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We present numerical solutions for stationary and axisymmetric equilibriums of compact stars associated with extremely strong magnetic fields. The interior of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD) conditions, while in the region of negligible mass density the force-free conditions or electromagnetic vacuum are assumed. Solving all components of Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free conditions, equilibriums of rotating compact stars associated with mixed poloidal and toroidal magnetic fields are obtained. It is found that in the extreme cases the strong mixed magnetic fields concentrating in a toroidal region near the equatorial surface expel the matter and form a force-free toroidal magnetotunnel. We also introduce a new differential rotation law for computing solutions associated with force-free magnetosphere, and present other extreme models without the magnetotunnel., Comment: 13 pages, 4 figures

We perform general relativistic simulations of self-gravitating black hole-disks in which the spin of the black hole is significantly tilted ($45^\circ$ and $90^\circ$) with respect to the angular momentum of the disk and the disk-to-black hole mass ratio is $16\%-28\%$. The black holes are rapidly spinning with dimensionless spins up to $\sim 0.97$. These are the first self-consistent hydrodynamic simulations of such systems, which can be prime sources for multimessenger astronomy. In particular tilted black hole-disk systems lead to: i) black hole precession; ii) disk precession and warping around the black hole; iii) earlier saturation of the Papaloizou-Pringle instability compared to aligned/antialigned systems, although with a shorter mode growth timescale; iv) acquisition of a small black-hole kick velocity; v) significant gravitational wave emission via various modes beyond, but as strong as, the typical $(2,2)$ mode; and vi) the possibility of a broad alignment of the angular momentum of the disk with the black hole spin. This alignment is not related to the Bardeen-Petterson effect and resembles a solid body rotation. Our simulations suggest that any electromagnetic luminosity from our models may power relativistic jets, such as those characterizing short gamma-ray bursts. Depending on the black hole-disk system scale the gravitational waves may be detected by LIGO/Virgo, LISA and/or other laser interferometers.

We perform general relativistic, magnetohydrodynamic (GRMHD) simulations of merging binary neutron stars incorporating neutrino transport and magnetic fields. Our new radiative transport module for neutrinos adopts a general relativistic, truncated-moment (M1) formalism. The binaries consist of two identical, irrotational stars modeled by the SLy nuclear equation of state (EOS). They are initially in quasicircular orbit and threaded with a poloidal magnetic field that extends from the stellar interior into the exterior, as in typical pulsars. We insert neutrino processes shortly after the merger and focus on the role of neutrinos in launching a jet following the collapse of the hypermassive neutron star (HMNS) remnant to a spinning black hole (BH). We treat two microphysical versions: one (a "warm-up") evolving a single neutrino species and considering only charged-current processes, and the other evolving three species $(\nu_e, \bar{\nu}_e, \nu_{\rm x})$ and related processes. We trace the evolution until the system reaches a quasiequilibrium state after BH formation. We find that the BH + disk remnant eventually launches an incipient jet. The electromagnetic Poynting luminosity is $\sim 10^{53} \rm \, erg\, s^{-1}$, consistent with that of typical short gamma-ray bursts (sGRBs). The effect of neutrino cooling shortens the lifetime of the HMNS, and lowers the amplitude of the major peak of the gravitational wave (GW) power spectrum somewhat. After BH formation, neutrinos help clear out the matter near the BH poles, resulting in lower baryon-loaded surrounding debris. The neutrino luminosity resides in the range $\sim 10^{52-53} \rm \,erg\,s^{-1}$ once quasiequilibrium is achieved. Comparing with the neutrino-free models, we observe that the inclusion of neutrinos yields similar ejecta masses and is inefficient in carrying off additional angular momentum., Comment: 32 page, 16 figures

We perform the first magnetohydrodynamic simulations in full general relativity of self-consistent rotating neutron stars (NSs) with ultrastrong mixed poloidal and toroidal magnetic fields. The initial uniformly rotating NS models are computed assuming perfect conductivity, stationarity, and axisymmetry. Although the specific geometry of the mixed field configuration can delay or accelerate the development of various instabilities known from analytic perturbative studies, all our models finally succumb to them. Differential rotation is developed spontaneously in the cores of our magnetars which, after sufficient time, is converted back to uniform rotation. The rapidly rotating magnetars show a significant amount of ejecta, which can be responsible for transient kilonova signatures. However no highly collimated, helical magnetic fields or incipient jets, which are necessary for gamma-ray bursts, arise at the poles of these magnetars by the time our simulations are terminated., 8 pages

