Context : The average Doppler shift shown by spectral lines formed from the chromosphere to the corona reveals important information on the mass and energy balance of the solar atmosphere , providing an important observational constraint to any models of the solar corona .
Previous spectroscopic observations of vacuum ultra-violet ( VUV ) lines have revealed a persistent average wavelength shift of lines formed at temperatures up to 1 MK .
At higher temperatures , the behaviour is still essentially unknown .

Aims : Here we analyse combined SUMER ( Solar Ultraviolet Measurements of Emitted Radiation ) /SoHO ( Solar and Heliospheric Observatory ) and EIS ( EUV Imaging Spectrometer ) /Hinode observations of the quiet Sun around disk centre to determine , for the first time , the average Doppler shift of several spectral lines formed between 1 and 2 MK , where the largest part of the quiet coronal emission is formed .

Methods : The measurements are based on a novel technique applied to EIS spectra to measure the difference in Doppler shift between lines formed at different temperatures .
Simultaneous wavelength-calibrated SUMER spectra allow establishing the absolute value at the reference temperature of T \approx 1 MK .

Results : The average line shifts at 1 MK ~ { } < T < 1.8 MK are modestly , but clearly bluer than those observed at 1 MK .
By accepting an average blue shift of about ( -1.8 \pm 0.6 ) ~ { } km~ { } s ^ { -1 } at 1 MK ( as provided by SUMER measurements ) , this translates into a maximum Doppler shift of ( -4.4 \pm 2.2 ) ~ { } km~ { } s ^ { -1 } around 1.8 MK .
The measured value appears to decrease to about ( -1.3 \pm 2.6 ) ~ { } km~ { } s ^ { -1 } at the Fe xv formation temperature of 2.1 MK .

Conclusions : The measured average Doppler shift between 0.01 and 2.1 MK , for which we provide a parametrisation , appears to be qualitatively and roughly quantitatively consistent with what foreseen by 3-D coronal models where heating is produced by dissipation of currents induced by photospheric motions and by reconnection with emerging magnetic flux .