2014ApJ...781...26A

The rotation frequencies of young pulsars are systematically below their theoretical Kepler limit. r-modes have been suggested as a possible explanation for this observation. With the help of semi-analytic expressions that make it possible to assess the uncertainties of the r-mode scenario due to the impact of uncertainties in underlying microphysics, we perform a quantitative analysis of the spin-down and the emitted gravitational waves of young pulsars. We find that the frequency to which r-modes spin-down a young neutron star (NS) is surprisingly insensitive to both the microscopic details and the saturation amplitude. Comparing our result to astrophysical data, we show that for a range of sufficiently large saturation amplitudes r-modes provide a viable spin-down scenario and that all observed young pulsars are very likely already outside the r-mode instability region. Therefore, the most promising sources for gravitational wave detection are unobserved NSs associated with recent supernovae, and we find that advanced LIGO should be able to see several of them. Our analysis shows that despite the coupling of the spin-down and thermal evolution, a power-law spin-down with an effective braking index n_rm≤ 7 is realized. Because of this, the gravitational wave strain amplitude is completely independent of both the r-mode saturation amplitude and the microphysics and depends on the saturation mechanism only within some tens of percent. However, the gravitational wave frequency depends on the amplitude, and we provide the required expected timing parameter ranges to look for promising sources in future searches.