Constraining Star Formation Histories of Blue Galaxies using the Scatter between Stellar Mass and Halo Mass

We present constraints on the timescale of star formation variability and the correlation between star formation and host halo accretion histories of star-forming (SF) central galaxies from the scatter of the stellar-to-halo mass relation (SHMR). SF galaxies are found to have a tight relationship between their star formation rates and stellar masses on the so-called "star-forming sequence" (SFS), which characterizes their SF histories and $M_*$ growths. Meanwhile, observed SHMR constraints connect $M_*$ growth to halo accretion history. Combining these observed trends with a cosmological $N$-body simulation, we present flexible models that track the SF, $M_*$, and halo accretion histories of SF central galaxies at $z<1$ while reproducing the observed stellar mass function and SFS in SDSS DR7. We find that the scatter in SHMR at $M_h=10^{12}M_\odot$, $σ_{M_*|M_h=10^{12}M_\odot}$, is sensitive to the timescale of star formation variability, $t_{\rm duty}$, and the correlation coefficient, $r$, between SF and halo accretion histories: shorter $t_{\rm duty}$ and higher $r$ both result in tighter $σ_{M_*|M_h=10^{12}M_\odot}$. To reproduce a constant 0.2 dex scatter over $z=1-0$, our models require $t_{\rm duty}\leq1.5$ Gyr for $r=0.99$ or $r>0.6$ for $t_{\rm duty}=0.1$ Gyr. For $r\sim0.6$, as found in the literature, $t_{\rm duty}<0.2$ Gyr is necessary. Meanwhile, to reproduce the tightening of $σ_{M_*|M_h=10^{12}M_\odot}=0.35$ to 0.2 dex from $z=1-0$ in hydrodynamical simulations, our models require $t_{\rm duty}=0.1$ Gyr for $r>0.5$. Although, the lack of consensus on $σ_{M_*|M_h=10^{12}M_\odot}$ at $M_h=10^{12}M_\odot$ and at $z=1$ from observations and galaxy formation models remains the main bottleneck in precisely constraining $r$ and $t_{\rm duty}$, we demonstrate that SHMR can be used to constrain the SF and host halo accretion histories of SF central galaxies.