Dynamical evolution of stellar binaries in galactic centers

TL;DR

This paper investigates how stellar binaries near a massive black hole evolve under the combined influence of ZLK oscillations, diffusive tidal friction, flybys, and vector resonant relaxation (VRR). By incorporating dynamical tides, VRR, and impulsive flyby perturbations into secular simulations, the authors show that a large fraction of binaries contract to near-contact separations while still on the main sequence, with the contraction probability increasing closer to the MBH. They introduce and exploit the ZLK loss wedge framework, showing that refilling by VRR and flybys makes contraction common, not rare, and predict a radial trend from roughly 60% contraction at 0.05 pc down to ~20% at 1 pc. These results imply substantial impacts on the post-MS evolution of nuclear binaries, potentially affecting the population of X-ray binaries, Hills-type hypervelocity events, and gravitational-wave sources in galactic centers. The work emphasizes that many near-contact binaries could be hidden in the Galactic Center, offering new observational avenues and demanding refined modeling of GC binary populations.

Abstract

Stellar binaries in galactic centers are relevant to several observable phenomena, including hypervelocity stars, X-ray binaries, and mergers of stars and compact objects; however, we know little about the properties of these binaries. Past works have suggested that a small fraction of them should contract to a few stellar radii or collide, due to the co-operation of stellar tides and the eccentricity oscillations induced by the strong tidal field of the central massive black hole. We revisit this model with several updates. We first argue that when a binary's pericenter separation is driven down to a few stellar radii, diffusive excitation of stellar tides should quickly contract the orbit, saving the stars from collision. Instead, the stars should end up as a very tight binary. We then show that vector resonant relaxation and perturbations from passing stars -- effects not included in past models -- dramatically increase the prevalence of such encounters. In numerical experiments, we find that 1 in 5 binaries around 1 pc from Sgr A* should tidally contract in this way while still on the main sequence. This rate climbs to 3 in 5 around 0.01 pc, inward of which it plateaus. We briefly discuss observable implications of these results, with particular attention to young stellar binaries in the Galactic Center.

Figures (10)

• Figure 1: Stellar binaries in galactic centers form a hierarchical triple with an MBH, leading to oscillations of the inner-orbit eccentricity. For systems in a favorable region of parameter space (see Fig. \ref{['fig:ie_space']}), these oscillations bring the inner orbit into the diffusive-tide regime, where it should rapidly contract (Section \ref{['sec:dynamics']}). Flybys and VRR bring more systems into this favorable region (Section \ref{['sec:evolution']}); flybys impulsively alter all properties of the inner orbit, while VRR continuously changes the mutual inclination $i$.
• Figure 2: The orbital energy change after a single pericenter passage drops steeply with increasing pericenter separation (eq. \ref{['eq:delta_E']}). Profiles are shown in the diffusive regime, where $|\Delta P_{\rm in}|\geq \omega_f^{-1}$. Each colored line is for a different primary mass $m_1$, labelled in $M_\odot$. The fractional change is $\propto a_{\rm in}$; here we show $a_{\rm in} = 10$ au. Shaded regions show the sum of stellar radii for the listed mass ratios, assuming $r_2=r_1(m_2/m_1)^{1/2}$.
• Figure 3: For typical semimajor axes, diffusive tides begin at wider $q_{\rm in}$ than collisions. This is not necessarily true at very small $a_{\rm in}$, though in this regime our tidal calculations assuming $1-e_{\rm in} \ll 1$ likely underestimate the fractional energy change per orbit. The dependence on $m_1$ arises solely from stellar structure. Thin, dotted lines show the approximation (\ref{['eq:qt']}). Lines are dashed in regions where $1-e_{\rm in} \not\ll 1$. Shaded regions show the sum of stellar radii for the listed mass ratios, as in Figure \ref{['fig:n_to_shrink']}.
• Figure 4: $\mathcal{I}$ determines the maximum eccentricity a binary can reach during ZLK oscillations, while $\mathcal{E}$ encodes the inner-orbit energy. If $\mathcal{I}$ is small enough for a given $\mathcal{E}$, then we say the system is in the "ZLK loss wedge" (condition \ref{['eq:condition']}; green region). Here, oscillations may bring the binary to the diffusive regime ($q_{\rm in} \leq q_t$; see eq. \ref{['eq:qt']}), where it should tidally contract (Section \ref{['sec:fates']}). Evolution in in $(\mathcal{I},\,\mathcal{E})$, driven by VRR and flybys, brings binaries into the loss wedge (e.g., blue path in cartoon); however, flybys may first widen the inner orbit to the point of becoming unbound (e.g., orange path; see eq. \ref{['eq:unbind']}).
• Figure 5: Binaries closer to the MBH tend to be solidly within the "refilling" regime, where contraction is more common (see Section \ref{['sec:regimes']}). This colormap shows $\mathcal{R}_{\max}$, the ratio between the ZLK oscillation period and the faster of the evaporation and VRR timescales. The red contour denotes $\mathcal{R}_{\max} = 0.1$, a rough boundary between the refilling and sporadic regimes. Below the grey contour, VRR acts faster than flybys. In the grey region, binaries become unbound by the tidal potential of the MBH (i.e., they satisfy condition \ref{['eq:unbind']}); in the gold region binaries are "hard" and will not evaporate. (All values are calculated for $m_b=2\,M_\odot$. Galactic Center properties are given in Appendix \ref{['sec:setup_details']}.)