Table 3.
Characteristic length scales of the overshooting layers obtained with the radial profiles of the convective flux, the EVT, and the mixture model.
Convective flux | Extreme value theory | Mixture model | |||
---|---|---|---|---|---|
![]() |
(ℓovL, max,ℓovU, max) | (ℓsoL,ℓsoU) | (ℓsoL, 90%,ℓsoU, 90%) | ||
ceph5 | (0.6, 0.6) | (1.56, 1.66) | (0.47 ± 0.07, 0.47 ± 0.29) | (0.59, 1.06) | |
ceph6 | (1.0, 1.1) | (1.73, 2.41) | (1.37 ± 0.33, 1.49 ± 0.54) | (2.02, 2.53) | |
ceph7a | (1.1, 1.6) | (1.86, 2.84) | (1.21 ± 0.35, 1.30 ± 0.47) | (1.89, 2.19) | |
ceph7b | (1.2, 1.9) | (1.87, 3.23) | (1.29 ± 0.37, 1.76 ± 0.61) | (2.02, 2.92) | |
ceph8 | (1.0, 1.3) | (1.48, 2.60) | (1.31 ± 0.27, 1.69 ± 0.49) | (1.83, 2.60) | |
ceph9 | (1.2, 1.7) | (2.08, 3.36) | (1.43 ± 0.37, 2.14 ± 0.74) | (2.15, 3.51) |
Notes. The length scale
is a width of the lower (upper) overshooting layer defined using the convective flux that is first averaged over the angular direction and then averaged in time. ℓovL, max (ℓovU, max) is a length defined by the EVT analysis, which provides a maximal width of the lower (upper) overshooting layer. For simulations ceph7a, ceph7b, ceph8 and ceph9, the value of the EVT result for the upper overshooting layer is the full width of the radiative layer. The value in italics for the 6 M⊙ Cepheid has been obtained from the incomplete PDF(Δrmax) and therefore associated with a higher uncertainty. ℓsoL (ℓsoU) is a characteristic length-scale associated with the lower (upper) overshooting layer, defined by the mean of the SO gamma distribution. The standard deviation of the SO gamma distribution is indicated as an error on the mean. ℓsoL, 90% (ℓsoU, 90%) is the distance at which 90% of the plumes have stopped below (above) the CZ, defined as the 90th percentile of the SO Gamma distribution. All values are given in units of the pressure scale height at the convective boundary, Hp, CB.
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