The Hubble Constant

TL;DR

This work synthesizes the cosmological role and measurement of the Hubble constant, organizing six high‑precision distance indicators—Cepheids, TRGB, masers, SBF, Tully‑Fisher, and SNe Ia—into an integrated framework for constraining $H_0$. It outlines the underlying physics, calibration strategies, and pertinent systematics, emphasizing geometric and standardizable‑candle approaches to anchor the distance scale. The authors report a current best estimate of $H_0 = 73 \pm 2$ (random) $\pm 4$ (systematic) ${\rm km\,s^{-1}\,Mpc^{-1}}$, and discuss how future missions (GAIA, Spitzer, JWST, Planck, etc.) and additional maser and SN calibrators aim to reduce uncertainties to ~2%. The paper also highlights the broader significance of a precise $H_0$ for constraining dark energy, neutrino masses, and cosmological curvature, and outlines a concrete path toward achieving this precision in the coming decade.

Abstract

Considerable progress has been made in determining the Hubble constant over the past two decades. We discuss the cosmological context and importance of an accurate measurement of the Hubble constant, and focus on six high-precision distance-determination methods: Cepheids, tip of the red giant branch, maser galaxies, surface brightness fluctuations, the Tully-Fisher relation and Type Ia supernovae. We discuss in detail known systematic errors in the measurement of galaxy distances and how to minimize them. Our best current estimate of the Hubble constant is 73 +/-2 (random) +/-4 (systematic) km/s/Mpc. The importance of improved accuracy in the Hubble constant will increase over the next decade with new missions and experiments designed to increase the precision in other cosmological parameters. We outline the steps that will be required to deliver a value of the Hubble constant to 2% systematic uncertainty and discuss the constraints on other cosmological parameters that will then be possible with such accuracy.

Figures (13)

• Figure 1: From Hubble (1929a): radial velocities, corrected for solar motion, plotted versus distances estimated from stars and mean luminosities of galaxies in clusters. The solid dots and line represent the solution for solar motion using individual galaxies. Hubble wrote: "The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect, and hence that numerical data may be introduced into discussions of the general curvature of space."
• Figure 2: The cumulative probability density distribution of 180 distance modulus estimates to the LMC culled from the recent literature, provided by NED. Individual estimates are shown by unit-area gaussians with a dispersion set to their quoted statistical errors. The thin solid line represents the renormalized sum of those gaussians. The thick broken line represents the value of 18.39 mag and a systematic error of $\pm$0.03 mag for the true (Wesenheit) distance modulus to the LMC, based on the Galactic parallax calibration for Cepheids and corrected for metallicity by -0.05 mag. For comparison the median value of the published, non-Cepheid distance moduli is 18.44$\pm$0.16 mag (shown as the circled point and error bar); the mode of the non-Cepheid moduli is 18.47 mag. The Cepheid value is statistically indistinguishable from this highly heterogeneous, but fairly complete, set of independently published determinations.
• Figure 3: Composite multiwavelength Period-Luminosity relations (Leavitt Laws) for Galactic (circled filled dots) and LMC (open circles) Cepheids from the optical (BVI) through the near-infrared (JHK). There is a monotonic increase in the slope, coupled with a dramatic decrease in total dispersion of the PL relations as one goes to longer and longer wavelengths.
• Figure 4: Standard extinction-curve fit to six multiwavength (BVIJHK) apparent distance moduli to the LMC scaled to the HST Galactic parallax sample (Benedict et al. 2007). The minimized-$\chi^2$ scaled fit gives a true distance modulus (intercept) of 18.40$\pm$0.01 mag, uncorrected for metallicity, and a total line-of-sight color excess (slope) of E(B-V) = 0.10 mag.
• Figure 5: The reddening-free VI Wesenheit PL relation showing the combined data for Galactic Cepheids having individually-determined trigonometric parallaxes (circled dots) and Large Magellanic Cloud Cepheids (open circles) brought into coincidence with the Galactic calibration after an offset of 18.44 mag between their apparent magnitudes. The solid line is a fit to the combined data. The dashed line is the calibration used by Freedman et al. (2001) at the conclusion of the Key Project. The inner bounding box shows the period and luminosity range used by the Key Project to determine extragalactic distances. The correspondence between the two calibrations is very close, but it should be noted that the Galactic calibration is for Galactic metallicity.