1 A gravitational-wave standard siren measurement of the 2 Hubble constant 1 2 3 3 B. Abbott , M. Others & E. M. Partners 1 4 LIGO 2 5 Virgo 3 6 Everywhere 7 P1700296-v3 8 September 29, 2017 9 We report the first determination of the Hubble constant, which is the local expansion rate 10 of the Universe, using gravitational wave measurements. The spiraling together of two com- 11 pact objects, such as neutron stars or black holes, is a “standard siren”: the waves emitted 12 tell us the distance to the binary. The observation by the LIGO and Virgo detectors of the 13 neutron-star merger event GW170817, combined with follow-up optical observations of the 14 post-merger explosion, allows us to measure both the distance and the recession velocity of 15 the standard siren’s host galaxy, NGC 4993, and thereby infer the Hubble constant. Our 16 measured value is consistent with existing estimates, while being completely independent of 17 them. Future gravitational wave observations of merger events will enable more precise mea- 18 surements of the Hubble constant. 1 19 The detection of GW170817 heralds the age of multi-messenger astronomy, with the obser- 1 20 vations of gravitational-wave (GW) and electromagnetic (EM) emission from the same transient 21 source. On 17 August 2017 the network of Advanced Laser Interferometer Gravitational-wave 2 3 22 Observatory (LIGO) and Virgo detectors observed GW170817, a strong signal from the merger 2 23 of a compact-object binary. The source was localized to a region of 28 deg (90% credible re- 4 24 gion). Independently, the Fermi Gamma-Ray Burst Monitor (GBM) detected a weak Gamma Ray 25 Burst (GRB) event GRB170817A consistent with the same sky region, less than 2 seconds after the 5–7 26 compact binary merger . The LIGO-Virgo localization region was subsequently observed by a 8 27 number of optical astronomy facilities , resulting in the identification of an optical transient signal 28 within ∼ 10 arcsec of the galaxy NGC 4993 (Swope, DECam, DLT40 2017 in prep., Valenti et 29 al. ApJL, accepted, LCOGT, VISTA, MASTER). GW170817 is therefore the first source to have 30 been detected in both GWs and EM waves, and the first GW source with a known host galaxy. This 9–13 31 event can therefore be used as a standard siren to determine the Hubble constant, combining the 32 distance inferred purely from the GW signal with the Hubble flow velocity of the galaxy contain- 33 ing the electromagnetic transient. Such measurements do not require any form of cosmic “distance 14 34 ladder” ; the GW analysis directly estimates the luminosity distance out to cosmological scales. 35 The Hubble constant H0 measures the mean expansion rate of the Universe. At nearby 36 distances (d . 100 Mpc) it is well approximated by the expression vH = H0d; (1) 37 where vH is the local “Hubble flow” velocity of a source, and d is the distance to the source. At 38 this nearby distance all cosmological distance measures (such as luminosity distance and comoving 39 distance) differ by less than 1%, so we do not distinguish among them. We are similarly insensitive 2 40 to the values of other cosmological parameters, such as Ωm and ΩΛ. An analysis of the GW +2:9 1 41 data finds that GW170817 occurred at a distance d = 43:8−6:9 Mpc . (All values are quoted as 42 the maximum posterior value with the minimal width 68:3% credible interval). To obtain the 43 Hubble flow velocity at the position of GW170817, we use the optical identification of the host 8 44 galaxy NGC 4993 . This identification is based solely on the 2-dimensional projected offset and 45 is independent of any assumed value of H0. The position and redshift of this galaxy allow us to 46 estimate the appropriate value of the Hubble flow velocity. 9 47 The original standard siren proposal did not rely on the unique identification of a host galaxy. 48 As long as a possible set of host galaxies can be identified for each GW detection, by combining 49 information from ∼ 100 independent detections, an estimate of H0 with ∼ 5% uncertainty can be 15 50 obtained event without the detection of any transient optical counterparts . If an EM counterpart 51 has been identified but the host galaxy is unknown, the same statistical method can be applied 52 but using only those galaxies in a narrow beam around the location of the optical counterpart. 53 However, such statistical analyses are sensitive to a number of complicating effects, including the 16 54 incompleteness of current galaxy catalogs or the need for dedicated follow-up surveys, as well 17 55 as a range of selection effects . In what follows we exploit the identification of NGC 4993 as the 10–13 56 host galaxy of GW170817 to perform a standard siren measurement of the Hubble constant . 