Relative positions of marginally stable circular orbits shown for several values of polytropic parameter n. For n = 3.8 we can see the onset of extremely large polytropes for higher values of parameter σ, since values of the absolute positions ξ_MSCO are only slightly affected by σ and all remain in the interval (0.8,  2.4). Solid circles show the maximum considered value of sigma σ_causal ≡ n/(n + 1).