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. Fundamentally, this new method is only able to recover the relative durations of different evolutionary phases. It therefore requires a "reference time-scale" to convert the relative time-scales into absolute values. The phase over which the star formation rate (SFR) tracer is visible is the logical choice to assign this reference time-scale to, since it can be characterised using stellar population synthesis models. In this paper, we use hydrodynamical disc galaxy simulations to produce synthetic emission maps of several SFR tracers and apply our statistical method to measure the associated characteristic time-scale of each tracer. These cover 12 ultraviolet (UV) filters (from GALEX, Swift, and HST) covering a wavelength range 150-350 nm, as well as H$\alpha$. For solar-metallicity environments, we find the characteristic time-scales for H$\alpha$ with (without) continuum subtraction to be ~4.3 (6-16) Myr and for the UV filters to be in the range 17-33 Myr, monotonically increasing with wavelength. We find that the characteristic time-scale decreases towards higher metallicities, as well as to lower star formation rate surface densities, if the stellar initial mass function is not well-sampled. We provide fitting functions to the resulting reference time-scales to facilitate observational applications of our statistical method across a wide range of galactic environments. More generally, our results predict the time-scales over which photoionisation and UV heating take place around star-forming regions.