tokens: 11 . For the most massive bin, the HSE mass is biased low at a constant level of about 24%. This bias drops with decreasing halo mass, with the mean bias in the radial range being , and 10% for the three lower-mass bins. These findings are in good agreement with the HSE mass biases for halos found in previous NR simulations (Kay et al. 2004 ; Nelson et al. 2012 ). Here we have assumed full information on both the density and temperature profiles in Equation ( 9 ). Incomplete knowledge on either of these quantities has the potential to further bias the HSE estimate. Figure 11. Bias between the HSE mass estimate and simulation mass at z = 0. Each line traces the median relation, with the red (black) error bars showing the 25th and 75th percentiles of the highest-mass (lowest-mass) bin. We show the result down to only , as the relation becomes dominated by noise on smaller scales. We can obtain a better understanding of the HSE mass bias by measuring the nonthermal pressure for each individual halo. Following Battaglia et al. ( 2012a ), we focus here on bulk flows, which should capture the major contribution to nonthermal support. We compute the corresponding kinetic pressure based on mass-averaged velocity fluctuations:The velocity fluctuations are made with respect to the baryon center of mass, , and mass-averaged velocity, , within R 200 :The resulting kinetic pressure profiles are shown in Figure 12 as the fraction of the total pressure. These are compared to the fitting function from Battaglia et al. ( 2012a ), which is based on the Shaw et al. ( 2010 ) power-law fitting function with an additional mass dependency that scales as . Figure 12. Fraction of the kinetic pressure with respect to the total (kinetic plus thermal) pressure for each of the four mass bins in the NR run at z = 0. The light-shaded solid lines trace the fitting function from Battaglia et al. ( 2012a ), which is based on power-law slopes of 4/5 in radius and 1/5 in mass. The fitting function is computed using the median halo mass in each bin. We show the 25th and 75th percentiles of the highest-mass (lowest-mass) bin as the red (black) error bars. The fitting function does a good job at matching our simulation results for but dramatically underestimates the kinetic pressure on smaller scales. In this case, a broken power law with a shallower slope on small scales would be more appropriate. We expect the NR results to be accurate for since bulk flows on these scales will be gravitationally sourced and mostly unaffected by cooling and feedback processes occurring on smaller scales (Battaglia et al. 2012a ; Nelson et al. 2014 ). Indeed, the fitting function in Figure 12 was calibrated against simulations with cooling and feedback. Earlier works have shown that kinetic pressure is greater in less relaxed systems that have undergone recent major mergers (Jeltema et al. 2008 ; Piffaretti Valdarnini 2008 ; Lau et al. 2009 ; Nelson et al. 2014 ). The rise of the kinetic
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