Temperature dependence of ultraviolet line average Doppler shifts in the quiet Sun

The existence of prevailing redshifts in the UV lines formed in the solar transition region raises an important question concerning its physical origin and its role in the mass and energy balance of the outer solar atmosphere. A series of UV spectral lines observed by SUMER has been analyzed to obtain the spatial average of Doppler shifts in the quiet Sun as a function of temperature. The UV lines used for the analysis cover temperatures ranging from 10(4) to 10(6) K. The wavelength calibration has been done in reference to the coolest chromospheric lines such as neutral lines of silicon and sulfur. The positioning of the line center in blended lines has been made by employing a constrained multi-Gaussian fitting technique. The error in the measured average of the Doppler shifts is estimated to be smaller than 1 km s(-1). Our results show that the average Doppler shift at the base of the transition region is about 1-2 km s(-1), increasing with temperature with a peak value of 11 km s(-1) near T = 2.3 x 10(5) K. Then it decreases but remains still above zero (5 km s(-1) in Ne VIII lines and 4 km s(-1) in Mg x lines). We find that this behavior can be explained by the dominance of emission from plasma flowing downward from the upper hot region to the lower cool region along flux tubes with varying cross section. Assuming that pressure and mass flux are constant along a flux tube, the cross section of a typical flux tube has been estimated as a function of temperature. It turns out that the cross section is nearly constant below T = 10(5) K and then expands by a factor of about 30 at T = 10(6) K. This behavior is fairly well represented by an analytical functional form, A(T)/A(T-h) = [1 + (Gamma(2) - 1)(T/T-h)(v)](1/2)/Gamma with parameters of T-h = 10(6) K, Gamma = 30, and v = 3.6.