Open Access
Table C.1.
Comparison of the slopes of the PL relations for BL Her stars of the mathematical form: Mλ = 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⊙) | ||||||||
| u | Zall (Set A) | -0.834±0.044 | 0.815±0.015 | 0.39 | 3266 | ... | ... | ... |
| u | Zall (Set B) | -0.589±0.046 | 0.848±0.015 | 0.352 | 2260 | (3.843,0.0 | ... | ... |
| u | Zall (Set C) | -0.475±0.05 | 0.944±0.017 | 0.418 | 2632 | (5.412,0.0) | (1.69,0.091) | ... |
| u | Zall (Set D) | -0.405±0.052 | 0.952±0.018 | 0.4 | 2122 | (6.308,0.0) | (2.65,0.008) | (0.961,0.336) |
| g | Zall (Set A) | -1.423±0.035 | -0.089±0.012 | 0.312 | 3266 | ... | ... | ... |
| g | Zall (Set B) | -1.164±0.036 | -0.077±0.012 | 0.278 | 2260 | (5.121,0.0) | ... | ... |
| g | Zall (Set C) | -1.241±0.038 | 0.033±0.013 | 0.319 | 2632 | (3.53,0.0) | (1.45,0.147) | ... |
| g | Zall (Set D) | -1.095±0.039 | 0.023±0.013 | 0.302 | 2122 | (6.241,0.0) | (1.297,0.195) | (2.669,0.008) |
| r | Zall (Set A) | -1.829±0.028 | -0.23±0.01 | 0.253 | 3266 | ... | ... | ... |
| r | Zall (Set B) | -1.602±0.03 | -0.232±0.01 | 0.231 | 2260 | (5.466,0.0) | ... | ... |
| r | Zall (Set C) | -1.705±0.031 | -0.146±0.011 | 0.26 | 2632 | (2.947,0.003) | (2.387,0.017) | ... |
| r | Zall (Set D) | -1.563±0.032 | -0.159±0.011 | 0.249 | 2122 | (6.199,0.0) | (0.888,0.375) | (3.193,0.001) |
| i | Zall (Set A) | -2.01±0.025 | -0.238±0.009 | 0.225 | 3266 | ... | ... | ... |
| i | Zall (Set B) | -1.804±0.027 | -0.245±0.009 | 0.209 | 2260 | (5.509,0.0) | ... | ... |
| i | Zall (Set C) | -1.902±0.028 | -0.175±0.01 | 0.232 | 2632 | (2.871,0.004) | (2.514,0.012) | ... |
| i | Zall (Set D) | -1.771±0.029 | -0.188±0.01 | 0.224 | 2122 | (6.189,0.0) | (0.826,0.409) | (3.262,0.001) |
| z | Zall (Set A) | -2.099±0.024 | -0.217±0.008 | 0.214 | 3266 | ... | ... | ... |
| z | Zall (Set B) | -1.903±0.026 | -0.226±0.009 | 0.199 | 2260 | (5.507,0.0) | ... | ... |
| z | Zall (Set C) | -2.001±0.026 | -0.162±0.009 | 0.219 | 2632 | (2.751,0.006) | (2.647,0.008) | ... |
| z | Zall (Set D) | -1.876±0.028 | -0.174±0.009 | 0.213 | 2122 | (6.093,0.0) | (0.718,0.473) | (3.294,0.001) |
| y | Zall (Set A) | -2.15±0.023 | -0.21±0.008 | 0.209 | 3266 | ... | ... | ... |
| y | Zall (Set B) | -1.957±0.026 | -0.22±0.008 | 0.196 | 2260 | (5.537,0.0) | ... | ... |
| y | Zall (Set C) | -2.061±0.025 | -0.158±0.009 | 0.214 | 2632 | (2.565,0.01) | (2.869,0.004) | ... |
| y | Zall (Set D) | -1.936±0.027 | -0.17±0.009 | 0.208 | 2122 | (5.979,0.0) | (0.569,0.569) | (3.367,0.001) |
