arXiv subjects

Pablo Marchant

Publications and source records attributed to Pablo Marchant.

At least 55 records · Page 3Linked to original sources

arXiv2020

Effects of close binary evolution on the main-sequence morphology of young star clusters

Star clusters are the building blocks of galaxies. They are composed of stars of nearly equal age and chemical composition, allowing us to use them as chronometers and as testbeds for gauging stellar evolution. It has become clear recently that massive stars are formed preferentially in close binaries, in which mass transfer will drastically change the evolution of the stars. This is expected to leave a significant imprint in the distribution of cluster stars in the Hertzsprung-Russell diagram. Our results, based on a dense model grid of more than 50,000 detailed binary-evolution calculations, indeed show several distinct, coeval main-sequence (MS) components, most notably an extended MS turnoff region, and a group of near-critical rotating stars that is spread over a large luminosity range on the red side of the classical MS. We comprehensively demonstrate the time evolution of the features in an animation, and we derive analytic expressions to describe these features. We find quantitative agreement with results based on recent photometric and spectroscopic observations. We conclude that while other factors may also be at play, binary evolution has a major impact on the MS morphology of young star clusters.

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arXiv2019

No signature of the orbital motion of a putative 70 solar mass black hole in LB-1

Liu et al. (2019) recently reported the detection of a 68 [+11/-13] solar mass (Msun) black hole (BH) paired with an 8.2 [+0.9/-1.2] Msun B-type sub-giant star in the 78.9-day spectroscopic binary system LB-1. Such a black hole is over twice as massive as any other known stellar-mass black hole with non-compact companions2 and its mass approaches those that result from BH-BH coalescences that are detected by gravitational wave interferometers. Its presence in a solar-like metallicity environment challenges conventional theories of massive binary evolution, stellar winds and core-collapse supernovae, so that more exotic scenarios seem to be needed to explain the existence and properties of LB-1. Here, we show that the observational diagnostics used to derive the BH mass results from the orbital motion of the B-type star, not that of the BH. As a consequence, no evidence for a massive BH remains in the data, therefore solving the existing tension with formation models of such a massive BH at solar metallicity and with theories of massive star evolution in general.

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arXiv2019

Eclipses of continuous gravitational waves as a probe of stellar structure

Although gravitational waves only interact weakly with matter, their propagation is affected by a gravitational potential. If a gravitational wave source is eclipsed by a star, measuring these perturbations provides a way to directly measure the distribution of mass throughout the stellar interior. We compute the expected Shapiro time delay, amplification and deflection during an eclipse, and show how this can be used to infer the mass distribution of the eclipsing body. We identify continuous gravitational waves from neutron stars as the best candidates to detect this effect. When the Sun eclipses a far-away source, depending on the depth of the eclipse the time-delay can change by up to $\sim 0.034$ ms, the gravitational-wave strain amplitude can increase by $\sim 4$%, and the apparent position of the source in the sky can vary by $4''$. Accreting neutron stars with Roche-lobe filling companion stars have a high probability of exhibiting eclipses, producing similar time delays but undetectable changes in amplitude and sky location. Even for the most rapidly rotating neutron stars, this time delay only corresponds to a few percent of the phase of the gravitational wave, making it an extremely challenging measurement. However, if sources of continuous gravitational waves exist just below the limit of detection of current observatories, next-generation instruments will be able to observe them with enough precision to measure the signal of an eclipsing star. Detecting this effect would provide a new direct probe to the interior of stars, complementing asteroseismology and the detection of solar neutrinos.

