Simin Mahmoodifar, Tod Strohmayer
The r-mode oscillations of neutron stars can be potentially powerful probes of cold ultra-dense matter. In this paper we present upper limits on the amplitude of r-mode oscillations, and their gravitational-radiation-induced spin-down rates, in low mass X-ray binary (LMXB) neutron stars under the assumption that the quiescent neutron star luminosity is powered by dissipation from a steady-state r-mode. We compute results for neutron star models constructed with the APR equation of state for masses of 1.4, 2 and 2.21 M_{sun}. For the lower mass models (1.4 and 2 M_{sun}) we find dimensionless r-mode amplitudes in the range from about 1x10^{-8} to 1.5x10^{-6}. For the accreting millisecond X-ray pulsar (AMXP) sources with known quiescent spin-down rates these limits suggest that about 1% of the observed rate can be due to an unstable r-mode. Interestingly, the AMXP with the highest amplitude limit, NGC 6640, could have an r-mode spin-down rate comparable to the observed, quiescent rate for SAX J1808-3658. Thus, quiescent spin-down measurements for this source would be particularly interesting. For all the sources considered here our amplitude limits suggest that their gravitational wave signals are likely too weak for detection with Advanced LIGO. Our highest mass model (2.21 M_{sun}) can support enhanced, direct Urca neutrino emission in the core and thus can have higher r-mode amplitudes. Indeed, the inferred r-mode spin-down rates at these higher amplitudes are inconsistent with the observed spin-down rates for some of the sources, such as IGR J00291+5934 and XTE J1751-305. This can be used to place an upper limit on the masses of these sources if they are made of normal nuclear matter, or alternatively it could be used to probe the existence of exotic matter in them if their masses were known.
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http://arxiv.org/abs/1302.1204
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