We combine electromagnetic (EM) and gravitational wave (GW) information on the binary neutron star (NS) merger GW170817 in order to constrain the radii $R_{\rm ns}$ and maximum mass $M_{\rm max}$ of NSs. GW170817 was followed by a range of EM counterparts, including a weak gamma-ray burst (GRB), kilonova (KN) emission from the radioactive decay of the merger ejecta, and X-ray/radio emission consistent with being the synchrotron afterglow of a more powerful off-axis jet. The type of compact remnant produced in the immediate merger aftermath, and its predicted EM signal, depend sensitively on the high-density NS equation of state (EOS). For a soft EOS which supports a low $M_{\rm max}$, the merger undergoes a prompt collapse accompanied by a small quantity of shock-heated or disk wind ejecta, inconsistent with the large quantity $\gtrsim 10^{-2}M_{\odot}$ of lanthanide-free ejecta inferred from the KN. On the other hand, if $M_{\rm max}$ is sufficiently large, then the merger product is a rapidly-rotating supramassive NS (SMNS), which must spin-down before collapsing into a black hole. A fraction of the enormous rotational energy necessarily released by the SMNS during this process is transferred to the ejecta, either into the GRB jet (energy $E_{\rm GRB}$) or the KN ejecta (energy $E_{\rm ej}$), also inconsistent with observations. By combining the total binary mass of GW170817 inferred from the GW signal with conservative upper limits on $E_{\rm GRB}$ and $E_{\rm ej}$ from EM observations, we constrain the likelihood probability of a wide-range of previously-allowed EOS. These two constraints delineate an allowed region of the $M_{\rm max}-R_{\rm ns}$ parameter space, which once marginalized over NS radius places an upper limit of $M_{\rm max} \lesssim 2.17M_{\odot}$ (90\%), which is tighter or arguably less model-dependent than other current constraints.

https://iopscience.iop.org/article/10.3847/2041-8213/aa991c/pdf

Constraining the Maximum Mass of Neutron Stars from Multi-messenger Observations of GW170817

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst-active x-ray pulsars, the anomalous x-ray pulsars (AXPs) and the soft gamma repeaters (SGRs); the latter emitted also three 'giant flares', extremely powerful events during which luminosities can reach up to 10(47) erg s(-1) for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or 'outbursting', and 'low-field' magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent x-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.

http://iopscience.iop.org/article/10.1088/0034-4885/78/11/116901/pdf

Magnetars: the physics behind observations. A review.

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares," extremely powerful events during which luminosities can reach up to 10^47 erg/s for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or "outbursting," and "low-field" magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent X-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.

Magnetars: the physics behind observations

Constraining the Maximum Mass of Neutron Stars From Multi-Messenger Observations of GW170817

The Sun and other stars are magnetic: magnetism pervades their interiors and affects their evolution in a variety of ways In the Sun, both the fields themselves and their influence on other phenomena can be uncovered in exquisite detail, but these observations sample only a moment in a single star's life By turning to observations of other stars, and to theory and simulation, we may infer other aspects of the magnetism-eg, its dependence on stellar age, mass, or rotation rate-that would be invisible from close study of the Sun alone Here, we review observations and theory of magnetism in the Sun and other stars, with a partial focus on the "Solar-stellar connection": ie, ways in which studies of other stars have influenced our understanding of the Sun and vice versa We briefly review techniques by which magnetic fields can be measured (or their presence otherwise inferred) in stars, and then highlight some key observational findings uncovered by such measurements, focusing (in many cases) on those that offer particularly direct constraints on theories of how the fields are built and maintained We turn then to a discussion of how the fields arise in different objects: first, we summarize some essential elements of convection and dynamo theory, including a very brief discussion of mean-field theory and related concepts Next we turn to simulations of convection and magnetism in stellar interiors, highlighting both some peculiarities of field generation in different types of stars and some unifying physical processes that likely influence dynamo action in general We conclude with a brief summary of what we have learned, and a sampling of issues that remain uncertain or unsolved

