The metallicity dependence of long-duration gamma-ray bursts

TL;DR

This work addresses whether long-duration gamma-ray bursts (LGRBs) require low metallicity by integrating a metallicity- and mass-dependent cosmic star formation history with an LGRB production efficiency that declines with $Z_{O/H}$. The authors implement a comprehensive model incorporating the galaxy stellar mass function, a mass–metallicity relation, a star formation–mass relation, and scatter at multiple levels, including an asymmetric metallicity distribution within galaxies. By comparing model predictions to LGRB host metallicities, host masses, and the cosmic LGRB rate, they find that a sharp cutoff at near-solar metallicity, $Z_{O/H}=8.6\pm0.1$, best explains the data, while low-metallicity thresholds are disfavored. The results imply that LGRB progenitors may arise from multiple channels and that metallicity alone at the global galaxy scale is not the sole determinant; these findings have implications for using LGRBs as probes of star formation and galaxy evolution, with future high-resolution metallicity mapping (e.g., JWST, IFU observations) poised to refine constraints.

Abstract

Both theoretical models and observations of collapsar created gamma-ray bursts -- typically long-duration gamma-ray bursts (LGRBs) -- suggest that these transients cannot occur at high metallicity, likely due to angular momentum losses via stellar winds for potential progenitor stars. However, the precise metallicity threshold (if it is a hard threshold) above which the formation of LGRBs is suppressed is still a topic of discussion. We investigated observed LGRBs and the properties of their host galaxies to constrain this metallicity dependence. In order to compute LGRB rates we modelled the cosmic history of star formation, as a function of host galaxy metallicity and stellar mass, and added a LGRB efficiency function that can include various shapes including abrupt cutoffs and more gradual variations in the GRB yield with metallicity. In contrast to previous work, this model includes scatters in the relations between mass, metallicity, and star formation rate, as well as a scatter in the metallicity distribution inside galaxies. We then varied both the threshold value and shape, and compared it to observed LGRBs and the properties of their host galaxies. In our model a sharp cutoff at an oxygen abundance $Z_{\text{O/H}}=12+\log(\text{O/H})=8.6\pm0.1$ (corresponding to $\sim0.6Z_{\odot}$) provides the best explanation for the observed LGRB data. In contrast, a lower threshold proposed in literature (i.e. at $Z_{\text{O/H}}=8.3$ or $\sim0.3Z_{\odot}$) fits observations poorly. We therefore conclude that, in contrast to most theoretical LGRB models, a relatively high metallicity threshold at near-solar values provides the best match between our model and observed LGRBs.

Figures (12)

• Figure 1: Galaxy stellar mass function (Eq. \ref{['eq2']}), for $0\leq z\leq10$ (colour scale), containing both $\Phi_{\text{high}}$ (solid lines, Eq. \ref{['eq3']} and Table \ref{['tab1']}), $\Phi_{\text{low}}$ (dashed lines, Eq. \ref{['eq4']}) and $M_{\text{lim}}$ (dots, Eq. \ref{['eq1']}).
• Figure 2: Mass-metallicity relation (Eqs. \ref{['eq7']}, \ref{['eq8']}, and \ref{['eq9']}, of which the parameters are listed in Table \ref{['tab2']}), extrapolated from Sanders_2021, for $0\leq z\leq10$ (colour scale), comparing metallicities given in $Z_{\text{O/H}}$ (left axis) and $Z$ (right axis, through Eq. \ref{['eq6']}). The dashed lines show the Kobulnicky_2004 MZR Chruslinska_2019 and the grey dotted line shows solar metallicity.
• Figure 3: Star formation--mass relation (Eq. \ref{['eq11']}) for $0\leq z\leq10$ (colour scale), which becomes flattened at $\log_{10}(M_*/M_{\sun})>9.7$.
• Figure 4: Gamma-ray burst efficiency ($\eta_{\text{LGRB}}$, Eq. \ref{['eq16']}), relative to the maximum efficiency ($\eta_0$) for different values of $\kappa$---a parameter that allows for a range of steepness of cutoff toward higher metallicities. The parameter $Z_{\text{th}}$ is the central metallicity at which this cutoff occurs.
• Figure 5: Scattered metallicity distribution within galaxies relative to the median metallicity as described by the MZR ($\Delta Z_{\text{scat}}$), showing our adopted distribution: an asymmetric Gaussian Disberg_2023 with $\sigma_-=0.13$ and $\sigma_+=0.05$. This distribution is, to a certain degree, similar to the results of Pessi_2023a. The median of the distribution is centred at $\Delta Z_{\text{scat}}=0$.