The time-scales probed by star formation rate indicators for realistic,
  bursty star formation histories from the FIRE simulations
  Understanding the rate at which stars form is central to studies of galaxy
formation. Observationally, the star formation rates (SFRs) of galaxies are
measured using the luminosity in different frequency bands, often under the
assumption of a time-steady SFR in the recent past. We use star formation
histories (SFHs) extracted from cosmological simulations of star-forming
galaxies from the FIRE project to analyze the time-scales to which the
H${\alpha}$ and far-ultraviolet (FUV) continuum SFR indicators are sensitive.
In these simulations, the SFRs are highly time variable for all galaxies at
high redshift, and continue to be bursty to z=0 in dwarf galaxies. When FIRE
SFHs are partitioned into their bursty and time-steady phases, the best-fitting
FUV time-scale fluctuates from its ~10 Myr value when the SFR is time-steady to
>~100 Myr immediately following particularly extreme bursts of star formation
during the bursty phase. On the other hand, the best-fitting averaging
time-scale for H${\alpha}$ is generally insensitive to the SFR variability in
the FIRE simulations and remains ~5 Myr at all times. These time-scales are
shorter than the 100 Myr and 10 Myr time-scales sometimes assumed in the
literature for FUV and H${\alpha}$, respectively, because while the FUV
emission persists for stellar populations older than 100 Myr, the
time-dependent luminosities are strongly dominated by younger stars. Our
results confirm that the ratio of SFRs inferred using H${\alpha}$ vs. FUV can
be used to probe the burstiness of star formation in galaxies.
