A gravitational-wave standard siren measurement of the Hubble constant

Abstract

The detection of GW170817 in both gravitational waves and electromagnetic waves heralds the age of gravitational-wave multi-messenger astronomy. On 17 August 2017 the Advanced LIGO and Virgo detectors observed GW170817, a strong signal from the merger of a binary neutron-star system. Less than 2 seconds after the merger, a gamma-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO-Virgo-derived location of the gravitational-wave source. This sky region was subsequently observed by optical astronomy facilities, resulting in the identification of an optical transient signal within $\sim 10$ arcsec of the galaxy NGC 4993. These multi-messenger observations allow us to use GW170817 as a standard siren, the gravitational-wave analog of an astronomical standard candle, to measure the Hubble constant. This quantity, which represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Our measurement combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using electromagnetic data. This approach does not require any form of cosmic "distance ladder;" the gravitational wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be $70.0^{+12.0}_{-8.0} \, \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$ (maximum a posteriori and 68% credible interval). This is consistent with existing measurements, while being completely independent of them. Additional standard-siren measurements from future gravitational-wave sources will provide precision constraints of this important cosmological parameter.

Figures (5)

• Figure 1: GW170817 measurement of $H_0$. Marginalized posterior density for $H_0$ (blue curve). Constraints at $1$- and $2\sigma$ from Planck Planck2016 and SHoES Riess2016 are shown in green and orange. The maximum a posteriori value and minimal $68.3\%$ credible interval from this PDF is $H_0 = 70.0^{+12.0}_{-8.0}\, \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$. The $68.3\%$ ($1\sigma$) and $95.4\%$ ($2\sigma$) minimal credible intervals are indicated by dashed and dotted lines.
• Figure 1: Graphical model illustrating the statistical relationships between the data and parameters. Open circles indicate parameters which require a prior; filled circles described measured data, which are conditioned on in the analysis. Here we assume we have measurements of the GW data, $x_{\mathrm{GW}}$, a recessional velocity (i.e. redshift), $v_r$, and the mean peculiar velocity in the neighborhood of NGC 4993, $\left\langle v_p \right\rangle$. Arrows flowing into a node indicate that the conditional probability density for the node depends on the source parameters; for example, the conditional distribution for the observed GW data, $p\left( x_{\mathrm{GW}} \mid d, \cos \iota \right)$, discussed in the text, depends on the distance and inclination of the source (and additional parameters, here marginalized out).
• Figure 2: Inference on $H_0$ and inclination. Posterior density of $H_0$ and $\cos \iota$ from the joint GW-EM analysis (blue contours). Shading levels are drawn at every $5\%$ credible level, with the $68.3\%$ ($1\sigma$, solid) and $95.4\%$ ($2\sigma$, dashed) contours in black. Values of $H_0$ and $1$- and $2\sigma$ error bands are also displayed from Planck Planck2016 and SHoES Riess2016. As noted in the text, inclination angles near $180\deg$ ($\cos \iota = -1$) indicate that the orbital angular momentum is anti-parallel with the direction from the source to the detector.
• Figure 2: Using different assumptions compared to our canonical analysis. The posterior distribution on $H_0$ discussed in the main text is shown in black, the alternative flat prior on $z$ (discussed in the Methods section) gives the distribution shown in blue, and the increased uncertainty ($250 \, \mathrm{km} \, \mathrm{s}^{-1}$) applied to our peculiar velocity measurement (also discussed in the Methods section) is shown in pink. Minimal $68.3\%$ ($1\sigma$) credible intervals are shown by dashed lines.
• Figure 3: Constraints on the inclination angle of GW170817. Posterior density on $\cos \iota$, for various assumptions about the prior distribution of $H_0$. The analysis of the joint GW and EM data with a $1/H_0$ prior density gives the blue curve; using values of $H_0$ from Planck Planck2016 and SHoES Riess2016 as a prior on $H_0$ give the green and red curves, respectively. Choosing a narrow prior on $H_0$ converts the precise Hubble velocity measurements for the group containing NGC 4993 to a precise distance measurement, breaking the distance inclination degeneracy, and leading to strong constraints on the inclination. Minimal $68.3\%$ ($1\sigma$) credible intervals are indicated by dashed lines. Because our prior on inclination is flat on $\cos \iota$ the densities in this plot are proportional to the marginalised likelihood for $\cos \iota$.