Stochastic modeling of star-formation histories I: the scatter of the star-forming main sequence. (arXiv:1901.07556v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Caplar_N/0/1/0/all/0/1">Neven Caplar</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tacchella_S/0/1/0/all/0/1">Sandro Tacchella</a>
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. Specifically, we
show how the measurements of the normalisation and width ($sigma_{rm MS}$) of
the main sequence, measured in several passbands that probe different
timescales, give a constraint on the parameters of the underlying power
spectrum density. We first derive these results analytically for a simplified
case where we model observations by averaging over the recent star-formation
history. We then run numerical simulations to find results for more realistic
observational cases. As a proof of concept, we use observational estimates of
the main sequence scatter at $zsim0$ and $M_{star}approx10^{10}~M_{odot}$
measured in H$alpha$, UV+IR and the u-band, and show that combination of these
point to $tau_{rm break}=178^{+104}_{-66}$ Myr, when assuming $alpha=2$.
This implies that star-formation histories of galaxies lose “memory” of their
previous activity on a timescale of $sim200$ Myr, highlighting the importance
of baryonic effects that act over the dynamical timescales of galaxies.
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. Specifically, we
show how the measurements of the normalisation and width ($sigma_{rm MS}$) of
the main sequence, measured in several passbands that probe different
timescales, give a constraint on the parameters of the underlying power
spectrum density. We first derive these results analytically for a simplified
case where we model observations by averaging over the recent star-formation
history. We then run numerical simulations to find results for more realistic
observational cases. As a proof of concept, we use observational estimates of
the main sequence scatter at $zsim0$ and $M_{star}approx10^{10}~M_{odot}$
measured in H$alpha$, UV+IR and the u-band, and show that combination of these
point to $tau_{rm break}=178^{+104}_{-66}$ Myr, when assuming $alpha=2$.
This implies that star-formation histories of galaxies lose “memory” of their
previous activity on a timescale of $sim200$ Myr, highlighting the importance
of baryonic effects that act over the dynamical timescales of galaxies.
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