The role of the galaxy stellar mass function in determining the cosmological distribution of astrophysical transients with applications to fast radio bursts and merging binary black holes

TL;DR

This paper argues that population studies of cosmological transients such as FRBs and merging BBHs must incorporate the galaxy stellar mass function (SMF) and its redshift evolution, not just the redshift-dependent star formation rate density (SFRD). The authors model FRB formation as a mixture of SFRD- and SMF-traced channels, with a fiducial fraction $f_Y=0.3$, and demonstrate that matching the local FRB rate requires roughly a threefold boost in formation efficiency per stellar mass relative to prior assumptions. Using the observed SMF from Euclid/Cosmic Dawn and a filter $F(\mathcal{M})$ for potential FRB hosts, they show that the stellar-mass-weighted density (SMD) probed by FRB hosts is about a third of the total SMD implied by all galaxies, and that FRB hosts do not fully track the global SMD. They further illustrate that inference of $f_Y$ using the traditional Madau–Dickinson SFRD template can be biased due to SMF evolution, and they explore mild redshift evolution of FRB-host masses with only modest effects. Extending the framework to BBH mergers, they fit $f_Y$ to GW-rate data and show that BBH hosting can be consistent with both MD-like or FRB-like tracers, highlighting the potential to constrain host-galaxy properties from GW catalogs in the future. Overall, the work provides a systematic method to connect transient populations to host-galaxy statistics, with implications for FRB energetics, host demographics, and the interpretation of GW event hosts.

Abstract

The cosmological distribution and formation rate of compact astrophysical objects such as fast radio bursts (FRBs) are typically assumed to be proportional to a linear combination of cosmological star formation rate and stellar mass. In the literature, a template for star formation rate, which is just a function of redshift, is typically used. In this work, we point out the importance of galaxy stellar mass function which captures the host galaxy information of observed FRBs as well as the redshift evolution of galaxy stellar mass. Using this information, we find that FRB formation efficiency per stellar mass has to be more efficient (by a factor of $\approx 3$) than previously calculated, in order to reproduce the observed volumetric rate of FRBs at $z=0$. We show that cosmological population studies of FRBs have to include host galaxy information along with its redshift evolution in order to obtain unbiased results. This consideration is also applicable to other transients, e.g. gamma-ray bursts and merging binary black hole events. We show that our approach may open up the possibility to infer the host galaxy stellar mass of merging binary black holes with a detection of few thousand gravitational wave events.

Figures (7)

• Figure 1: Evolution of SMD as a function of redshift. (Left panel) The inferred SMD from galaxy SMF is shown in black points. Our smooth fit to the data points is shown in solid green. We consider galaxies with masses between $10^8-10^{13}$$M_{\odot}$. In dashed green, we plot the SMD from potential FRB host galaxies with an appropriate filter function. We also plot a scenario where we isolate the contribution from host galaxies with $M_*> 10^{10}$$M_{\odot}$. (Right panel) We scaled the SMD inferred from galaxy SMF, in a redshift dependent way, to match the improved MD fit. We apply the same scale factor to the other curves in green in the left panel.
• Figure 2: Cumulative distribution function (CDF) of FRB filter function and the normalized mass weighted galaxy SMF or $\Phi(\mathcal{M})\mathcal{M}$ at the lowest redshift bin with central $z=0.35$. The maximum difference between the two CDFs is shown in the double-headed magenta line.
• Figure 3: Plot of ratio ${\rm SFRD/SFRD(z=0)}$ and ${\rm SMD/SMD(z=0)}$ for improved MD fit (red) and with galaxy SMF with FRB specific galaxies (green) (left panel). The inferred $f_{Y,{\rm t}}$ using the galaxy SMF where we simulated FRB distribution with $f_Y=0.3$ (see text for details).
• Figure 4: SMD using Eq. \ref{['eq:SMD_SMF']} with lognormal $f(\mathcal{M})$ and redshift dependent $\mu$ as shown in Fig. We have not applied any scaling to the SMD as opposed to the right panel of Fig. \ref{['fig:euclid_data_fit']}.
• Figure 5: The inferred merger rate of BBHs in the comoving frame as a function of redshift (left panel). The solid black line shows the best fit and the grey band show 50 percent confidence interval. The cosmological SFRD (Eq. \ref{['eq:SFRD']}) is shown in red line. The best fit assuming FRB specific galaxies (Sec. \ref{['app:stellarmass_data']}) is shown in blue dashed line. (Right panel) Value of $\chi^2$ as a function of $f_Y$ for two cases discussed in text. We caution the reader that the magnitude of $\chi^2$ should not be taken at face-value and we are only interested in the value of $f_Y$ where $\chi^2$ is minimum.