tokens: et al. 2015b ). The contaminated regions of the SMICA map were further removed with the Galaxy, point-source, and SMICA -specific temperature and polarization masks, which leave ≈67% of the sky for the minimum-variance lensing reconstruction analysis. Given the sensitivity and angular resolutions of the Planck mission, the analysis thus results in the most significant measurement of the CMB lensing potential map to date. The online data provided by the Planck science team are in the standard HEALPix format (Górski et al. 2005 ). The spherical harmonics coefficients of lensing convergence, , are given for multipoles up to instead of the lensing potential, . We use the standard definition of lensing convergence to calculate fromWe then use the HEALPix synfast package to synthesize the lensing potential map, . The generated map has a resolution of (i.e., pixels). The projected lensing potential map is shown in Figure 1 . This reconstructed lensing potential map is used to cross-correlate with the cosmic void catalog, where the azimuthally averaged potential around each void is extracted, scaled, and then combined to constrain the void density profile. For our analysis, we shall use only those regions that pass the analysis mask (Galaxy + point-source + SMICA ). Figure 1. Lensing potential map, , constructed from Planck lensing convergence, . The gray shaded area marks the rejected pixels excluded by the analysis mask. 2.2. Cosmic Void Catalog In this work, we use the “Public Cosmic Void Catalog” (Sutter et al. 2012b ) constructed using a modified and extended version of the watershed algorithm ZOBOV , called “Void IDentification and Examination” (VIDE; Sutter et al. 2014b ). We applied the code to the SDSS Data Release 7 (Abazajian et al. 2009 ) main galaxy sample and SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 (Ahn et al. 2014 ) LOWZ and CMASS samples. This results in individually detected voids. The samples represent volume-limited catalogs of voids at various redshift bins. To minimize any possible evolution of the profile parameters, we choose to work with voids in individual redshift bins and do not stack voids across the bins. In order to have as many voids in a single bin as possible, we chose a high-redshift bin to increase the volume. Here, we report on the analysis using the “dr10cmass1” (, , ) and “dr10cmass2” samples (, , ), hereafter called “cmass1” and “cmass2,” respectively. We therefore stacked the Planck lensing potential map (Section 2.1 ) around the central positions of cosmic voids taken from the Sutter et al. ( 2014b ) “dr10cmass1” and “dr10cmass2” samples as two separated measurements. However, during our analysis we found that considerable numbers (106 and 303 for cmass1 and cmass2, respectively) of the voids are located in the negative lensing potential regions, which could be due to a number of reasons and warrants further investigations. We therefore restrict our analysis to 123 and
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