Magnetic flares and induced oscillations of magnetars (super-magnetized neutron stars) are promising sources of gravitational waves (GWs). We suggest that the GW emission, if any, would last longer than the observed X-ray quasi-periodic oscillations (X-QPOs), calling for the longer-term GW analyses from a day to months than the current searches. Like the pulsar timing, the oscillation frequency would also evolve with time because of the decay or reconfiguration of magnetic field, which is crucial for the GW detection. With the observed GW frequency and its time-derivatives, we can probe the interior magnetic field strength and its evolution to open a new GW asteroseismology with the next generation interferometers like advanced LIGO, advanced VIRGO, LCGT and ET.
State-of-the-art numerical simulations of core-collapse supernovae reveal that the main source of gravitational waves is the excitation of proto-neutron star modes during post-bounce evolution. In this work we derive universal relations that relate the frequencies of the most common oscillation modes observed, i.e. g-modes, p-modes and the f-mode, with fundamental properties of the system, such as the surface gravity of the proto-neutron star or the mean density in the region enclosed by the shock. These relations are independent of the equation of state, the neutrino treatment, and the progen…
Magnetars are neutron stars with exceptionally strong dipole magnetic fields which are observed to display a range of x-ray flaring behavior, but the flaring mechanism is not well understood. The third observing run of Advanced LIGO and Virgo extended from April 1, 2019 to March 27, 2020, and contained x-ray flares from known magnetar SGR 1935+2154, as well as the newly-discovered magnetar, Swift J1818-1607. We search for gravitational waves coincident with these magnetar flares with minimally modeled, coherent searches which specifically target both short-duration gravitational waves produced…
Understanding the evolution of the angle $χ$ between a magnetar's rotation and magnetic axes sheds light on the star's birth properties. This evolution is coupled with that of the stellar rotation $Ω$, and depends on the competing effects of internal viscous dissipation and external torques. We study this coupled evolution for a model magnetar with a strong internal toroidal field, extending previous work by modelling -- for the first time in this context -- the strong proto-magnetar wind acting shortly after birth. We also account for the effect of buoyancy forces on viscous dissipation at la…
We examine the gravitational wave frequencies from neutron stars during thermal evolution, adopting the relativistic Cowling approximation. We particularly focus on the neutron star models, in which the direct Urca (rapid cooling process) does not work, without the superfluidity and superconductivity. For such models, the cooling curve hardly depends on the equation of state (EOS) as well as the mass of neutron star, while we show that the gravitational wave frequencies strongly depend on the both properties. Then, we find that the frequencies of the fundamental and the 1st pressure mode multi…
We investigate the direct contribution of the magnetic field to the gravitational wave generation. To do so, we study the post-Newtonian energy-momentum tensor of the magnetized fluid and the post-Newtonian expansion of the gravitational potential in the wave zone. We show that the magnetic field appears even in the first post-Newtonian order of the multipole moment tensor. Then, we find an explicit relativistic correction containing the magnetic field contribution to the well-known quadrupole formula. As an application of this derivation, we find that the B-field part of the gravitational wav…
We construct new, multivariate empirical relations for measuring neutron star radii and tidal deformabilities from the dominant gravitational wave frequency in the post-merger phase of binary neutron star mergers. The relations determine neutron star radii and tidal deformabilities for specific neutron star masses with consistent accuracy and depend only on two observables: the post-merger peak frequency $f_{\rm peak}$ and the chirp mass $M_{\rm chirp}$. The former could be measured with good accuracy from gravitational waves emitted in the post-merger phase using next-generation detectors, wh…
Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the proto-neutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS-shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation …
Magnetic-distortion-induced ellipticity and gravitational wave radiation of neutron stars: millisecond magnetars in short GRBs, Galactic pulsars, and magnetars