We have evolved mergers of equal-mass binary quark stars, the total mass of which is close to the mass shedding limit of uniformly rotating configurations, in fully general relativistic hydrodynamic simulations, aimed at investigating the post-merger outcomes. In particular, we have identified the threshold mass for prompt black hole formation after the merger, by tracing the minimum lapse function as well as the amount of ejected material during the merger simulation. A semi-analytical investigation based on the angular momentum contained in the merger remnant is also performed to verify the results. For the equation of state considered in this work, the maximum mass of TOV solutions for which is 2.10 $M_\odot$, the threshold mass is found between 3.05 and 3.10 $M_\odot$. This result is consistent (with a quantitative error smaller than 1%) with the universal relation derived from the numerical results of symmetric binary neutron star mergers. Contrary to the neutron star case, the threshold mass is close to the mass shedding limit of uniformly rotating quark star. Consequently, we have found that binary quark stars with total mass corresponding to the long-lived supramassive remnant for neutron star case, could experience collapse to black hole within several times dynamical timescale, making quark stars as exceptions of the commonly accepted post-merger scenarios for binary neutron star mergers. We have suggested explanation for both the similarity and the difference, between quark stars and neutron stars., Comment: 6 pages, 4 figures. Comments are welcome

The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short $\gamma$-ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and played a pivotal role in furthering our understanding on a number of longstanding questions. Numerical modelling of such multimessenger sources is an important tool to understand the physics of compact objects and, more generally, the physics of matter under extreme conditions. In this review we present a unified view of various techniques used to obtain equilibrium and quasiequilibrium solutions for three astrophysically relevant relativistic, self-gravitating fluid systems: Binary neutron stars, black hole-disks, and magnetized rotating neutron stars. These solutions are necessary not only for modeling such compact objects, but equally important, for providing self-consistent initial data in numerical relativity simulations. Instead of presenting the full details of the formulations and numerical algorithms, we focus on painting the broadbrush picture of the methods developed to address these problems, and facilitate future work in the area., Comment: Invited review, 74 pages, no figures. This article is dedicated to the memory of Yoshiharu Eriguchi, whose work on self-gravitating fluids has been a source of inspiration

We perform general relativistic, magnetohydrodynamic (GRMHD) simulations of binary neutron stars in quasi-circular orbit that merge and undergo delayed or prompt collapse to a black hole (BH). The stars are irrotational and modeled using an SLy or an H4 nuclear equation of state. To assess the impact of the initial magnetic field configuration on jet launching, we endow the stars with a purely poloidal magnetic field that is initially unimportant dynamically and is either confined to the stellar interior or extends from the interior into the exterior as in typical pulsars. Consistent with our previous results, we find that only the BH + disk remnants originating from binaries that form hypermassive neutron stars (HMNSs) and undergo delayed collapse can drive magnetically-powered jets. We find that the closer the total mass of the binary is to the threshold value for prompt collapse, the shorter is the time delay between the gravitational wave peak amplitude and jet launching. This time delay also strongly depends on the initial magnetic field configuration. We also find that seed magnetic fields confined to the stellar interior can launch a jet over $\sim 25\,\rm ms$ later than those with pulsar-like magnetic fields. The lifetime of the jet [$\Delta t\lesssim 150\,\rm ms$] and its outgoing Poynting luminosity [$L_{\rm EM}\sim 10^{52\pm 1}\rm erg/s$] are consistent with typical short gamma-ray burst central engine lifetimes, as well as with the Blandford--Znajek mechanism for launching jets and their associated Poynting luminosities. Our numerical results also suggest that the dynamical ejection of matter can be enhanced by the magnetic field. Therefore, GRMHD studies are required to fully understand kilonova signals from GW170818-like events., Comment: 21 pages, 12 figures. Matches published version

