  We establish that two-dimensional dipolar quantum gases admit a universal
description, i.e., their thermodynamic properties are independent of details of
the interaction at short distances. The only relevant parameters are the dipole
length as well as the scattering length of the combined short-range plus
dipolar interaction potential. We derive adiabatic relations that link the
change in the thermodynamic potentials with respect to the scattering length
and the dipole length to a generalized Tan contact parameter and a new dipolar
contact, which involves an integral of a short-distance regularized pair
distribution function. These two quantities determine the scale anomaly in the
difference between pressure and energy density and also the internal energy in
the presence of a harmonic confinement. For a weak transverse confinement,
configurations with attractive interactions appear, which lead to a
density-wave instability beyond a critical strength of the dipolar interaction.
We show that this instability essentially coincides with the onset of a roton
minimum in the excitation spectrum and may be understood in terms of a quantum
analog of the Hansen-Verlet criterion for freezing of a classical fluid.
