\'{e} number" $\mathrm{Po}$) is sufficiently large. We constrain the contribution of the precessional instability to tidal dissipation and heat transport, using Cartesian hydrodynamical simulations in a small patch of a planet, and study its interaction with turbulent convection, modelled as rotating Rayleigh-B\'{e}nard convection. The precessional instability without convection results in laminar flow at low values and turbulent flow at sufficiently high values of $\mathrm{Po}$. The associated tidal dissipation rate scales as $\mathrm{Po}^2$ and $\mathrm{Po}^3$ in each regime, respectively. With convection, the Poincar\'e number at which turbulent flow is achieved shifts to lower values for stronger convective driving. Convective motions also act on large-scale tidal flows like an effective viscosity, resulting in continuous tidal dissipation (scaling as $\mathrm{Po}^2$), which obfuscates or suppresses tidal dissipation due to precessional instability. The effective viscosities obtained agree with scaling laws previously derived using (rotating) mixing-length theory. By evaluating our scaling laws using interior models of Hot Jupiters, we find that the precessional instability is significantly more efficient than the effective viscosity of convection. The former drives alignment in 1 Gyr for a Jupiter-like planet orbiting within 23 days. Linearly excited inertial waves can be even more effective for wider orbits, aligning spins for orbits within 53-142 days.

astro-ph.EP↗

arXiv2025

From proto-neutron star dynamo to low-field magnetars

Low-field magnetars have dipolar magnetic fields that are 10-100 times weaker than the threshold, $B \gtrsim 10^{14}$ G, used to define classical magnetars, yet they produce similar X-ray bursts and outbursts. Using the first direct numerical simulations of magneto-thermal evolution starting from a dynamo-generated magnetic field, we show that the low-field magnetars can be produced as a result of a Tayler--Spruit dynamo inside the proto-neutron star. We find that these simulations naturally explain key characteristics of low-field magnetars: (1) weak ($\lesssim 10^{13}$ G) dipolar magnetic fields, (2) strong small-scale fields, and (3) magnetically induced crustal failures producing X-ray bursts. These findings suggest two distinct formation channels for classical and low-field magnetars, potentially linked to different dynamo mechanisms.

astro-ph.HE↗

arXiv2023

Tidal dissipation in stably stratified and semi-convective regions of rotating giant planets: incorporating Coriolis forces

We study how stably stratified or semi-convective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial and surface gravity waves in rotating giant planets. We explore scenarios in which stable (non-convective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealised spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semi-convective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors $Q'$) -- sufficient to explain the observed migration rates of Saturn's moons -- are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance-locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters, and hot Neptunes, providing efficient tidal circularisation rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.

astro-ph.EP↗

arXiv2023

Three-dimensional magneto-thermal evolution of off-centred dipole magnetic field configurations in neutron stars

Off-centred dipole configurations have been suggested to explain different phenomena in neutron stars, such as natal kicks, irregularities in polarisation of radio pulsars and properties of X-ray emission from millisecond pulsars. Here for the first time we model magneto-thermal evolution of neutron stars with crust-confined magnetic fields and off-centred dipole moments. We find that the dipole shift decays with time if the initial configuration has no toroidal magnetic field. The decay timescale is inversely proportional to magnetic field. The octupole moment decreases much faster than the quadrupole. Alternatively, if the initial condition includes strong dipolar toroidal magnetic field, the external poloidal magnetic field evolves from centred dipole to off-centred dipole. The surface thermal maps are very different for configurations with weak $B = 10^{13}$ G and strong $B = 10^{14}$ G magnetic fields. In the former case, the magnetic equator is cold while in the latter case it is hot. We model lightcurves and spectra of our magneto-thermal configurations. We found that in the case of cold equator, the pulsed fraction is small (below a few percent in most cases) and spectra are well described with a single blackbody. Under the same conditions models with stronger magnetic fields produce lightcurves with pulsed fraction of tens of percent. Their spectra are significantly better described with two blackbodies. Overall, the magnetic field strength has a more significant effect on bulk thermal emission of neutron stars than does the field geometry.

