Precessing Neutron Star Research Articles

Observational clues to the magnetic evolution of magnetars

ABSTRACT Utilizing four archival X-ray data sets taken with the Hard X-ray Detector onboard Suzaku, timing studies were performed on three magnetars, 1E 1841−045 (observed in 2006), SGR 0501+4516 (2008), and 1RXS J170849.0−400910 (2009 and 2010). Their pulsations were reconfirmed, typically in an energy range of 12–50 keV. The 11.783 s pulses of 1E 1841−045 and those of SGR 0501+4516 at 5.762 s were periodically phase modulated, with a long period of $\approx 23.4$ and $\approx 16.4$ ks, respectively. The pulse-phase modulation was also observed, at $\approx 46.5$ ks, from two data sets of 1RXS J170849.0−400910. In all these cases, the modulation amplitude was 6 per cent to 16 per cent of the pulse cycle. Including previously confirmed four objects, this characteristic timing behaviour is now detected from seven magnetars in total, and interpreted as a result of free precession of neutron stars that are deformed to an asphericity of $\sim 10^{-4}$. Assuming that the deformation is due to magnetic stress, these magnetars are inferred to harbour toroidal magnetic fields of $B_{\rm t}\sim 10^{16}$ G. By comparing the estimated $B_{\rm t}$ of these objects with their poloidal dipole field $B_{\rm d}$, the $B_{\rm t}/B_{\rm d}$ ratio is found to increase with their characteristic age. Therefore, the toroidal fields of magnetars are likely to last longer than their poloidal fields. This explains the presence of some classes of neutron stars that have relatively weak $B_{\rm d}$ but are suspected to hide strong $B_{\rm t}$ inside them.

Empirical Assessment of Aperiodic and Periodic Radio Bursts from Young Precessing Magnetars

We analyze the slow periodicities identified in burst sequences from FRB 121102 and FRB 180916 with periods of about 16 and 160 days, respectively, while also addressing the absence of any fast periodicity that might be associated with the spin of an underlying compact object. Both phenomena can be accounted for by a young, highly magnetized, precessing neutron star that emits beamed radiation with significant imposed phase jitter. Sporadic narrow-beam emission into an overall wide solid angle can account for the necessary phase jitter, but the slow periodicities with 25%–55% duty cycles constrain beam traversals to be significantly smaller. Instead, phase jitter may result from variable emission altitudes that yield large retardation and aberration delays. A detailed arrival time analysis for triaxial precession includes wobble of the radio beam and the likely larger, cyclical torque resulting from the changes in the spin–magnetic moment angle. These effects will confound identification of the fast periodicity in sparse data sets longer than about a quarter of a precession cycle unless fitted for and removed as with orbital fitting. Stochastic spin noise, likely to be much larger than in radio pulsars, may hinder detection of any fast periodicity in data spans longer than a few days. These decoherence effects will dissipate as sources of fast radio bursts age, so they may evolve into objects with properties similar to Galactic magnetars.

Triaxially deformed freely precessing neutron stars: continuous electromagnetic and gravitational radiation

ABSTRACT The shape of a neutron star (NS) is closely linked to its internal structure and the equation of state of supranuclear matters. A rapidly rotating, asymmetric NS in the Milky Way undergoes free precession, making it a potential source for multimessenger observation. The free precession could manifest in (i) the spectra of continuous gravitational waves (GWs) in the kilohertz (kHz) band for ground-based GW detectors, and (ii) the timing behaviour and pulse-profile characteristics if the NS is monitored as a pulsar with radio and/or X-ray telescopes. We extend previous work and investigate in great detail the free precession of a triaxially deformed NS with analytical and numerical approaches. In particular, its associated continuous GWs and pulse signals are derived. Explicit examples are illustrated for the continuous GWs, as well as timing residuals in both time and frequency domains. These results are ready to be used for future multimessenger observation of triaxially deformed freely precessing NSs, in order to extract scientific implication as much as possible.

