Measuring the Galactic Binary Fluxes with LISA: Metamorphoses and Disappearances of White Dwarf Binaries

The space gravitational wave detector LISA is expected to detect $\sim {10}^4$ of nearly monochromatic Galactic binaries, after $\sim 10\mathrm{yr}$ operation. We propose to measure the inspiral and outspiral binary fluxes in the frequency space, by processing tiny frequency drifts of these numerous binaries. Rich astrophysical information is encoded in the frequency dependencies of the two fluxes, and we can read the long-term evolution of white dwarf binaries, resulting in metamorphoses or disappearances. This measurement will thus help us to deepen our understanding on the strongly interacting exotic objects. Using a simplified model for the frequency drift speeds, we discuss the primary aspects of the flux measurement, including the prospects with LISA.

Figure 1

The schematic picture for the inspiral or outspiral binary fluxes in the frequency space. The black curve shows the total inspiral flux $F_{+}(f)=F_{+}^M(f)+F_{+}^T(f)$ that is subdivided into the merger (green) and turnover (orange) components. The latter generates the outspiral flux $F_{-}(f)=-F_{+}^T(f)$ (blue). The information of the merger and turnover is clearly imprinted in the frequency dependencies of the two fluxes $F_{\pm }(f)$.

Figure 2

The drift speeds $|\dot{f}|$ for the binaries with initial masses $0.35M_{\odot }+0.46M_{\odot }$ (green) and $0.15M_{\odot }+0.3M_{\odot }$ (orange: inspiral, blue: outspiral phases). The dotted and dashed curves show the estimations errors $\mathrm{\Delta }\dot{f}$ for corresponding binaries at $d=20\mathrm{kpc}$ with the observational periods $T_o=10$ and 4 yr.

Figure 3

The number densities of binaries per unit frequency. The black line is that for total inspiral binaries ${\rho }_{+}(f)$ composed by the merger (green) and turnover (orange) components. The blue curve is ${\rho }_{-}(f)$ for the outspiral binaries. The horizontal red lines show the critical densities for the source confusion. The inset shows the characteristic frequency resolutions $\delta f_{\pm }$ in Eq. (14). The relative Poisson fluctuations are given by $[{\rho }_{\pm }(f)\delta f_{\pm }{]}^{-1/2}$.

Figure 4

The angular-averaged signal-to noise ratios for WDBs at $d=20\mathrm{kpc}$ and $T_o=10\mathrm{yr}$. The green curve is for the initial masses $0.35M_{\odot }+0.42M_{\odot }$, resulting in the merger. The WDB initially with $0.15M_{\odot }+0.3M_{\odot }$ turns over at 7.2 mHz.