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Table 5:

Concentration bias of 2D fits.

Model
$R_{\rm max}$ $c_{\rm 2D}/c_{\rm 3D}^{\rm best}$

  no v-cut   v-cut
    no bg fixed bg free bg   no bg fixed bg free bg
NFW 1 0.86 $\pm $ 0.07 1.01 $\pm $ 0.08 0.99 $\pm $ 0.05   0.96 $\pm $ 0.06 1.02 $\pm $ 0.07 1.01 $\pm $ 0.07
Einasto m=5 1 0.82 $\pm $ 0.06 0.97 $\pm $ 0.08 0.96 $\pm $ 0.05   0.93 $\pm $ 0.06 0.99 $\pm $ 0.07 0.97 $\pm $ 0.07
NFW 1.35 0.78 $\pm $ 0.06 0.98 $\pm $ 0.08 0.98 $\pm $ 0.05   0.91 $\pm $ 0.06 1.01 $\pm $ 0.07 0.96 $\pm $ 0.05
Einasto m=5 1.35 0.72 $\pm $ 0.06 0.93 $\pm $ 0.07 0.95 $\pm $ 0.05   0.87 $\pm $ 0.06 0.96 $\pm $ 0.06 0.94 $\pm $ 0.05
NFW 3 0.37 $\pm $ 0.04 0.85 $\pm $ 0.09 0.98 $\pm $ 0.11   0.68 $\pm $ 0.04 0.96 $\pm $ 0.06 0.96 $\pm $ 0.10
Einasto m=5 3 0.32 $\pm $ 0.03 0.71 $\pm $ 0.08 0.92 $\pm $ 0.16   0.59 $\pm $ 0.04 0.83 $\pm $ 0.05 0.89 $\pm $ 0.05

Notes. The biases highlighted in bold (respectively blue italics) show the cases where the best-fit surface density profile was consistent with the data to better than 5% (between 0.01% and 5%) confidence (see last column of Table 4). The errors are the statistical (MLE fit) and cosmic variance (from the 3 cartesian stacked halos) errors of Table 4 added in quadrature together and with the analogous errors on the best-fit (bold in Table 1) 3D concentration, with $\sigma^2(c_{\rm
2D}/c_{\rm 3D}^{\rm best})=\sigma^2(c_{\rm 2D})/\left\langle c...
...le c_{\rm 2D}\right\rangle^2/\left\langle
c_{\rm 3D}^{\rm best}\right \rangle^4$.


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