Black hole mass function shift in proto-stellar clusters driven by gas accretion

Open Access

Table 1

BH mass growth, Δm, with respect to the initial mass, m₀.

	Subsolar Z	Low Z
r_h = 1.0 pc	$Δ m = {(\frac{m_{0}}{22.4})}^{4.6}$ $\Delta m = {\left( {{{{m_0}} \over {22.4}}} \right)^{4.6}}$	$Δ m = {(\frac{m_{0}}{25.0})}^{4.3}$ $\Delta m = {\left( {{{{m_0}} \over {25.0}}} \right)^{4.3}}$
ε = 0.06
r_h = 0.7 pc	$Δ m = {(\frac{m_{0}}{21.7})}^{6.0}$ $\Delta m = {\left( {{{{m_0}} \over {21.7}}} \right)^{6.0}}$	$Δ m = {(\frac{m_{0}}{24.5})}^{5.4}$ $\Delta m = {\left( {{{{m_0}} \over {24.5}}} \right)^{5.4}}$
ε = 0.1
r_h = 0.5 pc	$Δ m = {(\frac{m_{0}}{25.0})}^{5.3}$ $\Delta m = {\left( {{{{m_0}} \over {25.0}}} \right)^{5.3}}$	$Δ m = {(\frac{m_{0}}{27.0})}^{4.9}$ $\Delta m = {\left( {{{{m_0}} \over {27.0}}} \right)^{4.9}}$
ε = 0.2

Notes. Initial cluster’s total mass, M = 10⁶ M_⊙. The overall fit of Δm for BHs of the main branch CCSN-BH and direct-collapse-BH, displayed in the panels of Figure 3 for the same, several ε and r_h values.

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