Renormalization group flow and fragmentation in the self-gravitating thermal gas - art. no. 125021

The self-gravitating thermal gas (non-relativistic particles of mass m at t emperature T) is exactly equivalent to a field theory with a single scalar field phi(x) and exponential self-interaction. We build up perturbation the ory around a space dependent stationary point phi(0)(r) in a finite size do main delta less than or equal to r less than or equal to R (delta much less than R), which is relevant for astrophysical applications (interstellar me dium, galaxy distributions). We compute the correlations of the gravitation al potential (phi) and of the density and find that they scale; the latter scales as r(-2). A rich structure emerges in the two-point correlators from . the phi fluctuations around phi(0)(r). The n-point correlators are explic itly computed to the one-loop level. The relevant effective coupling turns out to be lambda = 4 pi Gm(2)/(TR). The renormalization group (RG) equation s for the n-point correlator are derived and the RG flow for the effective coupling lambda(tau), tau = ln(R/delta), explicitly obtained. A novel depen dence on T emerges here. lambda(tau) vanishes each time tau approaches disc rete values tau = tau(n) = 2 pi n/root 7 - 0, n = 0,1,2,... . Such RC stabl e behavior [lambda(tau) decreasing with increasing tau] is here connected w ith low density self-similar fractal structures fitting one into another. F or sizes smaller than the points tau(n), RG unstable behavior appears which we connect to the Jeans unstable behavior, growing density and fragmentati on. Remarkably, we get a hierarchy of scales and Jeans lengths following th e geometric progression R-n = R-0 e(2 pi n/root 7) = R-0[10.749087 ...](n). A hierarchy of this type is expected for non-spherical geometries, with a ratio different from e(2)pi/root 7. [S0556-2821(99)05510-1].