We perform the first fully general relativistic, magnetohydrodynamic simulations of dynamically stable hypermassive neutron stars with and without ergoregions to assess the impact of ergoregions on launching magnetically--driven outflows. The hypermassive neutron stars are modeled by a compressible and causal equation of state and are initially endowed with a dipolar magnetic field extending from the stellar interior into its exterior. We find that, after a few Alfv\'en times, magnetic field lines in the ergostar (star that contains ergoregions) and the normal star have been tightly wound in both cases into a helical funnel within which matter begins to flow outward. The maximum Lorentz factor in the outflow is $\Gamma_L \sim 2.5$, while the force-free parameter holds at $B^2/8\pi\rho_0\lesssim 10$. These values are incompatible with highly relativistic, magnetically-driven outflows (jets) and short $\gamma$-ray bursts. We compare these results with those of a spinning black hole surrounded by a magnetized, massless accretion disk that launches a bona fide jet. Our simulations suggest that the Blandford-Znajek mechanism for launching relativistic jets only operates when a black hole is present, though the Poynting luminosity in all cases is comparable. Therefore, one cannot distinguish a magnetized, accreting black hole from a magnetized hypermassive neutron star in the so-called mass-gap based solely on the value of the observed Poynting luminosity. These results complement our previous studies of supramassive remnants and suggest that it would be challenging for either normal neutron stars or ergostars in a hypermassive state to be the progenitors of short $\gamma$-ray bursts., Comment: 7 pages, 3 figures. Matches published version

The recent discovery by LIGO/Virgo of a merging binary having a $\sim 23 M_\odot$ black hole and a $\sim 2.6 M_\odot$ compact companion has triggered a debate regarding the nature of the secondary, which falls into the so-called mass gap. Here we explore some consequences of the assumption that the secondary was a neutron star (NS). We show with concrete examples of heretofore viable equations of state (EOSs) that rapid uniform rotation may neither be necessary for some EOSs nor sufficient for others to explain the presence of a NS. Absolute upper limits for the maximum mass of a spherical NS derived from GW170817 already suggest that this unknown compact companion might be a slowly or even a nonrotating NS. However several soft NS EOSs favored by GW170817 with maximum spherical masses $\lesssim 2.1 M_\odot$ cannot be invoked to explain this object, even allowing for maximum uniform rotation. By contrast, sufficiently stiff EOSs that yield $2.6 M_\odot$ NSs which are slowly rotating or, in some cases, nonrotating, and are compatible with GW170817 and the results of NICER, can account for the black hole companion., 7 pages, 2 figures. Matches published version

Binary neutron star (NSNS) mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of spinning NSNSs initially on quasicircular orbits that merge and undergo delayed collapse to a black hole (BH). The NSNSs consist of two identical stars modeled as $\Gamma=2$ polytropes with spin $\chi_{NS}= 0.36$ aligned along the direction of the total orbital angular momentum $L$. Each star is initially threaded by a dynamical unimportant interior dipole B-field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment $\mu$ is either aligned or perpendicular to $L$ and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where $\mu$ in both stars is aligned along $L$. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta are very sensitive to the B-field orientation. By contrast, the physical properties of the BH + disk remnant, such as the mass and spin of the BH, the accretion rate, and the electromagnetic luminosity, are roughly independent of the initial B-field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results show that an incipient jet emerges only when the seed B-field has a sufficiently large-scale poloidal component aligned to $L$. The lifetime [$\Delta t\gtrsim 140(M_{NS}/1.625M_\odot)\rm ms$] and Poynting luminosities [$L_{EM}\simeq 10^{52}$erg/s] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford--Znajek mechanism for launching jets., Comment: 16 pages, 12 figures. Matches published version

Recently, we have shown that dynamically stable ergostar solutions (equilibrium neutron stars that contain an ergoregion) with a compressible and causal equation of state exist [A. Tsokaros, M. Ruiz, L. Sun, S. L. Shapiro, and K. Ury\=u, Phys. Rev. Lett. 123, 231103 (2019)]. These stars are hypermassive, differentially rotating, and highly compact. In this work, we make a systematic study of equilibrium models in order to locate the position of ergostars in parameter space. We adopt four equations of state that differ in the matching density of a maximally stiff core. By constructing a large number of models both with uniform and differential rotation of different degrees, we identify the parameters for which ergostars appear. We find that the most favorable conditions for the appearance of dynamically stable ergostars are a significant finite density close to the surface of the star (i.e., similar to self-bound quark stars) and a small degree of differential rotation., Comment: 8 pages, 3 figures. Matches published version

