From Wide Triples to UCXBs: Multimessenger Signatures of Dynamically-formed Black Hole-White Dwarf Systems in the LISA Band

TL;DR

This work presents a coherent formation channel for BH–WD ultracompact X-ray binaries via dynamically excited wide BH–WD binaries in hierarchical triples. By coupling EKL dynamics, general relativistic precession, GW emission, WD dynamical tides, and subsequent mass transfer, the authors predict that a non-negligible fraction of BH–WD triples evolve into UCXBs that are observable in both X-rays and the mHz GW band. They estimate a Milky Way formation rate of $\Gamma_{\rm UCXB}\approx1.5\times10^{-7}\ \rm yr^{-1}$, with a combined GW-detectable lifetime of $\sim$ a few Myr and an X-ray detectable lifetime of $\sim$ 20–180 Myr, yielding a modest but testable Galactic population ($N_{\rm GW,UCXB}\sim1$, $N_{\rm UCXB}\sim3$–$27$). The study highlights the potential to identify tertiary companions as a smoking-gun signature of this channel and presents LISA verification binaries as a key multimessenger outcome, advancing our understanding of UCXB demographics and WD tidal physics.

Abstract

Ultracompact X-ray binaries (UCXBs) are a subclass of low-mass X-ray binaries characterized by tight orbits and degenerate donors, which pose significant challenges to our understanding of their formation. Recent discoveries of black hole (BH) candidates with main-sequence (MS) or red giant (RG) companions suggest that BH-white dwarf (BH-WD) binaries are common in the Galactic field. Motivated by these observations and the fact that most massive stars are born in triples, we show that wide BH-WD systems can naturally form UCXBs through the eccentric Kozai-Lidov (EKL) mechanism. Notably, EKL-driven eccentricity excitations combined with gravitational wave (GW) emission and WD dynamical tides can effectively shrink and circularize the orbit, leading to mass-transferring BH-WD binaries. These systems represent promising multimessenger sources in both X-ray and GW observations. Specifically, we predict that the wide triple channel can produce $\sim3-27$ ($\sim1-5$) detectable UCXBs in the Milky Way (Andromeda galaxy), including $\sim1$ system observable by the mHz GW detection of LISA. If the final WD mass can reach sufficiently small values, this channel could contribute up to $\sim 10^3$ UCXBs in the Galaxy. Furthermore, the identification of tertiary companions in observed UCXBs would provide direct evidence for this formation pathway and yield unique insights into their dynamical origins.

Figures (6)

• Figure 1: Comparison between the energy transfer rate of dynamical tides and GW radiation, for a highly eccentric BH–WD system. Here we consider a $10$–$0.6~\rm M_{\odot}$ BH–WD binary with $e=0.95$, WD radius $R_2=5.3\times 10^{-5}$ au, and WD dimensionless tidal torque $\hat{F}(\omega)\sim 150\omega^5$. The energy transfer rates from WD dynamical tides and from GW radiation are plotted as functions of the binary’s pericenter distance $r_p$. We show two cases for dynamical tides: the zero-spin case (red solid line, fixing $\Omega_s=0$) and the synchronized-spin case (blue dashed line, when $\Omega_s$ synchronizes with pericenter frequency and satisfies $\dot{J}_{\rm tide}=0$). The energy loss due to GW radiation is shown as the grey dash-dotted line. We note that when eccentricity is nonzero, there will be a residual tidal heating rate (blue dashed line) even when there is no net torque on the WD. This rate will vanish in the circular limit.
• Figure 2: Time evolution of an example BH-WD system that undergoes strong EKL oscillations during the dynamical formation stage (left column) and transitions into a mass-transferring UCXB (right column). Here we show the time evolution of a representative BH-WD system from our simulation, with initial mass $m_1=10$$\rm M_{\odot}$, $m_2=0.6$$\rm M_{\odot}$, orbit separation $a_0=95.3$ au, eccentricity $e_0=0.199$. This binary is orbited by a tertiary companion with mass $m_3=0.836$$\rm M_{\odot}$, outer orbit separation $a_2=4997$ au, eccentricity $e_2=0.602$, and mutual inclination $i = 91.8^\circ$ to the inner binary. We define $t_c$ as the time when the BH–WD binary becomes fully circularized ($e < 0.01$). The system's evolution during the dynamical formation stage is shown in the left column as a function of $t_c - t$ (log-scale), while its post-circularization evolution is shown in the right column as a function of $t - t_c$. The first row shows the inner binary's orbital eccentricity, as $1-e$. The second row shows the inner orbital separation (red solid line, $a$), the WD–BH mass ratio (blue dash-dotted line, $m_2/m_1$), the Roche lobe radius (black dashed line, $R_{\rm lobe}$, see, e.g., eq.28 in Ye_2023), and the WD radius (black dotted line, $R_2$). The third row plots two ratios: the tidal energy dissipation rate (red solid line, see Equation (\ref{['eq:Edot']})) to the GW radiation power (see, e.g., eq. 5.4 in Peters64), and the WD spin angular frequency $\Omega_s$ to the binary’s pericenter frequency $\Omega_p = \Omega (1 - e)^{-3/2}$ (blue dash-dotted line). The bottom row shows the expected gravitational wave SNR at distance $D_l=8$ kpc (red solid line) for a 4-year LISA observation, and the binary’s X-ray luminosity $L_X$ (blue dash-dotted line), normalized by $0.1\%$ of the BH Eddington luminosity, $L_0=10^{-3}L_{\rm Edd} \sim 1.26\times 10^{36}$erg s$^{-1}$.
• Figure 3: The population of BH-WD systems from simulated Milky Way Galactic field, and their estimated GW SNR as a function of semi-major axis and eccentricity (for a 4-yr LISA observation). Here, we plot the semi-major axis, $a$, and eccentricity, as $1-e$, of each simulated BH-WD system (see the white stars). The Left Panel shows the initial conditions, while the Right Panel represents the final state of each system, either when its dynamical evolution ends at the Hubble time or when the orbit separation shrinks to $\lesssim10^{-3}$ au and triggers the mass transfer. The background color maps the binary's expected gravitational wave SNR, assuming a fixed distance $D_l=8$ kpc and a 4-yr LISA observation. In the Right Panel, we also plot intermediate evolutionary stages (pink dots) for binaries that eventually evolve into UCXBs. These dots represent the evolution track of UCXBs formed via the wide triple channel, and highlight the region of parameter space where they may become detectable.
• Figure 4: Parameters of detached BH-WD systems in triples after main sequence evolution. Here we plot the semimajor axis of inner ($a_1$) and outer orbits ($a_2$) for the BH–WD binaries and their tertiary companions, immediately after the inner binary has evolved into a BH–WD configuration. Red circles represent all systems, while blue triangles indicate those that later form UCXBs in our simulations. The dashed line indicates $a_2/a_1=1$.
• Figure 5: Comparison between tidal angular momentum and energy transfer rate, $\dot{J}_{\rm tide}$ and $\dot{E}_{\rm tide}$, as functions of the WD spin. Here we consider a $10-0.6$ M$_{\odot}$ BH-WD system with $e=0.9,\, r_p =3\times10^{-3}$ au, $\hat{F}(\omega)=150\omega^5$, and plot $\dot{J}_{\rm tide}$ and $\dot{E}_{\rm tide}$ as functions of the ratio between the WD spin angular frequency, $\Omega_s$, and orbital pericenter frequency, $\Omega_p$.