We examine isothermal dark matter halos in hydrostatic equilibrium with a “ \Lambda –field ” , or cosmological constant \Lambda = \Omega _ { \Lambda } \rho _ { \textrm { \tiny { crit } } } c ^ { 2 } , where \Omega _ { \Lambda } \simeq 0.7 , and \rho _ { \textrm { \tiny { crit } } } is the present value of the critical density with h \simeq 0.65 .
Modeling cold dark matter as a self–gravitating Maxwell-Boltzmann gas , the Newtonian limit of General Relativity yields equilibrium equations that are different from those arising by merely coupling an “ isothermal sphere ” to the \Lambda –field within a Newtonian framework .
Using the conditions for the existence and stability of circular geodesic orbits , the numerical solutions of the equilibrium equations ( Newtonian and Newtonian limit ) show the existence of ( I ) an “ isothermal region ” ( 0 \leq r < r _ { 2 } ) , where circular orbits are stable and all variables behave almost identically to those of an isothermal sphere ; ( II ) an “ asymptotic region ” ( r > r _ { 1 } ) dominated by the \Lambda –field , where the Newtonian potential oscillates and circular orbits only exist in disconnected patches of the domain of r ; ( III ) a “ transition region ” ( r _ { 2 } \leq r < r _ { 1 } ) between ( I ) and ( II ) , where circular orbits exist but are unstable .
We also find that no stable configuration can exist with central density , \rho _ { c } , smaller than 2 \Lambda , hence any galactic haloes which virialized at z < 30 
in a \Lambda –CDM cosmological background must have central densities of \rho _ { c } > 0.008 \textrm { M } _ { \odot } / \textrm { pc } ^ { 3 } , in interesting agreement with rotation curve studies of dwarf galaxies .
Since r _ { 2 } marks the largest radius of a stable circular orbit , it provides a characteristic boundary or “ cut off ” maximal radius for isothermal spheres in equilibrium with a \Lambda –field .
For current estimates of \rho _ { c } and velocity dispersion of virialized galactic structures , this cut off scale ranges from 90 kpc for dwarf galaxies , up to to 3 Mpc for large galaxies and 22 Mpc for clusters .
In a purely Newtonian framework these length scales are about 10 % smaller , though in either case r _ { 2 } is between five and seven times larger than physical cut off scales of isothermal halos , such as the virialization radius or the critical radius for the onset of Antonov instability .
These results indicate that the effects of the \Lambda –field can be safely ignored in studies of virialized structures , but could be significant in the study of structure formation models and the dynamics of superclusters still in the linear regime or of gravitational clustering at large scales ( r \approx 30 Mpc ) .