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Table A.1

Mass accreted before critical rotation is reached (ΔM) by the different models.

M τ KH k 2 ΔMP81 Ṁ j a ΔM j a ΔM j a ΔM j a ΔM j a ΔM j a ΔM
Z = 10-4; MAGB = 1.0 M⊙; tmt = 6.3 Gyr; uniform rotation
0.600 65.0 0.128 0.091 0.01 0.2 > 0.35 0.5 0.236 1.0 0.103 2.0 0.050 1.758 0.050 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.098 1.0 0.079 2.0 0.050 1.758 0.050 ... ...
... ... ... ... 1.0 0.2 0.275 0.5 0.258 1.0 0.112 2.0 0.054 1.758 0.054 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.758 − ... ...
0.625 56.2 0.120 0.088 0.01 0.2 > 0.35 0.5 0.228 1.0 0.103 2.0 0.049 1.836 0.048 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.099 1.0 0.060 2.0 0.045 1.836 0.044 ... ...
... ... ... ... 1.0 0.2 0.183 0.5 0.184 1.0 0.105 2.0 0.051 1.836 0.051 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.836 − ... ...
0.650 48.7 0.112 0.085 0.01 0.2 > 0.35 0.5 0.220 1.0 0.101 2.0 0.047 1.914 0.046 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.104 1.0 0.052 2.0 0.038 1.914 0.037 ... ...
... ... ... ... 1.0 0.2 0.132 0.5 0.116 1.0 0.092 2.0 0.048 1.914 0.047 ... ...
... ... ... ... 10.0 0.2 − 0.5 > 0.35 1.0 − 2.0 − 1.914 − ... ...
0.675 42.1 0.105 0.081 0.01 0.2 > 0.35 0.5 0.213 1.0 0.099 2.0 0.047 1.995 0.045 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.111 1.0 0.052 2.0 0.029 1.995 0.028 ... ...
... ... ... ... 1.0 0.2 0.127 0.5 0.065 1.0 0.066 2.0 0.044 1.995 0.041 ... ...
... ... ... ... 10.0 0.2 > 0.35 0.5 > 0.35 1.0 0.109 2.0 0.048 1.995 0.046 ... ...
0.700 36.5 0.097 0.077 0.01 0.2 > 0.35 0.5 0.206 1.0 0.096 2.0 0.047 2.080 0.042 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.123 1.0 0.054 2.0 0.028 2.080 0.024 ... ...
... ... ... ... 1.0 0.2 0.135 0.5 0.056 1.0 0.035 2.0 0.034 2.080 0.033 ... ...
... ... ... ... 10.0 0.2 0.297 0.5 0.236 1.0 0.099 2.0 0.046 2.080 0.042 ... ...
0.725 31.6 0.089 0.073 0.01 0.2 > 0.35 0.5 0.202 1.0 0.094 2.0 0.046 2.168 0.040 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.137 1.0 0.056 2.0 0.029 2.168 0.024 ... ...
... ... ... ... 1.0 0.2 0.157 0.5 0.060 1.0 0.032 2.0 0.019 2.168 0.017 ... ...
... ... ... ... 10.0 0.2 0.118 0.5 0.117 1.0 0.079 2.0 0.042 2.168 0.036 ... ...
0.750 27.3 0.082 0.068 0.01 0.2 > 0.35 0.5 0.199 1.0 0.091 2.0 0.045 2.262 0.037 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.152 1.0 0.060 2.0 0.030 2.262 0.023 ... ...
... ... ... ... 1.0 0.2 0.184 0.5 0.066 1.0 0.035 2.0 0.020 2.262 0.015 ... ...
... ... ... ... 10.0 0.2 0.051 0.5 0.037 1.0 0.039 2.0 0.032 2.262 0.028 ... ...
0.775 23.6 0.075 0.063 0.01 0.2 > 0.35 0.5 0.201 1.0 0.089 2.0 0.043 2.361 0.035 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.168 1.0 0.064 2.0 0.030 2.361 0.023 ... ...
... ... ... ... 1.0 0.2 0.220 0.5 0.072 1.0 0.037 2.0 0.020 2.361 0.015 ... ...
... ... ... ... 10.0 0.2 0.048 0.5 0.027 1.0 0.018 2.0 0.012 2.361 0.011 ... ...
0.800 20.2 0.067 0.058 0.01 0.2 > 0.35 0.5 0.210 1.0 0.087 2.0 0.042 2.466 0.033 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.183 1.0 0.068 2.0 0.032 2.466 0.023 ... ...
... ... ... ... 1.0 0.2 0.269 0.5 0.078 1.0 0.040 2.0 0.022 2.466 0.015 ... ...
