Probing bursty star formation by cross-correlating extragalactic background light and galaxy surveys

Understanding the star formation rate (SFR) variability and how it depends on physical properties of galaxies is important for developing and testing the theory of galaxy formation. We investigate how statistical measurements of the extragalactic background light (EBL) can shed light on this topic and complement traditional methods based on observations of individual galaxies. Using semi-empirical models of galaxy evolution and SFR indicators sensitive to different star formation timescales (e.g., H$\alpha$ and UV continuum luminosities), we show that the SFR variability, quantified by the joint probability distribution of the SFR indicators (i.e., the bivariate conditional luminosity function), can be characterized as a function of galaxy mass and redshift through the cross-correlation between deep, near-infrared maps of the EBL and galaxy distributions. As an example, we consider combining upcoming SPHEREx maps of the EBL with galaxy samples from Rubin/LSST. We demonstrate that their cross-correlation over a sky fraction of $f_\mathrm{sky}\sim0.5$ can constrain the joint SFR indicator distribution at high significance up to $z\sim2.5$ for mass-complete samples of galaxies down to $M_{*}\sim10^9\,M_{\odot}$. These constraints not only allow models of different SFR variability to be distinguished, but also provide unique opportunities to investigate physical mechanisms that require large number statistics such as environmental effects. The cross-correlations investigated illustrate the power of combining cosmological surveys to extract information inaccessible from each data set alone, while the large galaxy populations probed capture ensemble-averaged properties beyond the reach of targeted observations towards individual galaxies.