Parameters

a = separation
q = mass ratio = M2/M1
Wo = orbital angular velocity
n = polytropic index [ P = Kir1 + 1/n ]
Ki = polytropic constant [ i = 1, 2 ]
G = adiabatic exponent [ Homentropic if G = 1 + 1/n ]

NOTE: Models are all initially tidally locked so that Wspin = Wframe = Wo.

Equal Mass (q = 1):

Fix "n" and set K2 = K1, then generate a one-parameter sequence of initial models (e.g., vary the separation "a"). Unequal Mass: Fix "q" and "n", then at various choices of "a", the values of K1 and K2 can be adjusted to have each binary component fill a specified fraction of its Roche Lobe. Hence the parameter space becomes very large!

One interesting regime to note for polytropes: If q > qstable, where,

qstable = (9 - 4n)/[3 (3 - n)] ,
then the system is expected to be dynamically unstable toward mass transfer, once the donor star fills its Roche Lobe. For n = 3/2, this gives qstable = 2/3.



Return to Binaries