Void profile from Planck lensing potential map

Abstract

We use the lensing potential map from Planck CMB lensing reconstruction analysis and the "Public Cosmic Void Catalog" to measure the stacked void lensing potential. In this profile, four parameters are needed to describe the shape of voids with different characteristic radii $R_V$. However, we have found that after reducing the background noise by subtracting the average background, there is a residue lensing power left in the data. The inclusion of the environment shifting parameter, ${\gamma }_V$, is necessary to get a better fit to the data with the residue lensing power. We divide the voids into two redshift bins: cmass1 ($0.45<z<0.5$) and cmass2 ($0.5<z<0.6$). Our best-fit parameters are $\alpha =1.989\pm 0.149$, $\beta =12.61\pm 0.56$, ${\delta }_c=-0.697\pm 0.025$, $R_S/R_V=1.039\pm 0.030$, ${\gamma }_v=(-7.034\pm 0.150)\times 10^{-2}$ for the cmass1 sample with 123 voids and $\alpha =1.956\pm 0.165$, $\beta =12.91\pm 0.60$, ${\delta }_c=-0.673\pm 0.027$, $R_S/R_V=1.115\pm 0.032$, ${\gamma }_v=(-4.512\pm 0.114)\times 10^{-2}$ for the cmass2 sample with 393 voids at 68% C.L. The addition of the environment parameter is consistent with the conjecture that the Sloan Digital Sky Survey voids reside in an underdense region.

8 pages, 5 figures, 1 table, accepted for publication in ApJ

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