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arXiv2019

Progenitors of Type IIb Supernovae: I. Evolutionary Pathways and Rates

Type IIb supernovae (SNe) are important candidates to understand mechanisms that drive the stripping of stripped-envelope (SE) supernova (SN) progenitors. While binary interactions and their high incidence are generally cited to favor them as Type IIb SN progenitors, this idea has not been tested using models covering a broad parameter space. In this paper, we use non-rotating single- and binary-star models at solar and low metallicities spanning a wide parameter space in primary mass, mass ratio, orbital period, and mass transfer efficiencies. We find that our single- and binary-star models contribute to roughly equal, however small, numbers of Type IIb SNe at solar metallicity. Binaries only dominate as progenitors at low metallicity. We also find that our models can account for less than half the observationally inferred rate for Type IIb SNe at solar metallicity, with computed rates ~<4% of core-collapse (CC) SNe. On the other hand, our models can account for the rates currently indicated by observations at low metallicity, with computed rates as high as 15% of CC SNe. However, this requires low mass transfer efficiencies (~<0.1) to prevent most progenitors from entering contact. We suggest that the stellar wind mass-loss rates at solar metallicity used in our models are too high. Lower mass-loss rates would widen the parameter space for binary Type IIb SNe at solar metallicity by allowing stars that initiate mass transfer earlier in their evolution to reach CC without getting fully stripped.

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arXiv2019

Modules for Experiments in Stellar Astrophysics (MESA): Pulsating Variable Stars, Rotation, Convective Boundaries, and Energy Conservation

We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). RSP is a new functionality in MESAstar that models the non-linear radial stellar pulsations that characterize RR Lyrae, Cepheids, and other classes of variable stars. We significantly enhance numerical energy conservation capabilities, including during mass changes. For example, this enables calculations through the He flash that conserve energy to better than 0.001 %. To improve the modeling of rotating stars in MESA, we introduce a new approach to modifying the pressure and temperature equations of stellar structure, and a formulation of the projection effects of gravity darkening. A new scheme for tracking convective boundaries yields reliable values of the convective-core mass, and allows the natural emergence of adiabatic semiconvection regions during both core hydrogen- and helium-burning phases. We quantify the parallel performance of MESA on current generation multicore architectures and demonstrate improvements in the computational efficiency of radiative levitation. We report updates to the equation of state and nuclear reaction physics modules. We briefly discuss the current treatment of fallback in core-collapse supernova models and the thermodynamic evolution of supernova explosions. We close by discussing the new MESA Testhub software infrastructure to enhance source-code development.

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arXiv2019

On the Origin of Black Hole Spin in High-mass X-Ray Binaries

Black hole (BH) spins in low-mass X-ray binaries (LMXBs) cover a range of values that can be explained by accretion after BH birth. In contrast, the three BH spin measurements in high-mass X-ray binaries (HMXBs) show only values near the maximum and likely have a different origin connected to the BH stellar progenitor. We explore here two possible scenarios to explain the high spins of BHs in HMXBs: formation in binaries that undergo mass transfer (MT) during the main sequence (MS; Case-A MT), and very close binaries undergoing chemically homogeneous evolution (CHE). We find that both scenarios are able to produce high-spin BHs if internal angular momentum (AM) transport in the progenitor star after its MS evolution is not too strong (i.e., weak coupling between the stellar core and its envelope). If instead efficient AM transport is assumed, we find that the resulting BH spins are always too low with respect to observations. The Case-A MT model provides a good fit for the BH spins, the masses of the two components, and the final orbital periods for two of the three BHs in HMXBs with measured spins. For one of them, the mass predicted for the BH companion is significantly lower than observed, but this depends strongly on the assumed efficiency of mass transfer. The CHE models predict orbital periods that are too large for all three cases considered here. We expect the Case-A MT to be much more frequent at the metallicities involved, so we conclude that the Case-A MT scenario is preferred. Finally, we predict that the stellar companions of HMXBs formed through the Case-A MT have enhanced nitrogen surface abundances, which can be tested by future observations.