... ... ... ... 10.0 0.2 0.053 0.5 0.029 1.0 0.019 2.0 0.011 2.466 0.008 ... ...
0.825 17.4 0.061 0.054 0.01 0.2 > 0.35 0.5 0.220 1.0 0.086 2.0 0.041 2.578 0.031 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.196 1.0 0.072 2.0 0.034 2.578 0.024 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 0.086 1.0 0.043 2.0 0.023 2.578 0.016 ... ...
... ... ... ... 10.0 0.2 0.059 0.5 0.031 1.0 0.020 2.0 0.012 2.578 0.008 ... ...
Z = 10-4; MAGB = 1.5 M⊙; tmt = 1.8 Gyr; uniform rotation
0.600 72.2 0.135 0.098 0.01 0.2 > 0.35 0.5 0.247 1.0 0.109 2.0 0.054 1.736 0.054 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.113 1.0 0.089 2.0 0.054 1.736 0.054 ... ...
... ... ... ... 1.0 0.2 − 0.5 0.330 1.0 0.120 2.0 0.058 1.736 0.058 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.736 − ... ...
0.625 63.5 0.128 0.095 0.01 0.2 > 0.35 0.5 0.242 1.0 0.110 2.0 0.052 1.809 0.052 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.104 1.0 0.072 2.0 0.050 1.809 0.050 ... ...
... ... ... ... 1.0 0.2 0.229 0.5 0.228 1.0 0.116 2.0 0.055 1.809 0.055 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.809 − ... ...
0.650 56.1 0.122 0.093 0.01 0.2 > 0.35 0.5 0.238 1.0 0.110 2.0 0.051 1.881 0.051 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.108 1.0 0.055 2.0 0.045 1.881 0.044 ... ...
... ... ... ... 1.0 0.2 0.164 0.5 0.160 1.0 0.108 2.0 0.053 1.881 0.052 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.881 − ... ...
0.675 49.6 0.115 0.091 0.01 0.2 > 0.35 0.5 0.235 1.0 0.109 2.0 0.051 1.954 0.049 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.117 1.0 0.055 2.0 0.037 1.954 0.036 ... ...
... ... ... ... 1.0 0.2 0.142 0.5 0.102 1.0 0.092 2.0 0.051 1.954 0.049 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.954 − ... ...
0.700 44.1 0.109 0.088 0.01 0.2 > 0.35 0.5 0.232 1.0 0.109 2.0 0.052 2.028 0.048 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.130 1.0 0.057 2.0 0.031 2.028 0.028 ... ...
... ... ... ... 1.0 0.2 0.152 0.5 0.066 1.0 0.064 2.0 0.047 2.028 0.044 ... ...
... ... ... ... 10.0 0.2 > 0.35 0.5 0.349 1.0 0.121 2.0 0.053 2.028 0.049 ... ...
0.725 39.3 0.103 0.086 0.01 0.2 > 0.35 0.5 0.231 1.0 0.108 2.0 0.052 2.102 0.046 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.148 1.0 0.060 2.0 0.031 2.102 0.027 ... ...
... ... ... ... 1.0 0.2 0.176 0.5 0.064 1.0 0.038 2.0 0.036 2.102 0.035 ... ...
... ... ... ... 8.0 0.2 0.228 0.5 0.210 1.0 0.107 2.0 0.051 2.102 0.046 ... ...
0.750 35.2 0.098 0.083 0.01 0.2 > 0.35 0.5 0.233 1.0 0.108 2.0 0.052 2.178 0.045 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.168 1.0 0.064 2.0 0.032 2.178 0.026 ... ...
... ... ... ... 1.0 0.2 0.215 0.5 0.069 1.0 0.037 2.0 0.022 2.178 0.020 ... ...
... ... ... ... 10.0 0.2 0.142 0.5 0.143 1.0 0.093 2.0 0.048 2.178 0.042 ... ...
0.775 31.6 0.092 0.080 0.01 0.2 > 0.35 0.5 0.237 1.0 0.107 2.0 0.052 2.255 0.044 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.192 1.0 0.070 2.0 0.034 2.255 0.026 ... ...
... ... ... ... 1.0 0.2 0.278 0.5 0.077 1.0 0.040 2.0 0.022 2.255 0.018 ... ...
... ... ... ... 8.0 0.2 0.067 0.5 0.061 1.0 0.061 2.0 0.042 2.255 0.036 ... ...
0.800 28.4 0.087 0.077 0.01 0.2 > 0.35 0.5 0.251 1.0 0.107 2.0 0.052 2.334 0.042 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.220 1.0 0.076 2.0 0.036 2.334 0.027 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 0.085 1.0 0.044 2.0 0.024 2.334 0.018 ... ...
