A Bayesian approach to the halo galaxy – supermassive black hole connection through cosmic time

Open Access

Table C.1.

Summary of modelled population statistics, their parameter, and asymptotic behaviour.

Number Density Function	Parameter	Interpretation	Low-Mass Slope	High-Mass Slope
Galaxy Stellar Mass Function	A_⋆	Average stellar mass – halo mass ratio at M_h = M_c^*.	$\frac{α_{HMF}}{(1 + γ_{⋆})}$ $\frac{\alpha_{\mathrm{HMF}}}{(1+\gamma_\star)}$	exponential
	γ_⋆	Strength of stellar feedback.
	δ_⋆	Strength of AGN feedback.
	M_c^*	Turnover (halo) mass for stellar and AGN feedback-dominated regime.

Galaxy UV Luminosity Function	A_UV	Average UV luminosity – halo mass ratio at M_h = M_c.			$\frac{α_{HMF}}{(1 + γ_{UV})}$ $\frac{\alpha_{\mathrm{HMF}}}{(1+\gamma_{\mathrm{UV}})}$	exponential
	γ_UV	Strength of stellar feedback.
	δ_UV	Strength of AGN feedback.
	$M_{c}^{UV}$ $M_{\mathrm{c}}^{\mathrm{UV}}$	Turnover (halo) mass for stellar and AGN feedback-dominated regime

Black Hole Mass Function	B	Average mass of SMBH at M_h = M_c^•.	$\frac{α_{HMF}}{η}$ $\frac{\alpha_{\mathrm{HMF}}}{\eta}$	exponential
	η	Slope of BH mass growth with halo mass for acreeting SMBHs.
	M_c^•	Critical (halo) mass for SMBH mass model.

Quasar Luminosity Function	C	Average bolometric AGN luminosity at $M_{h} = M_{c}^{bol}$ $M_{\mathrm{h}}=M_{\mathrm{c}}^{\mathrm{bol}}$ and λ = 1.			$\frac{α_{HMF}}{θ}$ $\frac{\alpha_{\mathrm{HMF}}}{\theta}$	−ρ
	θ	Slope of luminosity increase with halo mass for acreeting SMBHs.
	λ_c	Critical Eddington ratio for power law drop-off of ERDF.
	ρ	Slope of ERDF drop-off.
	$M_{c}^{bol}$ $M_{\mathrm{c}}^{\mathrm{bol}}$	Critical (halo) mass for AGN luminosity model.

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