Diagonal Ridge pattern of different age populations 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 mean radial velocity and find this feature is presented from very young (OB stars, few hundred \,Myr) to very old populations ($\tau$ = 9$-$14 \,Gyr). Meanwhile, some ridge features are also revealed in the metallicity [Fe/H], [$\alpha$/Fe] and $v_{z}$ distributions. In the $L_{Z}, v_{\phi}$ plane, one of the ridge patterns, with constant angular momentum per unit mass, shows variations with different age populations compared. However, the remaining two ones are relatively stable, implying there might have two kinds of ridge patterns with different dynamical origins and evolution.