R modes and neutron star recycling scenario

Abstract

To put new constraints on the r-mode instability window, we analyse the formation of millisecond pulsars (MSPs) within the recycling scenario, making use of three sets of observations: (a) X-ray observations of neutron stars (NSs) in low-mass X-ray binaries; (b) timing of millisecond pulsars; and (c) X-ray and UV observations of MSPs. As shown in previous works, r-mode dissipation by shear viscosity is not sufficient to explain observational set (a), and enhanced r-mode dissipation at the red-shifted internal temperatures $T^\infty\sim 10^8$ K is required to stabilize the observed NSs. Here, we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set (a) due to strong neutrino emission, which is typical for these models (unrealistically powerful energy source is required to keep NSs at the observed temperatures). We also demonstrate that the observational set (b), combined with the theory of internal heating and NS cooling, provides evidence of enhanced r-mode dissipation at low temperatures, $T^\infty\sim 2\times 10^7$ K. Observational set (c) allows us to set an upper limit on the internal temperatures of MSPs, $T^\infty<2\times 10^7$ K (assuming a canonical NS with the accreted crust). Recycling scenario can produce MSPs at these temperatures only if r-mode instability is suppressed in the whole MSP spin frequency range ($\nu\lesssim 750$ Hz) at temperatures $2\times 10^7\lesssim T^\infty\lesssim 3 \times 10^7$ K, providing thus a new constraint on the r-mode instability window. These observational constraints are analysed in more details in application to the resonance uplift scenario of Gusakov et al. [Phys. Rev. Lett., 112 (2014), 151101].