A blinded determination of $H_0$ from low-redshift Type Ia supernovae, calibrated by Cepheid variables

TL;DR

This study conducts a blinded, end-to-end reanalysis of Riess et al. (2011) to measure the Hubble constant $H_0$ by tying the local Cepheid distance scale to nearby SNe Ia and a larger low-$z$ SN sample via a covariance-based treatment of SN systematics. The authors implement a three-step fitting strategy—Cepheid-only, SN-only, and a global joint fit—using a Bayesian framework with priors and offsets to blind the $H_0$ value. Anchored by NGC 4258, LMC, and Milky Way distances, they obtain $H_0 = 72.5 ext{ km s}^{-1} ext{ Mpc}^{-1}$ with a statistical uncertainty of $3.1$ and a systematic of $0.77$ km s$^{-1}$ Mpc$^{-1}$, with a total relative uncertainty of about 4.4%. The analysis demonstrates the importance of incorporating SN covariance matrices and a simultaneous fit to all data, and confirms a persistent tension with Planck's CMB-derived $H_0$, while highlighting avenues for reducing systematics in future work (notably with Riess et al. 2016 data).

Abstract

Presently a ${>}3σ$ tension exists between values of the Hubble constant $H_0$ derived from analysis of fluctuations in the Cosmic Microwave Background by Planck, and local measurements of the expansion using calibrators of type Ia supernovae (SNe Ia). We perform a blinded reanalysis of Riess et al. 2011 to measure $H_0$ from low-redshift SNe Ia, calibrated by Cepheid variables and geometric distances including to NGC 4258. This paper is a demonstration of techniques to be applied to the Riess et at. 2016 data. Our end-to-end analysis starts from available CfA3 and LOSS photometry, providing an independent validation of Riess et al. 2011. We obscure the value of $H_0$ throughout our analysis and the first stage of the referee process, because calibration of SNe Ia requires a series of often subtle choices, and the potential for results to be affected by human bias is significant. Our analysis departs from that of Riess et al. 2011 by incorporating the covariance matrix method adopted in SNLS and JLA to quantify SN Ia systematics, and by including a simultaneous fit of all SN Ia and Cepheid data. We find $H_0 = 72.5 \pm 3.1$ (stat) $\pm 0.77$ (sys) km s$^{-1}$ Mpc$^{-1}$ with a three-galaxy (NGC 4258+LMC+MW) anchor. The relative uncertainties are 4.3% statistical, 1.1% systematic, and 4.4% total, larger than in Riess et al. 2011 (3.3% total) and the Efstathiou 2014 reanalysis (3.4% total). Our error budget for $H_0$ is dominated by statistical errors due to the small size of the supernova sample, whilst the systematic contribution is dominated by variation in the Cepheid fits, and for the SNe Ia, uncertainties in the host galaxy mass dependence and Malmquist bias.

Figures (10)