astro-ph.HE↗

arXiv2023

Tidal dissipation due to the elliptical instability and turbulent viscosity in convection zones in rotating giant planets and stars

Tidal dissipation in star-planet systems can occur through various mechanisms, among which is the elliptical instability. This acts on elliptically deformed equilibrium tidal flows in rotating fluid planets and stars, and excites inertial waves in convective regions if the dimensionless tidal amplitude ($\epsilon$) is sufficiently large. We study its interaction with turbulent convection, and attempt to constrain the contributions of both elliptical instability and convection to tidal dissipation. For this, we perform an extensive suite of Cartesian hydrodynamical simulations of rotating Rayleigh-B\'{e}nard convection in a small patch of a planet. We find that tidal dissipation resulting from the elliptical instability, when it operates, is consistent with $\epsilon^3$, as in prior simulations without convection. Convective motions also act as an effective viscosity on large-scale tidal flows, resulting in continuous tidal dissipation (scaling as $\epsilon^2$). We derive scaling laws for the effective viscosity using (rotating) mixing-length theory, and find that they predict the turbulent quantities found in our simulations very well. In addition, we examine the reduction of the effective viscosity for fast tides, which we observe to scale with tidal frequency ($\omega$) as $\omega^{-2}$. We evaluate our scaling laws using interior models of Hot Jupiters computed with MESA. We conclude that rotation reduces convective length scales, velocities and effective viscosities (though not in the fast tides regime). We estimate that elliptical instability is efficient for the shortest-period Hot Jupiters, and that effective viscosity of turbulent convection is negligible in giant planets compared with inertial waves.

astro-ph.EP↗

arXiv2023

Tidal dissipation in stratified and semi-convective regions of giant planets

We study how stably stratified or semi-convective layers alter the tidal dissipation rates associated with the generation of internal waves in planetary interiors. We consider if these layers could contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. We use an idealised global spherical Boussinesq model to study the influence of stable stratification and semi-convective layers on tidal dissipation rates. We carry out analytical and numerical calculations considering realistic tidal forcing and measure how the viscous and thermal dissipation rates depend on the parameters relating to the internal stratification profile. We find that the strongly frequency-dependent tidal dissipation rate is highly dependent on the parameters relating to the stable stratification, with strong resonant peaks that align with the internal modes of the system. The locations and sizes of these resonances depend on the form and parameters of the stratification, which we explore both analytically and numerically. Our results suggest that stable stratification can significantly enhance the tidal dissipation in particular frequency ranges. Analytical calculations in the low frequency regime give us scaling laws for the key parameters, including the tidal quality factor $Q'$ due to internal gravity waves. Stably stratified layers can significantly contribute to tidal dissipation in solar and extrasolar giant planets, and we estimate substantial tidal evolution for hot Neptunes. Further investigation is needed to robustly quantify the significance of the contribution in realistic interior models, and to consider the contribution of inertial waves.

astro-ph.EP↗

arXiv2022

Three-dimensional numerical simulations of ambipolar diffusion in NS cores in the one-fluid approximation: instability of poloidal magnetic field

We numerically model evolution of magnetic fields inside a neutron star under the influence of ambipolar diffusion in the weak-coupling mode in the one-fluid MHD approximation. Our simulations are three-dimensional and performed in spherical coordinates. Our model covers the neutron star core and includes crust where the magnetic field decay is due to Ohmic decay. We discover an instability of poloidal magnetic field under the influence of ambipolar diffusion. This instability develops in the neutron star core and grows on a timescale of 0.2 dimensionless times, reaching saturation by 2 dimensionless times. The instability leads to formation of azimuthal magnetic field with azimuthal wavenumber $m=14$ (at the moment of saturation) which keeps merging and reaches $m=4$ by 16 dimensionless times. Over the course of our simulations (16 dimensionless times) the surface dipolar magnetic field decays, reaching 20 percent of its original value and keeps decaying. The decay timescale for the total magnetic energy is six dimensionless times. The ambipolar diffusion induces electric currents in the crust where these currents dissipate efficiently. Strong electric currents in the crust lead to heating, which could correspond to luminosities of $\approx 10^{29}$ erg s$^{-1}$ during hundreds of Myrs for an initial magnetic field of $10^{14}$ G. Ambipolar diffusion leads to formation of small-scale magnetic fields at the neutron star surface.