Periodic fast radio bursts from forcedly precessing neutron stars, anomalous torque, and internal magnetic field for FRB 180916.J0158+65 and FRB 121102

ABSTRACT A recent discovery of the periodic activity of the repeating fast radio burst source FRB 180916.J0158+65 in the Canadian Hydrogen Intensity Mapping Experiment (CHIME) hints at possible origin of the FRB from a freely precessing neutron star with a magnetar magnetic field of about 1016 G. However, the absence of simultaneously detected high-energy emission in the Swift and AGILE observations imposes stringent constraints on the field magnitude and questions the possibility of such a progenitor. We show that consideration of forced precession of a neutron star does not encounter the difficulty. This kind of precession takes place even if the neutron star is not deformed and is brought about by the anomalous moment of electromagnetic forces induced by stellar rotation and determined by non-corotational currents. Contrary to what is expected for the currents of corotation, the anomalous torque calculated by the direct method appears to be non-zero. If the observed 16.35-d period corresponds to the period of stellar precession, the inferred internal magnetic field appears to be about 6 × 1014 G for rotational period 1 s. For another possibly periodic FRB 121102 with 157-d period, the magnetic field is even lower, 2 × 1014 G, thereby justifying earlier considerations and not ruling out the hypothesis of FRB origin from precessing neutron stars.

Novel Clues to the Physics of Magnetars as Probed with Detailed Pulse-Timing Studies

AbstractBroadband X-ray data of five magnetars show that their hard X-ray pulses suffer periodic phase modulations, at a period ∼ 104 times their pulse period. The phenomenon is interpreted as a result of free precession of neutron stars that are prolately deformed to an asphericity of ∼ 10−4, by the magnetic stress of toroidal fields reaching ∼ 1016 G. The behavior is absent in their soft X-ray pulses, probably due to a higher emission symmetry. The ultra-high toroidal fields, considered common to magnetars, may persist longer than their dipole fields.

Possible periodic activity in the repeating FRB 121102

ABSTRACTThe discovery that at least some Fast Radio Bursts (FRBs) repeat has ruled out cataclysmic events as the progenitors of these particular bursts. FRB 121102 is the most well-studied repeating FRB but despite extensive monitoring of the source, no underlying pattern in the repetition has previously been identified. Here, we present the results from a radio monitoring campaign of FRB 121102 using the 76 m Lovell telescope. Using the pulses detected in the Lovell data along with pulses from the literature, we report a detection of periodic behaviour of the source over the span of 5 yr of data. We predict that the source is currently ‘off’ and that it should turn ‘on’ for the approximate MJD range 59002−59089 (2020 June 2 to 2020 August 28). This result, along with the recent detection of periodicity from another repeating FRB, highlights the need for long-term monitoring of repeating FRBs at a high cadence. Using simulations, we show that one needs at least 100 h of telescope time to follow-up repeating FRBs at a cadence of 0.5–3 d to detect periodicities in the range of 10–150 d. If the period is real, it shows that repeating FRBs can have a large range in their activity periods that might be difficult to reconcile with neutron star precession models.

Periodic modulation in pulse arrival times from young pulsars: a renewed case for neutron star precession

In a search for periodic variation in the arrival times of pulses from 151 young, energetic pulsars, we have identified seven cases of modulation consistent with one or two harmonics of a single fundamental with time-scale 0.5-1.5 yr. We use simulations to show that these modulations are statistically significant and of high quality (sinusoidal) even when contaminated by the strong stochastic timing noise common to young pulsars. Although planetary companions could induce such modulation, the large implied masses and 2:1 mean motion resonances challenge such an explanation. Instead, the modulation is likely to be intrinsic to the pulsar, arising from quasi-periodic switching between stable magnetospheric states, and we propose that precession of the neutron star may regulate this switching.

