Gravitational Waves from Neutron Stars: a Review

Publications of the Astronomical Society of Australia (PASA) c Astronomical Society of Australia 2015; published by Cambridge University Press. doi: 10.1017/pas.2015.xxx. Gravitational Waves from Neutron Stars: A Review Paul D. Lasky1∗ 1Monash Centre for Astrophysics, School of Physics and Astronomy, Monash University, VIC 3800, Australia Abstract Neutron stars are excellent emitters of gravitational waves. Squeezing matter beyond nuclear densities invites exotic physical processes, many of which violently transfer large amounts of mass at relativistic velocities, disrupting spacetime and generating copious quantities of gravitational radiation. I review mechanisms for generating gravitational waves with neutron stars. This includes gravitational waves from radio and millisecond pulsars, magnetars, accreting systems and newly born neutron stars, with mechanisms including magnetic and thermoelastic deformations, various stellar oscillation modes and core superfluid turbulence. I also focus on what physics can be learnt from a gravitational wave detection, and where additional research is required to fully understand the dominant physical processes at play. Keywords: Gravitational Waves { Neutron Stars 1 Introduction ing neutron stars, and primordial perturbations dur- ing inflation. Continuous gravitational waves are almost The dawn of gravitational wave astronomy is one of monochromatic signals generated typically by rotating, the most anticipated scientific advances of the coming non-axisymmetric neutron stars. decade. The second generation, ground-based gravita- The above laundry list of gravitational wave sources tional wave interferometers, Advanced LIGO (aLIGO prominently features neutron stars in their many guises. Aasi et al. 2015b) and Virgo (Acernese et al. 2015), are While supranuclear densities, relativistic velocities and due to start observing later in 2015 and in 2016, respec- enormous magnetic fields are exactly what makes neu- tively. The first aLIGO observing run is expected to be tron stars amenable to emitting gravitational waves of a few times more sensitive than initial LIGO, with a sufficient amplitude to be detectable on Earth, it is also full order of magnitude increase in strain sensitivity by these qualities that makes it difficult to provide accu- ∼ 2019 (for a review, see Aasi et al. 2013). rate predictions of the gravitational wave amplitudes, The inspiral and merger of compact binary systems and hence detectability, of their signals. A positive grav- (neutron stars and/or black holes) are commonly ex- itational wave detection from a neutron star would en- pected to be the first detections with aLIGO. The most gender great excitement, but it is the potential to un- robust predictions for event rates come from obser- derstand the interior structure of neutron stars that will vations of the binary neutron star population within make this field truly revolutionary. our galaxy, with an expected binary neutron-star de- In this review, I provide a detailed overview of many tection rate for the aLIGO/Virgo network at full sen- proposed gravitational wave generation mechanisms in sitivity between 0.4 and 400 per year (Abadie et al. neutron stars, including state-of-the-art estimates of the arXiv:1508.06643v1 [astro-ph.HE] 26 Aug 2015 2010b). But there are many other exciting astrophysi- gravitational wave detectability. These include gravita- cal and cosmological sources of gravitational waves (for tional waves generated from magnetic deformations in a brief review, see Riles 2013). Loosely, these can be newly-born and older isolated radio pulsars (section2), divided into four categories: compact binary coales- accreting systems (section3), impulsive and continuous- cences, bursts, stochastic backgrounds and continuous wave emission from pulsar glitches (section4), magne- waves. Burst sources include gravitational waves gener- tar flares (section5), and from superfluid turbulence in ated in nearby supernova explosions, magnetar flares, the stellar cores (section6). As well as discussing grav- and cosmic string cusps. Stochastic backgrounds arise itational wave detectability, I also concentrate on what from the incoherent sum of sources throughout the Uni- physics can be learnt from a future, positive gravita- verse, including from compact binary systems, rotat- tional wave detection. ∗email: [email protected] 1 2 Lasky It is worth stressing that this is not a review of all 1 are the projected strain sensitivities for aLIGO and gravitational wave sources in the audio band, but is ET (solid and dashed black curves respectively), and instead designed to review the theory of gravitational the strain sensitivity for the S5 run of initial LIGO (for wave sources from neutron stars. The article is but one details, see Aasi et al. 2014a). Age-based upper limits in a series highlighting Australia's contribution to grav- on the gravitational wave strain can also be calculated itational wave research (Howell 2015; Kerr 2015; Slag- for neutron stars with unknown spin frequencies (Wette molen 2015). et al. 2008). 