Table 3.
Main features of the relaxed high-density rotating polytropes (ρmax = 1014 g cm−3 prior to relaxation) calculated with γ = 5/3 and mass M = 2 M⊙.
| m | A | J | ρmax | j | Np | hmin | EI/EG | Ek/EG | ET/E0 | V.T | Ωc | F | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ×1049 erg s | ×1014 g cm−3 | ×106 | km | ×10−5 | ×10−3 | s−1 | |||||||
| B1 | 1 | 2 | 2.3354 | 0.656 | 0.05129 | 1.0 | 0.55 | 0.429 | 0.0685 | −7.822 | 4.4 | 1336 | 0.68 |
| EM1 | – | – | 0.05129 | – | – | 0.432 | 0.0679 | −7.759 | 0.43 | – | 0.68 | ||
| B2 | 1 | 0.2 | 1.2946 | 0.664 | 0.02849 | 1.0 | 0.55 | 0.469 | 0.0385 | −2.583 | 3.0 | 7116 | 0.76 |
| EM2 | – | – | 0.02849 | – | – | 0.463 | 0.0377 | −2.633 | 0.54 | – | 0.77 | ||
| B3 | 1 | 0.2 | 2.1707 | 0.422 | 0.04429 | 1.0 | 0.63 | 0.413 | 0.0852 | −6.275 | 3.2 | 10937 | 0.54 |
| EM3 | – | – | 0.04429 | – | – | 0.419 | 0.0808 | −6.280 | 0.49 | – | 0.55 | ||
| B4 | 1/2 | 2 | 2.4306 | 0.647 | 0.05326 | 1.0 | 0.55 | 0.427 | 0.0747 | −8.320 | 2.7 | 1260 | 0.60 |
| EM4 | – | – | 0.05326 | – | – | 0.427 | 0.0731 | −8.386 | 0.40 | – | 0.65 | ||
| B5 | 1/2 | 0.2 | 3.0946 | 0.368 | 0.06173 | 1.0 | 0.67 | 0.388 | 0.1110 | −12.0 | 2.2 | 4429 | 0.54 |
| EM5 | – | – | 0.06173 | – | – | 0.396 | 0.1037 | −11.8 | 0.45 | – | 0.57 | ||
Notes. Models Bn refer to the 3D-SPH calculations and EMn are the reference results by Eriguchi & Mueller (1985). Columns: model name, exponent in the rotation law of Eq. (3) (m), A = Rc/RNS, total angular momentum (J), maximum density (ρmax), dimensionless angular momentum (j), number of SPH particles (Np), minimum smoothing length (hmin), internal-to-gravitational energy ratio, kinetic-to-gravitational energy ratio, total energy conservation, virial theorem, central angular velocity, and polar-to-equatorial radius ratio. The symbol “–” indicates that the corresponding magnitude was not available in the paper by EM.
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