The Host Galaxies of Fast Radio Bursts Track a Combination of Stellar Mass and Star Formation, Similar to Type Ia Supernovae

TL;DR

The paper addresses determining FRB progenitors by exploiting host-galaxy statistics across redshift. It introduces a multivariate, redshift-aware framework that weights galaxies in the stellar-mass–SFR plane against a redshift-dependent background distribution $ ho(M,{\rm SFR},z)$, using a likelihood-based Monte Carlo testing procedure. Applying this to 51 FRB hosts, the study rules out models where FRBs track only SFR or globular-cluster mass, and finds that a mixed model with a small SFR contribution ($A/B\approx 10^{-10.5}\,{\rm yr}^{-1}$) best describes the data, mirroring Type Ia SNe host demographics. The approach demonstrates that incorporating redshift evolution and the full bivariate host-galaxy information yields robust constraints on progenitor scenarios and offers a general framework for similar population tests in transients; the authors provide publicly available code for broader use.

Abstract

We develop a new statistical framework for studying the host galaxies of astrophysical sources that accounts for both redshift evolution and the multi-variate nature of host-galaxy properties. These aspects are critical when dealing with sources that span a wide range of redshifts, and/or with unknown redshift-dependent selection effects. We apply our method to a sample of Fast Radio Burst (FRB) host-galaxies as a means of probing the uncertain progenitor(s) of these events. Using our method we are able to rule out that FRBs track star-formation rate (SFR), as would be expected if FRBs are associated exclusively with young neutron stars born via core-collapse supernovae (SNe). Furthermore, we rule out a recently proposed metallicity-dependent model whereby FRBs track SFR only above an oxygen abundance of 12+log(O/H) ~ 8. Motivated by the fact that at least one FRB has been localized to a globular cluster (GC), we also investigate the hypothesis that FRB sources track GC mass and explicitly rule out this scenario. Alternatively, we find that a `mixed' model whereby FRBs track a linear combination of both SFR and stellar-mass best explains the data. The preferred parameters of such a mixed model are similar to those inferred for Type Ia SNe, and implies a possible connection between the progenitors of these different transients.

Figures (4)

• Figure 1: Weighted galaxy distributions in the stellar-mass--SFR plane, illustrated here at a fixed redshift of $z=0.3$. The unweighted distribution of field galaxies $\rho \left( M,{\rm SFR} | z \right)$ is based on a continuous model from Leja+22. Panels (a), (b), and (c), show the mass-weighted, SFR-weighted, and GC-weighted distributions, respectively, as defined via Equations (\ref{['eq:weights_mass']},\ref{['eq:weights_SFR']},\ref{['eq:weights_GC']}). In each panel, black, yellow, and white contours show regions that enclose 10%, 50%, and 75% of the probability. A $z=0.3$ sample of FRB host-galaxies would follow one of these distributions if FRBs tracked stellar mass, SFR, or the mass of stars in GCs. Colored points show the FRB host-galaxy sample considered in this paper (§\ref{['sec:sample']}; Sharma+24) for illustrative comparison purposes. As these galaxies span a range of redshifts, they cannot be directly compared to the background distributions which are at fixed $z=0.3$. Our analysis takes this into account by comparing each FRB host to field galaxies at its redshift.
• Figure 2: Methodology for calculating the p-value of models. Random samples are drawn from a model distribution, effectively generating many mock data sets. The likelihood of every mock dataset is then calculated via Equation (\ref{['eq:likelihood']}). Black curves in each panel show the cumulative distribution of likelihoods for the mock data sets. This is compared to the likelihood obtained for the observed FRB host-galaxy sample, shown in blue. The vertical dark-blue curve shows the likelihood obtained using the nominal (median) inferred masses and SFRs for the 51 FRB host galaxies in our full sample. The light-blue shaded region shows the range of values that can be obtained accounting for the uncertainties on the inferred masses and SFRs. The nominal p-value of a given model, $p_{\rm nom}$, is defined via Equation (\ref{['eq:pval']}) and is found by the value of the CDF at the intersection of the dark-blue curve with the black curve. Similarly, a more conservative $p_{90}$ p-value is defined by the intersection of the black curve with the upper bound of the shaded light-blue region. A model is considered to be ruled out if the p-value is less than $p=0.05$.
• Figure 3: Consistency of 'mixed' models which assume that FRB progenitors track a linear combination of stellar mass and star formation as parameterized via Equation (\ref{['eq:weights_AB']}). The p-value of this model is shown as a function of $A/B$, the relative weight of each component. Orange points show the nominal p-value, while blue points show the more conservative $p_{90}$ (see §\ref{['sec:model_testing']} and Figure \ref{['fig:pvals']} for further details). As $\log_{10}(A/B) \to \infty$ the mixed model reduces to the mass-weighted scenario. Conversely, the left end of the plot shows the limit $\log_{10}(A/B) \to -\infty$ which describes the SFR-weighted scenario. Points that fall below the dashed-grey curve have $p<0.05$ and are considered ruled out at this threshold. The peak near the center of the plot indicates that a mixed model is most consistent with the data. Our preferred model has $A/B = 10^{-10.5}\,{\rm yr}^{-1} \approx 0.03\,{\rm Gyr}^{-1}$ and is marked with a dashed-green vertical curve.
• Figure 4: Marginalized stellar-mass (top panels) and SFR (bottom) distribution functions, split into three redshift bins. Blue curves show the CDFs of the FRB hosts within each redshift bin, and shaded grey areas show the 95% CI on these CDFs obtained by bootsrapping. The colored curves in each panel show different models discussed in the text: the mass-weighted model (yellow), the SFR-weighted model (bright red), the SFR+Z model proposed by Sharma+24 (pink), and our preferred mixed model for which $A/B = 10^{-10.5}\,{\rm yr}^{-1}$ (green). The p-values resulting from KS tests of each model against the FRB data are listed in the top-left corner of each plot. See §\ref{['sec:CDFs']} for further details. The model samples in each subplot are generated at a redshift corresponding to the median redshift of FRB host galaxies within that bin.