Formation of the Dormant Black Holes with Luminous Companions from Binary or Triple Systems

TL;DR

This work investigates the formation of dormant black holes with luminous companions (dBH-LCs) via isolated binary evolution (IBE) and hierarchical triple evolution in the Milky Way. It uses MOBSE for binary evolution and the TSE code for triple evolution to sample up-to-date initial-multiplicity distributions, compute orbital and mass distributions, and estimate birthrates, defining dBH-LCs by low X-ray luminosity and detached states. The main finding is that triple evolution dominates dBH-LC production by 1–2 orders of magnitude, with the principal channel being post-merger binaries formed through von Zeipel-Lidov-Kozai oscillations, and it can yield heavier BHs, including a minority in the PISN mass range; the study predicts on the order of 8.7×10^4 dBH-LCs with P_orb < 10 years in the MW, many of which Gaia could detect. These results imply that triple dynamics are essential for accurate population synthesis of dBH-LCs and have important implications for interpreting Gaia and future surveys.

Abstract

Recently, a class of dormant black hole binaries with luminous companions (dBH-LC) has been observed, such as $Gaia$ BH1, BH2, and BH3. Unlike previously discovered X-ray BH binaries, this type of dBH-LC has relatively long orbital periods (typically more than several tens to a few hundred days) and shows very weak X-ray emission. Therefore, studying the formation and evolution of the whole dBH-LC population is also a very interesting problem. Our aim is to study the contribution of massive stars to the dBH-LC population under different evolutionary models (isolated binary evolution (IBE) and hierarchical triple evolution), and different formation channels (such as mass transfer, common envelope evolution). Using the Massive Objects in Binary Stellar Evolution (MOBSE) code, the Triple Stellar Evolution (TSE) code, and the latest initial multiple-star distributions, we model the populations of massive stars. Finally, we calculate the orbital properties, mass distributions, and birthrates of the BH-LC populations formed under these different conditions. In the Milky Way, we calculate that the birthrate of dBH-LC formed through IBE is about 4.35$\times$$10^{-5}$ ${\rm yr}^{-1}$, while the birthrate through triple evolution is about 1.47$\times$$10^{-3}$ ${\rm yr}^{-1}$. This means that the birthrate from triple evolution is one to two orders of magnitude higher than that from IBE. We find that in triple evolution, the main formation channel of dBH-LC is post-merger binaries formed from inner binary mergers triggered by von Zeipel$-$Lidov$-$Kozai oscillations.

Figures (7)

• Figure 1: The top-left panel shows the companion frequency for a primary mass of 20 $M_{\odot}$ at different orbital periods. The blue line represents the companion frequency from 2017ApJS..230...15M for a 20 $M_{\odot}$ primary, while the other colors show extrapolated companion frequencies for different minimum mass ratios ($q_{\rm min}$). The top-right panel shows the initial orbital distribution of isolated binaries with a $q_{\rm min}$ = 0.001. The two bottom panels show the initial inner and outer orbital distributions of triple with $q_{\rm min}$ = 0.001.
• Figure 2: Examples of dBH-LC formation through SN or inner binary merger in triple evolution are shown. Both panels display the evolution of component mass, radius, orbital separation, and eccentricity as functions of time. In both panels, the gray region indicates the phase when the inner binary undergoes RLOF, and the red region marks the dBH-LC phase. In addition, the initial parameters of the two triples shown in the figure are as follows: In the left panel, the masses of the system are $m_{\rm 1}$ = 23.57 $M_{\odot}$, $m_{\rm 2}$ = 14.96 $M_{\odot}$, and $m_{\rm 3}$ = 0.13 $M_{\odot}$. The semi-major axes and eccentricities are $a_{\rm in}$ = 1902.10 $R_{\odot}$, $a_{\rm out}$ = 19130.05 $R_{\odot}$, $e_{\rm in}$ = 0.51, and $e_{\rm out}$ = 0.46. The inclinations and arguments of pericenter are $\cos i_{\rm in}$ = 0.80, $\cos i_{\rm out}$ = 0.04, $\omega_{\rm in}$ = 6.00, and $\omega_{\rm out}$ = 0.07. In the right panel, the masses of the triple are $m_{\rm 1}$ = 52.84 $M_{\odot}$, $m_{\rm 2}$ = 8.07 $M_{\odot}$, and $m_{\rm 3}$ = 9.00 $M_{\odot}$. The semi-major axes and eccentricities are $a_{\rm in}$ = 66.26 $R_{\odot}$, $a_{\rm out}$ = 2666.19 $R_{\odot}$, $e_{\rm in}$ = 0.18, and $e_{\rm out}$ = 0.66. The inclinations and arguments of pericenter are $\cos i_{\rm in}$ = -0.98, $\cos i_{\rm out}$ = -0.99, $\omega_{\rm in}$ = 0.79, and $\omega_{\rm out}$ = 2.99.
• Figure 3: At the metallicity of the MW, the birthrate distributions of the physical parameters of dBH-MS and dBH-PMS formed through IBE and triple evolution.
• Figure 4: The birthrate 2D distribution of dBH-MS in the MW is shown as a function of LC mass ($M_{\rm LC}$), BH mass ($M_{\rm BH}$), orbital period ($P_{\rm orb}$), and eccentricity ($e$). The color in each pixel is scaled according to the birthrate of dBH-LC binaries. The left panels show dBH-MS formed through IBE, and the right panels show those formed through triple evolution. The darkgreen crosses represent the observational data from Table 1. It is worth noting that our study focuses more on the differences between the dBH-LC populations formed through IBE and triple evolution. Therefore, in Table 1, we classify the observations only by the stellar types of the LCs. We emphasize that explaining these observations still requires attention to additional physical properties (for example, the metallicity of each observation).
• Figure 5: Similar to Fig. \ref{['fig:4']}, but for dBH-PMS.