The gravitational wave signal from diverse populations of double white dwarf binaries in the Galaxy

Shenghua Yu and C. Simon Jeffery

Fig. 6. The GW signal due to different types of DWD. log h represents the strain amplitude (left panel). The number distribution is shown in the middle panel. The right panel illustrates the distribution of chirp mass due to different DWD types, normalized by the total number (2.76×108) of DWDs in the Galaxy (bin size ΔM = 0.001M). The LISA sensitivity and frequency bins are as in Fig. 5.

Context. The gravitational wave (GW) background in the range 0.01 − 30 mHz has been assumed to be dominated by unresolved radiation from double white dwarf binaries (DWDs). Recent investigations indicate that, at short periods, a number of DWDs should be resolvable sources of GW.

Aims. To characterize the GW signal which would be detected by LISA from DWDs in the Galaxy.

Methods. We have constructed a Galactic model in which we consider distinct contributions from the bulge, thin disc, thick disc, and halo, and subsequently executed a population synthesis approach to determine the birth rates, numbers, and period distributions of DWDs within each component.

Results. In the Galaxy as a whole, our model predicts the current birth rate of DWDs to be 3.21 × 10−2 yr−1, the local density to be 2.2×10−4pc−3 and the total number to be 2.76 × 108. Assuming SNIa are formed from the merger of two CO white dwarfs, the SNIa rate should be 0.0013 yr−1. The frequency spectra of DWD strain amplitude and number distribution are presented as a function of galactic component, DWD type, formation channel, and metallicity.

Conclusions. We confirm that CO+He and He+He white dwarf (WD) pairs should dominate the GW signal at very high frequencies (log f Hz−1 > −2.3), while CO+CO and ONeMg WD pairs have a dominant contribution at log f Hz−1 ≤ −2.3. Formation channels involving two common-envelope (CE) phases or a stable Roche lobe overflow phase followed by a CE phase dominate the production of DWDs detectable by LISA at log f Hz−1 > −4.5. DWDs with the shortest orbital periods will come from the CE+CE channel. The Exposed Core plus CE channel is a minor channel. A number of resolved DWDs would be detected, making up 0.012% of the total number of DWDs in the Galaxy. The majority of these would be CO+He and He+He pairs formed through the CE+CE channel.

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Last Revised: 2010 July 23rd