Re-assessing the stellar population scaling relations of the galaxies in the Local Universe

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Volume 703 (November 2025)

A&A, 703 (2025) A5

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Table A.1.

Summary table of the parameters used to generate the CSP library.

Parameters	Description	Prior PDF
Secular SFH: ${SFR}_{τ} (t) \propto \frac{(t - t_{form})}{τ} exp (- \frac{{(t - t_{form})}^{2}}{τ^{2}})$ ${{SFR}}_\tau(t)\propto\frac{(t-t_{\mathrm{form}})}{\tau}\exp\left(-\frac{(t-t_{\mathrm{form}})^2}{\tau^2}\right)$

t_form, lb
≡t₀ − t_form	Time elapsed since the beginning of the SFH	Log-uniform between 5 ⋅ 10⁸ and 2 ⋅ 10¹⁰ yr

τ	Time scale/peak	From log-uniform of τ/t_form, lb between 1/20 and 2

Secular Chemical Enrichment History:
$Z_{} (t) = Z_{} (M (t)) = Z_{* final} - (Z_{* final} - Z_{* 0}) {(1 - \frac{M (t)}{M_{} final})}^{α}$ $Z_(t) = Z_\left(M(t)\right) = Z_{\,\text{ final}}-\left(Z_{\,\text{ final}}-Z_{*\,\text{0}}\right)\left(1-\frac{M(t)}{M_\text{ final}}\right)^\alpha$

⟨Z_{* fm − w}⟩	Formed-mass-weighted metallicity (non-generative, constraint for generative pars.)	tanh distribution of P(log⟨Z_{* fm − w}⟩): P(1/50 Z_⊙) = 0, P(0.1 Z_⊙) = 0.9, P(3.8 Z_⊙) = 1, ⟨Z_{* fm − w}⟩ < 3.8 Z_⊙

α	Swiftness of chemical enrichment	0.25 ≤ α ≤ 19, from a uniform distribution in $β \equiv \frac{1}{1 + α}, 0.05 \leq β \leq 0.80$ $\beta\equiv\frac{1}{1+\alpha},\, 0.05 \leq \beta \leq 0.80$

Z_* 0	Initial metallicity	Log-uniform between log(Z_min/Z_⊙)≡log(1/50) and min(log Z_0 max/Z_⊙ ≡ log(0.05),⟨Z_{* fm − w}⟩)

Z_* final	Final metallicity	Derived from Z_min, α, and ⟨Z_{* fm − w}⟩, with the constraint Z_* final ≤ 4Z_* ⊙

Bursts

N_burst	Number of bursts	1/3 of models without bursts; for the remaining 2/3: N_burst ≤ 6, P(N_burst)∝e^−N_burst

t_burst, i	Age of the ith burst (instantaneous)	Log-uniform distribution between 10⁵ yr and the t_form of the secular component

Z_{* burst, i}	Metallicity of the ith burst	Gaussian distribution in log-Z, with mean equal to the metallicity value of the secular component at t = t_burst, i and width σ_{Z_* burst} = 0.2 dex

ℳ_burst, i	Mass fraction formed in the ith burst relative to the mass formed in secular mode	Log-uniform distribution between 10⁻³ and 2. More restrictive upper limits applied for t_burst, i < 10⁸ yr

Dust attenuation (Charlot & Fall 2000)

τ_V	Total optical depth due to diffuse ISM and birth cloud (affects stars younger than 10⁷ yr)	P(τ_V)∝1 − tanh(1.5τ_V − 6.7), constant at low values, exponential drop to 0 between τ_V = 4 and τ_V = 6

μ	Fraction of total optical depth in diffuse ISM	P(μ)∝1 − tanh(8μ − 6), exponential drop to 0 between μ = 0.5 and μ = 1

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