  We investigate the two-halo galactic conformity effect for central galaxies,
which is the spatial correlation of the star formation activities for central
galaxies to several Mpcs, by studying the dependence of the star formation
activities of central galaxies on their large-scale structure in our local
Universe using the SDSS data. Here we adopt a novel environment metric using
only central galaxies quantified by the distance to the $n$-th nearest central
galaxy. This metric measures the environment within an aperture from $\sim$ 1
Mpc to $\gtrsim$ 10 Mpc, with a median value of $\sim$ 4 Mpc. We found that two
kinds of conformity effects in our local Universe. The first one is that
low-mass central galaxies are more quenched in high-density regions, and we
found that this effect mainly comes from low-mass centrals that are close to a
more massive halo. A similar trend is also found in the IllustrisTNG
simulation, which can be entirely explained by backsplash galaxies. The second
conformity effect is that massive central galaxies in low-density regions are
more star-forming. This population of galaxies also possesses a higher fraction
of spiral morphology and lower central stellar velocity dispersion, suggesting
that their low quiescent fraction is due to less-frequent major merger events
experienced in the low-density regions, and as a consequence, less-massive
bulges and central black holes.
