A Cross-internal Linear Combination Approach to Probe the Secondary CMB Anisotropies: Kinematic Sunyaev–Zel’dovich Effect and CMB Lensing

Abstract

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–Zel’dovich (tSZ) signals in kinematic Sunyaev–Zel’dovich (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 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 and tSZ are negligible. We also compute the impact of unmodeled CIB/tSZ residuals on kSZ and cosmological parameters, finding 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 current and upcoming CMB surveys such as the South Pole Telescope (SPT), Simons Observatory (SO), and CMB-S4. With the cross-ILC approach, we find that the total kSZ power spectrum can be measured at very high significance in the coming years: 35 σ by SPT, 22 σ by SO, and 80 σ by CMB-S4. Finally, we forecast constraints on the epoch of reionization using the kSZ power spectrum and find that the duration of reionization, currently unconstrained by Planck, can be constrained to σ ( Δ z re ) = 1.5 or 0.5 depending on the choice of the prior on the optical depth to reionization. The data products and the associated codes can be downloaded from this link ( https://github.com/sriniraghunathan/cross_ilc_methods_paper ).