Stretch to stretch, dust to dust: Lower-value local H0 measurements from the two-population modelling of type Ia supernovae

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Table 1.

Best-fit hyperparameters of the prior probability distributions of the two-population mixture model.

	Hubble flow		Hubble flow + calibration sample
	old pop (low X₁)	young pop (high X₁)	old pop (low X₁)	young pop (high X₁)
${\hat{M}}_{B}$ $\widehat{M}_{\mathrm{B}}$	$- 19 . 37_{- 0.03}^{+ 0.03} (h = 0.7)$ $-19.37 ^{+ 0.03 }_{- 0.03 }\,(h=0.7)$	$- 19 . 33_{- 0.03}^{+ 0.03} (h = 0.7)$ $-19.33 ^{+ 0.03 }_{- 0.03 }\,(h=0.7)$	$- 19 . 34_{- 0.05}^{+ 0.05}$ $-19.34 ^{+ 0.05 }_{- 0.05 }$	$- 19 . 28_{- 0.04}^{+ 0.04}$ $-19.28 ^{+ 0.04 }_{- 0.04 }$
${\hat{X}}_{1, HF}$ $\widehat{X}_{1,\mathrm{HF}}$	$- 1 . 09_{- 0.13}^{+ 0.13}$ $-1.09 ^{+ 0.13 }_{- 0.13 }$	$0 . 60_{- 0.07}^{+ 0.07}$ $0.60 ^{+ 0.07 }_{- 0.07 }$	$- 1 . 12_{- 0.11}^{+ 0.11}$ $-1.12 ^{+ 0.11 }_{- 0.11 }$	$0 . 59_{- 0.06}^{+ 0.06}$ $0.59 ^{+ 0.06 }_{- 0.06 }$
σ_X₁, HF	$0 . 73_{- 0.08}^{+ 0.08}$ $0.73 ^{+ 0.08 }_{- 0.08 }$	$0 . 52_{- 0.04}^{+ 0.04}$ $0.52 ^{+ 0.04 }_{- 0.04 }$	$0 . 72_{- 0.07}^{+ 0.07}$ $0.72 ^{+ 0.07 }_{- 0.07 }$	$0 . 53_{- 0.04}^{+ 0.04}$ $0.53 ^{+ 0.04 }_{- 0.04 }$
$\hat{c_{int}}$ $\widehat{c_{\mathrm{int}}}$	$- 0 . 072_{- 0.011}^{+ 0.011}$ $-0.072 ^{+ 0.011 }_{- 0.011 }$	$- 0 . 075_{- 0.012}^{+ 0.012}$ $-0.075 ^{+ 0.012 }_{- 0.012 }$	$- 0 . 074_{- 0.011}^{+ 0.011}$ $-0.074 ^{+ 0.011 }_{- 0.011 }$	$- 0 . 067_{- 0.012}^{+ 0.012}$ $-0.067 ^{+ 0.012 }_{- 0.012 }$
σ_{c_int}	$0 . 041_{- 0.010}^{+ 0.010}$ $0.041 ^{+ 0.010 }_{- 0.010 }$	$0 . 051_{- 0.009}^{+ 0.009}$ $0.051 ^{+ 0.009 }_{- 0.009 }$	$0 . 039_{- 0.010}^{+ 0.010}$ $0.039 ^{+ 0.010 }_{- 0.010 }$	$0 . 059_{- 0.008}^{+ 0.008}$ $0.059 ^{+ 0.008 }_{- 0.008 }$
τ	$0 . 082_{- 0.011}^{+ 0.011}$ $0.082 ^{+ 0.011 }_{- 0.011 }$	$0 . 055_{- 0.012}^{+ 0.011}$ $0.055 ^{+ 0.011 }_{- 0.012 }$	$0 . 083_{- 0.011}^{+ 0.011}$ $0.083 ^{+ 0.011 }_{- 0.011 }$	$0 . 050_{- 0.012}^{+ 0.011}$ $0.050 ^{+ 0.011 }_{- 0.012 }$
$\hat{R_{B}}$ $\widehat{R_{\mathrm{B}}}$	$3 . 030_{- 0.177}^{+ 0.177}$ $3.030 ^{+ 0.177 }_{- 0.177 }$	$4 . 074_{- 0.494}^{+ 0.510}$ $4.074 ^{+ 0.510 }_{- 0.494 }$	$3 . 018_{- 0.171}^{+ 0.169}$ $3.018 ^{+ 0.169 }_{- 0.171 }$	$4 . 281_{- 0.610}^{+ 0.676}$ $4.281 ^{+ 0.676 }_{- 0.610 }$
σ_{R_B}	$0 . 323_{- 0.207}^{+ 0.191}$ $0.323 ^{+ 0.191 }_{- 0.207 }$	$0 . 915_{- 0.279}^{+ 0.313}$ $0.915 ^{+ 0.313 }_{- 0.279 }$	$0 . 316_{- 0.202}^{+ 0.188}$ $0.316 ^{+ 0.188 }_{- 0.202 }$	$0 . 934_{- 0.297}^{+ 0.329}$ $0.934 ^{+ 0.329 }_{- 0.297 }$
σ_{M_B}	$0 . 104_{- 0.011}^{+ 0.011}$ $0.104 ^{+ 0.011 }_{- 0.011 }$	$0 . 059_{- 0.017}^{+ 0.017}$ $0.059 ^{+ 0.017 }_{- 0.017 }$	$0 . 104_{- 0.011}^{+ 0.011}$ $0.104 ^{+ 0.011 }_{- 0.011 }$	$0 . 051_{- 0.018}^{+ 0.018}$ $0.051 ^{+ 0.018 }_{- 0.018 }$
α	$0 . 175_{- 0.014}^{+ 0.014}$ $0.175 ^{+ 0.014 }_{- 0.014 }$		$0 . 185_{- 0.012}^{+ 0.012}$ $0.185 ^{+ 0.012 }_{- 0.012 }$
β	$2 . 797_{- 0.231}^{+ 0.229}$ $2.797 ^{+ 0.229 }_{- 0.231 }$		$2 . 821_{- 0.182}^{+ 0.181}$ $2.821 ^{+ 0.181 }_{- 0.182 }$
f_o, HF = 1 − f_y, HF	$0 . 484_{- 0.055}^{+ 0.054}$ $0.484 ^{+ 0.054 }_{- 0.055 }$		$0 . 471_{- 0.047}^{+ 0.047}$ $0.471 ^{+ 0.047 }_{- 0.047 }$
f_o, cal = 1 − f_y, cal	–		≡0

Notes. These results were obtained from fitting type Ia supernovae in the Hubble flow (left) or from a joint analysis of the Hubble flow and calibration samples (right). Best-fit results are provided as the posterior mean values and errors given by credible intervals containing 68 per cent of the marginalised probabilities. Two parameters (α and β) are assumed to be the same in the two supernova populations. The parameters, ‘HF’ and ‘cal’, denote those used exclusively in the Hubble flow or the calibration sample.

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