An analytical approach to binary populations in globular clusters

Abstract

Globular clusters (GCs) display much lower binary fractions than found among main-sequence stars in the solar neighborhood. The physical cause of this difference is debatable: does it reflect different star formation outcomes at low metallicity and/or high density, the dynamical processing of primordial binaries over cluster lifetimes, or a combination of the two? Starting from the assumption that the initial binary distribution in GCs is the same as the binary distribution observed in the solar neighborhood, we show with straightforward analytical calculations that the dynamical dissolution of "soft" primordial binaries can fully explain the main-sequence binary fractions in present-day GCs. We validate our estimates against a detailed N-body simulation with the Cluster Monte Carlo code. Adopting the view that the observed binary fraction in a given cluster constrains the location of the hard/soft boundary at birth, we infer that surviving Milky Way GCs had a similar distribution of birth radii to young massive clusters in the local universe. Our findings underscore the crucial role of stellar black holes (through "black hole burning") in sculpting GC binary populations and reinforce the need for realistic initial conditions in theoretical modeling of GC dynamics.

Figures (6)

• Figure 1: Map of the primary mass--semimajor axis parameter space for binary systems embedded in fiducial Plummer-sphere clusters. Solid lines show the hard/soft boundary as a function of $m_{1}$ in each cluster for binaries with mass ratio $q = 0.5$; the color of each line indicates the cluster parameters described in the text: blue for model A, amber for B, green for C, and red for D. Dashed lines of the corresponding colors shows $a_{\rm max}$ in the same clusters. The dotted black curve shows $a_{\rm min}$. Binaries cannot exist in the shaded regions under our assumptions.
• Figure 2: Binary fraction as a function of primary mass. The black points are the measured MF among MS stars in the solar neighborhood as compiled in Table 1 of Offner2023binaries, with the mass bins and quoted uncertainties shown as horizontal and vertical error bars. The black curve is given by Eq. \ref{['eq:offner_mf_fit']}. Dashed colored curves show the predicted primordial hard binary fractions at the half-mass radii of our three fiducial Plummer-sphere clusters, using the same color scheme as in Fig. \ref{['fig:logm_loga_map']}. The shaded regions highlight areas of observational relevance: light blue shows the range of MS stellar masses and observed binary fractions in GCs, while grey shows the approximate mass range for BH progenitor stars.
• Figure 3: Like Fig. \ref{['fig:hardbinfracs']}, but for a log-normal distribution of semi-major axes with median $\mu_{a} = 30 \,\mathrm{AU}$ and dispersion $\sigma_{a} = 1.5 \, {\rm dex}$.
• Figure 4: Key timescales related to soft binary evolution within GCs, as computed for fiducial models A through D. The background stars assumed to have an average mass of $\bar{m} = 0.6 M_{\odot}$ and a binary fraction of $F_{\rm b} = 0.3$. Colored curves show the strong encounter interval as a function of $\eta$ for soft binaries of various masses. The black horizontal lines indicate the cluster's half-mass crossing time $T_{\rm cross}$, the mass segregation time $T_{\rm seg}$ for $10 M_{\odot}$ BHs, and the half-mass relaxation time $T_{\rm rh}$. Note that the ages of the Milky Way GCs are generally $\gtrsim 10 \,\mathrm{Gyr}$.
• Figure 5: Results of a CMC simulation of a GC with a primordial binary population realized according to our fiducial IBD. Clockwise from the top left, the four panels show (i) the total number of bound stars (blue) and total bound mass (amber), normalized to their initial values; (ii) the half-mass radius (blue) and theoretical (density-weighted) core radius (amber); (iii) the number of bound BHs (blue) and binary BHs (amber); and (iv) the binary fractions of all bound stars (blue), stars in the core (amber), and bound BHs (black). The core and BH data have been smoothed to a moderate degree to enhance visual clarity.