Ultracompact binary pulsars as continuous dual-line gravitational wave sources

Binary millisecond pulsars (MSPs) are detached systems consisting of a MSP and a He white dwarf. If the initial orbital periods of binary MSPs are shorter than 0.3 day, they would evolve toward ultracompact binary pulsars due to the rapid orbital shrinkage by the gravitational wave (GW) radiation. During the orbital decay, the MSP with an ellipticity would spin down due to GW radiation and magnetic dipole radiation. Our calculations indicate that the angular momentum loss is dominated by the GW radiation when the ellipticities of the neutron stars (NSs) are in the range of $(1–50)\times {10}^{-7}$, and the frequencies of high-frequency GW signals from the rotating NSs are 10–100 Hz when the binary pulsars can be visible as low-frequency GW sources. These high-frequency GW signals are possible to be detected by aLIGO and the third-generation GW detectors such as Einstein Telescope, depending on the frequencies and the distances. Therefore, ultracompact binary pulsars have an opportunity to become intriguing dual-line GW sources. By detecting low-frequency GW signals, the NS mass can be accurately derived. A dual-line detection of two band GW signals could provide a constraint on the moment of inertia and the ellipticity of the NS. Thus dual-line GW sources can be potentially applied to constrain the equation of state of NSs.

Figure 1

Evolution of the low-frequency GW signals producing by the orbital motion of binary MSP in the characteristic strain vs the GW frequency diagram. The solid curve is the LISA sensitivity curve. The initial orbital periods of binary MSPs are assume to be 0.3 days. The dashed, and dotted curves corresponds to a distance $d=1$, and 10 kpc, respectively.

Figure 2

Evolution of the frequency of the high-frequency GW signals producing by the spin motion of MSPs with an ellipticity. In this figure, we take $f_{\mathrm{high},0}=1000\mathrm{Hz}$, and $I_{45}=1$. The solid, dashed, dotted, and dashed-dotted curves corresponds to an ellipticity ${\epsilon }_{-7}=1$, 10, 0.1, and 100, respectively.

Figure 3

Distribution of some NS samples that can emitting high-frequency GW signals in the characteristic strain vs the GW frequency diagram. The distances of the solid stars and the open stars are 1 kpc, and 10 kpc, respectively. The upper and bottom curves correspond to the sensitivity curves of the aLIGO and ET, respectively. The designed power spectral densities $S_{\mathrm{n}}(f)$ of aLIGO and ET arise from the analytical models (see also [51, 52, 53]).