A Cross-Internal Linear Combination Approach to Probe the Secondary CMB Anisotropies: Kinematic Sunyaev-Zel{'}dovich Effect and CMB Lensing

We propose a cross-internal linear combination (cross-ILC) approach to measure the small-scale cosmic microwave background (CMB) anisotropies robustly against the contamination from astrophysical signals. In particular, we focus on the mitigation of systematics from cosmic infrared background (CIB) and thermal Sunyaev-Zeldovich (tSZ) signals in kinematic SZ (kSZ) power spectrum and CMB lensing. We show the cross-spectrum measurement between two CMB maps created by nulling the contributions from CIB (CIB-free map) and tSZ (tSZ-free map) to be robust for kSZ as the approach significantly suppresses the total contribution of CIB and tSZ signals. Similarly, for CMB lensing, we use the approach introduced by Madhavacheril & Hill (2018) but with a slight modification by using the tSZ-free and CIB-free maps in the two legs of the quadratic estimator. By cross-correlating the CMB lensing map created using this technique with galaxy surveys, we show that the biases from both CIB/tSZ are negligible. We also compute the impact of unmodeled CIB/tSZ residuals on kSZ and cosmological parameters finding that the kSZ measured using the standard ILC to be significantly biased. The kSZ estimate from the cross-ILC remains less affected by CIB/tSZ making it crucial for CMB surveys such as the South Pole Telescope (SPT), Simons Observatory (SO) and CMB-S4. With the cross-ILC method, we find the total kSZ power spectrum can be measured at very high significance: $35\sigma$ by SPT, $22\sigma$ by SO, and $80\sigma$ by CMB-S4. We forecast constraints on the epoch of reionization using the kSZ power spectrum and find that the duration of reionization, currently unconstrained by {\it Planck}, can be constrained to $\sigma(z_{\rm dur})$= 1.5 (or) 0.5 depending on the choice of $\tau_{\rm re}$ prior. The data products and codes can be downloaded from https://github.com/sriniraghunathan/cross_ilc_methods_paper.