Spinning down newborn neutron stars: Nonlinear development of ther-mode instability

Abstract

We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial modes that couple to it. We find that the spectrum of evolutions is more diverse than previously thought. We start our evolutions with a star of temperature ∼ 10 10 K and a spin frequency close to the Kepler break-up frequency. We assume that hyperon bulk viscosity dominates at high temperatures (T ∼ 10 9 − 10 10 K) and boundary layer viscosity dominates at lower temperatures (∼ a few × 10 8 K). To explore possible nonlinear behavior, we vary properties of the star such as the hyperon superfluid transition temperature, the strength of the boundary layer viscosity, and the fraction of the star that cools via direct URCA reactions. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects become important when the r-mode amplitude grows above its first parametric instability threshold. The balance between neutrino cooling and viscous heating plays an important role in the evolution. Depending on the initial r-mode amplitude, and on the strength of the viscosity and of the cooling this balance can occur at different temperatures. If thermal equilibrium occurs on the r-mode stability curve, where gravitational driving equals viscous damping, the evolution may be adequately described by a one-mode model. Otherwise, nonlinear effects are important and lead to various more complicated scenarios. Once thermal balance occurs, the star spinsdown oscillating between thermal equilibrium states until the instability is no longer active. The average evolution of the mode amplitudes can be approximated by quasi-stationary states that are determined algebraically. For lower viscosity we observe runaway behavior in which the r-mode amplitude passes several parametric instability thresholds. In this case more modes need to be included to model the evolution accurately. In the most optimistic case, we find that gravitational radiation from the r-mode instability in a very young, fast spinning neutron star within about 1 Mpc of Earth may be detectable by advanced LIGO for years, and perhaps decades, after formation. Details regarding the amplitude and duration of the emission depend on the internal dissipation of the modes of the star, which would be probed by such detections.

Differential rotation and r-modes in magnetized neutron stars

“…1.2 of the initial one according to Kastaun 2011) can strongly affect magnetic field (formally, it does not contradict with our estimates, which predict enhancement of the magnetic field up to ≈ 10 17 G for α ≈ 3). However, r-mode saturation amplitudes calculated by Bondarescu et al (2009) ;Bondarescu & Wasserman (2013) are small α ≪ 1. Thus it seems reasonable to restrict consideration to small amplitudes.…”

Long gravitational-wave transients and associated detection strategies for a network of terrestrial interferometers

“…Potential astrophysical sources of GWs from r-modes are accreting neutron stars in low-mass X-ray binaries (e.g., [58,61,62]) and, more relevant in the present context, newborn, rapidly spinning neutron stars [28,29,57]. In the latter, r-modes may play an important role in the early spin evolution [29,63].…”

“…The parameter α ∈ [0, 1] is the dimensionless saturation amplitude of the r-modes and its true value has been the topic of much debate. Most recent work suggests (see [29,58] and references therein) that α ≪ 0.1 and, perhaps, does not exceed ∼ 10 −5 due to non-linear mode coupling effects [59]. Generally, r-modes are expected to be a source of verylong-lasting quasi-continuous GW emission, though long GW transients may be possible in the case of high saturation amplitudes (e.g., [60]).…”

“…The GW signature of CCSNe (recently reviewed in [2]) may be composed of contributions from rotating collapse and core bounce [14], post-bounce protoneutron star (PNS) convection [2,15,16], neutrino-driven convection and the standing-accretion-shock instability (SASI) [17][18][19], PNS pulsations [20], nonaxisymmetric rotational instabilities (both dynamical and secular) [21,22], asymmetric neutrino emission [2,18,19], aspherical outflows [23][24][25][26][27], magnetic stresses [26,27], and r-mode pulsations in rotating PNSs (see, e.g., [28,29]). Depending on the particular CCSN mechanism in operation, some emission processes may dominate while others are suppressed [13].…”

First Search for Nontensorial Gravitational Waves from Known Pulsars

“…The nature of these three quantities depends on the specifics of the underlying theory of gravity and the associated emission mechanism (for different emission mechanisms within GR, see, e.g., Refs. [31][32][33]). While we treat a p and ϕ p as free parameters, we take ϕðtÞ to be the same as in the traditional GR analysis [25]:…”