Open Access
Table C.2.
Comparison of the slopes of the PW relations for BL Her stars of the mathematical form: Wλ = alog(P)+b.
| Band | Source | a | b | σ | N | (|T|, p(t)) w.r.t. | ||
|---|---|---|---|---|---|---|---|---|
| (LSST) | Set A | Set B | Set C | |||||
| Complete set of models (0.5 − 0.8 M⊙) | ||||||||
| Wug | Zall (Set A) | -3.249±0.053 | -2.892±0.018 | 0.469 | 3266 | ... | ... | ... |
| Wug | Zall (Set B) | -2.946±0.064 | -2.942±0.021 | 0.488 | 2260 | (3.653,0.0) | ... | ... |
| Wug | Zall (Set C) | -3.615±0.063 | -2.792±0.022 | 0.529 | 2632 | (4.45,0.0) | (7.444,0.0) | ... |
| Wug | Zall (Set D) | -3.232±0.07 | -2.857±0.024 | 0.541 | 2122 | (0.194,0.846) | (3.009,0.003) | (4.057,0.0) |
| Wur | Zall (Set A) | -3.081±0.031 | -1.545±0.011 | 0.279 | 3266 | ... | ... | ... |
| Wur | Zall (Set B) | -2.876±0.038 | -1.589±0.012 | 0.29 | 2260 | (4.167,0.0) | ... | ... |
| Wur | Zall (Set C) | -3.254±0.037 | -1.517±0.013 | 0.307 | 2632 | (3.575,0.0) | (7.155,0.0) | ... |
| Wur | Zall (Set D) | -3.018±0.041 | -1.557±0.014 | 0.316 | 2122 | (1.218,0.223) | (2.554,0.011) | (4.282,0.0) |
| Wgr | Zall (Set A) | -2.965±0.019 | -0.624±0.007 | 0.172 | 3266 | ... | ... | ... |
| Wgr | Zall (Set B) | -2.826±0.023 | -0.665±0.008 | 0.178 | 2260 | (4.59,0.0) | ... | ... |
| Wgr | Zall (Set C) | -3.005±0.021 | -0.645±0.007 | 0.179 | 2632 | (1.386,0.166) | (5.671,0.0) | ... |
| Wgr | Zall (Set D) | -2.87±0.024 | -0.668±0.008 | 0.185 | 2122 | (3.054,0.002) | (1.341,0.18) | (4.179,0.0) |
| Wgi | Zall (Set A) | -2.765±0.017 | -0.431±0.006 | 0.152 | 3266 | ... | ... | ... |
| Wgi | Zall (Set B) | -2.628±0.02 | -0.462±0.007 | 0.154 | 2260 | (5.144,0.0) | ... | ... |
| Wgi | Zall (Set C) | -2.754±0.019 | -0.442±0.006 | 0.156 | 2632 | (0.439,0.661) | (4.555,0.0 | ... |
| Wgi | Zall (Set D) | -2.642±0.021 | -0.459±0.007 | 0.16 | 2122 | (4.548,0.0) | (0.482,0.63) | (3.991,0.0) |
| Wiz | Zall (Set A) | -2.384±0.02 | -0.149±0.007 | 0.181 | 3266 | ... | ... | ... |
| Wiz | Zall (Set B) | -2.219±0.023 | -0.164±0.007 | 0.174 | 2260 | (5.383,0.0) | ... | ... |
| Wiz | Zall (Set C) | -2.318±0.022 | -0.12±0.008 | 0.184 | 2632 | (2.207,0.027) | (3.115,0.002) | ... |
| Wiz | Zall (Set D) | -2.21±0.024 | -0.131±0.008 | 0.182 | 2122 | (5.574,0.0) | (0.282,0.778) | (3.344,0.001) |
| Wgy | Zall (Set A) | -2.557±0.018 | -0.278±0.006 | 0.164 | 3266 | ... | ... | ... |
| Wgy | Zall (Set B) | -2.401±0.021 | -0.3±0.007 | 0.161 | 2260 | (5.538,0.0) | ... | ... |
| Wgy | Zall (Set C) | -2.521±0.02 | -0.264±0.007 | 0.167 | 2632 | (1.341,0.18) | (4.095,0.0) | ... |
| Wgy | Zall (Set D) | -2.407±0.022 | -0.279±0.007 | 0.168 | 2122 | (5.243,0.0) | (0.191,0.849) | (3.835,0.0) |
| Low-mass models only (0.5 − 0.6 M⊙) | ||||||||