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 0.024 2.334 0.024 ... ...
0.825 25.6 0.082 0.075 0.01 0.2 > 0.35 0.5 0.271 1.0 0.108 2.0 0.052 2.412 0.041 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 0.247 1.0 0.082 2.0 0.038 2.412 0.027 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 0.093 1.0 0.048 2.0 0.026 2.412 0.019 ... ...
... ... ... ... 10.0 0.2 0.059 0.5 0.033 1.0 0.021 2.0 0.014 2.412 0.011 ... ...
Z = 0.008; MAGB = 3.0 M⊙; tmt = 422 Myr; uniform rotation
1.000 25.27 0.075 0.082 0.01 0.2 > 2.0 0.5 0.275 1.0 0.136 2.0 0.070 3.0 0.045 2.954 0.045
... ... ... ... 0.1 0.2 > 2.0 0.5 0.196 1.0 0.088 2.0 0.047 3.0 0.033 2.954 0.031
... ... ... ... 1.0 0.2 0.255 0.5 0.086 1.0 0.046 2.0 0.029 3.0 0.029 2.954 0.029
... ... ... ... 10.0 0.2 0.181 0.5 0.181 1.0 0.127 2.0 0.067 3.0 0.045 2.954 0.043
1.250 12.60 0.045 0.059 0.01 0.2 > 2.0 0.5 0.490 1.0 0.160 2.0 0.071 3.0 0.046 3.844 0.035
... ... ... ... 0.1 0.2 > 2.0 0.5 0.410 1.0 0.139 2.0 0.062 3.0 0.041 3.844 0.030
... ... ... ... 1.0 0.2 > 2.0 0.5 0.174 1.0 0.083 2.0 0.044 3.0 0.031 3.844 0.022
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 3.0 − 3.844 −
1.500 7.27 0.044 0.069 0.01 0.2 > 2.0 0.5 1.052 1.0 0.240 2.0 0.102 3.0 0.065 4.370 0.042
... ... ... ... 0.1 0.2 > 2.0 0.5 1.041 1.0 0.225 2.0 0.094 3.0 0.060 4.370 0.039
... ... ... ... 1.0 0.2 > 2.0 0.5 0.365 1.0 0.139 2.0 0.069 3.0 0.047 4.370 0.030
... ... ... ... 10.0 0.2 0.286 0.5 − 1.0 0.069 2.0 − 3.0 − 4.370 −
1.735 4.63 0.044 0.080 0.01 0.2 > 2.0 0.5 > 2.0 1.0 0.338 2.0 0.137 3.0 0.087 4.954 0.049
... ... ... ... 0.1 0.2 > 2.0 0.5 > 2.0 1.0 0.327 2.0 0.133 3.0 0.083 4.954 0.047
... ... ... ... 1.0 0.2 > 2.0 0.5 > 2.0 1.0 0.218 2.0 0.100 3.0 0.066 4.954 0.038
... ... ... ... 8.0 0.2 > 2.0 0.5 0.234 1.0 0.117 2.0 0.064 3.0 0.045 4.954 0.027
2.000 2.84 0.042 0.089 0.1 0.2 > 2.0 0.5 > 2.0 1.0 0.470 2.0 0.180 3.0 0.112 5.770 0.054
... ... ... ... 1.0 0.2 > 2.0 0.5 > 2.0 1.0 0.358 2.0 0.143 3.0 0.092 5.770 0.045
... ... ... ... 10.0 0.2 > 2.0 0.5 0.379 1.0 0.171 2.0 0.089 3.0 0.062 5.770 0.032
2.250 1.77 0.039 0.093 0.1 0.2 > 2.0 0.5 > 2.0 1.0 0.635 2.0 0.229 3.0 0.141 6.809 0.056
... ... ... ... 1.0 0.2 > 2.0 0.5 > 2.0 1.0 0.535 2.0 0.191 3.0 0.120 6.809 0.049
... ... ... ... 10.0 0.2 > 2.0 0.5 0.732 1.0 0.253 2.0 0.124 3.0 0.085 6.809 0.037
2.500 1.07 0.034 0.088 0.1 0.2 > 2.0 0.5 > 2.0 1.0 0.746 2.0 0.278 3.0 0.170 8.460 0.054
... ... ... ... 1.0 0.2 > 2.0 0.5 > 2.0 1.0 0.728 2.0 0.246 3.0 0.149 8.460 0.048
... ... ... ... 10.0 0.2 > 2.0 0.5 > 2.0 1.0 0.373 2.0 0.168 3.0 0.112 8.460 0.039
Z = 10-4; MAGB = 1.0 M⊙; tmt = 6.3 Gyr; differential rotation
0.600 65.0 0.128 0.091 0.01 0.2 > 0.35 0.5 > 0.35 1.0 − 2.0 − 1.758 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.004 2.0 0.004 1.758 0.004 ... ...
