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Table A.1.
PL relations of the form M = α + β log P.
| α | β | N | Constraints | |
|---|---|---|---|---|
| GDR2 parallaxes | ||||
| V band | ||||
| −1.984 ± 0.121 | −2.326 ± 0.115 | 425 | all | |
| −1.985 ± 0.136 | −2.321 ± 0.134 | 419 | |GOF|< 100 | |
| −1.956 ± 0.043 | −2.337 ± 0.049 | 376 | |GOF|< 20 | |
| −2.033 ± 0.051 | −2.220 ± 0.061 | 293 | |GOF|< 10 | |
| −2.049 ± 0.055 | −2.201 ± 0.066 | 250 | |GOF|< 8 | |
| −2.138 ± 0.074 | −2.084 ± 0.092 | 197 | |GOF|< 6 | |
| −2.134 ± 0.090 | −2.093 ± 0.110 | 113 | |GOF|< 4 | |
| −2.047 ± 0.055 | −2.202 ± 0.067 | 248 | |GOF|< 8, ɛi < 0.001 |GOF|< 8, ɛ i < 0.001, and ... | |
| −1.881 ± 0.057 | −2.416 ± 0.065 | 211 | FU | |
| −2.661 ± 0.176 | −1.344 ± 0.247 | 37 | FO | |
| −1.852 ± 0.060 | −2.446 ± 0.068 | 205 | FU, P >2.5d | |
| −1.857 ± 0.060 | −2.441 ± 0.068 | 200 | FU, P >3.0d | |
| −1.869 ± 0.059 | −2.431 ± 0.070 | 185 | FU, P >3.5d | |
| −1.911 ± 0.080 | −2.393 ± 0.093 | 159 | FU, P >2.5d, |GOF|< 6 | |
| −1.882 ± 0.115 | −2.363 ± 0.131 | 90 | FU, P >2.5d, |GOF|< 4 | |
| −1.847 ± 0.072 | −2.457 ± 0.086 | 202 | FU, P >2.5d, P <35 | |
| −1.886 ± 0.060 | −2.415 ± 0.068 | 207 | FU, no uncertain types | |
| −1.794 ± 0.058 | −2.385 ± 0.066 | 205 | FU, P >2.5d, ZPoff =−0.029 mas | |
| −1.759 ± 0.057 | −2.353 ± 0.065 | 205 | FU, P >2.5d, ZPoff =−0.046 mas | |
| −1.883 ± 0.113 | −2.443 ± 0.126 | 205 | FU, P >2.5d, δ PL = 0.20 | |
| K band | ||||
| −2.980 ± 0.031 | −3.060 ± 0.038 | 425 | all | |
| −2.985 ± 0.029 | −3.051 ± 0.035 | 419 | |GOF|< 100 | |
| −3.008 ± 0.031 | −3.023 ± 0.036 | 376 | |GOF|< 20 | |
| −3.073 ± 0.036 | −2.929 ± 0.045 | 294 | |GOF|< 10 | |
| −3.083 ± 0.039 | −2.907 ± 0.048 | 250 | |GOF|< 8 | |
| −3.171 ± 0.053 | −2.787 ± 0.067 | 197 | |GOF|< 6 | |
| −3.209 ± 0.063 | −2.769 ± 0.081 | 113 | |GOF|< 4 | |
| −3.081 ± 0.039 | −2.907 ± 0.045 | 248 | |GOF|< 8, ɛi < 0.001 |GOF|< 8, ɛi < 0.001, and ... | |
| −2.985 ± 0.041 | −3.083 ± 0.048 | 211 | FU | |
| −3.622 ± 0.125 | −1.974 ± 0.192 | 37 | FO | |
| −2.953 ± 0.044 | −3.119 ± 0.051 | 205 | FU, P >2.5d | |
| −2.964 ± 0.044 | −3.107 ± 0.052 | 200 | FU, P >3.0d | |
| −2.992 ± 0.052 | −3.079 ± 0.060 | 185 | FU, P >3.5d | |
| −3.017 ± 0.057 | −3.053 ± 0.069 | 159 | FU, P >2.5d, |GOF|< 6 | |