Black hole-neutron star (BHNS) mergers are thought to be sources of gravitational waves (GWs) with coincident electromagnetic (EM) counterparts. To further probe whether these systems are viable progenitors of short gamma-ray bursts (sGRBs) and kilonovae, and how one may use (the lack of) EM counterparts associated with LIGO/Virgo candidate BHNS GW events to sharpen parameter estimation, we study the impact of neutron star spin in BHNS mergers. Using dynamical spacetime magnetohydrodynamic simulations of BHNSs initially on a quasicircular orbit, we survey configurations that differ in the BH spin ($a_{\rm BH}/M_{\rm BH}=0$ and $0.75$), the NS spin ($a_{\rm NS}/M_{\rm NS}=-0.17,\,0,\,0.23$ and $0.33$), and the binary mass ratio ($q\equiv M_{\rm BH}:M_{\rm NS}=3:1$ and $5:1$). The general trend we find is that increasing the NS prograde spin increases both the rest mass of the accretion disk onto the remnant black hole, and the rest mass of dynamically ejected matter. By a time~$\Delta t\sim 3500-5500M\sim 88-138(M_{\rm NS}/1.4M_\odot)\,\rm ms$ after the peak gravitational wave amplitude, a magnetically--driven jet is launched only for $q=3:1$ regardless of the initial NS spin. The lifetime of the jets [$\Delta t\sim 0.5-0.8(M_{\rm NS}/1.4 M_\odot)\,\rm s$] and their outgoing Poynting luminosity [$L_{\rm Poyn}\sim 10^{51.5\pm 0.5}\,\rm erg/s$] are consistent with typical sGRBs luminosities and expectations from the Blandford-Znajek mechanism. By the time we terminate our simulations, we do not observe either an outflow or a large-scale magnetic field collimation for the other systems we considered. The mass range of dynamically ejected matter is $10^{-4.5}-10^{-2}~(M_{\rm NS}/1.4M_\odot)M_\odot$, which can power kilonovae with peak bolometric luminosities $L_{\rm knova}\sim 10^{40}-10^{41.4}$ erg/s with rise times $\lesssim 6.5\,\rm h$ and potentially detectable by the LSST., Comment: 15 pages, 10 figures. Matches published version

We present fully general-relativistic numerical evolutions of self-gravitating tori around spinning black holes with dimensionless spin $a/M = 0.7$ parallel or anti-parallel to the disk angular momentum. The initial disks are unstable to the hydrodynamic Papaloizou-Pringle Instability which causes them to grow persistent orbiting matter clumps. The effect of black hole spin on the growth and saturation of the instability is assessed. We find that the instability behaves similarly to prior simulations with non-spinning black holes, with a shift in frequency due to spin-induced changes in disk orbital period. Copious gravitational waves are generated by these systems, and we analyze their detectability by current and future gravitational wave observatories for large range of masses. We find that systems of $10 M_\odot$ - relevant for black hole-neutron star mergers - are detectable by Cosmic Explorer out to $\sim300$ Mpc, while DECIGO (LISA) will be able to detect systems of $1000 M_\odot$ ($10^5M_\odot$) - relevant for disks forming in collapsing supermassive stars - out to cosmological redshift of $z\sim5$ ($z\sim 1$). Computing the accretion rate of these systems we find that these systems may also be promising sources of coincident electromagnetic signals., Comment: 15 pages, 12 figures

