On the evolution of Diagonal Ridge pattern found in Gaia DR2 with LAMOST Main-Sequence-Turn-Off and OB type Stars

We revisit the diagonal ridge feature (diagonal distributions in the $R, v_{\phi}$ plane) found in $Gaia$ and present timing analysis for it between Galactocentric distances of $R=7.5$ and 12 \,kpc, using Main-Sequence-Turn-Off and OB stars selected from the LAMOST Galactic spectroscopic surveys. We recover the ridge pattern in the $R$-$v_{\phi}$ plane color coded by stellar number density and mean radial velocity and find this feature is presented from very young (OB stars, few hundred \,Myr) to very old populations ($\tau > $ 9 \,Gyr), accompanying with the north-south asymmetrical ridges. One of the ridge patterns, with constant angular momentum per unit mass, shows clear variations with different age populations compared. However, the remaining two ones are very stable, clearly implying there might have two kinds of ridge patterns with different dynamical origins and evolution. For the vertical velocity and height, there are no ridge features corresponding to the in-plane Galactoseismogy features, but the metallicity and [$\alpha/Fe$] have some weak signals. This first temporal chemo-kinematical analysis for ridge strongly supports that the ridge pattern might be originated from the phase mixing of disrupting spiral arms implying different ridges have different physical processes and no coupling phenomenon, although other possible scenarios such as Sgr perturbations could not be ruled out.