| −3.146 ± 0.075 | −2.869 ± 0.094 | 90 | FU, P >2.5d, |GOF|< 4 | |
| −3.181 ± 0.091 | −2.829 ± 0.107 | 76 | FU, P >3.5d, |GOF|< 4 | |
| −2.957 ± 0.044 | −3.117 ± 0.053 | 201 | FU, P >2.5d, no uncertain | |
| −2.918 ± 0.047 | −3.166 ± 0.060 | 202 | FU, P >2.5d, P <35 | |
| −2.894 ± 0.042 | −3.055 ± 0.048 | 205 | FU, P >2.5d, ZPoff =−0.029 mas | |
| −2.861 ± 0.040 | −3.021 ± 0.047 | 205 | FU, P >2.5d, ZPoff =−0.046 mas | |
| −2.957 ± 0.053 | −3.114 ± 0.061 | 205 | FU, P >2.5d, δ PL = 0.066 | |
| WVK band | ||||
| −3.114 ± 0.031 | −3.158 ± 0.038 | 425 | all | |
| −3.118 ± 0.030 | −3.149 ± 0.036 | 419 | |GOF|< 100 | |
| −3.149 ± 0.031 | −3.113 ± 0.037 | 376 | |GOF|< 20 | |
| −3.213 ± 0.035 | −3.020 ± 0.045 | 293 | |GOF|< 10 | |
| −3.221 ± 0.038 | −2.998 ± 0.048 | 250 | |GOF|< 8 | |
| −3.311 ± 0.052 | −2.876 ± 0.068 | 197 | |GOF|< 6 | |
| −3.360 ± 0.063 | −2.849 ± 0.082 | 113 | |GOF|< 4 | |
| −3.221 ± 0.038 | −2.998 ± 0.045 | 248 | |GOF|< 8, ɛ i < 0.001 | |
| |GOF|< 8, ɛ i < 0.001, and ... | ||||
| −3.136 ± 0.042 | −3.167 ± 0.049 | 211 | FU | |
| −3.747 ± 0.134 | −2.027 ± 0.204 | 37 | FO | |
| −3.101 ± 0.043 | −3.203 ± 0.051 | 205 | FU, P >2.5d | |
| −3.113 ± 0.043 | −3.191 ± 0.052 | 200 | FU, P >3.0d | |
| −3.145 ± 0.051 | −3.159 ± 0.060 | 200 | FU, P >3.5d | |
| −3.168 ± 0.057 | −3.133 ± 0.068 | 159 | FU, P >2.5d, |GOF|< 6 | |
| −3.322 ± 0.075 | −2.926 ± 0.092 | 90 | FU, P >2.5d, |GOF|< 4 | |
| −3.374 ± 0.091 | −2.864 ± 0.106 | 76 | FU, P >3.5d, |GOF|< 4 | |
| −3.105 ± 0.044 | −3.202 ± 0.053 | 201 | FU, P >2.5d, no uncertain | |
| −3.062 ± 0.048 | −3.256 ± 0.060 | 202 | FU, P >2.5d, P <35 | |
| −3.043 ± 0.041 | −3.140 ± 0.048 | 205 | FU, P >2.5d, ZPoff =−0.029 mas | |
| −3.009 ± 0.040 | −3.105 ± 0.046 | 205 | FU, P >2.5d, ZPoff =−0.046 mas | |
| −3.103 ± 0.049 | −3.201 ± 0.057 | 205 | FU, P >2.5d, δ PL = 0.049 | |
| −3.064 ± 0.054 | −3.257 ± 0.066 | 202 | FU, P >2.5d, δ PL = 0.049, P <35 | |
| −3.032 ± 0.058 | −3.278 ± 0.070 | 157 | FU, P >2.5d, δ PL = 0.049, P <35, π > 0, σ π /π < 0.2 | |
| −2.994 ± 0.065 | −3.296 ± 0.082 | 85 | FU, P >2.5d, δ PL = 0.049, P <35, π > 0, σ π /π < 0.1 | |
| −2.995 ± 0.118 | −3.294 ± 0.159 | 23 | FU, P >2.5d, δ PL = 0.049, P <35, π > 0, σ π /π < 0.05 | |
| GDR2+external parallaxes | ||||
| V band | ||||