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arXiv2018

Constraints on the Progenitor System of SN 2016gkg from a Comprehensive Statistical Analysis

Type IIb supernovae (SNe) present a unique opportunity for understanding the progenitors of stripped-envelope (SE) SNe as the stellar progenitor of several Type IIb SNe have been identified in pre-explosion images. In this paper, we use Bayesian inference and a large grid of non-rotating solar-metallicity single and binary stellar models to derive the associated probability distributions of single and binary progenitors of the Type IIb SN 2016gkg using existing observational constraints. We find that potential binary star progenitors have smaller pre-SN hydrogen-envelope and helium-core masses than potential single-star progenitors typically by 0.1 Msun and 2 Msun, respectively. We find that, a binary companion, if present, is a main-sequence or red-giant star. Apart from this, we do not find strong constraints on the nature of the companion star. We demonstrate that the range of progenitor helium-core mass inferred from observations could help improve constraints on the progenitor. We find that the probability that the progenitor of SN 2016gkg was a binary is 22% when we use constraints only on the progenitor luminosity and effective temperature. Imposing the range of pre-SN progenitor hydrogen-envelope mass and radius inferred from SN light-curves the probability the progenitor is a binary increases to 44%. However, there is no clear preference for a binary progenitor. This is in contrast to binaries being the currently favored formation channel for Type IIb SNe. Our analysis demonstrates the importance of statistical inference methods to constrain progenitor channels.

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arXiv2018

Modules for Experiments in Stellar Astrophysics (MESA): Convective Boundaries, Element Diffusion, and Massive Star Explosions

We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective core mass during both hydrogen and helium burning phases. Stars with $M<8\,{\rm M_\odot}$ become white dwarfs and cool to the point where the electrons are degenerate and the ions are strongly coupled, a realm now available to study with MESA due to improved treatments of element diffusion, latent heat release, and blending of equations of state. Studies of the final fates of massive stars are extended in MESA by our addition of an approximate Riemann solver that captures shocks and conserves energy to high accuracy during dynamic epochs. We also introduce a 1D capability for modeling the effects of Rayleigh-Taylor instabilities that, in combination with the coupling to a public version of the STELLA radiation transfer instrument, creates new avenues for exploring Type II supernovae properties. These capabilities are exhibited with exploratory models of pair-instability supernova, pulsational pair-instability supernova, and the formation of stellar mass black holes. The applicability of MESA is now widened by the capability of importing multi-dimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, and four new software tools -- MESAWeb, MESA-Docker, pyMESA, and mesastar.org -- to enhance MESA's education and research impact.

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arXiv2017

Ultra-luminous X-ray sources and neutron-star-black-hole mergers from very massive close binaries at low metallicity

Gravitational waves from the binary black hole (BH) merger GW150914 may enlighten our understanding of ultra-luminous X-ray sources (ULXs), as BHs>30Msun can reach luminosities>4x10^39 erg s^-1 without exceeding their Eddington limit. It is then important to study variations of evolutionary channels for merging BHs, which might instead form accreting BHs and become ULXs. It was recently shown that massive binaries with mass ratios close to unity and tight orbits can undergo efficient rotational mixing and evolve chemically homogeneously, resulting in a compact BH binary. We study similar systems by computing ~120000 detailed binary models with the MESA code covering a wide range of initial parameters. For initial mass ratios M2/M1~0.1-0.4, primaries >40Msun can evolve chemically homogeneously, remaining compact and forming a BH without undergoing Roche-lobe overflow. The secondary then expands and transfers mass to the BH, initiating a ULX phase. We predict that ~1 out of 10^4 massive stars evolves this way, and that in the local universe 0.13 ULXs per Msun yr^-1 of star-formation rate are observable, with a strong preference for low-metallicities. At metallicities log Z>-3, BH masses in ULXs are limited to 60Msun due to the occurrence of pair-instability supernovae which leave no remnant, resulting in an X-ray luminosity cut-off. At lower metallicities, very massive stars can avoid exploding as pair-instability supernovae and instead form BHs with masses above 130Msun, producing a gap in the ULX luminosity distribution. After the ULX phase, neutron-star-BH binaries that merge in less than a Hubble time are produced with a formation rate <0.2 Gpc^-3 yr^-1. We expect that upcoming X-ray observatories will test these predictions, which together with additional gravitational wave detections will provide strict constraints on the origin of the most massive BHs that can be produced by stars.

