Title: Constraints on Fluctuating Star Formation Rates for Intermediate-mass Galaxies with H$α$ and UV Luminosities

Abstract: We study the recent star formation histories (SFHs) of 575 intermediate-mass galaxies (IMGs, $10^{9} \leq M/M_{\odot} \leq 10^{10}$) in COSMOS at $0.3<z<0.4$ by comparing their H$\alpha$ and UV luminosities. These two measurements trace star formation rates (SFRs) on different timescales and together reveal fluctuations in recent activity. We compute $L_{{\rm H}\alpha}$ from Magellan IMACS spectroscopy while $L_{\rm UV}$ is derived from rest-frame 2800 $\text{\r{A}}$ photometry. Dust corrections are applied to each band independently. We compare the deviation of $L_{{\rm H}\alpha}$ and $L_{\rm UV}$ from their respective star forming sequences (i.e., $\Delta\log L_{{\rm H}\alpha}$ and $\Delta\log L_{\rm UV}$) and after accounting for observational uncertainties we find a small intrinsic scatter between the two quantities ($\sigma_{\delta} \lesssim 0.03$ dex). This crucial observational constraint precludes strong fluctuations in the recent SFHs of IMGs: simple linear SFH models indicate that a population of IMGs would be limited to only factors of $\lesssim 2$ change in SFR over $200$ Myr and $\lesssim 30\%$ on shorter timescales of $20$ Myr. No single characteristic SFH for IMGs, such as an exponentially rising/falling burst, can reproduce the individual and joint distribution of $\Delta\log L_{{\rm H}\alpha}$ and $\Delta\log L_{\rm UV}$. Instead, an ensemble of SFHs is preferred. Finally, we find that IMG SFHs predicted by recent hydrodynamic simulations, in which feedback drives rapid and strong SFR fluctuations, are inconsistent with our observations.