| −1.924 ± 0.046 | −2.355 ± 0.054 | 426 | all | |
| −1.931 ± 0.045 | −2.353 ± 0.054 | 425 | no Polaris | |
| −1.813 ± 0.051 | −2.490 ± 0.057 | 374 | FU | |
| −2.417 ± 0.144 | −1.680 ± 0.197 | 52 | FO | |
| −2.437 ± 0.139 | −1.659 ± 0.196 | 51 | FO, no Polaris | |
| −1.813 ± 0.052 | −2.490 ± 0.059 | 373 | FU, GOF < 100 | |
| −1.831 ± 0.045 | −2.464 ± 0.051 | 345 | FU, GOF < 20 | |
| −1.887 ± 0.051 | −2.379 ± 0.058 | 265 | FU, GOF < 10 | |
| −1.882 ± 0.058 | −2.380 ± 0.065 | 225 | FU, GOF < 8 | |
| −1.878 ± 0.054 | −2.384 ± 0.062 | 223 | FU, GOF < 8, ɛ i < 0.001 |GOF|< 8, ɛ i < 0.001, and ... | |
| −1.856 ± 0.058 | −2.407 ± 0.068 | 217 | FU, P >2.5d | |
| −1.856 ± 0.060 | −2.405 ± 0.066 | 212 | FU, P >3.0d | |
| −1.852 ± 0.055 | −2.411 ± 0.064 | 197 | FU, P >3.5d | |
| −1.858 ± 0.056 | −2.410 ± 0.065 | 213 | FU, P >2.5d, no uncertain | |
| −1.840 ± 0.070 | −2.430 ± 0.081 | 213 | FU, P >2.5d, P <35 | |
| −1.795 ± 0.057 | −2.361 ± 0.066 | 217 | FU, P >2.5d, ZPoff =−0.029 mas | |
| −1.760 ± 0.056 | −2.335 ± 0.065 | 217 | FU, P >2.5d, ZPoff =−0.046 mas | |
| −1.882 ± 0.105 | −2.406 ± 0.117 | 217 | FU, P >2.5d, δ PL = 0.20 | |
| −1.886 ± 0.056 | −2.378 ± 0.063 | 221 | FU, GOF < 8, no uncertain | |
| −1.812 ± 0.054 | −2.346 ± 0.061 | 221 | FU, GOF < 8, no uncertain, ZPoff =−0.029 mas | |
| −1.771 ± 0.054 | −2.328 ± 0.062 | 221 | FU, GOF < 8, no uncertain, ZPoff =−0.046 mas | |
| −1.767 ± 0.062 | −2.323 ± 0.069 | 221 | FU, GOF < 8, no uncertain, ZPoff =−0.046 mas, σ π · 1.3 | |
| −2.14 ± 0.18 | −1.98 ± 0.27 | 112 | FU, GOF < 8, P < 6 | |
| −1.81 ± 0.085 | −2.45 ± 0.085 | 113 | FU, GOF < 8, P > 6 | |
| −1.87 ± 0.10 | −2.40 ± 0.14 | 157 | FU, GOF < 8, P < 8 | |
| −1.68 ± 0.15 | −2.54 ± 0.13 | 68 | FU, GOF < 8, P > 8 | |
| −1.870 ± 0.060 | −2.433 ± 0.069 | 358 | FU, V > 6.3 | |
| −1.884 ± 0.059 | −2.411 ± 0.068 | 214 | FU, V > 6.3, GOF < 8 | |
| −1.539 ± 0.035 | −2.81 fixed | 1 | Polaris | |
| −1.542 ± 0.015 | −2.81 fixed | 225 | FU, GOF < 8 K band | |
| −2.912 ± 0.029 | −3.076 ± 0.035 | 426 | all | |
| −2.907 ± 0.034 | −3.151 ± 0.040 | 374 | FU | |
| −2.977 ± 0.042 | −3.048 ± 0.049 | 225 | FU, GOF < 8 | |
| −2.981 ± 0.039 | −3.045 ± 0.047 | 221 | FU, GOF < 8, no uncertain |GOF|< 8, ɛ i < 0.001, and ... | |
| −2.943 ± 0.042 | −3.084 ± 0.051 | 217 | FU, GOF < 8, P > 2.5d | |
