Corolla:  The entire set of petals of a flower.  In composite species, the capitula are composed of multiple tiny florets, each having its own corolla.  The disk florets are the rayless ones located in the center of a composite flower head.  The petals (corollas) of these florets are fused or united to form a narrow vase-shaped tube, called the "limb".  The "lobes" comprise the flaring, upper-most portion of the limb.  Depending on the species, the lobes will flare to various degrees.  For some species the lobes hardly flare at all, whereas for others they flare a great deal.  This is one of the post important characteristics used to distinguish the aster species from each other.  In the upper image (of Ionactis linariifolius), the lobes flare only slightly.  In the lower image (of Symphyotrichum lateriflorum), the lobes are strongly reflexed.