We have selelcted 556 Red Horizontal Branch ( RHB ) stars along the streams of the Sagittarius dwarf galaxy ( Sgr ) from SDSS DR7 spectroscopic data using a theoretical model .
The metallicity and \alpha -elements distributions are investigated for stars in the Sgr streams and for Galactic stars at the same locations .
We find that the Sgr stars have two peaks in the metallicity distribution while the Galactic stars have a more prominent metal-poor peak .
Meanwhile , [ \alpha /Fe ] ratios of the Sgr stars are lower than those of the Galactic stars .
Among the Sgr stars , we find a difference in the metallicity distribution between the leading and trailing arms of the Sgr tidal tails .
The metallicity and [ \alpha /Fe ] distribution of the leading arm is similar to that of the Galaxy .
The trailing arm is composed mainly of a metal rich component and [ \alpha /Fe ] is obviously lower than that of the Galactic stars .
The metallicity gradient is - ( 1.8 \pm 0.3 ) \times 10 ^ { -3 } dex degree ^ { -1 } in the first wrap of the trailing arm and - ( 1.5 \pm 0.4 ) \times 10 ^ { -3 } dex degree ^ { -1 } in the first wrap of the leading arm .
No significant gradient exists along the second wraps of the leading or trailing arms .
It seems that the Sgr dwarf galaxy initially lost the metal poor component in the second wrap ( older ) arms due to the tidal force of our Galaxy and then the metal rich component is disrupted in the first wrap ( younger ) arms .
Finally , we found that the velocity dispersion of the trailing arm from 88 ^ { \circ } < \Lambda _ { \odot } < 112 ^ { \circ } is \sigma = 9.808 \pm 1.0 km s ^ { -1 } , which is consistent with previous work in the literature .