Chemical evolution in nuclear stellar discs | Astronomy & Astrophysics (A&A)

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Table A.1

Adopted yield grids and prescriptions for the timescales important to chemical evolution modelling.

Process	Shape	Values	Yields
		n₁ = 1.4
Star formation	${\dot{Σ}}_{} = {\begin{cases} κ Σ_{gas}^{n 1} & Σ_{cold} > Σ_{c u t - o f f} \\ κ {(Σ_{c u t - o f f} + Σ_{hot})}^{n_{1} - n_{2}} Σ_{gas}^{n_{2}} & otherwise \end{cases}$ $\[\dot{\Sigma}_= \begin{cases}\kappa \Sigma_{\text {gas }}^{n 1} & \Sigma_{\text {cold }}>\Sigma_{\mathrm {cut-off }} \\ \kappa\left(\Sigma_{\mathrm {cut-off }}+\Sigma_{\text {hot }}\right)^{n_1-n_2} \Sigma_{\text {gas }}^{n_2} & \text { otherwise }\end{cases}\]$	n₂ = 4.0
		κ = 2.2(10⁹ M_⊙)^−n₁+n₂ Gyr⁻¹
		Σ_cut–off = 0.004 · 10⁹ M_⊙ kpc⁻²
ccSNe & AGB	PARSEC isochrones (1,2,3) including the thermally pulsing-AGB phase (4,5,6)	τ_PARSEC(M_*, Z)	(7,8,9)
		t_SNIa,delay = 0.45 Gyr
SNeIa	$Ψ_{SNIa} (t) = {\begin{cases} 0 & t < t_{SNIa,delay} \\ f_{SNIa,short} e^{- t / τ_{SNla,short}} + (1 - f_{SNla,short}) e^{- t / τ_{SNla,long}} & otherwise \end{cases}$ $\[\Psi_{\text {SNIa}}(t)= \begin{cases}0 & t<t_{\text {SNIa,delay }} \\ f_{\text {SNIa,short}} \mathrm{e}^{-t / \tau_{\text {SNla,short}}}+\left(1-f_{\text {SNla,short}}\right) \mathrm{e}^{-t / \tau_{\text {SNla,long}}} & \text { otherwise }\end{cases}\]$	f_SNIa,short = 0.01
		τ_SNIa,short = 100 Myr	W70 yields (10)
		τ_SNIa,long = 1.5 Gyr
NSMs	$Ψ_{N S M} (t) = {\begin{cases} 0 & t < t_{N S M, delay} \\ e^{- t / τ_{N S M}} & otherwise \end{cases}$ $\[\Psi_{\mathrm{NSM}}(t)= \begin{cases}0 & t<t_{\mathrm{NSM}, \text {delay}} \\ e^{-t / \tau_{\mathrm{NSM}}} & \text { otherwise}\end{cases}\]$	t_NSM,delay = 20 Myr	unclear, a fixed Eu yield is assumed and calibrated to the solar neighbourhood abundance by scaling the fraction of neutron stars undergoing a merger at each time step
		τ_NSM = 300 Myr
cooling	${\dot{M}}_{h, cooling} = - Λ M_{h}$ $\[\dot{M}_{\mathrm{h}, \text { cooling }}=-\Lambda M_{\mathrm{h}}\]$	Λ = 1 Gyr
		R₀ = 1.5 kpc
		R_end = 3.75 kpc
inside-out formation	$R_{g a s} (t) = R_{0} + N [\arctan (\frac{t - t_{0}}{t_{g}}) - \arctan (\frac{t_{0}}{t_{g}})]$ $\[R_{\mathrm{gas}}(t)=R_0+N\left[\arctan \left(\frac{t-t_0}{t_g}\right)-\arctan \left(\frac{t_0}{t_g}\right)\right]\]$	t₀ = 1.0 Gyr
		t_g = 0.6 Gyr
		t_end = 12 kpc

References. (1) Bressan et al. (2012), (2) Chen et al. (2015), (3) Tang et al. (2014), (4) Marigo et al. (2017), (5) Pastorelli et al. (2019), (6) Pastorelli et al. (2020), (7) Maeder (1992), (8) Marigo (2001), (9) Chieffi & Limongi (2004), (10) Iwamoto et al. (1999).

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