astro-ph.HE↗

arXiv2021

Evolution of neutron star magnetic fields

Neutron stars are natural physical laboratories allowing us to study a plethora of phenomena in extreme conditions. In particular, these compact objects can have very strong magnetic fields with non-trivial origin and evolution. In many respects its magnetic field determines the appearance of a neutron star. Thus, understanding the field properties is important for interpretation of observational data. Complementing this, observations of diverse kinds of neutron stars enable us to probe parameters of electro-dynamical processes at scales unavailable in terrestrial laboratories. In this review we first briefly describe theoretical models of formation and evolution of magnetic field of neutron stars, paying special attention to field decay processes. Then we present important observational results related to field properties of different types of compact objects: magnetars, cooling neutron stars, radio pulsars, sources in binary systems. After that, we discuss which observations can shed light on obscure characteristics of neutron star magnetic fields and their behaviour. We end the review with a subjective list of open problems.

astro-ph.HE↗

arXiv2021

3D Magneto-thermal Simulations of Tangled Crustal Magnetic Field in Central Compact Objects

Central compact objects are young neutron stars emitting thermal X-rays with bolometric luminosities $L_X$ in the range $10^{32}$-$10^{34}$ erg/s. Gourgouliatos, Hollerbach and Igoshev recently suggested that peculiar emission properties of central compact objects can be explained by tangled magnetic field configurations formed in a stochastic dynamo during the proto-neutron star stage. In this case the magnetic field consists of multiple small-scale components with negligible contribution of global dipolar field. We study numerically three-dimensional magneto-thermal evolution of tangled crustal magnetic fields in neutron stars. We find that all configurations produce complicated surface thermal patterns which consist of multiple small hot regions located at significant separations from each other. The configurations with initial magnetic energy of $2.5-10\times 10^{47}$ erg have temperatures of hot regions that reach $\approx 0.2$ keV, to be compared with the bulk temperature of $\approx 0.1$ keV in our simulations with no cooling. A factor of two in temperature is also seen in observations of central compact objects. The hot spots produce periodic modulations in light curve with typical amplitudes of $\leq 9-11$ %. Therefore, the tangled magnetic field configuration can explain thermal emission properties of some central compact objects.

astro-ph.HE↗

arXiv2020

Sleeping beasts: strong toroidal magnetic field in quiescent magnetars explains their large pulsed fraction

Magnetars are neutron stars (NSs) with extreme magnetic fields of strength $5 \times 10^{13}$ - $10^{15}$ G. They exhibit transient, highly energetic events, such as short X-ray flashes, bursts and giant flares, all of which are powered by their enormous magnetic energy. Quiescent magnetars have X-ray luminosities between $10^{29}$ and $10^{35}$ erg/s, and are further classified as either persistent or transient magnetars. Their X-ray emission is modulated with the rotational period of the NS, with a typical relative amplitude (so-called pulsed fraction) between 10-58 per cent, implying that the surface temperature is significantly non-uniform despite the high thermal conductivity of the star's crust. Here, we present the first 3D magneto-thermal MHD simulations of magnetars with strong toroidal magnetic fields. We show that these models, combined with ray propagation in curved space-time, accurately describe the light-curves of most transient magnetars in quiescence and allow us to further constrain their rotational orientation. We find that the presence of a strong toroidal magnetic field explains the observed asymmetry in the surface temperature, and is the main cause of the strong modulation of thermal X-ray emission in quiescence.