| −2.950 ± 0.042 | −3.075 ± 0.048 | 212 | FU, GOF < 8, P > 3.0d | |
| −2.957 ± 0.049 | −3.069 ± 0.056 | 197 | FU, GOF < 8, P > 3.5d | |
| −2.911 ± 0.048 | −3.130 ± 0.058 | 213 | FU, GOF < 8, P > 2.5, P <35d | |
| −2.882 ± 0.040 | −3.037 ± 0.048 | 217 | FU, GOF < 8, P > 2.5d, ZPoff =−0.029 mas | |
| −2.848 ± 0.039 | −3.011 ± 0.047 | 217 | FU, GOF < 8, P > 2.5d, ZPoff =−0.046 mas | |
| −2.946 ± 0.052 | −3.084 ± 0.060 | 217 | FU, GOF < 8, P > 2.5d, δ PL = 0.066 | |
| −2.976 ± 0.042 | −3.051 ± 0.050 | 220 | FU, GOF < 8, no uncertain, P > 2d | |
| −2.956 ± 0.042 | −3.074 ± 0.051 | 209 | FU, GOF < 8, no uncertain, P > 3d | |
| −2.959 ± 0.050 | −3.070 ± 0.058 | 180 | FU, GOF < 8, no uncertain, P > 4d | |
| −2.805 ± 0.061 | −3.214 ± 0.066 | 140 | FU, GOF < 8, no uncertain, P > 5d | |
| −2.915 ± 0.076 | −3.119 ± 0.077 | 110 | FU, GOF < 8, no uncertain, P > 6d | |
| −2.917 ± 0.071 | −3.012 ± 0.072 | 110 | FU, GOF < 8, no uncertain, P > 6d, ZPoff =−0.029 mas | |
| −2.915 ± 0.071 | −2.956 ± 0.070 | 110 | FU, GOF < 8, no uncertain, P > 6d, ZPoff =−0.046 mas | |
| −2.897 ± 0.095 | −3.111 ± 0.096 | 110 | FU, GOF < 8, no uncertain, P > 6d, ZPoff =−0.000 mas, σ π · 1.3 | |
| −2.765 ± 0.008 | −3.26 fixed | 426 | all | |
| −2.484 ± 0.028 | −3.26 fixed | 1 | Polaris | |
| −2.735 ± 0.010 | −3.26 fixed | 269 | GOF < 8 | |
| −2.807 ± 0.010 | −3.26 fixed | 225 | FU, GOF < 8 WVK band | |
| −3.045 ± 0.030 | −3.174 ± 0.035 | 426 | all | |
| −3.122 ± 0.036 | −3.026 ± 0.045 | 269 | GOF < 8 | |
| −3.125 ± 0.042 | −3.133 ± 0.048 | 225 | GOF < 8, FU | |
| −3.609 ± 0.042 | −2.093 ± 0.200 | 44 | GOF < 8, FO | |
| −3.092 ± 0.042 | −3.166 ± 0.050 | 218 | GOF < 8, FU, P > 2.5d | |
| −3.099 ± 0.041 | −3.161 ± 0.047 | 213 | GOF < 8, FU, P > 3.0d | |
| −3.108 ± 0.048 | −3.151 ± 0.055 | 197 | GOF < 8, FU, P > 3.5d | |
| −3.060 ± 0.048 | −3.210 ± 0.060 | 214 | GOF < 8, FU, P > 2.5, P <35d | |
| −3.031 ± 0.041 | −3.119 ± 0.048 | 218 | GOF < 8, FU, P > 2.5d, ZPoff =−0.029 mas | |
| −2.996 ± 0.040 | −3.093 ± 0.048 | 218 | GOF < 8, FU, P > 2.5d, ZPoff =−0.046 mas | |
| −3.095 ± 0.047 | −3.166 ± 0.053 | 218 | GOF < 8, FU, P > 2.5d, δ PL = 0.049 | |
Notes. N is the number of stars in the solution.
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