Table 3.
Comparison of the β term of the PLZ relations for RR Lyrae models with those for BL Her models.
| Band | Mode | α | β | γ | σ | N | (|T|, p(t)) w.r.t. BL Her models from this work(a) | |||
|---|---|---|---|---|---|---|---|---|---|---|
| (LSST) | Set A | Set B | Set C | Set D | ||||||
| Complete set of models (0.5 − 0.8 M⊙) | ||||||||||
| r | F | 0.25 ± 0.02 | −1.35 ± 0.08 | 0.163 ± 0.014 | 0.128 | 155 | (5.476,0.0) | (2.786,0.005) | (3.888,0.0) | (2.298,0.022) |
| i | F | 0.21 ± 0.02 | −1.6 ± 0.07 | 0.163 ± 0.011 | 0.099 | 155 | (5.357,0.0) | (2.586,0.01) | (3.807,0.0) | (2.112,0.035) |
| z | F | 0.23 ± 0.02 | −1.73 ± 0.06 | 0.168 ± 0.01 | 0.087 | 155 | (5.648,0.0) | (2.554,0.011) | (4.012,0.0) | (2.114,0.035) |
| y | F | 0.23 ± 0.02 | −1.75 ± 0.06 | 0.167 ± 0.01 | 0.086 | 155 | (6.112,0.0) | (3.059,0.002) | (4.618,0.0) | (2.721,0.007) |
| Low-mass models only (0.5 − 0.6 M⊙) | ||||||||||
| r | F | 0.25 ± 0.02 | −1.35 ± 0.08 | 0.163 ± 0.014 | 0.128 | 155 | (0.606,0.545) | (0.666,0.505) | (1.843,0.066) | (1.558,0.12) |
| i | F | 0.21 ± 0.02 | −1.6 ± 0.07 | 0.163 ± 0.011 | 0.099 | 155 | (0.518,0.605) | (0.853,0.394) | (1.761,0.078) | (1.394,0.164) |
| z | F | 0.23 ± 0.02 | −1.73 ± 0.06 | 0.168 ± 0.01 | 0.087 | 155 | (0.389,0.698) | (1.155,0.248) | (1.787,0.074) | (1.315,0.189) |
| y | F | 0.23 ± 0.02 | −1.75 ± 0.06 | 0.167 ± 0.01 | 0.086 | 155 | (0.964,0.335) | (0.581,0.561) | (2.401,0.017) | (1.872,0.062) |
Notes. The PLZ relation is of the mathematical form Mλ = α + βlog(P)+γ[Fe/H]. The table includes our grid of BL Her models computed using four sets of convection parameters and fundamental-mode RR Lyrae models from Marconi et al. (2015). N is the total number of fundamental mode RR Lyrae 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 slopes can be rejected. aThe PLZ relations for the BL Her models are provided in Table C.3.
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