Stochastic modeling of star-formation histories I: the scatter of the star-forming main sequence

Understand

We present a framework for modelling the star-formation histories of galaxies as a stochastic process.

• We define this stochastic process through a power spectrum density with a functional form of a broken power-law.
• Star-formation histories are correlated on short timescales, the strength of this correlation described by a power-law slope, $\alpha$, and they decorrelate to resemble white noise over a timescale that is proportional to the timescale of the break in the power spectrum density, $\tau_{\rm break}$.
• We use this framework to explore the properties of the stochastic process that, we assume, gives rise to the log-normal scatter about the relationship between star-formation rate and stellar mass, the so-called galaxy star-forming main sequence.