Binary stars in the Milky Way nuclear stellar cluster

TL;DR

The paper investigates the fate of low-mass binaries in the Milky Way's nuclear stellar cluster under the combined influence of a central SMBH, dynamical three-body encounters, and tidal dissipation. By simulating binaries at $0.1$ and $0.3$ pc with von Zeipel-Lidov-Kozai cycles and tides over $\sim 10$ Gyr, the study shows that inward migration typically destroys binaries via mergers or evaporation, while outward migration helps preserve them; outcomes near the hard-soft boundary are stochastic. It identifies three key pathways to observable remnants: mergers that can produce blue straggler-like products, collisions that trigger three-body pile-ups (3BPUs), and a population of merger products migrating toward the inner arcsec, potentially contributing to the S-cluster and G-objects. The work links NSC binary evolution to the presence of S-cluster-like objects and dust-enshrouded merger remnants, offering a framework to interpret observed populations and to constrain star-formation-evolution histories in the Galactic Center.

Abstract

Intermediate-mass galaxies, including the Milky Way, typically host both a supermassive black hole (SMBH) and a nuclear stellar cluster (NSC). Binaries in an NSC evolve via close encounters with surrounding stars and secular processes related to the SMBH. We study moderately soft and hard binaries ($0.03$-$2.5\,\mathrm{au}$, $M \lesssim 2\,M_\odot$) initially at galactocentric radii 0.1 and 0.3 pc using three-body simulations including von Zeipel-Lidov-Kozai oscillations and tidal dissipation over $\sim 10$ Gyr. Binaries migrate both inward and outward as a consequence of kicks received in the three-body encounters. Inward migration leads to destruction via mergers and evaporation, while outward migration is a pathway to retaining intact binaries for $\gtrsim 10$ Gyr. All surviving binaries are hard and circular, but outcomes for binaries initially at the hard-soft boundary are stochastic. We find that: (i) about $0.3$ percent of evaporated binaries fall into the SMBH's loss cone, (ii) at least $1$ percent of mergers occur late enough to appear as blue straggler stars (BSSs) on the main sequence or as recently evolved red giants, (iii) about $1$ percent of binaries initially at 0.1 pc merge within the inner arcsec of the NSC, and (iv) less than about $80$ percent of field-star collisions with a binary star lead to a subsequent merger; a three-body pile up, which are relatively common in the first 1-2 Gyr and could serve as a way to form more massive BSSs in the NSC. We predict that a small fraction of binaries originate closer to the SMBH than their present-day orbits, and vice versa for evaporated binaries and BSSs. The mergers confined to the inner arcsec occur after $\gtrsim 300$ Myr, too long to be directly related to the formation of the S-stars or G-objects, but suggest that the inner arcsec is contaminated with BSSs from earlier star formation events.

Figures (21)

• Figure 1: Initial (final) distribution of hardness ratio for binaries originating at $0.1$ and $0.3~\mathrm{pc}$ in solid (dashed) black and red lines, respectively. The vertical dotted line marks the H/SB. Each bin is normalised to the total sum.
• Figure 2: Flow chart of our routine which is described in Section \ref{['sect: Algorithm']}. The central sketch shows the overall setup of the three-body encounters; a binary ($m_1,~ m_2$) on an orbit at a distance of $d_\bullet$ around the SMBH ($M_\mathrm{SMBH}$) interacting with a tertiary ($m_3$). To the right of this sketch we show the possible outcomes from a three-body interaction. Group C contains interactions in which the binary remains intact and bound to the SMBH, and as a consequence will have a Continued evolution. Conversely, the evolution is Terminated by outcomes in group T. To the left of the sketch we illustrate how a binary is evolved. A timestep $\Delta t$ is set by the shortest timescale of ZLK (quadrupole approximation), encounters and circularisation (tides). The secular process with the shortest timescale $\min[\tau_\mathrm{quad},\tau_\mathrm{circ}]$ is then run for $\Delta t$. At every step $0.1\Delta t$, a three body encounter is sampled with the accept reject method described in Appendix \ref{['Accept/Reject']}; if accepted the three-body encounter is carried out with tsunami, if rejected we proceed to the next $0.1\Delta t$ and sample again. After a time $\Delta t$ has passed, or after a three-body encounter, a new $\Delta t$ is calculated. In this example, the encounter occurs after $\Delta t_1 + 0.1\Delta t_2 + t_\mathrm{enc}$. This process is then continued until an outcome in group T occurs, or until the simulation time exceeds $10\,\mathrm{Gyr}$.
• Figure 3: Left: Inner semi-major axes distribution of the initial population (black) and the corresponding final outcomes (colours). Yellow lines refer to binary mergers; green lines to binaries that evaporate; magenta lines to binaries that are ejected (unbound from the SMBH); red lines to intact binaries (i.e. binaries that survive to 10 Gyr); and blue lines to evolved binaries (stellar evolution of the primary occurs before binary destruction and by 10 Gyr). In the cases of evaporation and mergers, the properties shown in the Figure refers to the binary just before either destruction mechanism takes place. Ejection corresponds to the region the binaries were ejected from and not where they end up. The top row corresponds to binaries starting with $a_\bullet = 0.1~\mathrm{pc}$ from the SMBH, the bottom row to $a_\bullet = 0.3~\mathrm{pc}$. Right: Outer semi-major axis distributions. The vertical black lines represent the initial populations, the boxes the final outcomes coloured in the same way.
• Figure 4: Cumulative distribution of outcomes as a function of time. The outcomes are colour-coded the exact same way as in Figure \ref{['fig: sma distributions']}. The solid (dashed) lines refer to binaries initially $0.1~\mathrm{pc}$ ($0.3~\mathrm{pc}$) away from the SMBH.
• Figure 5: Cumulative distribution of the eccentricities for the inner (panel a) and outer (panel b) orbit, colour-coded as in the previous Figures (outcome). The dotted grey lines follow specific power-law distribution $e^\eta$ where $\eta = -1$ correspond to mostly circular orbits, $\eta = 0$ to a uniform distribution and $\eta = 1$ to a thermal distribution (e.g. mostly eccentric orbits). As in Figure \ref{['fig: sma distributions']}, the coloured distributions consider the final state of a binary where it can still be considered a binary (and not destroyed). Best-fit parameters can be found in Table \ref{['table: power law fits']}.