tokens: while the dark matter distribution in the interior of the halo hardly changes at low redshift (Prada et al. 2006 ; Diemand, Kuhlen Madau 2007 ; Cuesta et al. 2008 ). Recently More, Diemer Kravtsov ( 2015 ) proposed that the best physically based definition of halo radius is the ‘splashback radius’ R sp ≈ 2 R 200m , where there is typically a sharp drop in the density; using this definition, there is actually more halo mass increase than for R vir , R 200m , or R 200c . What is actually relevant to star formation of the central galaxy in the halo is the amount of gas that enters the halo and eventually reaches its central regions. Wetzel Nagai ( 2015 ) have used adaptive refinement tree (ART) hydrodynamic galaxy simulations with a best resolution of about 0.5 kpc to show that infalling gas decouples from dark matter starting at about 2 R 200m and roughly tracks the growth of M 200m . Thus, they argue that pseudo-evolution is relevant to the accretion of dark matter, but not to that of gas. Further evidence that the gas falling into the central regions of haloes roughly tracks the halo MAR is provided by Dekel et al. ( 2013 ), who used a suite of ART hydrodynamic zoom-in galaxy simulations with M vir /10 12 M ⊙ = 0.1 to 2 at z = 2 and best resolution of 35 pc, and found that the gas inflow rate is proportional to the halo MAR, with about half the gas penetrating to 0.1 R vir at redshifts from z = 4 to 2, and with the fraction increasing from z = 2 to 1. Analysis of a subsequent suite of ART hydrodynamic zoom-in galaxy simulations with better resolution and feedback showed that these simulated star-forming galaxies grow stellar mass at the same rate as the specific halo mass increase (Tacchella et al. 2015 ; Zolotov et al. 2015 ). A similar result has been reported in González-Samaniego et al. ( 2014 ) for galaxies formed in haloes of . Star-forming galaxies are known to show a tight dependence of SFR on stellar mass, which is known as the ‘main sequence’ of galaxy formation (Daddi et al. 2007 ; Elbaz et al. 2007 ; Noeske et al. 2007 ; Salim et al. 2007 ), in analogy with the tight dependence on stellar mass of the properties of stars on the stellar main sequence. Dark matter haloes also have an MAR that is roughly proportional to their mass, and we show in Section 2.1 of this paper that the dispersion of the halo MAR at a given halo mass is 0.3 to 0.4 dex, similar to the dispersion of the SFR on the main sequence. It was this equality that originally motivates us to examine more closely the connection between mass accretion and star formation. Our analysis is limited to the connection between distinct haloes and central galaxies only. One reason is that subhaloes lose mass via tidal stripping, resulting in negative values of accretion rates (see e.g. van den Bosch, Tormen Giocoli 2005 ). Satellite galaxies are also affected in other ways by their proximity to central galaxies. Therefore, studying the connection between subhalo mass accretion
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