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arXiv2017

Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions

We substantially update the capabilities of the open-source software instrument Modules for Experiments in Stellar Astrophysics (MESA). MESA can now simultaneously evolve an interacting pair of differentially rotating stars undergoing transfer and loss of mass and angular momentum, greatly enhancing the prior ability to model binary evolution. New MESA capabilities in fully coupled calculation of nuclear networks with hundreds of isotopes now allow MESA to accurately simulate advanced burning stages needed to construct supernova progenitor models. Implicit hydrodynamics with shocks can now be treated with MESA, enabling modeling of the entire massive star lifecycle, from pre-main sequence evolution to the onset of core collapse and nucleosynthesis from the resulting explosion. Coupling of the GYRE non-adiabatic pulsation instrument with MESA allows for new explorations of the instability strips for massive stars while also accelerating the astrophysical use of asteroseismology data. We improve treatment of mass accretion, giving more accurate and robust near-surface profiles. A new MESA capability to calculate weak reaction rates "on-the-fly" from input nuclear data allows better simulation of accretion induced collapse of massive white dwarfs and the fate of some massive stars. We discuss the ongoing challenge of chemical diffusion in the strongly coupled plasma regime, and exhibit improvements in MESA that now allow for the simulation of radiative levitation of heavy elements in hot stars. We close by noting that the MESA software infrastructure provides bit-for-bit consistency for all results across all the supported platforms, a profound enabling capability for accelerating MESA's development.

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arXiv2016

A New Model of Roche-lobe Overflow for Short-Period Gaseous Planets and Binary Stars

Some close-in gaseous exoplanets are nearly in Roche-lobe contact, and previous studies show tidal decay can drive hot Jupiters into contact during the main sequence of their host stars. Improving upon a previous model, we present a revised model for mass transfer in a semi-detached binary system that incorporates an extended atmosphere around the donor and allows for an arbitrary mass ratio. We apply this new formalism to hypothetical, confirmed, and candidate planetary systems to estimate mass loss rates and compare with models of evaporative mass loss. Overflow may be significant for hot Neptunes out to periods of $\sim$ 2 days, while for hot Jupiters, it may only be important inward of 0.5 days. We find that CoRoT-24 b may be losing mass at a rate of more than an Earth mass in a Gyr. The hot Jupiter WASP-12 b may lose an Earth mass in a Myr, while the putative planet orbiting a T-Tauri star PTFO8-8695 might shed its atmosphere in a few Myrs. We point out that the orbital expansion that can accompany mass transfer may be less effective than previously considered because the gas accreted by the host star removes some of the system's angular momentum from the orbit, but simple scaling arguments suggest that the Roche-lobe overflow might remain stable. Consequently, the recently discovered small planets in ultra-short-periods ($<$ 1 day) may not be the remnants of hot Jupiters/Neptunes. The new model presented here has been incorporated into Modules for Experiments in Stellar Astrophysics (MESA).

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arXiv2016

Models of low-mass helium white dwarfs including gravitational settling, thermal and chemical diffusion, and rotational mixing

A large number of extremely low-mass helium white dwarfs (ELM WDs) have been discovered in recent years. The majority of them are found in close binary systems suggesting they are formed either through a common-envelope phase or via stable mass transfer in a low-mass X-ray binary (LMXB) or a cataclysmic variable (CV) system. Here, we investigate the formation of these objects through the LMXB channel with emphasis on the proto-WD evolution in environments with different metallicities. We study, for the first time, the combined effects of rotational mixing and element diffusion (e.g. gravitational settling, thermal and chemical diffusion) on the evolution of proto-WDs and on the cooling properties of the resulting WDs. We present state-of-the-art binary stellar evolution models computed with MESA for metallicities between Z=0.0002 and Z=0.02, producing WDs with masses between 0.16-0.45 M$_{\odot}$. Our results confirm that element diffusion plays a significant role in the evolution of proto-WDs that experience hydrogen shell flashes. The occurrence of these flashes produces a clear dichotomy in the cooling timescales of ELM WDs, which has important consequences e.g. for the age determination of binary millisecond pulsars. Rotational mixing is found to counteract the effect of gravitational settling in the surface layers of young, bloated ELM proto-WDs and therefore plays a key role in determining their surface chemical abundances. We predict that these proto-WDs have helium-rich envelopes through a significant part of their lifetime, a crucial ingredient for understanding the newly observed ELM proto-WD pulsators. The hydrogen envelope at detachment, although small compared to the total mass of the WD, contains enough angular momentum such that the spin frequency of the resulting WD on the cooling track is well above the orbital frequency.

