Spin-up and spin distribution of stellar black holes grown by gas accretion in proto-stellar clusters

Open Access

Table 2

Number of high-mass/low-spin BH outliers per cluster for several clusters.

		$60 M_{⊙} \leq m_{B H}^{fin} < 150 M_{⊙}$ $Mathematical equation: $\[60 ~\mathrm{M}_{\odot} \leq m_{\mathrm{BH}}^{\text {fin}}<150 ~\mathrm{M}_{\odot}\]$$		$150 M_{⊙} \leq m_{B H}^{fin} \leq 500 M_{⊙}$ $Mathematical equation: $\[150 ~\mathrm{M}_{\odot} \leq m_{\mathrm{BH}}^{\text {fin}} \leq 500 ~\mathrm{M}_{\odot}\]$$		$500 M_{⊙} < m_{B H}^{fin} \leq 10^{3} M_{⊙}$ $Mathematical equation: $\[500 ~\mathrm{M}_{\odot}<m_{\mathrm{BH}}^{\text {fin}} \leq 10^{3} ~\mathrm{M}_{\odot}\]$$
M_⋆[M_⊙]	r_c,⋆[pc]	$\bar{n} (a_{} \leq 0.1)$ $Mathematical equation: $\[\bar{n}\left(a_{} \leq 0.1\right)\]$$	$\bar{n} (0.1 < a_{} \leq 0.3)$ $Mathematical equation: $\[\bar{n}\left(0.1<a_{} \leq 0.3\right)\]$$	$\bar{n} (0.1 \leq a_{} < 0.3)$ $Mathematical equation: $\[\bar{n}\left(0.1 \leq a_{}<0.3\right)\]$$	$\bar{n} (0.3 \leq a_{} \leq 0.5)$ $Mathematical equation: $\[\bar{n}\left(0.3 \leq a_{} \leq 0.5\right)\]$$	$\bar{n} (0.1 \leq a_{} < 0.3)$ $Mathematical equation: $\[\bar{n}\left(0.1 \leq a_{}<0.3\right)\]$$	$\bar{n} (0.3 \leq a_{} \leq 0.5)$ $Mathematical equation: $\[\bar{n}\left(0.3 \leq a_{} \leq 0.5\right)\]$$
10⁶	1.0	0.70	2.80	0.40	1.20	0.10	0.50
10⁶	1.3	1.60	3.60	0.00	0.00	0.00	0.00

3.5 × 10⁵	0.6	0.00	0.20	0.05	0.30	0.00	0.09
3.5 × 10⁵	0.8	0.15	0.80	0.05	0.20	0.00	0.00

Notes. The cluster parameters correspond to the four first rows of Table 1. We denote as $\bar{n}$ $Mathematical equation: $\[\bar{n}\]$$ the number of BHs per cluster within the corresponding mass bin and spin range.

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