Formation of black holes from He stars

Abstract

Massive He stars are potential candidates of type Ib/c supernova (SN) progenitors. Understanding their final fates remains a key issue in astrophysics. In this work, we investigate the evolution of He stars with initial masses from 5 $M_\odot$ to 65 $M_\odot$, focusing on the presupernova (pre-SN) core structures to assess their explodability. Our simulations indicate that the final core structure is determined by the CO core mass and the central 12C mass fraction at the end of core He burning, affecting the properties of central C-burning and the locations of convective shells. The location of the last convective C-burning shell sets the mass of the C-free core, constraining the iron core mass and compactness. We found that the final compactness and iron core mass exhibit non-monotonic behavior with initial mass, suggesting that the boundary between neutron star and black hole formation is not a simple mass threshold. This is due to core C/Ne burning becoming neutrino dominated. This process drives stronger core contraction, ultimately increasing the iron core mass and the final compactness. In contrast, earlier core Ne/O/Si ignition and shell mergers inhibit core contraction, reducing both the iron core mass and final compactness. We also discuss the effects of metallicity and overshooting on the pre-SN core structure. These factors potentially affect the explodability of progenitors.

Figures (10)

• Figure 1: Evolutionary track of a 15 $M_{\odot}$ He star with solar metallicity ($Z = 0.02$) and overshooting parameter $f_{\mathrm{ov}} = 0.01$. Panel (a): Temporal evolution of the compactness parameter $\xi_{2.5}$ until seconds before core collapse. Key evolutionary phases are marked as follows: pentagram (central He depletion), square (central C ignition), triangle (central C depletion), cross (central Ne depletion), open circle (central O depletion), and left-pointing triangle (central Si depletion). Panel (b): Kippenhahn diagram from core He-burning to the onset of core collapse. The color bar shows the nuclear energy generation rate ($\epsilon_{\rm nuc}$, red) and neutrino loss rate ($\epsilon_{\nu}$, blue). The green, purple, and red-hatched regions represent the convective, overshooting, and semiconvective mixing regions, respectively. The gray solid indicate the classical Chandrasekhar mass, $M_{\rm Ch,0}$, as defined in Eq.$\,$\ref{['eq:M_ch']}. The dashed black, dotted red, and dash-dotted magenta lines denote the iron, He-free ($M_{\text{He-free}}$), and C-free ($M_{\text{C-free}}$) cores, respectively. Vertical dotted lines mark specific depletion and ignition events. Panel (c): Same as panel (b), but the color represents the specific gravothermal energy, $\epsilon_{\text{grav }} \equiv-T ds / dt$ (red: contraction , blue: expansion). Panel (d): Same as panel (b), but the color represents the electron degeneracy parameter, $\eta \equiv \mu/k_{\rm B}T$, where $\mu$ is the chemical potential, $k_{\rm B}$ is the Boltzmann constant, and $T$ is temperature. $\eta \ll -1$: non-degenerate; $\eta \approx 0$: partial degeneracy; $\eta \gg 1$: strong degeneracy.
• Figure 2: Same model as Fig. \ref{['fig:xi']}. The figure shows the core structure of the progenitor at the onset of core collapse. Panel (a): Radial infall velocity (black dotted line, left axis) and mass fraction profiles of $^{56}$Fe, $^{28}$Si, and $^{16}$O (dashed lines, right axis) versus the mass coordinate $M_{r}$. Panel (b): Radial profiles of the central density (dashed line) and specific entropy (dotted line) as functions of the mass coordinate $M_{r}$, where the iron core mass is 1.85 $M_{\odot}$. The dash-dotted blue line marks the mass coordinate where the central specific entropy $s_{\rm c}=4\, k_{\rm B}$, corresponding to the Si/O shell interface at $M_{r} = 2.32 \,M_{\odot}$.
• Figure 3: Key parameters at the onset of core collapse. Panel (a): Final compactness parameter $\xi_{2.5}$. Panel (b): Central specific entropy $s_c$. Panel (c): Iron core mass $M_{\rm Fe}$. Panel (d): Binding energy above the iron core $E_{\text{bind}}$. Panel (e): C-free core mass $M_{\rm C\text{-free}}$, all plotted as functions of the initial helium star mass $M_{\mathrm{He}}^{\mathrm{i}}$. The top axis shows the CO core masses of He stars at the end of core He burning. The light gray shading indicates radiative core C burning, while the darker gray shading represents radiative core Ne burning in the panel (a). The red dotted line at $\xi_{2.5} = 0.35$ separates models likely to explode (below the line) from those likely to implode (above the line). Black crosses indicate models predicted to explode according to both the explodability criteria of ertl2016two and muller2016simple. White crosses mark models predicted to explode by the ertl2016two criterion but not the muller2016simple criterion. Black circles indicate models predicted to fail to explode and collapse into BHs according to both criteria. The black dashed vertical line marks the $M_{\mathrm{He}}^{\mathrm{i}} = 21\,M_{\odot}$ model ($M_{\rm CO} = 9.86\,M_{\odot}$), serving as a proxy for the $\sim 10\,M_{\odot}$ threshold for the upper limit of successful explosions suggested by patton2020towards.
• Figure 4: Core properties at the end of core He burning as a function of initial mass. Panel (a): Central density $\rho_{\mathrm{c}}$ and CO core mass $M_{\mathrm{CO}}$ at the end of core He burning, shown as a function of the initial He star mass $M_{\mathrm{He}}^{\mathrm{i}}$. Panel (b): Corresponding central ${}^{12}\rm C$ mass fraction $X_{\rm C}$ at the end of core He burning, with the top axis indicating the CO core mass $M_{\mathrm{CO}}$ for each $M_{\mathrm{He}}^{\mathrm{i}}$. Light and dark gray shaded regions denote models undergoing radiative core C and Ne burning, respectively. The dotted and dashed lines represent the threshold ${}^{12}\rm C$ mass fractions separating convective and radiative burning regimes.
• Figure 5: Same as Fig. \ref{['fig:xi']}b, but for models with $M_{\mathrm{He}}^{\mathrm{i}}=12, 13, 15, 16, 17, 18, 23, 26, 29, 30, 35, \text{and}\, 40 \,M_{\odot}$, covering the evolution from core C-burning to the onset of core collapse. The gray dashed line indicates, $M_{\rm Ch}$, as defined by Eq. \ref{['eq:M_ch']}. The dotted vertical lines indicate, from left to right, the times of depletion of $^{12}$C, $^{20}$Ne, $^{16}$O, and $^{28}$Si in the core.