... ... ... ... 1.0 0.2 − 0.5 0.160 0.7 0.072 1.0 0.001 2.0 − 1.758 0.001
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.758 − ... ...
0.625 56.2 0.120 0.088 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 − 1.836 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 0.000 1.836 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 0.056 1.0 0.005 2.0 0.005 1.836 0.005
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.836 − ... ...
0.650 48.7 0.112 0.085 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 0.000 1.914 0.000 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 0.000 1.914 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 0.050 1.0 0.006 2.0 0.001 1.914 0.001
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.914 − ... ...
0.675 42.2 0.105 0.081 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 − 1.995 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 0.000 1.995 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 0.039 1.0 0.000 2.0 0.000 1.995 0.000
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 1.995 − ... ...
0.700 36.5 0.097 0.077 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 − 2.080 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 − 1.0 0.000 2.0 0.000 2.080 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 0.029 1.0 0.000 2.0 0.000 2.080 0.000
... ... ... ... 10.0 0.2 − 0.5 − 1.0 − 2.0 − 2.080 − ... ...
0.725 31.6 0.089 0.073 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 − 2.168 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.000 2.0 0.000 2.168 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 > 0.35 1.0 0.000 2.0 0.000 2.168 0.000
... ... ... ... 10.0 0.2 > 0.35 0.5 > 0.35 1.0 0.014 2.0 0.006 2.168 − ... ...
0.750 27.3 0.082 0.068 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.012 2.0 0.000 2.262 0.000 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.004 2.0 0.000 2.262 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 > 0.35 1.0 0.006 2.0 0.000 2.262 0.000
... ... ... ... 10.0 0.2 > 0.35 0.5 > 0.35 1.0 0.009 2.0 0.004 2.262 − ... ...
0.775 23.6 0.075 0.063 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.015 2.0 0.000 2.361 0.000 ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.001 2.0 0.000 2.361 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 > 0.35 1.0 0.002 2.0 0.000 2.361 0.000
... ... ... ... 10.0 0.2 > 0.35 0.5 > 0.35 1.0 0.004 2.0 0.000 2.361 − ... ...
0.800 20.2 0.067 0.059 0.01 0.2 > 0.35 0.5 > 0.35 1.0 0.015 2.0 0.000 2.466 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.001 2.0 0.000 2.466 0.000 ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 > 0.35 1.0 0.035 2.0 0.000 2.466 0.000
... ... ... ... 10.0 0.2 > 0.35 0.5 > 0.35 1.0 0.001 2.0 0.000 2.466 − ... ...
0.825 17.4 0.061 0.054 0.01 0.2 > 0.35 0.5 > 0.35 1.0 − 2.0 0.000 2.578 − ... ...
... ... ... ... 0.1 0.2 > 0.35 0.5 > 0.35 1.0 0.016 2.0 0.000 2.578 − ... ...
... ... ... ... 1.0 0.2 > 0.35 0.5 > 0.35 0.7 > 0.35 1.0 0.038 2.0 0.000 2.578 0.000
... ... ... ... 10.0 0.2 >0.35 0.5 >0.35 1.0 >0.35 2.0 0.000 2.578 − ... ...

Notes. The first five columns list the initial mass of the secondary (M); its Kelvin-Helmholtz timescale before mass addition (τKH, Myr); its gyration radius before mass addition (k2 = I/MR2); estimate of ΔM based on Packet (1981) (ΔMP81); mass accretion rate (Ṁ/ 10-6M⊙ yr-1). The remaining columns list pairs of specific angular momentum of the accreted material (ja in units of 1018 cm2 s-1) and the corresponding ΔM. The last pair in each row corresponds to ja = jK and the listed value of ja is the Keplerian specific angular momentum at the surface prior to mass addition. The table is sectioned according to the metallicity Z and initial primary mass MAGB (tmt is the age at which mass addition starts). All masses are in solar masses. If critical rotation was not reached by then, the CEMP and Ba star progenitor models were stopped when, respectively, 0.35 M⊙ and 2 M⊙ of material were accreted. A minus indicates failure of convergence. The values of tmt are from Lugaro et al. (2012) and Pols et al. (1998) for stars of Z = 10-4 and Z = 0.008, respectively.

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