| Low-mass models only (0.5 − 0.6 M⊙) | ||||||||
| u | Zall (Set A) | -0.235±0.071 | 0.858±0.023 | 0.351 | 1050 | ... | ... | ... |
| u | Zall (Set B) | -0.198±0.067 | 0.958±0.022 | 0.3 | 707 | (0.38,0.704) | ... | ... |
| u | Zall (Set C) | -0.252±0.081 | 1.122±0.028 | 0.396 | 856 | (0.155,0.877) | (0.512,0.609) | ... |
| u | Zall (Set D) | -0.388±0.08 | 1.169±0.028 | 0.384 | 711 | (1.428,0.153) | (1.811,0.07) | (1.196,0.232) |
| g | Zall (Set A) | -0.92±0.055 | -0.036±0.018 | 0.274 | 1050 | ... | ... | ... |
| g | Zall (Set B) | -0.798±0.049 | 0.025±0.016 | 0.218 | 707 | (1.666,0.096) | ... | ... |
| g | Zall (Set C) | -1.043±0.059 | 0.193±0.02 | 0.29 | 856 | (1.513,0.13) | (3.193,0.001) | ... |
| g | Zall (Set D) | -1.034±0.057 | 0.208±0.02 | 0.274 | 711 | (1.427,0.154) | (3.136,0.002) | (0.107,0.915) |
| r | Zall (Set A) | -1.433±0.043 | -0.155±0.014 | 0.213 | 1050 | ... | ... | ... |
| r | Zall (Set B) | -1.304±0.039 | -0.12±0.013 | 0.172 | 707 | (2.237,0.025) | ... | ... |
| r | Zall (Set C) | -1.544±0.046 | 0.011±0.016 | 0.226 | 856 | (1.765,0.078) | (4.001,0.0) | ... |
| r | Zall (Set D) | -1.502±0.045 | 0.015±0.016 | 0.213 | 711 | (1.109,0.267) | (3.355,0.001) | (0.662,0.508) |
| i | Zall (Set A) | -1.664±0.037 | -0.152±0.012 | 0.182 | 1050 | ... | ... | ... |
| i | Zall (Set B) | -1.544±0.033 | -0.126±0.011 | 0.149 | 707 | (2.413,0.016) | ... | ... |
| i | Zall (Set C) | -1.761±0.039 | -0.018±0.014 | 0.194 | 856 | (1.791,0.073) | (4.185,0.0) | ... |
| i | Zall (Set D) | -1.718±0.038 | -0.015±0.013 | 0.184 | 711 | (1.011,0.312) | (3.408,0.001) | (0.778,0.437) |
| z | Zall (Set A) | -1.773±0.034 | -0.127±0.011 | 0.169 | 1050 | ... | ... | ... |
| z | Zall (Set B) | -1.659±0.031 | -0.104±0.01 | 0.139 | 707 | (2.47,0.014) | ... | ... |
| z | Zall (Set C) | -1.868±0.037 | -0.006±0.013 | 0.179 | 856 | (1.902,0.057) | (4.357,0.0) | ... |
| z | Zall (Set D) | -1.826±0.036 | -0.003±0.012 | 0.171 | 711 | (1.068,0.286) | (3.521,0.0) | (0.829,0.407) |
| y | Zall (Set A) | -1.833±0.033 | -0.118±0.011 | 0.164 | 1050 | ... | ... | ... |
| y | Zall (Set B) | -1.718±0.03 | -0.098±0.01 | 0.135 | 707 | (2.56,0.011) | ... | ... |
| y | Zall (Set C) | -1.932±0.035 | -0.002±0.012 | 0.173 | 856 | (2.041,0.041) | (4.591,0.0) | ... |
| y | Zall (Set D) | -1.885±0.035 | -0.0±0.012 | 0.165 | 711 | (1.09,0.276) | (3.632,0.0) | (0.942,0.346) |
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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