• Figure 1: The best-fitting values for $b_W, Z_W$ from all Cepheid-only fits to the Leavitt law (Equation \ref{['eq:pl2']}), assuming various distance anchors and rejection algorithms, with and without a cut on the period. The different markers represent these properties as indicated in the legends, with the colour representing the outlier rejection algorithm, shape representing the distance anchor, and solidness reflecting the period cut. We consider all seven combinations of distance anchor galaxies NGC 4258, LMC, and MW (Appendix \ref{['sec:anchors']}), and all three rejection algorithms (Appendix \ref{['sec:rejection']}). This figure shows: (i) including the longer-period Cepheids increases both $b_W$ and $Z_W$ (empty markers lie up and to the right of solid markers) (ii) Systematic variation in parameters with distance anchor (e.g. for each choice of period cut, the NGC 4258 + MW anchor gives the lowest $b_W$ and the NGC 4258-only anchor gives the highest); meanwhile fits with both the LMC and MW as anchors (diamonds and upward triangles, with and without NGC 4258 respectively) are clustered tightly, indicating that these two galaxies together provide a strong constraint on both parameters. (iii) The R11 rejection results in less negative $Z_W$ and to a lesser extent $b_W$ (reflected in orange markers concentrated in the upper-right portion of the figure), while the E14 algorithm with rejection threshold $T=2.5$ (turquoise) results in higher $Z_W$ compared to $T=2.25$ (green) for fits other than those with both the LMC and MW anchors. The typical uncertainties, indicated by the arrows, are ${\sim}0.05$ for $b_W$ and ${\sim}0.1$ for $Z_W$ for most fits, but can be larger for some anchors or rejection algorithms. Evidently the scatter arising from varying the distance anchor, cut on period, and rejection far exceeds the statistical uncertainty. The histograms in the margins display distributions of $b_W$ and $Z_W$ values over all fits. The histogram for $b_W$ shows that values are clustered around $b_W{\sim}-3.25$ for fits with a $P<60$ day cut (reflective of the influence of the LMC Cepheids) and $b_W{\sim}-3.10$ for fits without. The histogram for $Z_W$ shows a spread centred at $Z_W{\sim}-0.3$, dependent on distance anchor; fits with both the LMC and MW anchors lie with $-0.2 < Z_W < 0$.
• Figure 2: The best-fitting values for $\alpha, \beta$ from all SN-only fits to Equation \ref{['eq:sn2']}, assuming various cuts on the low-$z$ SNe. The different markers represent the cuts described in Section \ref{['sec:SNcuts']}. The typical statistical uncertainties are indicated by the arrows. The variation in $\alpha$ is comparable to the statistical uncertainty, and the same is true for $\beta$ if we disregard the higher low-redshift cut.
• Figure 3: Constraints on parameters in $\Theta$ from an example global MultiNest fit (with $T=2.25$, NGC 4258+LMC+MW anchor, $P<60$ day cut Cepheid fit, default SN cuts) marginalised over $\{\Delta\mu_i\}$. The shaded regions in the PDFs represent 1$\sigma$ levels, and the 1$\sigma$, 2$\sigma$, and 3$\sigma$ regions are shown in the contours. Note the strong degeneracy between $\mathcal{H}$ and $M_B$, and slightly weaker degeneracies between $\mathcal{H}, M_B, \mu_{4258}$, and $M_W$. The other parameters appear uncorrelated.
• Figure 4: The same fit as Fig. \ref{['fig:8dim']}, also marginalised over $\{\alpha,\beta,b_W,Z_W, \mu_{4258}\}$. This shows the three parameters that are the most highly correlated.
• Figure 5: Results of all global fits to Equations \ref{['eq:pl2']}--\ref{['eq:sn2']} simultaneously, in the (a) $b_W,Z_W$- (b) $M_B,M_W$- (c) $\alpha,\beta$- and (d) $M_B,\mathcal{H}$-planes, when assuming various choices of SN cut and Cepheid fit. As shown in the legends the different combinations of colour and fill encapsulate information on the choice of Cepheid fit as described in Section \ref{['sec:selection']}, while the different shapes represent difference cuts on the supernovae from Section \ref{['sec:SNresults']}. The chosen reference fits (bolded in Table \ref{['tab:SNfinal']} and \ref{['tab:cepheidfinal']}) are indicated by the violet arrows in (a) and (c). The overlap of points with the same colour and fill in (a) demonstrate that the Cepheid parameters $b_W, Z_W$ depend only on the Cepheid fit; similarly, the clusters of points with the same shape in (c) show that the SN Ia parameters $\alpha,\beta$ depend mostly on the SN cut. Subplot (b) shows that $M_W$ and $M_B$ both depend predominantly on the choice of Cepheid fit, with the effect more strong in $M_W$. A strong degeneracy between $M_B$ and $\mathcal{H}$ is evident in (d), indicating that $\mathcal{H}$ depends primarily on the Cepheid fit, and secondarily on the SN cut. There is no systematic difference in $M_W, M_B$, and $\mathcal{H}$ between fits with and without an upper limit on Cepheid period.