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

Abstract: 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 $M_h=10^{12}M_\odot$, $\sigma_{M_|M_h=10^{12}M_\odot}$, 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 $\sigma_{M_|M_h=10^{12}M_\odot}$. 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 $\sigma_{M_|M_h=10^{12}M_\odot}=0.35$ 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 $\sigma_{M_*|M_h=10^{12}M_\odot}$ 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.