Non-monotonous character of single radio pulsar spin-down

Our paper is dedicated to the problem of anomalous values of braking indices n obs and spin frequency second derivatives \(\ddot \nu\) of isolated radio pulsars. Observations of these objects for over 40 years have shown that in addition to the complex short-term irregular component in the evolution of the pulsars’ frequency, secular values of its second derivative are orders of magnitude greater than the predicted theoretical ones, and in a good half of cases—they are even negative. We earlier attributed this behavior of secular values of the second derivative to the presence of a cyclic component in the secular evolution of ν(t), with a characteristic recurrence time of thousands to tens of thousand years. We continue to develop this hypothesis based on a more detailed statistical analysis of the characteristics of 297 isolated radio pulsars: we analyze the model of these objects spin-down, consisting of two components, monotonic and cyclic, and determine their parameters. We demonstrate that the monotonic spin-down component is described by the classical magnetodipolar power law with an braking index of about 3, while the large amplitude of the cyclic component causes a significant variation of the observed spin-down rate \((\dot \nu )\) (with respect to magnetodipolar one), and fully determines the anomalous values of \(\ddot \nu\) and n obs. An important consequence of the existence of a cyclic component of the pulsar rotational variations is the difference between their characteristic ages and respective secular values (by about 0.5–5 times). This allows to explainthe observed discrepancy of the characteristic and physical ages of some objects, as well as very large, up to 108 years, characteristic ages of some old pulsars. The paper argues that the cyclic component of the observed spin-down is due to the long-term precession of neutron stars around their magnetic axes, which, in particular, may be driven by the anomalous braking torque. In the model of purely magnetodipolar braking this torque is a consequence of emission in the near field zone.

The influence of nondipolar magnetic field and neutron star precession on braking indices of radiopulsars

Some of radiopulsars have anomalous braking index values $n = \Omega \ddot{\Omega} / \dot{\Omega}^2 \sim \pm (10^3 \div 10^4) $. It is shown that such values may be related with nondipolar magnetic field. The precession of neutron star lead to rotation (in reference frame related with neutron star) of vector of angular velocity $\vec{\Omega}$ along direction of neutron star magnetic dipole moment $\vec{m}$ with angular velocity $\vec{\Omega}_{p}$. This process may cause the altering of electric current flow through inner gap and consequently the current losses with the same time scale as precession period $T_{p} = 2\pi / \Omega_{p}$. It occurs because of electric current in inner gaps is determined by Goldreich-Julian charge density $\rho_{GJ} = -\frac{\vec{\Omega} \cdot \vec{B}}{2\pi c}$, which are depend on angle between direction of small scale magnetic field and angular velocity $\vec{\Omega}$. It is essential that pulsar tubes nearby neutron star surface are curved. In current paper it is considered the only inner gaps with steady, electron charge limited flow regime.

Dynamics of Quantum Vorticity in a Random Potential

I study the dynamics of a superfluid vortex in a random potential, as in the inner crust of a neutron star. Below a critical flow velocity of the ambient superfluid, a vortex is effectively immobilized by lattice forces even in the limit of zero dissipation. Low-velocity, translatory motion is not dynamically possible, a result with important implications for understanding neutron star precession and the dynamical properties of superfluid nuclear matter.

Do superfluid instabilities prevent neutron star precession?

We discuss short wavelength (inertial wave) instabilities present in the standard two-fluid neutron star model when there is sufficient relative flow along the superfluid neutron vortex array. We demonstrate that these instabilities may be triggered in precessing neutron stars, since the angular velocity vectors of the neutron and proton fluids are misaligned during precession. Our results suggest that the standard (Eulerian) slow precession that results for weak drag between the vortices and the charged fluid (protons and electrons) is not seriously affected by the instability. In contrast, the fast precession, which results when vortices are strongly coupled to the charged component, is generally unstable. The presence of this instability renders the standard (solid body) rotation model for free precession inconsistent and makes unsafe conclusions that have recently been drawn regarding neutron star interiors based on observations of precession in radio pulsars.

Does the accreting millisecond pulsar XTE J1814−338 precess?