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arXiv2016

A new route towards merging massive black holes

Recent advances in gravitational-wave astronomy make the direct detection of gravitational waves from the merger of two stellar-mass compact objects a realistic prospect. Evolutionary scenarios towards mergers of double compact objects generally invoke common-envelope evolution which is poorly understood, leading to large uncertainties in merger rates. We explore the alternative scenario of massive overcontact binary (MOB) evolution, which involves two very massive stars in a very tight binary which remain fully mixed due to their tidally induced high spin. We use the public stellar-evolution code MESA to systematically study this channel by means of detailed simulations. We find that, at low metallicity, MOBs produce double-black-hole (BH+BH) systems that will merge within a Hubble time with mass ratios close to one, in two mass ranges, ~25...60msun and >~ 130msun, with pair instability supernovae (PISNe) being produced in-between. Our models are also able to reproduce counterparts of various stages in the MOB scenario in the local Universe, providing direct support for it. We map the initial parameter space that produces BH+BH mergers, determine the expected chirp mass distribution, merger times, Kerr parameters and predict event rates. We typically find that for Z~<Z_sun/10, there is one BH+BH merger for ~1000 core-collapse supernovae. The advanced LIGO (aLIGO) detection rate is more uncertain and depends on the metallicity evolution. Deriving upper and lower limits from a local and a global approximation for the metallicity distribution of massive stars, we estimate aLIGO detection rates (at design limit) of ~19-550 yr^(-1) for BH+BH mergers below the PISN gap and of ~2.1-370 yr^(-1) above the PISN gap. Even with conservative assumptions, we find that aLIGO should soon detect BH+BH mergers from the MOB scenario and that these could be the dominant source for aLIGO detections.

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arXiv2015

Tidally-driven Roche-Lobe Overflow of Hot Jupiters with MESA

Many exoplanets have now been detected in orbits with ultra-short periods, very close to the Roche limit. Building upon our previous work, we study the possibility that mass loss through Roche lobe overflow (RLO) may affect the evolution of these planets, and could possibly transform a hot Jupiter into a lower-mass planet (hot Neptune or super-Earth). We focus here on systems in which the mass loss occurs slowly ("stable mass transfer" in the language of binary star evolution) and we compute their evolution in detail with the binary evolution code MESA. We include the effects of tides, RLO, irradiation and photo-evaporation of the planet, as well as the stellar wind and magnetic braking. Our calculations all start with a hot Jupiter close to its Roche limit, in orbit around a sun-like star. The initial orbital decay and onset of RLO are driven by tidal dissipation in the star. We confirm that such a system can indeed evolve to produce lower-mass planets in orbits of a few days. The RLO phase eventually ends and, depending on the details of the mass transfer and on the planetary core mass, the orbital period can remain around a few days for several Gyr. The remnant planets have a rocky core and some amount of envelope material, which is slowly removed via photo-evaporation at nearly constant orbital period; these have properties resembling many of the observed super-Earths and sub-Neptunes. For these remnant planets we also predict an anti-correlation between mass and orbital period; very low-mass planets ($M_{\rm pl}\,\lesssim\,5\,M_{\oplus}$) in ultra-short periods ($P_{\rm orb}$<1d) cannot be produced through this type of evolution.