astro-ph.HE↗

arXiv2020

Powering Central Compact Objects with a Tangled Crustal Magnetic Field

Central Compact Objects (CCOs) are X-ray sources with luminosity ranging between $10^{32}$-$10^{34}$ erg~s$^{-1}$, located at the centres of supernova remnants. Some of them have been confirmed to be neutron stars. Timing observations have allowed the estimation of their dipole magnetic field, placing them in the range $\sim10^{10}$-$10^{11}$ G. The decay of their weak dipole fields, mediated by the Hall effect and Ohmic dissipation, cannot provide sufficient thermal energy to power their X-ray luminosity, as opposed to magnetars whose X-ray luminosities are comparable. Motivated by the question of producing high X-ray power through magnetic field decay while maintaining a weak dipole field, we explore the evolution of a crustal magnetic field that does not consist of an ordered axisymmetric structure, but rather comprises a tangled configuration. This can be the outcome of a non-self-excited dynamo, buried inside the crust by fallback material following the supernova explosion. We find that such initial conditions lead to the emergence of the magnetic field from the surface of the star and the formation of a dipolar magnetic field component. An internal tangled magnetic field of the order of $10^{14}$ G can provide sufficient Ohmic heating to the crust and power CCOs, while the dipole field it forms is approximately $10^{10}$ G, as observed in CCOs.

astro-ph.HE↗

arXiv2020

Time-dependent Probability Density Functions and Information Geometry in the Fusion L-H Transition

We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a stochastic model. We highlight the limited utility of mean value and variance in understanding the L-H transition by showing strongly non-Gaussian PDFs, with the number of peaks changing in time. We also propose a new information geometric method by using information length, dynamical time scale, and information phase portrait, and show their utility in forecasting transitions and self-regulation between turbulence and zonal flows. In particular, we demonstrate the importance of intermittency (rare events of large amplitude) of zonal flows that can play an important role in promoting the L-H transition.

physics.plasm-ph↗

arXiv2020

Wave propagation in semi-convective regions of giant planets

Recent observations of Jupiter and Saturn suggest that heavy elements may be diluted in the gaseous envelope, providing a compositional gradient that could stabilise ordinary convection and produce a stably-stratified layer near the core of these planets. This region could consist of semi-convective layers with a staircase-like density profile, which have multiple convective zones separated by thin stably-stratified interfaces, as a result of double-diffusive convection. These layers could have important effects on wave propagation and tidal dissipation that have not been fully explored. We analyse the effects of these layers on the propagation and transmission of internal waves within giant planets, extending prior work in a local Cartesian model. We adopt a simplified global Boussinesq planetary model in which we explore the internal waves in a non-rotating spherical body. We begin by studying the free modes of a region containing semi-convective layers. We then analyse the transmission of internal waves through such a region. The free modes depend strongly on the staircase properties, and consist of modes with both internal and interfacial gravity wave-like behaviour. We determine the frequency shifts of these waves as a function of the number of steps to explore their potential to probe planetary internal structures. We also find that wave transmission is strongly affected by the presence of a staircase. Very large-wavelength waves are transmitted efficiently, but small-scale waves are only transmitted if they are resonant with one of the free modes. The effective size of the core is therefore larger for non-resonant modes.

astro-ph.EP↗

arXiv2018

Magnetorotational instability in Taylor-Couette flows between cylinders with finite electrical conductivity

