Higher Harmonics of Double White Dwarfs in the Centihertz Band: Linking LISA and DECIGO

TL;DR

This work assesses the detectability of post-Newtonian higher harmonics from Galactic double white dwarfs in the centihertz band, using a synthetic population to quantify LISA and decihertz mission capabilities. It demonstrates that while LISA will provide a near-complete census through quadrupole detections, DECIGO/BBO can detect the third harmonic for about 10% of inspiral binaries above roughly 5 mHz, enabling direct constraints on mass ratios. The results highlight a sequential, complementary observational strategy that leverages LISA for a census and decihertz missions for detailed binary parameter estimation, bridging millihertz and decihertz GW astronomy. The study also discusses astrophysical implications, including mass-ratio distributions and EM synergy, while acknowledging limitations related to population modeling and post-contact evolution.

Abstract

We investigate the detectability of post-Newtonian higher harmonics from Galactic double white dwarfs in the centihertz band ($\sim 0.01$ Hz). Using a synthetic population, we show that, unlike the quadrupole mode, higher harmonics remain undetectable with LISA except for rare nearby systems. In contrast, planned mid-band (decihertz) observatories such as DECIGO and BBO will be able to detect the third harmonic for about 10\% of inspiral binaries above $\sim 5$ mHz, enabling statistical constraints on mass ratios. These results highlight the successive roles of LISA and future decihertz missions in establishing a coherent strategy for space-based gravitational-wave astronomy.

Figures (8)

• Figure 1: Inclination dependence of the geometrical factors $E_k(I)=\sqrt{a_{k,+}^2+a_{k,\times}^2}$ for $k=1,2,3$. The odd-harmonic factors vanish for face-on configurations ($I=0$ or $\pi$).
• Figure 2: Adopted noise spectra for space-based detectors. The curves show the instrumental terms $S_{\rm inst}(f)$ (LISA, Taiji, TianQin, DECIGO, BBO) and the extra-galactic white-dwarf foreground $S_{\rm exgal}(f)$ from Eq. (\ref{['exg']}). The vertical axis shows $\sqrt{S(f)}$ (Hz$^{-1/2}$), where $S(f)$ denotes the respective spectra. The figure displays $S_{\rm inst}$ and $S_{\rm exgal}$ separately; it does not show the summed $S_n=S_{\rm inst}+S_{\rm exgal}$ nor the $S_n/3$ scaling used for the three independent DECIGO/BBO units.
• Figure 3: Histogram of quadrupole GW frequencies $f_2$ for the 1858 binaries with $f_2 \geq 5$ mHz in the analysis sample.
• Figure 4: Histogram of component masses for the 1858 binaries. Distinct peaks correspond to He and CO white dwarfs, with a high-mass tail associated with the CO component.
• Figure 5: Cumulative distribution of heliocentric distances $F(<d)$ for the disk, bulge, and total populations defined in Eq. (\ref{['eq:cdf_def']}).