An uncertainty principle for star formation -- III. The characteristic
  emission time-scales of star formation rate tracers
  We recently presented a new statistical method to constrain the physics of
star formation and feedback on the cloud scale by reconstructing the underlying
evolutionary timeline. However, by itself this new method only recovers the
relative durations of different evolutionary phases. To enable observational
applications, it therefore requires knowledge of an absolute 'reference
time-scale' to convert relative time-scales into absolute values. The logical
choice for this reference time-scale is the duration over which the star
formation rate (SFR) tracer is visible because it can be characterised using
stellar population synthesis (SPS) models. In this paper, we calibrate this
reference time-scale using synthetic emission maps of several SFR tracers,
generated by combining the output from a hydrodynamical disc galaxy simulation
with the SPS model SLUG2. We apply our statistical method to obtain
self-consistent measurements of each tracer's reference time-scale. These
include H${\alpha}$ and 12 ultraviolet (UV) filters (from GALEX, Swift, and
HST), which cover a wavelength range 150-350 nm. At solar metallicity, the
measured reference time-scales of H${\alpha}$ are ${4.32^{+0.09}_{-0.23}}$ Myr
with continuum subtraction, and 6-16 Myr without, where the time-scale
increases with filter width. For the UV filters we find 17-33 Myr, nearly
monotonically increasing with wavelength. The characteristic time-scale
decreases towards higher metallicities, as well as to lower star formation rate
surface densities, owing to stellar initial mass function sampling effects. We
provide fitting functions for the reference time-scale as a function of
metallicity, filter width, or wavelength, to enable observational applications
of our statistical method across a wide variety of galaxies.
