A joint 1% calibration of the RR Lyrae and type-II Cepheid Leavitt laws yields homogeneous distances to 93 Galactic globular clusters

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Volume 706 (February 2026)

A&A, 706 (2026) A87

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Table E.1

Fitting results for each variant.

Variant	$χ_{dof}^{2}$ $\chi_{\text {dof }}^{2}$	N^a/N^h	RRab				RRc				T2Cep
			$N_{}^{a} / N_{}^{h}$ $N_{}^{a}/N_{}^{h}$	α₀	β₀	α_M	$N_{}^{a} / N_{}^{h}$ $N_{}^{a}/N_{}^{h}$	Δ α₀	β₀	α_M	$N_{}^{a} / N_{}^{h}$ $N_{}^{a}/N_{}^{h}$	Δ α₀	β₀	α_M
Baseline	0.989	37/56	399/403	−0.300(20)	−2.582(47)	−0.028(8)	166/179	0.303(5)	−2.497(95)	0.013(10)	14/7	−3.107(19)	−2.506(39)	0.107(43)
MCMC	0.989	37/56	399/403	−0.299(20)	−2.582(47)	−0.028(8)	166/179	0.303(5)	−2.497(94)	0.013(10)	14/7	−3.107(19)	−2.506(39)	0.107(42)
Outlier Rejection
No OR	6.297	37/56	407/437	−0.278(20)	−2.497(47)	−0.061(8)	172/197	0.314(5)	−2.052(94)	0.025(9)	14/7	−3.128(19)	−2.292(38)	−0.089(42)
κ=5.0	1.410	37/56	404/424	−0.296(20)	−2.574(47)	−0.028(8)	170/192	0.295(5)	−2.387(94)	0.021(10)	14/7	−3.116(19)	−2.494(39)	0.048(42)
κ=3.5	1.069	37/56	400/405	−0.298(20)	−2.581(47)	−0.031(8)	166/185	0.301(5)	−2.499(95)	0.011(10)	14/7	−3.110(19)	−2.510(39)	0.107(43)
κ=3.0	0.723	37/56	392/387	−0.310(20)	−2.540(48)	0.015(9)	165/175	0.300(5)	−2.509(96)	0.022(10)	14/7	−3.080(19)	−2.421(40)	−0.046(45)
κ=2.5	0.497	36/56	366/335	−0.314(20)	−2.560(49)	0.016(9)	160/166	0.303(5)	−2.561(97)	0.024(10)	12/7	−3.076(20)	−2.431(41)	−0.049(45)
Metallicities
Muraveva	1.047	37/53	399/402	−0.298(20)	−2.599(50)	−0.031(10)	92/74	0.296(6)	−2.302(138)	0.030(22)	14/7	−3.109(19)	−2.495(40)	0.116(43)
Cluster	0.845	36/56	397/398	−0.293(21)	−2.562(48)	−0.015(55)	166/183	0.299(5)	−2.600(80)	0.006(56)	10/7	−3.075(20)	−2.398(41)	−0.102(70)
Parallaxes
Median	1.010	38/55	377/425	−0.312(20)	−2.585(47)	−0.027(8)	151/195	0.303(5)	−2.504(95)	0.012(10)	11/10	−3.107(19)	−2.505(39)	0.106(43)
G<19	0.990	37/56	399/403	−0.295(20)	−2.581(47)	−0.028(8)	166/179	0.303(5)	−2.497(95)	0.012(10)	14/7	−3.108(19)	−2.506(39)	0.107(43)
14.5<G<19	0.989	38/55	400/402	−0.299(20)	−2.581(47)	−0.028(8)	167/178	0.303(5)	−2.497(95)	0.012(10)	14/7	−3.108(19)	−2.509(39)	0.109(43)
VB21	0.989	40/53	402/400	−0.278(20)	−2.580(47)	−0.028(8)	168/177	0.303(5)	−2.498(95)	0.012(10)	14/7	−3.107(19)	−2.503(39)	0.106(43)
Models
No RRab*	0.578	29/43	−	−	−	−	164/182	−0.002(23)*	−2.526(102)	0.013(11)	7/7	−3.365(25)*	−2.328(67)	−0.198(70)
No RRc	1.170	35/52	399/405	−0.290(21)	−2.567(50)	−0.032(9)	−	−	−	−	14/7	−3.105(19)	−2.490(40)	0.114(43)
No T2Cep	0.897	34/55	399/402	−0.294(21)	−2.564(47)	−0.033(8)	166/182	0.302(5)	−2.508(95)	0.008(10)	−	−	−	−
