The role of triple evolution in the formation of LISA double white dwarfs

TL;DR

This paper quantifies the contribution of hierarchical triple evolution to the Galactic population of LISA-detectable double white dwarfs by coupling the MSE population synthesis code with a Milky Way-like galaxy from the TNG50 cosmological simulation. It finds that roughly equal numbers of DWDs in the LISA band originate from triple (about $7.2 imes10^{6}$) and binary (about $3.8 imes10^{6}$) channels, with about $1.7 imes10^{4}$ individually resolvable sources in total (roughly $1.1 imes10^{4}$ from triples and $6.5 imes10^{3}$ from binaries). The triple channel also yields a small fraction of highly eccentric DWDs (≈$3 imes10^{-6}$ of the population), though these produce burst-like signals unlikely to be detectable within four years. Additionally, about 57% of LISA-visible triples retain a bound tertiary, but most tertiaries are too distant to imprint detectable Doppler signatures on the inner binary GW signal. Overall, including triples modestly but meaningfully enriches the LISA DWD foreground and introduces new avenues for cross-messenger constraints on triple-star evolution.

Abstract

Galactic double white dwarfs will be prominent gravitational-wave sources for the Laser Interferometer Space Antenna (LISA). While previous studies have primarily focused on formation scenarios in which binaries form and evolve in isolation, we present the first detailed study of the role of triple stellar evolution in forming the population of LISA double white dwarfs. In this work, we present the first detailed study of the role of triple stellar evolution in forming the population of LISA double white dwarfs. We use the multiple stellar evolution code (MSE) to model the stellar evolution, binary interactions, and the dynamics of triple star systems then use a Milky Way-like galaxy from the TNG50 simulations to construct a representative sample of LISA double white dwarfs. In our simulations about $7\times10^6$ Galactic double white dwarfs in the LISA frequency bandwidth originate from triple systems, whereas $\sim4\times10^6$ form from isolated binary stars. The properties of double white dwarfs formed in triples closely resemble those formed from isolated binaries, but we also find a small number of systems $\sim\mathcal{O}(10)$ that reach extreme eccentricities $(>0.9)$, a feature unique to the dynamical formation channels. Our population produces $\approx 10^{4} $ individually resolved double white dwarfs (from triple and binary channels) and an unresolved stochastic foreground below the level of the LISA instrumental noise. About $57\,\%$ of double white dwarfs from triple systems retain a bound third star when entering the LISA frequency bandwidth. However, we expect the tertiary stars to be too distant to have a detectable imprint in the gravitational-wave signal of the inner binary.

Figures (13)

• Figure 1: Initial parameter distributions. The left panel shows the mass distributions ($m_{i}$), where $m_1$ and $m_2$ denote the masses of the inner binary components, and $m_3$ represents the mass of the tertiary. The middle panel displays the semi-major axis distributions($a_{i}$) for the inner ($a_1$) and outer ($a_2$) orbits, respectively. The right panel illustrates the eccentricity distributions($e_{i}$) of the inner ($e_1$) and outer ($e_2$) orbits, respectively. (See Sect. \ref{['sec: initial distributions']} for more details.)
• Figure 2: Diagram of possible key processes that drive the evolutionary phases of a triple evolution leading to the formation of a double white dwarf in the LISA frequency bandwidth. The diagram showcases key stages, including mass transfer, common envelope phases, ZLK oscillations that enhance eccentricity, and eventual binary evolution. The tertiary star plays a critical role in shaping the inner binary's dynamics, either by inducing orbital changes or facilitating interactions that lead to the formation of the LISA double white dwarf. The circles represent the index of the star, with blue, green, and red indicating the primary, secondary, and tertiary stars, respectively. The filling inside each circle represents the star's evolutionary phase: purple for the main-sequence and white for a white dwarf. A dashed arrow denotes a distant tertiary star that is too far to significantly influence the inner binary. A multi-colored circle represents a post-merger star, with the two colors signifying the components that have merged.
• Figure 3: Venn diagram illustrating the overlap of the different evolutionary processes. Among the five processes, the inner binary channel is the only one that does not require assistance from the tertiary star to produce a LISA double white dwarf. In contrast, the other four processes rely on the tertiary star to bring the system into the LISA frequency bandwidth. These processes are not mutually exclusive and exhibit significant overlap.
• Figure 4: Comparison of the evolution of a triple system with and without a tertiary star. Panels (a) and (b) illustrate the evolution of the inner binary with and without the third star respectively. In the system with the tertiary star, mass transfer is induced by perturbations from the third star, allowing the system to eventually enter the LISA frequency bandwidth. When evolved without a tertiary star the binary components remain too far apart to interact. Such a system does not enter the LISA frequency bandwidth. The legends are similar to those in Fig. \ref{['fig:schematic_diagram']}. In addition, the yellow filling represents a star in the Asymptotic giant branch phase.
• Figure 5: Comparative evolution of the properties of the inner binary of the triple with and without a third star. The three panels, from top to bottom, display the zoomed-in evolution of key parameters of the two stars: eccentricity, semi-major axis, and radius. In the case of the triple system, the inner binary experiences unstable mass transfer, causing it to shrink further and eventually enter the LISA band. Meanwhile, the inner binary when evolved without a tertiary star undergoes mass loss due to winds, resulting in an increase in its semi-major axis and a widening of the orbit. Here $a_1\,(\mathrm{triple})$ and $e_1\,(\mathrm{triple})$ represent the semi-major axis and eccentricity of the inner binary evolved with a tertiary star, while ${a}\,({\rm binary})$ and ${e}\,({\rm binary})$ show the semi-major axis and eccentricity of the same inner binary evolved without the tertiary star. Additionally, $r_1$ and $r_2$ represent the radii of the primary and secondary stars in the inner binary, respectively.