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arXiv2015

AM Canum Venaticorum Progenitors with Helium Star Donors and the resultant Explosions

We explore the outcome of mass transfer via Roche lobe overflow (RLOF) of $M_{\rm He}\lesssim0.51 M_\odot$ pure helium burning stars in close binaries with white dwarfs (WDs). The evolution is driven by the loss of angular momentum through gravitational wave radiation (GWR), and both stars are modeled using Modules for Experiments in Stellar Astrophysics (MESA). The donors have masses of $M_{\rm He}=0.35, 0.4, \&\ 0.51M_\odot$ and accrete onto WDs of mass $M_{\rm WD}$ from $0.6M_\odot$ to $1.26M_\odot$. The initial orbital periods ($P_{\rm{orb}}$) span 20 to 80 minutes. For all cases, the accretion rate onto the WD is below the stable helium burning range, leading to accumulation of helium followed by unstable ignition. The mass of the convective core in the donors is small enough so that the WD accretes enough helium-rich matter to undergo a thermonuclear runaway in the helium shell before any carbon-oxygen enriched matter is transferred. The mass of the accumulated helium shell depends on $M_{\rm WD}$ and the accretion rate. We show that for $M_{\rm He}\gtrsim0.4 M_\odot$ and $M_{\rm WD}\gtrsim0.8 M_\odot$, the first flash is likely vigorous enough to trigger a detonation in the helium layer. These thermonuclear runaways may be observed as either faint and fast .Ia SNe, or, if the carbon in the core is also detonated, Type Ia SNe. Those that survive the first flash and eject mass will have a temporary increase in orbital separation, but GWR drives the donor back into contact, resuming mass transfer and triggering several subsequent weaker flashes.

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arXiv2015

Testing eccentricity pumping mechanisms to model eccentric long period sdB binaries with MESA

Hot subdwarf-B stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts those objects to be circularised before the onset of Roche-lobe overflow (RLOF). We aim to find binary-evolution mechanisms that can explain these eccentric long-period orbits, and reproduce the currently observed period-eccentricity diagram. Three different processes are considered; tidally-enhanced wind mass-loss, phase-dependent RLOF on eccentric orbits and the interaction between a circumbinary disk and the binary. The binary module of the stellar-evolution code MESA (Modules for Experiments in Stellar Astrophysics) is extended to include the eccentricity-pumping processes. The effects of different input parameters on the final period and eccentricity of a binary-evolution model are tested with MESA. The end products of models with only tidally-enhanced wind mass-loss can indeed be eccentric, but these models need to lose too much mass, and invariably end up with a helium white dwarf that is too light to ignite helium. Within the tested parameter space, no sdBs in eccentric systems are formed. Phase-dependent RLOF can reintroduce eccentricity during RLOF, and could help to populate the short-period part of the period-eccentricity diagram. When phase-dependent RLOF is combined with eccentricity pumping via a circumbinary disk, the higher eccentricities can be reached as well. A remaining problem is that these models favour a distribution of higher eccentricities at lower periods, while the observed systems show the opposite. The models presented here are potentially capable of explaining the period-eccentricity distribution of long-period sdB binaries, but further theoretical work on the physical mechanisms is necessary.

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arXiv2014

Stability of Hall equilibria in neutron star crusts

In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are "Hall equilibria", i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the Ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution towards an attractor, just as the purely poloidal one.

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arXiv2013

Stability of magnetic fields in non-barotropic stars: an analytic treatment

Magnetic fields in upper main-sequence stars, white dwarfs, and neutron stars are known to persist for timescales comparable to their lifetimes. From a theoretical perspective this is problematic, as it can be shown that simple magnetic field configurations are always unstable. In non-barotropic stars, stable stratification allows for a much wider range of magnetic field structures than in barotropic stars, and helps stabilize them by making it harder to induce radial displacements. Recent simulations by Braithwaite and collaborators have shown that, in stably stratified stars, random initial magnetic fields evolve into nearly axisymmetric configurations with both poloidal and toroidal components, which then remain stable for some time. It is desirable to provide an analytic study of the stability of such fields. We write an explicit expression for a plausible equilibrium structure of an axially symmetric magnetic field with both poloidal and toroidal components of adjustable strengths, in a non-barotropic static fluid star, and study its stability using the energy principle. We construct a displacement field that should be a reasonable approximation to the most unstable mode of a toroidal field, and confirm Braithwaite's result that a given toroidal field can be stabilized by a poloidal field containing much less energy than the former. This is consistent with the speculation that the toroidal field is the main reservoir powering magnetar activity. The deformation of a neutron star caused by the hidden toroidal field can also cause emission of gravitational waves.

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