Gravitational Radiation Instability in Hot Young Neutron Stars

Abstract

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the l = 2 r-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the timescale needed to cool a young neutron star to about T = 10 9 K (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about 0.076ΩK , where ΩK is the Keplerian angular velocity where mass shedding occurs. In older colder neutron stars this instability is suppressed by viscous effects, allowing older stars to be spun up by accretion to larger angular velocities. (and Friedman and Morsink [2] confirmed more generally) that gravitational radiation tends to drive the r-modes of all rotating stars unstable. In this paper we examine the timescales associated with this instability in some detail. We show that gravitational radiation couples to these modes primarily through the current multipoles, rather than the usual mass multipoles. We also evaluate the effects of internal fluid dissipation which tends to suppress this instability. We find that gravitational radiation is stronger than viscosity in these modes and so this instability severely limits the rotation rates of hot young neutron stars. We show that such stars can spin down by the emission of gravitational radiation to about 7.6% of their maximum rotation rates on the timescale (about one year) needed to cool these stars to 10 9 K.The r-modes of rotating barotropic Newtonian stars are solutions of the perturbed fluid equations having (Eulerian) velocity perturbationswhere R and Ω are the radius and angular velocity of the unperturbed star, α is an arbitrary constant, and Y B l m is the magnetic type vector spherical harmonic defined byPapaloizou and Pringle [3] first showed that the Euler equation for r−modes determines the frequencies asFurther use of the Euler equation (as first noted by Provost, Berthomieu and Rocca [4]) in the barotropic case (a good approximation for neutron stars) determines that only the l = m r-modes exist, and that δ v must have the radial dependence given in Eq. (1). These expressions for the velocity perturbation and frequency are only the lowest order terms in expansions for these quantities in powers of Ω. The exact expressions contain additional terms of order Ω 3 . The lowest order expressions for the (Eulerian) density perturbation δρ can also be deduced from the perturbed fluid equations (Ipser and Lindblom [5]): δρ ρ = αR 2 Ω 2 dρ dp (4) where δΨ(r) is proportional to the gravitational potential δΦ and satisfies d 2 δΨ dr 2 + 2 r dδΨ dr + 4πGρ dρ dp − (l + 1)(l + 2) r 2 δΨ = − 8πGl 2l + 1 l l + 1 ρ dρ dp r R l+1 .Eq. (4) is the complete expression for δρ to order Ω 2 . The next order terms are proportional to Ω 4 . Our interest here is to study the evolution of these modes due to the dissipative influences of viscosity and gravitational radiation. For this purpose it is useful to consider the effects of radiation on t...

Chandra studies of the globular cluster 47 Tucanae: a deeper X-ray source catalogue, five new X-ray counterparts to millisecond radio pulsars and new constraints to r-mode instability window

“…Haskell 2015 for a recent review). The standard model of r-mode instability (suggested by Lindblom, Owen & Morsink 1998;Owen et al 1998, see also Gusakov, Chugunov & Kantor 2014a for discussion of recent microphysical updates) assumes a hadronic composition of the NS core and dissipation by shear and bulk viscosity. It stabilizes the NS in the grey region in Fig.…”

Quiescent Light Curve of Accreting Neutron Star MAXI J0556-332

“…15) Crustal heating has the following form: The other heating process is viscous heating, which originates because of the r-mode instability associated with the rapidly rotating NSs. 26,27) This process may affect the temperature evolution of NSs; 28) however, we do not include it in our study because the dimensionless amplitude of the r-mode is very uncertain, and the heating rates is unclear. 29) The accreted matter is assumed to have a uniform chemical composition with each mass fraction (X, Y, Z) = (0.73, 0.25, 0.02), where X, Y, and Z represent the mass fractions of hydrogen, helium, and heavy elements, respectively.…”

Stellar Collapse and Gravitational Waves

“…R-modes have been of particular interest to GW studies (e.g., Lindblom, Owen, & Morsink 1998;Andersson, Kokkotas, & Schutz 1999;) because they are unstable to GW emission: gravitational radiation tends to increase the amplitude of the mode. Lindblom, Owen, & Morsink (1998) first mapped out the range of stellar spin and temperature for which the viscosity was unlikely to damp away this runaway growth, and concluded that many hot, young neutron stars were likely to be important sources of GWs. Current thinking is that the rmodes of young hot neutron stars are actually unlikely to be important sources of GWs.…”

“…Understanding the physical nature of noise in GW detectors is an active field of current research; see Levin (1998), Liu & Thorne (2000, Santamore & Levin (2001), Buonanno & Chen (2001a,b), Hughes & Thorne (1998), Creighton (2000), and references therein for a glimpse of recent work. In all cases, the fundamental fact to keep in mind is that a GW acts coherently, whereas noise acts incoherently, and thus can be beaten down provided one is able to average away the incoherent noise sources.…”

“…GEO600 is a 600 meter interferometer constructed by a British-German collaboration near Hannover, Germany (Lück et al 2000). It uses advanced interferometry and advanced low noise multiple pendulum suspensions, serving as a testbed for advanced detector technology, and allowing it to achieve sensitivities comparable to the multi-kilometer instruments.…”