Unveiling acoustic physics of the CMB using nonparametric estimation of
  the temperature angular power spectrum for Planck
  Estimation of the angular power spectrum is one of the important steps in
Cosmic Microwave Background (CMB) data analysis. Here, we present a
nonparametric estimate of the temperature angular power spectrum for the Planck
2013 CMB data. The method implemented in this work is model-independent, and
allows the data, rather than the model, to dictate the fit. Since one of the
main targets of our analysis is to test the consistency of the $\Lambda$CDM
model with Planck 2013 data, we use the nuisance parameters associated with the
best-fit $\Lambda$CDM angular power spectrum to remove foreground contributions
from the data at multipoles $\ell \geq50$. We thus obtain a combined angular
power spectrum data set together with the full covariance matrix, appropriately
weighted over frequency channels. Our subsequent nonparametric analysis
resolves six peaks (and five dips) up to $\ell \sim1850$ in the temperature
angular power spectrum. We present uncertainties in the peak/dip locations and
heights at the $95\%$ confidence level. We further show how these reflect the
harmonicity of acoustic peaks, and can be used for acoustic scale estimation.
Based on this nonparametric formalism, we found the best-fit $\Lambda$CDM model
to be at $36\%$ confidence distance from the center of the nonparametric
confidence set -- this is considerably larger than the confidence distance
($9\%$) derived earlier from a similar analysis of the WMAP 7-year data.
Another interesting result of our analysis is that at low multipoles, the
Planck data do not suggest any upturn, contrary to the expectation based on the
integrated Sachs-Wolfe contribution in the best-fit $\Lambda$CDM cosmology.