57 The gravitational wave observation 58 Analysis of the GW data associated with GW170817 produces estimates for the parameters of the 1The distance quoted here differs from that in other studies1, since here we assume that the optical counterpart represents the true sky position of the GW source instead of marginalizing over a range of potential sky positions. 3 59 source, under the assumption that General Relativity is the correct model of gravity. Parameters 18 1 60 are inferred within a Bayesian framework by comparing strain measurements in the two LIGO 61 detectors and the Virgo detector with the gravitational waveforms expected from the inspiral of two 19 62 point masses under general relativity. We are most interested in the joint posterior distribution on 63 the luminosity distance and binary orbital inclination angle. For the analysis in this paper we fix 20 64 the location of the GW source on the sky to the identified location of the counterpart . This anal- 1, 21 65 ysis uses algorithms for removing short-lived detector noise artifacts and employs approximate 19, 22, 23 66 point-particle waveform models . We have verified that the systematic changes in the results 24, 25 67 presented here from incorporating non-point-mass (tidal) effects and from different data pro- 68 cessing methods are much smaller than the statistical uncertainties in the measurement of H0 and 69 the binary orbital inclination angle. +2:9 70 The distance to GW170817 is estimated from the GW data alone to be 43:8−6:9 Mpc. The 71 ∼ 15% uncertainty is due to a combination of statistical measurement error from the noise in 1 72 the detectors, instrumental calibration uncertainties , and a geometrical factor dependent upon the 73 correlation of distance with inclination angle. The GW measurement is consistent with the distance 14, 26 74 to NGC 4993 measured using the Tully-Fisher relation, dTF = 41:1 ± 5:8 Mpc . 75 The measurement of the GW polarization is crucial for inferring the binary inclination. This 76 inclination, ι, is defined as the angle between the line of sight vector from the source to the detector 77 and the angular momentum vector of the binary system. Observable electromagnetic phenomena 78 cannot typically distinguish between face-on and face-off sources, and therefore are usually char- 4 79 acterized by a viewing angle: min (ι, 180 deg −ι). By contrast, GW measurements can identify 80 whether a source is rotating counter-clockwise or clockwise with respect to the line of sight, and 81 thus ι ranges from 0 to 180 deg. Previous GW detections by LIGO had large uncertainties in lu- 27 82 minosity distance and inclination because the two LIGO detectors that were involved are nearly 83 co-aligned, preventing a precise polarization measurement. In the present case, thanks to Virgo as 84 an additional detector, the cosine of the inclination can be constrained at 68:3% (1-σ) confidence 85 to the range [−1; −0:81] corresponding to inclination angles between [144; 180] deg. This implies 86 that the plane of the binary orbit is almost, but not quite, perpendicular to our line of sight to 5–7 87 the source (ι ≈ 180 deg), which is consistent with the observation of a coincident GRB (LVC, 88 GBM, INTEGRAL 2017 in prep., Goldstein et al. 2017, ApJL, submitted, and Savchenko et al. 89 2017, ApJL, submitted). 90 The electromagnetic observations 8 20, 28–31 91 EM follow-up of the GW sky localization region discovered an optical transient in close 92 proximity to the galaxy NGC 4993. The location of the transient was previously observed by the 93 Hubble Space Telescope on 2017 April 28 UT and no sources were found within 2.2 arcseconds 32 94 down to 25.9 mag . We estimate the probability of a random chance association between the 95 optical counterpart and NGC 4993 to be 0:004% (see the methods section for details). In what 96 follows we assume that the optical counterpart is associated with GW170817, and that this source 97 resides in NGC 4993. 98 To compute H0 we need to estimate the background Hubble flow velocity at the position 5 14 99 of NGC 4993. In the traditional electromagnetic calibration of the cosmic “distance ladder” , 100 this step is commonly carried out using secondary distance indicator information, such as the 26 101 Tully-Fisher relation , which allows one to infer the background Hubble flow velocity in the local 102 Universe scaled back from more distant secondary indicators calibrated in quiet Hubble flow. We 103 do not adopt this approach here, however, in order to preserve more fully the independence of our 104 results from the electromagnetic distance ladder.