Chemical enrichment of metal-poor stars orbiting massive black hole companions

TL;DR

The paper develops an analytical and numerical framework to quantify enhanced metal accretion onto low-mass stars in binaries with massive black hole companions. By extending Bondi-Hoyle-Lyttleton accretion to unequal-mass binaries and validating with 3D hydrodynamic simulations, it shows that the secondary’s accretion rate scales as $\dot{M}_{*,\rm bin} = \dot{M}_{*,\rm iso} (M_{\rm BH}/M_*)(a/R_a)^{-1}$, with density enhancements roughly proportional to $q^{-1}$. Applying this to Gaia BH3-like systems using Eris cosmological trajectories reveals substantial iron accretion on main-sequence companions (median $[\mathrm{Fe/H}]$ around $-3.4$ birth, up to $-2.2$ today for Gaia BH3-like configurations), while post-main-sequence dredge-up dilutes these signatures, making them harder to observe in evolved stars. The work highlights that surface metallicities of sun-like companions can diverge from their birth metallicities due to ISM accretion, especially in close, high-mass BH binaries, and discusses implications for globular clusters and LIGO-like binaries.

Abstract

There are millions of undetected black holes wandering through our galaxy. Observatories like {\it Chandra}, LIGO, and more recently, {\it Gaia}, have provided valuable insights into the configurations of these elusive objects when residing in binary systems. Motivated by these advances, we study, for the first time, the enhanced accretion of metals from the interstellar medium (ISM) onto low-mass companions in binary systems with highly unequal mass ratios, utilizing a series of hydrodynamical simulations. Our study demonstrates that a stellar companion's metal accretion history from the ISM alone, from its formation to the present, can significantly influence its surface abundances, especially when enhanced by a massive black hole companion. However, this effect is likely only measurable in stars that are still in the main sequence. Once a stellar companion evolves off the main sequence, similar to what has been observed with the {\it Gaia} BH3 companion, the initial dredge-up process are likely to erase any excess surface abundance resulting from the metals that were accreted. As we discover more unequal mass ratio binary systems, it is crucial to understand how the observed metallicity of sun-like companions may differ from their birth metallicity, especially if they are not yet evolved.

Figures (8)

• Figure 1: Left: Probability distribution of the mass ratio of binaries in three different catalogs: top: HMXBs (dark blue), radio pulsars (light blue), and bottom:Gaia wide binaries (purple) and Gaia DR3 binaries (pink). The locations of the three recently discovered Gaia black holes are labeled by the three black lines in the top pannel. Right: Semi-major axis distance between two orbiting bodies, $a$, versus accretion radius, $R_a$ for different detected binary systems. The diagonal lines shows the location where $a/R_a = 10, 1, 0.1, \ \text{and} \ 0.01$ from top to bottom (darker to lighter). In the upper left, denoted by purple stars, is a subset of the wide binaries detected by Gaia DR2. Lower down, in pink, is a subset of the binaries detected by Gaia in the DR3 non-single stars catalogue. In the bottom, in dark blue are the HMXBs and in light blue the radio pulsar binaries. The stars in yellow, orange and red, outlined in black, show the three Gaia black hole binaries.
• Figure 2: Density snapshots for two simulations at three different time stamps ($t=55, 61, 67 \ R_a/v_{\infty}$) as the system completes half of an orbit from left to right. Higher densities are denoted by lighter colors. The stellar companion is represented by the yellow star marker. The arrowed flow lines show the velocity streamlines of the incoming wind. Top row: Time evolution of a system with mass ratio $q^{-1}=2$ at a separation $a = 0.42\,R_a$. Bottom row: Time evolution of a system with mass ratio $q^{-1}={5}$ at a separation $a = 0.42\,R_a$.
• Figure 3: Density profiles from the center of mass of BH-star binaries for different mass ratios at a fixed initial separation of $a =0.42\,R_a$ (left) and $a =1.0\,R_a$ (right). From top to bottom, $q^{-1}=2,3,4,5$. The circles show the locations of the BHs and the star shaped symbols show the locations of the stars relative to the center of mass of the binary. We can see that the stars experience densities that are $\approx 6-10$ times larger than the background one. The gray dotted line shows the best fit to the single object between $0.1 \text{ and } 1.0 R_a$, $\rho \propto r^{-0.81}$. Left inset: Orbit averaged accretion rate for the stellar companion compared to its mass accretion rate in isolation. This is plotted for different inverse mass ratios $q^{-1}$, at fixed orbital separation of $a = 0.42$. The best fit line is plotted which yields the relation $\langle \dot{M} \rangle \propto \left( q^{-1} \right) ^{1.15\pm 0.2}$.
• Figure 4: Top: Evolution of $a/R_a$ for a Gaia BH3-like binary. Namely, a $0.8\,M_{\odot}$ companion star orbiting around a $32.7\,M_{\odot}$ black hole at a separation of $16\,\rm{AU}$. The components used from Eris simulations are the velocity of the star particles relative to the ISM, which determines $R_a$, as well as the gas density as a function of $z$. The gray dotted line denotes where $a/R_a=1$, such that for all values under the line, the binary has a shared accretion radius. Bottom: Distribution of the companion’s cumulative iron accretion history from formation to the present day, derived from the same set of trajectories and accounting for the spread in relative velocities. In both panels, dark curves show the median values and the shaded region show the $68$% scatter about the median.
• Figure 5: The surface abundance resulting from accretion for a main-sequence star companion with $0.8\,M_{\odot}$, orbiting a $M_{\rm{BH}}$ black hole at a separation $a/R_a$. We assume the star has a birth [Fe/H]$=-5$. The top panel shows the corresponding surface metallicity [Fe/H] calculated using the accretion history for stellar particles with Galactic locations similar to the Gaia BH3 system. The teal star-shaped marker denotes the conditions for the $Gaia$ BH3 system if it were in the main sequence and when it was actively accreting in the early universe (see Figure \ref{['fig:redshift']} where $a/R\approx 0.3$ for $z\lesssim 4$). The bottom panel calculates the accretion history of the binary using the mean values of $a/R_a$ across all stellar particle trajectories and scaling the accretion rate with the mean background density, $\rho_\infty$ (Figure \ref{['fig:redshift']}). For both cases, the surface abundance is progressively enhanced for stars residing at tighter separations with heavier black hole companions. Top panel distribution: In black, we show the probability density function of LIGO-Virgo-Kagra black hole masses LIGO. In blue, we show the probability density function of the masses of the black hole component of low mass X-ray binaries Fortin_2024. Right panel distribution: We show the probability density function of [Fe/H] of Gaia DR3 thick disc and halo stars Kim_2021.