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We present a detailed analysis of the specific star formation rate -- stellarmass ($\mathrm{sSFR}-M_*$) of $z\le 0.13$ disk central galaxies using amorphologically selected mass-complete sample ($M_* \ge 10^{9.5} M_{\odot}$).Considering samples of grouped and ungrouped galaxies, we find the$\mathrm{sSFR}-M_*$ relations of disk-dominated central galaxies to have nodetectable dependence on host dark-matter halo (DMH) mass, even whereweak-lensing measurements indicate a difference in halo mass of a factor$\gtrsim5$. We further detect a gradual evolution of the $\mathrm{sSFR}-M_*$relation of non-grouped (field) central disk galaxies with redshift, even overa $\Delta z \approx 0.04$ ($\approx5\cdot10^{8}\mathrm{yr}$) interval, whilethe scatter remains constant. This evolution is consistent with extrapolationof the "main-sequence-of-star-forming-galaxies" from previous literature thatuses larger redshift baselines and coarser sampling.  Taken together, our results present new constraints on the paradigm underwhich the SFR of galaxies is determined by a self-regulated balance between gasinflows and outflows, and consumption of gas by star-formation in disks, withthe inflow being determined by the product of the cosmological accretion rateand a fuelling-efficiency -- $\dot{M}_{\mathrm{b,halo}}\zeta$. In particular,maintaining the paradigm requires $\dot{M}_{\mathrm{b,halo}}\zeta$ to beindependent of the mass $M_{\mathrm{halo}}$ of the host DMH. Furthermore, itrequires the fuelling-efficiency $\zeta$ to have a strong redshift dependence($\propto (1+z)^{2.7}$ for $M_*=10^{10.3} M_{\odot}$ over $z=0 - 0.13$), eventhough no morphological transformation to spheroids can be invoked to explainthis in our disk-dominated sample. The physical mechanisms capable of givingrise to such dependencies of $\zeta$ on $M_{\mathrm{halo}}$ and $z$ for disksare unclear.

monthly notices of the royal astronomical society

Galaxy And Mass Assembly (GAMA): Gas Fuelling of Spiral Galaxies in the  Local Universe II. -- Direct Measurement of the Dependencies on Redshift and  Host Halo Mass of Stellar Mass Growth in Central Disk Galaxies