Magnetism, dynamo action and the solar-stellar connection

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

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

A strong candidate for a source of gravitational waves is a highly magnetized, rapidly rotating neutron star (magnetar) deformed by internal magnetic stresses. We calculate the mass quadrupole moment by perturbing a zeroth-order hydrostatic equilibrium by an axisymmetric magnetic field with a linked poloidal-toroidal structure. In this work, we do not require the model star to obey a barotropic equation of state (as a realistic neutron star is not barotropic), allowing us to explore the hydromagnetic equilibria with fewer constraints. We derive the relation between the ratio of poloidal to total field energy Λ and ellipticity e, and briefly compare our results to those obtained using the barotropic assumption. Then, we present some examples of how our results can be applied to astrophysical contexts. First, we show how our formulae, in conjunction with current gravitational wave (non-)detections of the Crab pulsar and the Cassiopeia A central compact object (Cas A CCO), can be used to constrain the strength of the internal toroidal fields of those objects. We find that, for the Crab pulsar (whose canonical equatorial dipole field strength, inferred from spin-down, is 4 × 108 T) to emit detectable gravitational radiation, the neutron star must have a strong toroidal field component, with maximum internal toroidal field strength Btm= 7 × 1012 T; for gravitational waves to be detected from the Cas A CCO at 300Hz, Btm∼ 1013 T, whereas detection at 100Hz would require Btm∼ 1014 T. Using our results, we also show how the gravitational wave signal emitted by a magnetar immediately after its birth (assuming it is born rapidly rotating, with Λ≲ 0.2) makes such a newborn magnetar a stronger candidate for gravitational wave detection than, for example, an SGR giant flare. © 2011 The Authors. Monthly Notices of the Royal Astronomical Society © 2011 RAS.

Gravitational wave emission from a magnetically deformed non-barotropic neutron star

In 1977, Flowers & Ruderman described a perturbation that destabilizes a purely dipolar magnetic field in a fluid star. They considered the effect of cutting the star in half along a plane containing the symmetry axis and rotating each half by 90 ◦ in opposite directions, which would cause the energy of the magnetic field in the exterior of the star to be greatly reduced, just as it happens with a pair of aligned magnets. We formally solve for the energy of the external magnetic field and check that it decreases monotonically along the entire rotation. We also describe the instability using perturbation theory, and show that it happens due to the work done by the interaction of the magnetic field with surface currents. Finally, we consider the stabilizing effect of adding a toroidal field by studying the potential energy perturbation when the rotation is not done along a sharp cut, but with a continuous displacement field that switches the direction of rotation across a region of small but finite width. Using these results, we estimate the relative strengths of the toroidal and poloidal fields needed to make the star stable to this displacement and show that the energy of the toroidal field required for stabilization is much smaller than the energy of the poloidal field. We also show that, contrary to a common argument, the Flowers–Ruderman instability cannot be applied many times in a row to reduce the external magnetic energy indefinitely.

Revisiting the Flowers-Ruderman instability of magnetic stars

In 1977, Flowers and Ruderman described a perturbation that destabilises a purely dipolar magnetic field in a fluid star. They considered the effect of cutting the star in half along a plane containing the symmetry axis and rotating each half by $90\degr$ in opposite directions, which would cause the energy of the magnetic field in the exterior of the star to be greatly reduced, just as it happens with a pair of aligned magnets. We formally solve for the energy of the external magnetic field and check that it decreases monotonously along the entire rotation. We also describe the instability using perturbation theory, and see that it happens due to the work done by the interaction of the magnetic field with surface currents. Finally, we consider the stabilising effect of adding a toroidal field by studying the potential energy perturbation when the rotation is not done along a sharp cut, but with a continuous displacement field that switches the direction of rotation across a region of small but finite width. Using these results, we estimate the relative strengths of the toroidal and poloidal field needed to make the star stable to this displacement and see that the energy of the toroidal field required for stabilisation is much smaller than the energy of the poloidal field. We also show that, contrary to a common argument, the Flowers-Ruderman instability cannot be applied many times in a row to reduce the external magnetic energy indefinitely.

Taner Akgün

Papers

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

Gravitational wave emission from a magnetically deformed non-barotropic neutron star

Revisiting the Flowers-Ruderman instability of magnetic stars

Revisiting the Flowers-Ruderman instability of magnetic stars