Correlation Analysis between Tibet AS-$\gamma$ TeV Cosmic Ray and WMAP
  Nine-year Data
  The Wilkinson Microwave Anisotropy Probe (WMAP) team subtracted
template-based foreground models to produce foreground-reduced maps, and masked
point sources and uncertain sky regions directly; however, whether foreground
residuals exist in the WMAP foreground-reduced maps is still an open question.
Here, we use Pearson correlation coefficient (PCC) analysis with AS-$\gamma$
TeV cosmic ray (CR) data to probe possible foreground residuals in the WMAP
nine-year data. The correlation results between the CR and foreground-contained
maps (WMAP foreground-unreduced maps, WMAP template-based and MEM foreground
models) suggest that: (1) CRs can trace foregrounds in the WMAP data; (2) at
least some TeV CRs originate from the Milky Way; (3) foregrounds may be related
to the existence of CR anisotropy (loss-cone and tail-in structures); (4) there
exist differences among different types of foregrounds in the declination range
of $< 15^{\circ}$. Then, we generate 10,000 mock CMB sky maps to describe the
cosmic variance, which is used to measure the effect of the fluctuations of all
possible CMB maps to the correlations between CR and CMB maps. Finally, we do
correlation analysis between the CR and WMAP foreground-reduced maps, and find
that: (1) there are significant anticorrelations; and (2) the WMAP
foreground-reduced maps are credible. However, the significant anticorrelations
may be accidental, and the higher signal-to-noise ratio (SNR) Planck SMICA map
cannot reject the hypothesis of accidental correlations. We therefore can only
conclude that the foreground residuals exist with $\sim$ 95\% probability.