中子星由于磁畸变而可能产生非轴对称形变，是地基干涉测量探测器的连续引力波（GW）源。经过几十年的搜索，使用现有的GW探测器，没有证据表明GW信号来自任何脉冲星。椭圆率的上限越来越严格地限制在银河系的恒星上。在这项工作中，我们使用的椭圆率推断从假定的毫秒磁星在短伽马射线暴（SGRB），以估计其可探测性目前和未来的GW探测器。对于从SGRB数据推断的$\sim 1$ ms磁星，高级LIGO（aLIGO）和爱因斯坦望远镜（ET）的探测视界分别为$\sim 30$ Mpc和$\sim 600$ Mpc。利用SGRB毫秒磁星的椭圆率作为刻度，在假设椭圆率是磁畸变引起的情况下，我们估算了银河系中的毫秒磁星和磁星的椭圆率和引力波应变。我们发现，该结果与aLIGO O 1对银河系恒星和磁星的零探测结果是一致的。我们进一步预测，GW信号从这些恒星/磁星可能无法检测到目前设计的aLIGO探测器。ET检测器可能能够检测来自这些天线中的一些天线的一些相对低频的信号（$<50$ Hz）。受其设计灵敏度的限制，eLISA探测器似乎不适合探测来自银河系恒星和磁星的信号。
We investigate correlated gravitational wave and neutrino signals from rotating core-collapse supernovae with simulations. Using an improved mode identification procedure based on mode function matching, we show that a linear quadrupolar mode of the core produces a dual imprint on gravitational waves and neutrinos in the early post-bounce phase of the supernova. The angular harmonics of the neutrino emission are consistent with the mode energy around the neutrinospheres, which points to a mechanism for the imprint on neutrinos. Thus, neutrinos carry information about the mode amplitude in the …
Weak and continuous gravitational-wave (GW) radiation can be produced by newborn magnetars with deformed structure and is expected to be detected by the Einstein telescope in the near future. In this work we assume that the deformed structure of a nascent magnetar is not caused by a single mechanism but by multiple time-varying quadrupole moments such as those present in magnetically induced deformation, starquake-induced ellipticity, and accretion column-induced deformation. The magnetar loses its angular momentum through accretion, magnetic dipole radiation, and GW radiation. Within this sce…
Gravitational-wave signals from coalescing binary neutron stars can yield important information about the properties of nuclear-matter equation of state from the early part of the signal through tidal effects to the properties and oscillation frequencies of the merger product. We investigate a direct link between the properties of isolated neutron stars and their merger, by comparing the frequency of the fundamental oscillation mode ($f$-mode) of neutron stars with the gravitational-wave frequency associated with the merger of two neutron stars. We calculate the quadrupolar ($l=2$) $f$-mode os…
We discuss some aspects of Pereira et al. (2018) concerning magnetars described by nonlinear theories of the electromagnetism and make the case for the Born-Infeld Lagrangian. We focus on the increase of toroidal magnetic fields in these systems with respect to ordinary magnetars and the subsequent increase of gravitational wave production. In summary, nonlinear theories of the electromagnetism would make it more likely for the detection of gravitational waves with future detectors, which could constrain nonlinear aspects of electrodynamics not entirely possible on Earth-based particle acceler…
In this paper we study the spin-evolution and gravitational-wave luminosity of a newly born millisecond magnetar, formed either after the collapse of a massive star or after the merger of two neutron stars. In both cases we consider the effect of fallback accretion, and consider the evolution of the system due to the different torques acting on the star, namely the spin up torque due to accretion and spin-down torques due to magnetic dipole radiation, neutrino emission, and gravitational wave emission linked to the formation of a `mountain' on the accretion poles. Initially the spin period is …
The binary neutron star merger GW170817/GRB170817A confirmed that at least some neutron star mergers are the progenitors of short gamma-ray bursts. Many short gamma-ray bursts have long-term x-ray afterglows that have been interpreted in terms of post-merger millisecond magnetars---rapidly rotating, highly magnetised, massive neutron stars. We review our current understanding of millisecond magnetars born in short gamma-ray bursts, focusing particularly three main topics. First, whether millisecond magnetars really do provide the most plausible explain for the x-ray plateau. Second, determinin…
Possessing the strongest magnetic fields in the Universe, magnetars mark an extremum of physical phenomena. The strength of their magnetic fields is sufficient to deform the shape of the stellar body, and when the rotational and magnetic axes are not aligned, these deformations lead to the production of gravitational waves (GWs) via a time-varying quadrupole moment. Such gravitational radiation differs from signals presently detectable by the Laser Interferometer Gravitational-Wave Observatory. These signals are continuous rather than the momentary 'chirp' waveforms produced by binary systems …
Electromagnetic responses driven by gravitational-wave memory in magnetar-flare outflows
