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Table G.1.

Results of the photometric parallax fit to the PWZ relations with variations with respect to the baseline (see text).

Wesenheit α σαlow σαhigh β σβlow σβhigh γ σγlow σγhigh ϵ σϵlow σϵhigh N μLMC σμLMC AIC BIC
PWZ relations using sigma Clipping

Gaia -6.038 0.022 0.022 -3.309 0.034 0.035 -0.585 0.061 0.058 -0.015 0.003 0.003 268 18.491 0.042 716 730
VI_C89 -6.078 0.022 0.023 -3.273 0.036 0.037 -0.628 0.063 0.062 -0.012 0.003 0.003 267 18.418 0.043 639 654
VI_F99 -5.871 0.022 0.021 -3.183 0.037 0.037 -0.393 0.059 0.058 -0.019 0.003 0.002 274 18.467 0.039 766 781
cVI -5.877 0.021 0.021 -3.183 0.036 0.035 -0.278 0.059 0.059 -0.016 0.003 0.003 272 18.406 0.037 684 699
cHVI -6.001 0.021 0.021 -3.212 0.033 0.033 -0.564 0.058 0.057 -0.008 0.003 0.003 269 18.387 0.039 671 685
VKs -6.056 0.021 0.022 -3.286 0.033 0.034 -0.527 0.058 0.056 -0.006 0.003 0.003 268 18.418 0.039 679 694
JKs_C89 -6.105 0.022 0.021 -3.354 0.034 0.035 -0.369 0.058 0.056 -0.008 0.003 0.003 271 18.447 0.038 717 732
JKs_F99 -6.149 0.022 0.022 -3.375 0.035 0.034 -0.374 0.057 0.057 -0.007 0.003 0.003 271 18.456 0.038 728 742

PWZ relations using F-mode pulsators only

Gaia -5.963 0.038 0.039 -3.37 0.071 0.073 -0.724 0.123 0.115 -0.005 0.005 0.005 170 18.329 0.076 240 252
VI_C89 -6.006 0.038 0.038 -3.3 0.074 0.075 -0.758 0.124 0.121 -0.002 0.005 0.005 168 18.278 0.078 204 216
VI_F99 -5.775 0.036 0.037 -3.162 0.07 0.071 -0.729 0.121 0.119 -0.005 0.005 0.005 172 18.244 0.075 233 245
cVI -5.808 0.035 0.036 -3.195 0.068 0.069 -0.478 0.118 0.114 -0.006 0.005 0.005 171 18.249 0.069 197 209
cHVI -5.937 0.035 0.036 -3.276 0.067 0.068 -0.648 0.112 0.108 -0.001 0.005 0.005 170 18.26 0.068 208 220
VKs -5.995 0.036 0.036 -3.346 0.068 0.068 -0.613 0.115 0.111 0.002 0.005 0.005 171 18.291 0.071 224 237
JKs_C89 -6.031 0.036 0.037 -3.374 0.069 0.069 -0.506 0.116 0.115 0.003 0.005 0.005 171 18.307 0.071 220 232
JKs_F99 -6.073 0.037 0.038 -3.395 0.069 0.069 -0.513 0.117 0.113 0.004 0.005 0.005 171 18.313 0.071 222 235

PWZ relations using the total metallicity [M/H]

Gaia -6.0 0.038 0.039 -3.31 0.052 0.054 -0.701 0.121 0.117 -0.014 0.004 0.004 270 18.555 0.056 352 366
VI_C89 -6.024 0.039 0.04 -3.268 0.056 0.057 -0.815 0.126 0.123 -0.01 0.005 0.004 267 18.463 0.059 298 313
VI_F99 -5.813 0.037 0.038 -3.163 0.056 0.055 -0.61 0.122 0.122 -0.015 0.004 0.004 274 18.461 0.056 350 364
cVI -5.834 0.036 0.037 -3.165 0.053 0.053 -0.452 0.117 0.114 -0.013 0.004 0.004 272 18.397 0.051 317 331
cHVI -5.96 0.036 0.036 -3.213 0.049 0.051 -0.699 0.111 0.109 -0.008 0.004 0.004 270 18.439 0.052 323 337
VKs -6.021 0.036 0.038 -3.28 0.049 0.05 -0.666 0.112 0.109 -0.005 0.004 0.004 271 18.47 0.053 344 359
JKs_C89 -6.057 0.037 0.037 -3.337 0.051 0.051 -0.554 0.115 0.113 -0.004 0.004 0.004 271 18.45 0.053 327 341
JKs_F99 -6.1 0.037 0.038 -3.357 0.051 0.052 -0.564 0.116 0.111 -0.004 0.004 0.004 271 18.458 0.053 331 345

PWZ relations using DCEPs with G < 12.5 mag only.

Gaia -6.072 0.045 0.046 -3.313 0.059 0.06 -0.453 0.12 0.117 -0.022 0.007 0.006 140 18.577 0.074 184 196
VI_C89 -6.102 0.045 0.045 -3.268 0.064 0.062 -0.518 0.127 0.123 -0.018 0.007 0.007 139 18.49 0.078 163 175
VI_F99 -5.869 0.044 0.043 -3.17 0.062 0.063 -0.367 0.127 0.121 -0.021 0.006 0.006 141 18.482 0.076 169 180
cVI -5.86 0.042 0.042 -3.166 0.058 0.059 -0.293 0.12 0.116 -0.014 0.006 0.006 140 18.391 0.07 154 166
cHVI -5.999 0.041 0.042 -3.207 0.055 0.056 -0.469 0.114 0.107 -0.009 0.006 0.006 140 18.426 0.068 173 185
VKs -6.057 0.042 0.042 -3.276 0.054 0.055 -0.401 0.109 0.109 -0.006 0.007 0.006 140 18.475 0.068 179 191
JKs_C89 -6.091 0.044 0.044 -3.333 0.056 0.057 -0.302 0.115 0.113 -0.006 0.007 0.007 140 18.471 0.071 159 170
JKs_F99 -6.134 0.043 0.045 -3.353 0.057 0.059 -0.314 0.117 0.114 -0.006 0.007 0.007 140 18.476 0.071 163 175

Notes. C89 and F99 refer to the Cardelli et al. (1989) and Fitzpatrick (1999) extinction laws, respectively. The values of σlow and σhigh list the 16th and 84th percentiles of the posterior probability, respectively (see text). The units of α,  β,  γ,  ϵ and of their uncertainties are mag, mag/dex, mag/dex and mas, respectively.

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