The nonaxisymmetric azimuthal magnetorotational instability is studied for hydromagnetic Taylor-Couette flows between cylinders of finite electrical conductivity. We find that the magnetic Prandtl number Pm determines whether perfectly conducting or insulating boundary conditions lead to lower Hartmann numbers for the onset of instability. Regardless of the imposed rotation profile, for small Pm the solutions for perfectly conducting cylinders become unstable for weaker magnetic fields than the solutions for insulating cylinders. The critical Hartmann and Reynolds numbers form monotonic functions of the ratio of the electrical conductivities of the cylinders and the fluid, such that a ratio of about 10 provides a very good approximation to perfectly conducting cylinders, and a ratio of about 0.1 a very good approximation to insulating cylinders. These results are of particular relevance for the super-rotating case where the outer cylinder rotates faster than the inner one; in this case the critical onset values are substantially different for perfectly conducting versus insulating boundary conditions. An experimental realization of the super-rotating instability, with liquid sodium as the fluid and cylinders made of copper, would require an electric current of at least 33.5 kAmp running along the central axis.

physics.flu-dyn↗

arXiv2018

Stability and instability of hydromagnetic Taylor-Couette flows

Decades ago S. Lundquist, S. Chandrasekhar, P.H. Roberts and R. J.~Tayler first posed questions about the stability of Taylor-Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new questions can now be answered numerically where the nonlinear simulations even provide the instability-induced values of several transport coefficients. The cylindrical containers are axially unbounded and penetrated by magnetic background fields with axial and/or azimuthal components. The influence of the magnetic Prandtl number $Pm$ on the onset of the instabilities is shown to be substantial. The potential flow subject to axial fields becomes unstable against axisymmetric perturbations for a certain supercritical value of the averaged Reynolds number $\overline{Rm}=\sqrt{Re\cdot Rm}$ (with $Re$ the Reynolds number of rotation, $Rm$ its magnetic Reynolds number). Rotation profiles as flat as the quasi-Keplerian rotation law scale similarly but only for $Pm\gg 1$ while for $Pm\ll 1$ the instability instead sets in for supercritical $Rm$ at an optimal value of the magnetic field. Among the considered instabilities of azimuthal fields, those of the Chandrasekhar-type, where the background field and the background flow have identical radial profiles, are particularly interesting. They are unstable against nonaxisymmetric perturbations if at least one of the diffusivities is non-zero. For $Pm\ll 1$ the onset of the instability scales with $Re$ while it scales with $\overline{Rm}$ for $Pm\gg 1$. - Even superrotation can be destabilized by azimuthal and current-free magnetic fields; this recently discovered nonaxisymmetric instability is of a double-diffusive character, thus excluding $Pm= 1$. It scales with $Re$ for $Pm\to 0$ and with $Rm$ for $Pm\to \infty$.

physics.plasm-ph↗

arXiv2018

Magnetic fields driven by tidal mixing in radiative stars

Stellar magnetism plays an important role in stellar evolution theory. Approximatively 10% of observed main sequence (MS) and pre-main-sequence (PMS) radiative stars exhibit surface magnetic fields above the detection limit, raising the question of their origin. These stars host outer radiative envelopes, which are stably stratified. Therefore, they are assumed to be motionless in standard models of stellar structure and evolution. We focus on rapidly rotating, radiative stars which may be prone to the tidal instability, due to an orbital companion. Using direct numerical simulations in a sphere, we study the interplay between a stable stratification and the tidal instability, and assess its dynamo capability. We show that the tidal instability is triggered regardless of the strength of the stratification (Brunt-V{ä}is{ä}l{ä} frequency). Furthermore, the tidal instability can lead to both mixing and self-induced magnetic fields in stably stratified layers (provided that the Brunt-V{ä}is{ä}l{ä} frequency does not exceed the stellar spin rate in the simulations too much). The application to stars suggests that the resulting magnetic fields could be observable at the stellar surfaces. Indeed, we expect magnetic field strengths up to several Gauss.Consequently, tidally driven dynamos should be considered as a (complementary) dynamo mechanism, possibly operating in radiative MS and PMS stars hosting orbital companions. In particular, tidally driven dynamos may explain the observed magnetism of tidally deformed and rapidly rotating Vega-like stars.

astro-ph.SR↗