Precession in an accretion-powered pulsar is expected to produce characteristic variations in the pulse properties. Assuming surface intensity maps with one and two hotspots, we compute theoretically the periodic modulation of the mean flux, pulse-phase residuals and fractional amplitudes of the first and second harmonic of the pulse profiles. These quantities are characterised in terms of their relative precession phase offsets. We then search for these signatures in 37 days of X-ray timing data from the accreting millisecond pulsar XTE J1814-338. We analyse a 12.2-d modulation observed previously and show that it is consistent with a freely precessing neutron star only if the inclination angle is < 0.1 degrees, an a priori unlikely orientation. We conclude that if the observed flux variations are due to precession, our model incompletely describes the relative precession phase offsets (e.g. the surface intensity map is over-simplified). We are still able to place an upper limit on \epsilon of 3.0 x 10^{-9} independently of our model, and estimate the phase-independent tilt angle \theta; to lie roughly between 5 and 10 degrees. On the other hand, if the observed flux variations are not due to precession, the detected signal serves as a firm upper limit for any underlying precession signal. We then place an upper limit on the product \epsilon cos(\theta) of \leq 9.9 x 10^{-10}. The first scenario translates into a maximum gravitational wave strain of 10^{-27} from XTE J1814-338 (assuming a distance of 8 kpc), and a corresponding signal-to-noise ratio of \leq 10^{-3} (for a 120 day integration time) for the advanced LIGO ground-based gravitational wave detector.

Tkachenko waves, glitches and precession in neutron stars

Here I discuss possible relations between free precession of neutron stars, Tkachenko waves inside them and glitches. I note that the proposed precession period of the isolated neutron star RX J0720.4-3125 (Haberl et al. 2006) is consistent with the period of Tkachenko waves for the spin period 8.4 s. Based on a possible observation of a glitch in RX J0720.4-3125 (van Kerkwijk et al. 2007), I propose a simple model, in which long period precession is powered by Tkachenko waves generated by a glitch. The period of free precession, determined by a NS oblateness, should be equal to the standing Tkachenko wave period for effective energy transfer from the standing wave to the precession motion. A similar scenario can be applicable also in the case of the PSR B1828-11.

Stability of Precessing Superfluid Neutron Stars

We discuss a new superfluid instability occurring in the interior of mature neutron stars with implications for free precession. This instability is similar to the instability which is responsible for the formation of turbulence in superfluid helium. We demonstrate that the instability is unlikely to affect slowly precessing systems with weak superfluid coupling. In contrast, fast precession in systems with strong coupling appears to be generically unstable. This raises serious questions about our understanding of neutron star precession and complicates attempts to constrain neutron star interiors using such observations.

Precession as a probe of the neutron star interior

Strong evidence that some neutron stars precess (nutate) with long periods (∼1 yr) challenges our current understanding of the neutron star interior. I describe how neutron star precession can be used to constrain the state of the interior in a new way. I argue that the standard picture of the outer core, in which superfluid neutrons coexist with type II, superconducting protons, requires revision. One possible resolution is that the protons are not type II, but type I. Another possibility is that the neutrons are normal in the outer core. I conclude with a brief discussion of the implications for detectable gravitational wave emission from millisecond pulsars.

Propagation of light in the field of stationary and radiative gravitational multipoles

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of the propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. This paper suggests a physically-adequate and consistent solution of this problem in the first post-Minkowskian approximation of general relativity which accounts for all time-dependent multipole moments of an isolated astronomical system. We derive equations of propagation of electromagnetic wave in the retarded gravitational field of the localized source emitting gravitational waves of arbitrary multipolarity and integrate them analytically in closed form. We also prove that the leading terms in the observable relativistic effects (time delay, deflection angle and rotation of the plane of polarization of light) depend on the instantaneous value of the multipole moments of the isolated system and its time derivatives taken at the retarded instant of time but not on their integrated values. The influence of the multipolar gravitational field of the isolated system on the light propagation is examined for a general case when light propagates not only through the wave zone of the system but also through its intermediate and near zones. The gauge freedom of our formalism is carefully studied and all gauge-dependent terms are singled out and separated from observable quantities.