Can one distinguish a binary black hole undergoing a merger from a binary neutron star if the individual compact companions have masses that fall inside the so-called mass gap of $3-5\ M_\odot$? For neutron stars, achieving such masses typically requires extreme compactness and in this work we present initial data and evolutions of binary neutron stars initially in quasiequilibrium circular orbits having a compactness $C=0.336$. These are the most compact, nonvacuum, quasiequilibrium binary objects that have been constructed and evolved to date, including boson stars. The compactness achieved is only slightly smaller than the maximum possible imposed by causality, $C_{\rm max}=0.355$, which requires the sound speed to be less than the speed of light. By comparing the emitted gravitational waveforms from the late inspiral to merger and postmerger phases between such a binary neutron star vs a binary black hole of the same total mass we identify concrete measurements that serve to distinguish them. With that level of compactness, the binary neutron stars exhibit no tidal disruption up until merger, whereupon a prompt collapse is initiated even before a common core forms. Within the accuracy of our simulations the black hole remnants from both binaries exhibit ringdown radiation that is not distinguishable from a perturbed Kerr spacetime. However, their inspiral leads to phase differences of the order of $\sim 5$ rad over an $\sim 81$ km separation (1.7 orbits) while typical neutron stars exhibit phase differences of $\geq 20$ rad. Although a difference of $\sim 5$ rad can be measured by current gravitational wave laser interferometers (e.g., aLIGO/Virgo), uncertainties in the individual masses and spins will likely prevent distinguishing such compact, massive neutron stars from black holes., 8 pages, 9 figures. Matches published version

Following the detection of GW170817 and the accompanying kilonova AT2017gfo, it has become crucial to model and understand the various channels through which mass is ejected in neutron-star binary mergers. We discuss the impact that high stellar spins prior to merger have on the ejection of mass focussing, in particular, on the dynamically ejected mass by performing general-relativistic magnetohydrodynamic simulations employing finite-temperature equations of state and neutrino-cooling effects. Using eight different models with dimensionless spins ranging from $\chi\simeq-0.14$ to $\chi\simeq0.29$ we discuss how the presence of different spins affects the angular distribution and composition of the ejected matter. Most importantly, we find that the dynamical component of the ejected mass can be strongly suppressed in the case of high spins aligned with the orbital angular momentum. In this case, in fact, the merger remnant has an excess angular momentum yielding a more extended and "colder" object, with reduced ability to shed mass dynamically. We discuss how this result impacts the analysis of the recent merger event GW170817 and its kilonova afterglow., Comment: matches accepted version

We perform long-term simulations of spinning binary neutron stars, with our highest dimensionless spin being $\chi \sim 0.32$. To assess the importance of spin during the inspiral we vary the spin, and also use two equations of state, one that consists of plain nuclear matter and produces compact stars (SLy), and a hybrid one that contains both nuclear and quark matter and leads to larger stars (ALF2). Using high resolution that has grid spacing $\Delta x\sim 98$ m on the finest refinement level, we find that the effects of spin in the phase evolution of a binary system can be larger than the one that comes from tidal forces. Our calculations demonstrate explicitly that although tidal effects are dominant for small spins ($\lesssim 0.1$), this is no longer true when the spins are larger, but still much smaller than the Keplerian limit., Comment: 11 pages, 6 figures

The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: a) the boundary is not known a-priori, but constitutes part of the solution of the problem; b) various terms become singular at the boundary. In this work, we present a new method to solve the fluid Poisson equation for irrotational/spinning binary neutron stars. The advantage of the new method is that it does not require complex fluid surface fitted coordinates and it can be implemented in a Cartesian grid, which is a standard choice in numerical relativity calculations. This is accomplished by employing the source term method proposed by Towers, where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The issue of singular terms caused by vanishing density on the surface is resolved with an additional separation that shifts the computation boundary to the interior of the star. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver COCAL, we demonstrate agreement to approximately $1\%$. Our method can be used in other problems with non-smooth solutions like in magnetized neutron stars., Comment: 24 pages, 15 figures

We construct the first dynamically stable ergostars (equilibrium neutron stars that contain an ergoregion) for a compressible, causal equation of state. We demonstrate their stability by evolving both strict and perturbed equilibrium configurations in full general relativity for over a hundred dynamical timescales ($\gtrsim 30$ rotational periods) and observing their stationary behavior. This stability is in contrast to earlier models which prove radially unstable to collapse. Our solutions are highly differentially rotating hypermassive neutron stars with a corresponding spherical compaction of $C=0.3$. Such ergostars can provide new insights into the geometry of spacetimes around highly compact, rotating objects and on the equation of state at supranuclear densities. Ergostars may form as remnants of extreme binary neutron star mergers and possibly provide another mechanism for powering short gamma-ray bursts., 5 pages, 3 figures, to appear in PRL