Relatively Fast and Reasonably Furious: Evidence for Increased Burstiness in Smaller Halos at Cosmic Dawn

TL;DR

This work develops a fast analytic framework to model burstiness in early galaxy star formation by representing SFHs as lognormal fluctuations drawn from a power-spectrum. By jointly fitting UV luminosity functions, clustering, and Hα/UV ratios, the authors robustly constrain burstiness as a function of halo mass, finding that smaller halos host galaxies with significantly larger SFR variability on ~20 Myr timescales. The inferred mass dependence, combined with extrapolations to higher redshift, can reproduce UVLFs up to z~17 and has implications for the ionizing photon budget and reionization history. The results align with expectations from supernova feedback and hydrodynamical simulations, and the framework enables rapid, population-wide inferences to guide interpretation of JWST-era data and future surveys.

Abstract

We introduce an effective framework to model star-formation burstiness and use it to jointly fit galaxy UV luminosity functions (UVLFs), clustering, and H$α$/UV ratios, providing the first robust empirical evidence that early galaxies hosted in lower-mass halos are burstier. Using $z\sim 4-6$ observations, we find that galaxies show approximately $0.6$ dex of SFR variability if hosted in halos of $M_h = 10^{11}\, M_\odot$ (typical of $M_{\rm UV}\approx -19$ galaxies at $z = 6$). This translates into a scatter of $σ_{M_{\rm UV}}\approx 0.75$ in the UVLF, in line with past findings. Strikingly, we find that burstiness grows for galaxies hosted in smaller halos, reaching $\gtrsim 1$ dex for $M_h \leq 10^{9}\, M_\odot$ (corresponding to $σ_{M_{\rm UV}} \approx 1.5$ for faint $M_{\rm UV} \gtrsim -15$ galaxies). Extrapolating to higher redshifts, when small halos were more prevalent, the inferred mass-dependent burstiness can reproduce observed UVLFs up to $z\sim 17$ within 1$σ$, potentially alleviating the tension between pre- and post-JWST galaxy-formation models. Current observations allow us to constrain burst timescales to approximately $20$ Myr, consistent with expectations from supernova feedback, and suggest broad distributions of ionizing efficiencies at fixed $M_{\rm UV}$. Our results demonstrate that mass-dependent burstiness, as predicted by hydrodynamical simulations, is critical for understanding the mass assembly of early galaxies.

Figures (29)

• Figure 1: Left: Example star-formation histories for galaxies hosted in "low-mass" halos, with $M_h=10^{10}\,M_{\odot}$ at $z=5.5$. Top left shows the average star-formation rate of all galaxies (black dashed, with no bursts) and two example bursty galaxies drawn from the power spectrum models in the right panel (red and blue, corresponding to long vs short bursts). Bottom left shows the ${\rm H \alpha}$/UV ratio that would be measured at each time, where the gray band represents the no-burst equilibrium value. Right: Power spectra of $x$ (the log-SFR fluctuation; see Eq. \ref{['eq:defSFRx']}) for two illustrative bursty models as a function of frequency $\omega$. The red model has more power at low frequencies and a cutoff, corresponding to longer coherent star-formation bursts than its blue counterpart.
• Figure 2: Left: Green's function for UV (green) and ${\rm H \alpha}$ (purple) emission, which quantifies how much luminosity in each band is emitted by a 1$M_{\odot}$ burst of star formation of age $t_{\rm age}$, so it can be understood as a mass-to-light ratio. Our baseline is the BC03 model (solid), but we also show BPASS for single stars (dashed) and with a default binary fraction (dot-dashed), which differ more in ${\rm H \alpha}$ than UV but give rise to very similar burstiness constraints, as we show in Appendix \ref{['app:extraposteriors']}. Right: The normalized Fourier-space "window functions" $\tilde{W}$ for UV and H$\alpha$, which are meant to be integrated over frequencies $\omega$ along with the SFR power spectrum (e.g., to obtain $\sigma_{M_{\rm UV}}$). The H$\alpha$ window extends to higher frequencies, as ${\rm H \alpha}$ light can capture fluctuations on shorter timescales. The UV light captures bursts over a broader frequency range than the typically assumed 100 Myr timescale (shown as a gray dot-dashed line for comparison).
• Figure 3: Predicted PDFs of different observables for two illustrative models: one with long bursts (red) and another with short bursts (blue), in both cases for galaxies residing in halos of $M_h=10^{10}\,M_{\odot}$ at $z=6$. Left: Both models predict nearly identical $M_{\rm UV}$ distributions, as they have been calibrated to the same UVLFs. Center: Their PDFs for $\log_{10}L_{\rm H\alpha}$ differ somewhat, though not enough to distinguish the burstiness timescale. Right: The H$\alpha$/UV ratios can efficiently differentiate between these two example models. The long-burst model (red) predicts a narrower PDF, closer to the no-burst expectation (gray), whereas in the short-burst model (blue) the H$\alpha$ and UV are less correlated and thus the distribution is broader. In both cases the PDF is skewed towards smaller values of $\eta_{\rm H\alpha,UV}$, representing "off-mode" galaxies.
• Figure 4: Predicted PDFs for $M_{\rm UV}$ ( left) and the ${\rm H \alpha}$/UV ratio ( right) for galaxies hosted in halos with $M_h=10^{10}$ at $z=6$ as a function of the bursty power spectrum parameters. In the top panels we vary the amplitude $\sigma_{\rm PS}$ and in the bottom the timescale $\tau_{\rm PS}$. The former has a stronger impact on the width of the PDFs, so it will be easier to constrain. Still, the timescale $\tau_{\rm PS}$ affects the shape of the PDFs, so combining UV and ${\rm H \alpha}$ information will allow us to measure it.
• Figure 5: Predicted UVLF ( top) and bias ( bottom) at $z\sim 6$ for the two example models (with long and short bursts in red and blue, respectively), as well as one with mass-independent burstiness (black dotdashed). The three models predict very similar UVLFs, but the mass-independent case differs in bias at the bright end (where measurements lie). The long- and short-bursts models predict the same PDF $\mathcal{P}(M_{\rm UV}|M_h)$, as shown in Fig. \ref{['fig:PDFs_at_Mh']}, so even with clustering we cannot distinguish them. Black points show observations from HST Bouwens21 and HSC Harikane.