Gravitational wave from GRB center: A black hole-torus system

We discuss a possible gravitational wave radiation from a center of GRB, which consists of a rotating black hole and a torus. The gravitational waves can be generated by the precession as well as the local intrinsic inhomogeneity of the torus. Using the typical values relevant to GRB center, one can expect gravitational wave production with frequencies roughly in the range of 10 2 up to 10 3 Hz, which correspond basically to the Lense-Thirring frequency and the Keplerian frequency, respectively. For a rigid precession, the amplitude is found to be not smaller than the recent estimation for a precessing neutron star. For a Lense-Thirring precession, the line-broadening in the observed spectrum is expected due to the modulation of the torus orientation to the line of sight. The effect of the back reaction of gravitational radiation is estimated to be not so significant for long-duration GRBs.

The gravitational wave spectrum of non-axisymmetric, freely precessing neutron stars

Evidence for free precession has been observed in the radio signature of several pulsars. Freely precessing pulsars radiate gravitationally at frequencies near the rotation rate and twice the rotation rate, which for rotation frequencies greater than ∼10 Hz is in the LIGO band. In older work, the gravitational wave spectrum of a precessing neutron star has been evaluated to first order in a small precession angle. Here, we calculate the contributions to second order in the wobble angle, and we find that a new spectral line emerges. We show that for reasonable wobble angles, the second-order line may well be observable with the proposed advanced LIGO detectors for precessing neutron stars as far away as the galactic centre. Observation of the full second-order spectrum permits a direct measurement of the star's wobble angle, oblateness and deviation from axisymmetry, with the potential to significantly increase our understanding of neutron star structure.

Type-I superconductivity and neutron star precession

Type-I proton superconducting cores of neutron stars break up in a magnetic field into alternating domains of superconducting and normal fluids. We examine two channels of superfluid-normal fluid friction where (i) rotational vortices are decoupled from the nonsuperconducting domains and the interaction is due to the strong force between protons and neutrons; (ii) the nonsuperconducting domains are dynamically coupled to the vortices and the vortex motion generates transverse electric fields within them, causing electronic current flow and Ohmic dissipation. The obtained dissipation coefficients are consistent with the Eulerian precession of neutron stars.

Hydromagnetic and Gravitomagnetic Crust‐Core Coupling in a Precessing Neutron Star

We consider two types of mechanical coupling between the crust and the core of a precessing neutron star. First, we find that a hydromagnetic (MHD) coupling between the crust and the core strongly modifies the star's precessional modes when $t_a\le\sim (T_s\times T_p)^{1/2}$; here $t_a$ is the Alfven crossing timescale, and $T_s$ and $T_p$ are the star's spin and precession periods, respectively. We argue that in a precessing pulsar PSR B1828-11 the restoring MHD stress prevents a free wobble of the crust relative to the non-precessing core. Instead, the crust and the proton-electron plasma in the core must precess in unison, and their combined ellipticity determines the period of precession. Link has recently shown that the neutron superfluid vortices in the core of PSR B1828-11 cannot be pinned to the plasma; he has also argued that this lack of pinning is expected if the proton Fermi liquid in the core is type-I superconductor. In this case, the neutron superfluid is dynamically decoupled from the precessing motion. The pulsar's precession decays due to the mutual friction between the neutron superfluid and the plasma in the core. The decay is expected to occur over tens to hundreds of precession periods and may be measurable over a human lifetime. Such a measurement would provide information about the strong n-p interaction in the neutron-star core. Second, we consider the effect of gravitomagnetic coupling between the neutron superfluid in the core and the rest of the star and show that this coupling changes the rate of precession by about 10%. The general formalism developed in this paper may be useful for other applications.