Abstract
With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar “mountain” deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.
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Notes
- 1.
As pointed out in Doneva and Kokkotas (2015), this asteroseismology formalism could equally well have been based on the compactness M∕R rather than η.
- 2.
We note with some amusement that the literature contains a mechanical pendulum analogue of the viscosity-driven CFS instability in a 1908 paper by Lamb (1908). Another occurrence of a CFS-like instability in the context of wave dynamics can be found in the 1974 textbook by Pierce (1974, Chapter 11).
- 3.
Remarkably, a similar CFS dynamical instability is known to exist in an entirely different context, namely, that of a rotating liquid drop with surface tension playing the role of gravity. Laboratory experiments have probed the impact of the instability on the shape of the drop and have revealed a rich phenomenology, see e.g. Brown and Scriven (1980), Hill and Eaves (2008).
- 4.
The term “supramassive” refers to a rapidly rotating neutron star with mass above the maximum allowed mass for spherical non-rotating neutron stars. The excess mass is supported by rotation which means that a supramassive system is dynamically stable only above a certain spin rate.
- 5.
A relatively low mass remnant may settle down to a normal neutron star existence without ever collapsing to a black hole.
- 6.
Starting from the perturbed Faraday’s law, ∇× δ E = −iωδ B∕c, and applying the usual “circuit” argument across the crust-core boundary leads to \(\hat {\mathbf {n}} \times \langle \delta \mathbf {E} \rangle =0\), where \(\hat {\mathbf {n}}\) is the unit normal vector to the boundary and 〈…〉 stands for the jump across the boundary. Using cδ E = −δ v ×B for the r-mode-induced electric field, we find \( ( \hat {\mathbf {n}} \cdot \mathbf {B} ) \langle \delta v \rangle = 0\) which for a general magnetic field implies a vanishing slippage.
- 7.
It is worth noting that the authors of Zink et al. (2012) fit the numerical data with a power-law relation, finding that the GW amplitude is proportional to B 3.3. The authors of Ciolfi and Rezzolla (2012), instead, have h ∼ B 2, because they fit the data with a quadratic function; this choice is correct as a first approximation, since in the perturbative results of Levin and van Hoven (2011) the GW amplitude is a quadratic function of the magnetic field strength.
- 8.
In polar coordinates, the field-strength components B r, B 𝜗 are poloidal, while B φ is toroidal.
- 9.
The instability of purely toroidal configurations is also shown in Akgun and Wasserman (2008) for a superconducting neutron star, by studying the variations of an energy functional.
- 10.
In these models the magnetic field-strength has as the same order of magnitude on the surface and in the interior.
- 11.
It should be mentioned that the breaking strain found in Horowitz and Kadau (2009) is the result of numerical simulations with duration much shorter than the timescale associated with crust straining/relaxation.
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Acknowledgements
We thank Nils Andersson, Daniela Doneva, Brynmor Haskell, Wynn Ho, Ian Jones, Kostas Kokkotas, Cristiano Palomba, George Pappas, Andrea Passamonti and Kai Schwenzer for useful discussions during the course of this work and for providing data and figures.
This work was supported by the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904 and by the COST actions MP1304 and CA16104.
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Glampedakis, K., Gualtieri, L. (2018). Gravitational Waves from Single Neutron Stars: An Advanced Detector Era Survey. In: Rezzolla, L., Pizzochero, P., Jones, D., Rea, N., Vidaña, I. (eds) The Physics and Astrophysics of Neutron Stars. Astrophysics and Space Science Library, vol 457. Springer, Cham. https://doi.org/10.1007/978-3-319-97616-7_12
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