State Key Laboratory of Radio Astronomy and Technology, Shanghai Astronomical Observatory, CAS（中国科学院上海天文台射电天文技术与重点实验室）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学前沿科学与高等研究院基础物理与数学学院）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magnetic field deforms the star, making it axisymmetric with respect to the magnetic axis (the body symmetry axis). In magnetars, the rotation axis is tilted to the magnetic axis, and we have an oblique rotator. General relativistic treatment of the obliquely rotating magnetar gives rise to frame-dragging velocities both in the azimuthal and polar direction. Solving the Einstein equation up to first-order perturbation in rotation and second-order perturbation in the magnetic field, we calculate the geodes…
Two accretion columns have been argued to form over the surface of a newborn millisecond magnetar for an extremely high accretion rate $\gtrsim1.8\times10^{-2}M_\odot\ {\rm s^{-1}}$ that may occur in the core-collapse of a massive star. In this paper, we investigate the characteristics of these accretion columns and their gravitational wave (GW) radiation. For a typical millisecond magnetar (surface magnetic field strength $B\sim10^{15}$ G and initial spin period $P\sim1$ ms), we find (1) its accretion columns are cooled via neutrinos and can reach a height $\sim1$ km over the stellar surface;…
The first detection of gravitational waves (GWs) from the binary neutron star (NS) inspiral GW170817 has opened a unique channel for probing the fundamental properties of matter at supra-nuclear densities inaccessible elsewhere in the Universe. This observation yielded the first constraints on the equation of state (EoS) of NS matter from the GW imprint of tidal interactions. Tidal signatures in the GW arise from the response of a matter object to the spacetime curvature sourced by its binary companion. They crucially depend on the EoS and are predominantly characterised by the tidal deformabi…
We investigate the fundamental mode of non-radial oscillations of non-rotating compact stars in general relativity using a set of equations of state (EOS) connecting state-of-the-art calculations at low and high densities. Specifically, a low density model based on the chiral effective field theory (EFT) and high density results based on perturbative Quantum Chromodynamics (QCD) are matched through different interpolating polytropes fulfilling thermodynamic stability and subluminality of the speed of sound, together with the additional requirement that the equations of state support a two sola…
Improvements in ground-based, advanced gravitational wave (GW) detectors may allow in the near future to observe the GW signal of a nearby core-collapse supernova. For the most common type of progenitors, likely with slowly rotating cores, the dominant GW emission mechanisms are the post-bounce oscillations of the proto-neutron star (PNS) before the explosion. We present a new procedure to compute the eigenmodes of the system formed by the PNS and the stalled accretion shock in general relativity including spacetime perturbations. The new method improves on previous results by accounting for p…
Comparison of gravitational waves from central engines of gamma-ray bursts: neutrino-dominated accretion flows, Blandford-Znajek mechanisms, and millisecond magnetars
Two classes of X-ray/$γ$-ray sources, the Soft Gamma Repeaters and the Anomalous X-ray Pulsars have been identified with isolated, slowly spinning magnetars, neutron stars whose emission draws energy from their extremely strong magnetic field ($\sim 10^{15}-10^{16}$ G). Magnetars are believed to form with millisecond spin period and to represent an important fraction of the whole population of young neutron stars. Newborn magnetars can convert very quickly their rotational energy into electromagnetic and/or gravitational waves, by virtue of their strong magnetic fields and fast spins. This cha…
Magnetars are neutron stars presenting bursts and outbursts of X- and soft-gamma rays that can be understood with the presence of very large magnetic fields. Thus, nonlinear electrodynamics should be taken into account for a more accurate description of such compact systems. We study that in the context of ideal magnetohydrodynamics and make a realization of our analysis to the case of the well-known Born-Infeld (BI) electromagnetism in order to come up with some of its astrophysical consequences. We focus here on toroidal magnetic fields as motivated by already known magnetars with low dipola…
A newly-born magnetar is thought to be central engine of some long gamma-ray bursts (GRBs). We investigate the evolution of the electromagnetic (EM) emission from the magnetic dipole (MD) radiation wind injected by spin-down of a newly-born magnetar via both quadrupole gravitational-wave (GW) and MD radiations. We show that the EM luminosity evolves as $L_{\rm em}\propto (1+t/τ_c)^α$, and $α$ is $-1$ and $-2$ in the GW and MD radiation dominated scenarios, respectively. Transition from the GW to MD radiation dominated epoch may show up as a smooth break with slope changing from $-1$ to $-2$. I…
