Spectroscopic signature of Alfvén waves damping in a polar coronal hole up to 0.4 solar radii

Between February 24-25, 2009, the EIS spectrometer onboard the Hinode spacecraft performed special "sit & stare" observations above the South polar coronal hole continuously over more than 22 hours. Spectra were acquired with the 1" slit placed off-limb covering altitudes up to 0.48 R\(_\odot\) (\(3.34\times 10^2\) Mm) above the Sun surface, in order to study with EIS the non-thermal spectral line broadenings. Spectral lines such as Fe {\sc xii} \(\lambda\)186.88, Fe {\sc xii} \(\lambda\)193.51, Fe {\sc xii} \(\lambda\)195.12 and Fe {\sc xiii} \(\lambda\)202.04 are observed with good statistics up to high altitudes and they have been analyzed in this study. Results show that the FWHM of Fe {\sc xii} \(\lambda\)195.12 line increases up to \(\simeq 0.14\) R\(_\odot\), then decreases higher up. EIS stray light has been estimated and removed. Derived electron density and non-thermal velocity profiles have been used to estimate the total energy flux transported by Alfvén waves off-limb in polar coronal hole up to \(\simeq 0.4\) R\(_\odot\). The computed Alfvén wave energy flux density \(f_w\) progressively decays with altitude from \(f_w \simeq 1.2 \cdot 10^6\) erg cm\(^{-2}\) s\(^{-1}\) at 0.03 R\(_\odot\) down to \(f_w \simeq 8.5 \cdot 10^3\) erg cm\(^{-2}\) s\(^{-1}\) at 0.4 R\(_\odot\), with an average energy decay rate \(\Delta f_w / \Delta h \simeq -4.5 \cdot 10^{-5}\) erg cm\(^{-3}\) s\(^{-1}\). Hence, this result suggests energy deposition by Alfvén waves in a polar coronal hole, thus providing a significant source for coronal heating.