Table 1: Characteristics of the stellar models (with $[{\rm Fe/H}]=-2$) on the ZAMS and at 10 Gyr: effective temperature, luminosity, thickness of the external convective zone in stellar mass and radius, largest convective scale  $\ell _{\rm c}$, characteristic convective frequency  $\nu _{\rm c}$, and thermal diffusivity below the convective envelope $K_{\rm T}$. $\nu _{\rm max}$ is the maximum frequency required to capture the wave - mean flow interaction.
M* Age $T_{\rm eff}$ $L/L_{\odot}$ log $\left({M_{\rm cz}/{M_*}}\right)$ $R_{\rm cz}/{R_*}$ $\ell _{\rm c}$ $\nu _{\rm c}$ $K_{\rm T}$ $\nu _{\rm max}$
($M_{\odot}$) (Gyr) (K)         ($\mu$Hz) (cm2 s-1) ($\mu$Hz)
0.60 zams 4985 0.14 -1.18 0.271 57 0.517 $2.43 \times 10^5$ 1.25
  10 5125 0.18 -1.30 0.263 59 0.614 $4.38 \times 10^5$ 1.25
0.65 zams 5245 0.21 -1.44 0.236 67 0.751 $7.79 \times 10^5$ 1.25
  10 5436 0.29 -1.66 0.229 69 0.879 $1.71 \times 10^6$ 1.25
0.70 zams 5490 0.30 -1.77 0.206 78 1.05 $2.37 \times 10^6$ 1.25
  10 5725 0.47 -2.22 0.181 90 1.68 $1.14 \times 10^7$ 1.25
0.75 zams 5720 0.42 -2.18 0.176 92 1.50 $6.89 \times 10^6$ 1.25
  10 6015 0.78 -3.15 0.125 132 4.27 $1.68 \times 10^8$ 1.85
0.80 zams 5935 0.57 -2.79 0.131 126 3.29 $4.31 \times 10^7$ 1.85
  10 6342 1.37 -4.15 0.065 259 26.1 $1.42 \times 10^{10}$ 6.25
0.82 zams 6010 0.64 -3.04 0.119 140 3.96 $6.56 \times 10^7$ 1.85
  10 6503 1.80 -5.96 0.041 392 8.02 $2.91 \times 10^{11}$ 17.5
0.85 zams 6140 0.76 -3.55 0.094 175 7.02 $2.22 \times 10^8$ 2.50
  10 6810 2.92 -8.23 0.010 1110 384 $2.80 \times 10^{13}$ *
0.9 zams 6370 0.99 -4.56 0.062 270 20.9 $2.39 \times 10^9$ 3.75
* No oscillation occurs in this model.


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