Direct N-body simulations of rotating and extremely massive Population III star clusters

Abstract

Aims. We present eight direct N-body simulations with NBODY6++GPU of extremely massive, initially rotating Population III star clusters with 1.01 x 10^5 stars. Methods. Our models include primordial binaries, a continuous initial mass function, differential rotation, tidal mass loss, updated fitting formulae for extremely massive metal-poor Population III stars, and general-relativistic merger recoil kicks. We assess their impact on cluster dynamics. Results. All runs form black holes below, within, and above the pair-instability gap, with multi-generation growth. Faster-rotating clusters core-collapse earlier; post-collapse clusters host a rotating, axisymmetric subsystem of intermediate-mass black holes (IMBHs) at the centre and an expanding halo of lower-mass objects. Pair-instability supernovae and compact-object formation at ~2-3 Myr sharply reduce total mass and a large fraction of the cluster's angular momentum. All Population III clusters in our simulations have the gravothermal-gravogyro catastrophe phase. Conclusions. We confirm two of the hypothesized formation channels of galactic nuclei seed black holes: gravitational runaway mergers of black holes and of Population III stars, which core-collapse into IMBHs thereafter. Higher initial star cluster bulk rotation correlates with earlier core collapse and, in the event counts reported here, with more coalescences/collisions and lower retained (compact) binary abundances. Initial bulk rotation is a primary control parameter of cluster evolution: faster rotation accelerates early angular-momentum transport, gravothermal collapse, mass segregation, and amplifies post-collapse expansion, which also favours the formation of a compact central IMBH subsystem.

Figures (14)

• Figure 1: Initial-final-mass relation (IFMR) for the NoK0.0 run: black-hole mass $m_{\mathrm{BH}}$ versus progenitor ZAMS mass $m_{\mathrm{ZAMS}}$. The panels correspond to progenitors exploding as lCCSNe, PPISNe, PISNe, and hCCSNe. (IM)BH formation channels are shown in red.
• Figure 2: Binary distributions at 500 Myr. From top to bottom: $e^2$, cumulative semi-major axis $a$ (au), cumulative binary potential energy $E_{\mathrm{pot}}$ (N-body units), cumulative distance to the density centre $r_{\mathrm{dens}}$ (pc), and mass ratio $q\equiv m_2/m_1$. In the $r_{\mathrm{dens}}$ panel a blue line shows the half-mass radius $r_\mathrm{h}$ of the NoK0.0 model at 500 Myr ($\sim$9.77 pc).
• Figure 3: Plot showing the total cluster mass $M_\mathrm{cl}{}$, the tidal radius $r_\mathrm{tid}$, the half mass radius $r_\mathrm{h}$, the mass of the core $m_\mathrm{c}{}$ and the radius of the core $r_\mathrm{c}$ in the four panels for all eight simulations with and without GR recoil kicks for different $\omega_{0}$. Time is shown on a logarithmic scale to highlight the cluster's rapid early evolution. The models with K are plotted as solid curves and the models without (NoK models) are plotted as dash-dotted curves.
• Figure 4: Plots showing cumulative counts of escaping single stars $n_{\mathrm{esc,singles}}$, their total mass $M_{\mathrm{esc,singles}}$, and counts of escaping single MS, CHeB, ShHeB, NS and BH stars ($n_{\mathrm{escMS,s}}$, $n_{\mathrm{escCHeB,s}}$, $n_{\mathrm{escShHeB,s}}$, $n_{\mathrm{escNS,s}}$, $n_{\mathrm{escBH,s}}$) for all eight simulations. K: solid; NoK: dash-dotted.
• Figure 5: Six vertically stacked panels display the evolution of total star count and the counts of MS (main sequence star), CHeB (core-helium burning star), ShHeB (shell-helium burning star), NS (neutron star), and BH (black hole), for eight simulations.