We use a sample of 83 high-resolution cosmological zoom-in simulations and a semi-analytic model ( SAM ) to study the stochasticity of galaxy formation in haloes ranging from dwarf to Milky Way masses .
Our simulated galaxies reproduce the observed inefficiency of galaxy formation as expressed through the stellar , gas and baryonic Tully-Fisher relations .
For Hi velocities in the range ( 70 \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } % } V \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } % } 220 km/s ) , the scatter is just 0.08 to 0.14 dex , consistent with the observed intrinsic scatter at these scales .
At low velocities ( 20 \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } % } V \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } % } 70 km/s ) , the simulated scatter is 0.2-0.25 dex , which could be tested with future observations .
The scatter in the stellar mass versus dark halo velocity relation is constant for 30 \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } % } V \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } % } 180 km s ^ { -1 } , and smaller ( \simeq 0.17 dex ) when using the maximum circular velocity of the dark matter only simulation , V _ { max } ^ { DMO } , compared to the virial velocity ( V _ { 200 } or V _ { 200 } ^ { DMO } ) .
The scatter in stellar mass is correlated with halo concentration , and is minimized when using a circular velocity at a fixed fraction of the virial radius \simeq 0.4 R _ { 200 } or with V _ { \alpha } = V _ { 200 } ^ { DMO } ( V _ { max } ^ { DMO } / V _ { 200 } ^ { DMO } ) ^ { \alpha } with \alpha \simeq 0.7 , consistent with constraints from halo clustering .
Using the SAM we show the correlation between halo formation time and concentration is essential in order to reproduce this result .
This uniformity in galaxy formation efficiency we see in our hydrodynamical simulations and a semi-analytic model proves the simplicity and self-regulating nature of galaxy formation in a \Lambda Cold Dark Matter ( \Lambda CDM ) universe .