A principle of corresponding states for two-component, self-gravitating
  fluids
  Macrogases are defined as two-component, large-scale celestial objects where
the subsystems interact only via gravitation. The macrogas equation of state is
formulated and compared to the van der Waals equation of state for ordinary
gases. By analogy, it is assumed that real macroisothermal curves in macrogases
occur as real isothermal curves in ordinary gases, where a phase transition
takes place along a horisontal line in the macrovolume-macropressure (Mv-Mp)
plane. A simple guidance case and two density profiles which satisfactorily fit
to observations or simulations, are studied in detail. For sufficiently steep
density profiles, a critical macroisothermal curve exists as shown by ordinary
gases, where the critical point coincides with the horisontal inflexion point.
By analogy with ordinary gases, the first quadrant of the (Mv-Mp) plane may be
divided into three parts, namely (i) the G region, where only gas exists; (ii)
the S region, where only stars exist; (iii) the GS region, where both gas and
stars exist. An application is made to a subsample of elliptical galaxies
investigated within the SAURON project. Different models characterized by equal
subsystem mass ratio and different scaled truncation radii, are considered and
the related position of sample objects on the (Mv-Mp) plane is determined.
Tipically, fast rotators are found to lie within the S region, while slow
rotators are close (from both sides) to the boundary between the S and the GS
region. The net effect of the uncertainty affecting observed quantities, on the
position of sample objects on the (Mv-Mp) plane, is also investigated. Finally,
a principle of corresponding states is formulated for macrogases with assigned
density profiles and scaled truncation radii.