β_{0, RRc}=β_{0, RRab}	1.053	37/56	400/404	−0.299(20)	−2.568(43)	−0.030(8)	166/181	0.302(5)	RRab	0.007(8)	14/7	−3.110(19)	−2.509(39)	0.108(43)
β_0,T2Cep=β_0,RRab	1.018	37/56	399/404	−0.301(20)	−2.534(30)	−0.028(8)	166/179	0.305(5)	−2.487(95)	0.013(10)	14/7	−3.112(18)	RRab	0.122(40)
β_0,T2Cep=β_0,RRc	0.988	37/56	399/403	−0.299(20)	−2.582(47)	−0.028(8)	166/179	0.303(5)	−2.505(36)	0.012(8)	14/7	−3.107(18)	RRc	0.107(42)
β_0,T2Cep=β_0,RRc=β_0,RRab	1.017	37/56	399/404	−0.301(20)	−2.530(29)	−0.027(8)	166/179	0.305(5)	RRab	0.010(8)	14/7	−3.111(18)	RRab	0.120(40)
α_M,RRc=α_M,RRab	0.831	36/56	397/398	−0.296(20)	−2.531(47)	0.017(7)	166/181	0.301(5)	−2.567(77)	RRab	10/7	−3.075(20)	−2.397(41)	−0.093(44)
No α_M	0.857	36/56	398/403	−0.295(20)	−2.554(47)	−	166/181	0.299(5)	−2.647(71)	−	10/7	−3.094(19)	−2.454(34)	−
β → β₀+β_M[Fe/H]	0.964	37/56	399/402	−0.303(20)	−2.654(49) −0.393(78)	−0.003(9)	166/179	0.306(5)	−2.505(96) 0.048(110)	0.014(10)	14/7	−3.107(19)	−2.506(39)	0.103(43)
β → β₀+β_M[Fe/H] + No α_M	0.862	36/56	398/398	−0.299(20)	−2.590(50) −0.372(66)	−	166/183	0.304(5)	−2.586(80)0.083(102)	−	10/7	−3.071(20)	−2.401(41)	−0.098(44)
β → β₀+β_M[Fe/H]_Cl	0.863	36/56	398/403	−0.292(22)	−2.565(49) 0.015(151)	−0.015(56)	166/183	0.299(5)	−2.599(81) 0.059(171)	0.005(56)	10/7	−3.079(20)	−2.399(41)	−0.111(70)
⁻ β → β₀+β_M [Fe/H]Cl_Cl + No α_M	0.860	36/56	398/402	−0.295(20)	−2.546(47) −0.077(132)	−	166/183	0.301(5)	−2.635(75)0.105(167)	−	10/7	−3.077(20)	−2.400(41)	−0.105(44)
Pre-processing
σ_extra=0	36/56	2.283	400/401	−0.293(19)	−2.538(26)	−0.026(4)	166/181	0.294(3)	−2.495(50)	0.002(6)	10/6	−3.087(10)	−2.418(22)	−0.145(23)
σ_extra=0.025	36/56	1.462	400/403	−0.293(20)	−2.570(35)	−0.037(6)	166/182	0.299(4)	−2.506(69)	0.005(7)	10/6	−3.085(14)	−2.409(30)	−0.147(35)
σ_extra=0.075	36/56	0.482	396/401	−0.309(21)	−2.524(68)	0.015(12)	166/181	0.303(7)	−2.551(138)	0.019(14)	12/7	−3.083(29)	−2.394(57)	−0.114(64)
Anchors Criteria
S/N=5	1.024	71/22	608/195	−0.300(19)	−2.570(47)	−0.029(8)	269/76	0.305(5)	−2.494(95)	0.013(10)	18/3	−3.107(19)	−2.508(39)	0.106(43)
S/N=20	0.956	10/83	120/680	−0.334(25)	−2.611(48)	−0.004(9)	46/300	0.301(5)	−2.543(95)	0.018(10)	2/19	−3.117(19)	−2.522(40)	0.127(43)
E(B–V)=∞	0.989	38/55	401/401	−0.300(20)	−2.582(47)	−0.028(8)	166/179	0.303(5)	−2.497(95)	0.013(10)	15/6	−3.107(19)	−2.505(39)	0.107(43)
E(B–V)=0.5	0.818	29/63	354/440	−0.290(22)	−2.540(48)	0.013(9)	145/200	0.302(5)	−2.548(95)	0.019(10)	7/10	−3.071(20)	−2.403(41)	−0.057(45)

Notes. ^(*) In that case, the calibration of RRc is absolute (i.e., α_0,RRc) and not relative (Δ α_0,RRc). Similarly, the calibration of T2Cep (Δ α_0,RRc) is relative to RRc, as there is no RRab calibration.

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