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Table 1.

Results from the least-squares fit of an ABL function in the form of Eqs. (1) and (2) (upper portion of the table); Eqs. (3) and (4) (middle portion of the table), or Eqs. (5) and (6) (lower part of the table).

α β γ δ n nrej Mode Δϖ Case σABL AIC
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
MKS, 0 or W(J, KS) = α + β(logߕP −logߕP0)
−5.840 ± 0.023 −3.061 ± 0.070 – – 373 47 F 0.0490 (K) 0.0095 −2594
−5.794 ± 0.021 −3.027 ± 0.090 – – 373 55 F 0.0615 (K) 0.0091 −2533
−5.762 ± 0.028 −3.012 ± 0.086 – – 373 53 F 0.0700 (K) 0.0098 −2533
−6.131 ± 0.027 −3.219 ± 0.078 – – 373 45 F 0.0490 (K, JK) 0.0091 −2666
−6.072 ± 0.024 −3.185 ± 0.085 – – 373 51 F 0.0615 (K, JK) 0.0086 −2635
−6.027 ± 0.016 −3.200 ± 0.087 – – 373 40 F 0.0700 (K, JK) 0.0090 −2631
−4.223 ± 0.082 −2.836 ± 0.474 – – 50 2 1O 0.0490 (K) 0.0109 −366
−4.190 ± 0.117 −2.788 ± 0.533 – – 50 2 1O 0.0615 (K) 0.0101 −364
−4.166 ± 0.091 −2.780 ± 0.453 – – 50 2 1O 0.0700 (K) 0.0107 −365
−4.457 ± 0.101 −2.889 ± 0.425 – – 50 2 1O 0.0490 (K, JK) 0.0091 −382
−4.430 ± 0.092 −2.786 ± 0.371 – – 50 5 1O 0.0615 (K, JK) 0.0078 −363
−4.404 ± 0.082 −2.802 ± 0.428 – – 50 4 1O 0.0700 (K, JK) 0.0087 −370
MKS, 0 or W(J, KS) = α + β(logߕP −logߕP0)+γ[Fe/H]
−5.837 ± 0.030 −3.053 ± 0.093 −0.039 ± 0.151 – 373 46 F 0.0490 (K) 0.0096 −2600
−5.785 ± 0.027 −3.015 ± 0.089 −0.082 ± 0.138 – 373 55 F 0.0615 (K) 0.0091 −2532
−5.746 ± 0.022 −2.992 ± 0.077 −0.141 ± 0.140 – 373 54 F 0.0700 (K) 0.0098 −2527
−6.121 ± 0.027 −3.216 ± 0.067 −0.084 ± 0.145 – 373 41 F 0.0490 (K, JK) 0.0093 −2684
−6.033 ± 0.029 −3.171 ± 0.065 −0.284 ± 0.115 – 373 34 F 0.0615 (K, JK) 0.0093 −2698
−5.991 ± 0.027 −3.148 ± 0.069 −0.356 ± 0.171 – 373 33 F 0.0700 (K, JK) 0.0098 −2686
−4.237 ± 0.128 −2.869 ± 0.641 0.225 ± 0.255 – 50 1 1O 0.0490 (K) 0.0108 −368
−4.204 ± 0.106 −2.787 ± 0.426 0.161 ± 0.295 – 50 3 1O 0.0615 (K) 0.0098 −357
−4.175 ± 0.107 −2.739 ± 0.517 0.101 ± 0.298 – 50 5 1O 0.0700 (K) 0.0088 −341
−4.447 ± 0.120 −2.893 ± 0.412 −0.111 ± 0.228 – 50 2 1O 0.0490 (K, JK) 0.0101 −381
−4.408 ± 0.108 −2.788 ± 0.427 −0.253 ± 0.230 – 50 5 1O 0.0615 (K, JK) 0.0082 −363
−4.381 ± 0.099 −2.761 ± 0.484 −0.304 ± 0.254 – 50 5 1O 0.0700 (K, JK) 0.0079 −362
MKS, 0 or W(J, KS) = α + (β + δ[Fe/H])(logߕP − logߕP0)+γ[Fe/H]
−5.837 ± 0.023 −3.064 ± 0.101 −0.044 ± 0.170 0.086 ± 0.673 373 49 F 0.0490 (K) 0.0096 −2579
−5.771 ± 0.030 −3.112 ± 0.111 −0.185 ± 0.191 0.704 ± 0.650 373 30 F 0.0615 (K) 0.0111 −2626
−5.731 ± 0.033 −3.111 ± 0.095 −0.256 ± 0.158 0.866 ± 0.587 373 27 F 0.0700 (K) 0.0113 −2607
−6.130 ± 0.035 −3.274 ± 0.117 −0.078 ± 0.164 0.507 ± 0.528 373 38 F 0.0490 (K, JK) 0.0096 −2690
−6.044 ± 0.025 −3.234 ± 0.118 −0.237 ± 0.157 0.465 ± 0.592 373 35 F 0.0615 (K, JK) 0.0096 −2698
−6.005 ± 0.025 −3.241 ± 0.093 −0.283 ± 0.160 0.727 ± 0.564 373 26 F 0.0700 (K, JK) 0.0103 −2716

Notes.

The functional form of the PW relation is labelled in the table. P0 is the pivoting period, whose logarithm is equal to 1.0 and 0.3 for DCEP_Fs and DCEP_1Os, respectively. The different columns provide (1–4) coefficients of the non-linear fit and their relative errors; (5–6) total number of available DCEPs and number of sources rejected during the fitting procedure; (7) pulsation mode; (8) adopted Gaia parallax offset (in mas); (9) case; (10) rms of the residuals of the ABL function; (11) AIC value (see text).

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