In this paper dry-merger means a pure dissipationless merger of stellar systems, i.e., without any gas and star formation.

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This seems to be the case for nearly 50% of the merger events (Khochfar & Burkert 2006)

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... $\sigma$

This might happen if the progenitors are already bound to each other, as in the case in which they inhabit the same massive Dark Matter halo. However, the energy must have the exact value for the merger end-product to obey to the Fundamental Plane and therefore this case seems rather unlikely.

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... difficulties

Thomas & Kauffmann (1999) already showed that this is not the case for the class of earlier hierarchical models not taking into account the downsizing.

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