The metallicity dependence of long-duration gamma-ray bursts

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Table 1

Fitted parameters of the GSMF Schechter function (Eq. (3)) at M_* ≥ M_lim (Eq. (1)) for different redshift (z), including the normalisation constant (Φ_*), cutoff mass (M_GSMF), and exponent (α_high).

z	$\log_{10} (\frac{Φ_{}}{{M p c}^{- 3} {d e x}^{- 1}})$ $\[\log _{10}\left(\frac{\Phi_{}}{\mathrm{Mpc}^{-3} \mathrm{dex}^{-1}}\right)\]$	$\log_{10} (\frac{M_{GSMF}}{M_{⊙}})$ $\[\log _{10}\left(\frac{M_{\text {GSMF }}}{M_{\odot}}\right)\]$
0	−2.804	10.771	−1.321
1	−3.022	10.787	−1.338
2	−3.395	10.904	−1.372
3	−4.234	11.152	−1.660
4	−5.220	11.379	−2.033
5	−6.142	11.379	−2.596
6	−6.413	11.379	−2.671
7	−5.357	10.732	−2.336
8	−6.178	10.707	−2.323
9	−6.498	10.538	−2.759
10	−6.129	9.5	−2.000

Notes. For each redshift value, we use (double) Schechter estimates of the literature listed below and make a least-squares fit of a single Schechter function to their average. At intermediate redshifts we interpolated between the listed functions. Baldry et al. (2004); González et al. (2011); Baldry et al. (2012); Ilbert et al. (2013); Moustakas et al. (2013); Muzzin et al. (2013); Duncan et al. (2014); Tomczak et al. (2014); Grazian et al. (2015); Song et al. (2016); Weigel et al. (2016); Davidzon et al. (2017); Bhatawdekar et al. (2019); Stefanon et al. (2021); Navarro-Carrera et al. (2024); Weibel et al. (2024).

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