2 Magnetic Deformations 2.2 Magnetic field-induced ellipticities Spinning neutron stars possessing asymmetric deforma- As a general rule of thumb, a neutron star's ellipticity tions emit gravitational waves. Such deformations can scales with the square of the volume-averaged magnetic be generated through elastic strains in the crust (Bild- field inside the star, hBi (e.g., Haskell et al. 2008), im- sten 1998; Ushomirsky et al. 2000), or strong magnetic plying the characteristic gravitational wave strain also 2 fields in the core (Bonazzola & Gourgoulhon 1996). scales as h0 ∼ hBi . The dipole, poloidal component of A triaxial body rotating about one of it's principal the magnetic field at the surface of the star is inferred moments of inertia will emit radiation at frequency from the star's spin period and it's derivative, but very fgw = 2ν, where ν is the star's spin frequency. More little is known about the interior field strength and/or precisely, a freely precessing, axisymmetric body, with configuration. principal moment of inertia, Izz, and equatorial ellip- A considerable body of work has been devoted to un- ticity, , emits a characteristic gravitational wave strain derstanding possible magnetic field configurations2, in (Zimmerman & Szedenits 1979) part to answer the question of gravitational wave detectability, but also to understand the inverse problem 2 2 4π G Izzfgw regarding what can be learnt from future gravitational h0 = c4 d wave observations. Purely poloidal and purely toroidal P −2 d −1 fields are known to be unstable on dynamical timescales = 4:2 × 10−26 ; 10−6 10 ms 1 kpc (e.g., Wright 1973; Braithwaite & Spruit 2006; Braith- (1) waite 2007). Mixed fields, where a toroidal component threads the closed-field-line region of the poloidal field, where d is the distance to the source. For comparison, commonly termed `twisted-torus' fields, are generally the smallest, upper limit on stellar ellipticity for young believed to be dynamically stable (e.g., Braithwaite & neutron stars in supernova remnants comes from LIGO Nordlund 2006; Ciolfi et al. 2009; Akgünet al. 2013), observations of Vela Jr. (G266.2-1.2), with ≤ 2:3 × −7 although it has been suggested this is dependent on the 10 (Aasi et al. 2014b). The overall ellipticity record- equation of state (Lander & Jones 2012; Mitchell et al. holder is for the millisecond pulsars J2124{3358 and −8 −8 2015). Moreover, a recent study of the effect twisted- J2129{5721 with ≤ 6:7 × 10 and ≤ 6:8 × 10 , re- torus fields have on crust-core rotational coupling dur- spectively (Aasi et al. 2014a). Typical ellipticity con- 4 6 ing neutron star spin down suggest these fields may straints for isolated radio pulsars are . 10 { 10 (Aasi be unstable on a spin down timescale (Glampedakis & et al. 2014a). Lasky 2015). While generating solutions to the equations of New- 2.1 Spin down limit tonian and general relativistic magnetohydrostatics is a noble task, it is no substitute for understanding the An absolute upper limit on the gravitational wave strain initial-value problem that brings one towards realis- from individual pulsars, known as the spin down limit, tic magnetic field configurations. In Newtonian simu- can be calculated assuming the observed loss of rota- lations with soft equations of state (typically more ap- tional energy is all going into gravitational radiation. plicable to main-sequence stars than to neutron stars), The left hand panel of Figure1 shows the current upper Braithwaite and co. showed magnetic fields evolve either limits on the gravitational wave strain from a search for to axisymmetric, twisted-tori (Braithwaite & Nordlund known pulsars (red stars; Aasi et al. 2014a), as well as 2006; Braithwaite 2009), or non-axisymmetric config- the spin down limits for the known pulsars in the ATNF urations (Braithwaite 2008), depending on the initial 1 catalogue (Manchester et al. 2005) . The observed grav- conditions. General relativistic magnetohydrodynamic itational wave upper limits beat the spin down limit for both the Crab and Vela pulsars, while a further five pul- 2In Australia, work on possible magnetic field configurations in sars are within a factor of five. Also plotted in Figure the cores of stars dates back to the 1960's, where Monaghan (1965, 1966) calculated magnetic field equilibria in polytropes, which even included calculations of magnetic-field induced stel- 1http://www.atnf.csiro.au/people/pulsar/psrcat/ lar ellipticities. PASA (2015) doi:10.1017/pas.2015.xxx Gravitational waves from neutron stars 3 -23 10 ] -24 ] 10 2 2 / / 1 1 -24 − -26 − 10 10 z z H H [ [ -28 -25 10 y y 10 t t i i v v -30 i i t 10 t i i -26 s s 10 n n -32 e e 10 s s -27 n n 10 i -34 i a 10 a r r t t s s 10-28 10-36 100 101 102 103 100 101 102 103 gravitational wave frequency [Hz] gravitational wave frequency [Hz] Figure 1. Left panel: Current upper limits on the gravitational wave strain from known pulsars (red stars; data from Aasi et al.

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