| Wug | Zall (Set A) | -3.046±0.095 | -2.808±0.031 | 0.472 | 1050 | ... | ... | ... |
| Wug | Zall (Set B) | -2.658±0.111 | -2.866±0.036 | 0.492 | 707 | (2.662,0.008) | ... | ... |
| Wug | Zall (Set C) | -3.496±0.111 | -2.687±0.038 | 0.544 | 856 | (3.079,0.002) | (5.35,0.0) | ... |
| Wug | Zall (Set D) | -3.037±0.115 | -2.771±0.04 | 0.552 | 711 | (0.055,0.956) | (2.378,0.018) | (2.862,0.004) |
| Wur | Zall (Set A) | -2.94±0.054 | -1.43±0.017 | 0.266 | 1050 | ... | ... | ... |
| Wur | Zall (Set B) | -2.695±0.062 | -1.475±0.02 | 0.276 | 707 | (2.995,0.003) | ... | ... |
| Wur | Zall (Set C) | -3.17±0.062 | -1.387±0.021 | 0.302 | 856 | (2.817,0.005) | (5.437,0.0) | ... |
| Wur | Zall (Set D) | -2.903±0.064 | -1.436±0.022 | 0.306 | 711 | (0.445,0.657) | (2.338,0.02) | (3.007,0.003) |
| Wgr | Zall (Set A) | -2.866±0.027 | -0.488±0.009 | 0.134 | 1050 | ... | ... | ... |
| Wgr | Zall (Set B) | -2.718±0.031 | -0.524±0.01 | 0.137 | 707 | (3.606,0.0) | ... | ... |
| Wgr | Zall (Set C) | -2.946±0.029 | -0.499±0.01 | 0.145 | 856 | (1.992,0.046) | (5.332,0.0) | ... |
| Wgr | Zall (Set D) | -2.809±0.031 | -0.523±0.011 | 0.147 | 711 | (1.385,0.166) | (2.098,0.036) | (3.203,0.001) |
| Wgi | Zall (Set A) | -2.621±0.02 | -0.301±0.007 | 0.099 | 1050 | ... | ... | ... |
| Wgi | Zall (Set B) | -2.505±0.022 | -0.32±0.007 | 0.097 | 707 | (3.931,0.0) | ... | ... |
| Wgi | Zall (Set C) | -2.684±0.021 | -0.291±0.007 | 0.105 | 856 | (2.168,0.03) | (5.894,0.0) | ... |
| Wgi | Zall (Set D) | -2.598±0.022 | -0.302±0.008 | 0.105 | 711 | (0.779,0.436) | (3.001,0.003) | (2.823,0.005) |
| Wiz | Zall (Set A) | -2.122±0.026 | -0.045±0.009 | 0.131 | 1050 | ... | ... | ... |
| Wiz | Zall (Set B) | -2.026±0.025 | -0.033±0.008 | 0.111 | 707 | (2.655,0.008) | ... | ... |
| Wiz | Zall (Set C) | -2.212±0.028 | 0.035±0.009 | 0.135 | 856 | (2.364,0.018) | (5.015,0.0) | ... |
| Wiz | Zall (Set D) | -2.172±0.028 | 0.037±0.01 | 0.132 | 711 | (1.298,0.194) | (3.924,0.0) | (1.042,0.297) |
| Wgy | Zall (Set A) | -2.345±0.022 | -0.164±0.007 | 0.112 | 1050 | ... | ... | ... |
| Wgy | Zall (Set B) | -2.234±0.022 | -0.166±0.007 | 0.099 | 707 | (3.494,0.0) | ... | ... |
| Wgy | Zall (Set C) | -2.43±0.024 | -0.112±0.008 | 0.116 | 856 | (2.612,0.009) | (6.026,0.0) | ... |
| Wgy | Zall (Set D) | -2.362±0.024 | -0.117±0.008 | 0.114 | 711 | (0.54,0.59) | (3.926,0.0) | (2.008,0.045) |
Notes. The theoretical relations are derived for the cases of the complete set of models and for the low mass models. N is the total number of models. |T| represents the observed value of the t-statistic, and p(t) gives the probability of acceptance of the null hypothesis (equal slopes). The bold-faced entries indicate that the null hypothesis of the equivalent PL slopes can be rejected.
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