Investigation of cosmic ray penetration with wavelet cross-correlation analysis

Aims. We use Fermi-LATand Planck data to calculate the cross correlation between γ-ray signal and gas distribution in different scales in giant molecular clouds (GMCs). Then we investigate the cosmic rays (CRs) penetration in GMCs with these informations. Methods. We use the wavelet technique to decompose both the γ-ray and dust opacity maps in different scales, then we calculate the wavelet cross correlation functions in these scales. We also define wavelet response as an analog to the impulsive response in Fourier transform and calculate that in different scales down to Fermi-LATangular resolution. Results. The γ-ray maps above 2 GeV show strong correlation with the dust opacity maps, the correlation coefficient is larger than 0.9 above a scale of 0.4 degree.The derived wavelet response is uniform in different scales. Conclusions. We argue that the CR above 10 GeV can penetrate the GMC freely and the CRs distributions in the same energy range are uniform down to parsec scale