A gravitational-wave standard siren measurement of the Hubble constant

Journal name:
Nature
Volume:
551,
Pages:
85–88
Date published:
DOI:
doi:10.1038/nature24471
Received
Accepted
Published online

On 17 August 2017, the Advanced LIGO1 and Virgo2 detectors observed the gravitational-wave event GW170817—a strong signal from the merger of a binary neutron-star system3. Less than two seconds after the merger, a γ-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO–Virgo-derived location of the gravitational-wave source4, 5, 6. This sky region was subsequently observed by optical astronomy facilities7, resulting in the identification8, 9, 10, 11, 12, 13 of an optical transient signal within about ten arcseconds of the galaxy NGC 4993. This detection of GW170817 in both gravitational waves and electromagnetic waves represents the first ‘multi-messenger’ astronomical observation. Such observations enable GW170817 to be used as a ‘standard siren’14, 15, 16, 17, 18 (meaning that the absolute distance to the source can be determined directly from the gravitational-wave measurements) to measure the Hubble constant. This quantity represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Here we report a measurement of the Hubble constant that combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using the electromagnetic data. In contrast to previous measurements, ours does not require the use of a cosmic ‘distance ladder’19: 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 about 70 kilometres per second per megaparsec. This value is consistent with existing measurements20, 21, while being completely independent of them. Additional standard siren measurements from future gravitational-wave sources will enable the Hubble constant to be constrained to high precision.

At a glance

Figures

  1. GW170817 measurement of H0.
    Figure 1: GW170817 measurement of H0.

    The marginalized posterior density for H0, p(H0 | GW170817), is shown by the blue curve. Constraints at 1σ (darker shading) and 2σ (lighter shading) from Planck20 and SHoES21 are shown in green and orange, respectively. The maximum a posteriori value and minimal 68.3% credible interval from this posterior density function is . The 68.3% (1σ) and 95.4% (2σ) minimal credible intervals are indicated by dashed and dotted lines, respectively.

  2. Inference on H0 and inclination.
    Figure 2: Inference on H0 and inclination.

    The posterior density of H0 and cosι from the joint gravitational-wave–electromagnetic analysis are shown as blue contours. Shading levels are drawn at every 5% credible level, with the 68.3% (1σ; solid) and 95.4% (2σ; dashed) contours in black. Values of H0 and 1σ and 2σ error bands are also displayed from Planck20 and SHoES21. Inclination angles near 180° (cosι = −1) indicate that the orbital angular momentum is antiparallel to the direction from the source to the detector.

  3. Constraints on the inclination angle of GW170817.
    Figure 3: Constraints on the inclination angle of GW170817.

    The posterior density on cosι (p(cosι)) is shown for various assumptions about the prior distribution of H0. The analysis of the joint gravitational-wave and electromagnetic data with a 1/H0 prior density gives the blue curve; using values of H0 from Planck20 and SHoES21 as a prior on H0 gives the green and red curves, respectively. Choosing a narrow prior on H0 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% (1σ) credible intervals are indicated by dashed lines. Because our prior on inclination is flat on cosι, the densities in this plot are proportional to the marginalized likelihood for cosι.

  4. Graphical model illustrating the statistical relationships between the data and parameters.
    Extended Data Fig. 1: Graphical model illustrating the statistical relationships between the data and parameters.

    Open circles indicate parameters that require a prior; filled circles describe measured data, which are conditioned on in the analysis. Here we assume that we have measurements of the gravitational-wave data xGW, a recessional velocity (that is, redshift) vr, and the mean peculiar velocity in the neighborhood of NGC 4993 〈vp〉. 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 gravitational-wave data p(xGW | d, cosι) depends on the distance and inclination of the source (and additional parameters, here marginalized out).

  5. Using different assumptions compared to our canonical analysis.
    Extended Data Fig. 2: Using different assumptions compared to our canonical analysis.

    The posterior distribution on H0 discussed in the main text is shown in black, the alternative flat prior on z (discussed in Methods) gives the distribution shown in blue, and the increased uncertainty (250 km s−1) applied to our peculiar velocity measurement (also discussed in Methods) is shown in pink. Minimal 68.3% (1σ) credible intervals are shown by dashed lines.

Tables

  1. Summary of constraints on the Hubble constant, binary inclination and distance
    Extended Data Table 1: Summary of constraints on the Hubble constant, binary inclination and distance

Main

The Hubble constant H0 measures the mean expansion rate of the Universe. At nearby distances (less than about 50 Mpc) it is well approximated by the expression

where vH is the local ‘Hubble flow’ velocity of a source and d is the distance to the source. At such distances all cosmological distance measures (such as luminosity distance and comoving distance) differ at the order of vH/c, where c is the speed of light. Because vH/c ≈ 1% for GW170817, the differences between the different distance measures are much smaller than the overall errors in distance. Our measurement of H0 is similarly insensitive to the values of other cosmological parameters, such as the matter density Ωm and the dark-energy density ΩΛ.

To obtain the Hubble flow velocity at the position of GW170817, we use the optical identification of the host galaxy NGC 49937. This identification is based solely on the two-dimensional projected offset and is independent of any assumed value of H0. The position and redshift of this galaxy allow us to estimate the appropriate value of the Hubble flow velocity. Because the source is relatively nearby, the random relative motions of galaxies, known as peculiar velocities, need to be taken into account. The peculiar velocity is about 10% of the measured recessional velocity (see Methods).

The original standard siren proposal14 did not rely on the unique identification of a host galaxy. By combining information from around 100 independent gravitational-wave detections, each with a set of potential host galaxies, an estimate of H0 accurate to 5% can be obtained even without the detection of any transient optical counterparts22. This is particularly relevant, because gravitational-wave networks will detect many binary black-hole mergers over the coming years23 and these are not expected to be accompanied by electromagnetic counterparts. Alternatively, if an electromagnetic counterpart has been identified but the host galaxy is unknown, then the same statistical method can be applied but using only those galaxies in a narrow beam around the location of the optical counterpart. However, such statistical analyses are sensitive to several complicating effects, such as the incompleteness of current galaxy catalogues or the need for dedicated follow-up surveys, and to a range of selection effects24. Here we use the identification of NGC 4993 as the host galaxy of GW170817 to perform a standard siren measurement of the Hubble constant15, 16, 17, 18.

Analysis of the gravitational-wave data associated with GW170817 produces estimates for the parameters of the source, under the assumption that general relativity is the correct model of gravity3. We are most interested in the joint posterior distribution on the luminosity distance and binary orbital inclination angle. For the analysis we fix the location of the gravitational-wave source on the sky to the identified location of the counterpart8 (see Methods for details).

An analysis of the gravitational-wave data alone finds that GW170817 occurred at a distance (all values are quoted as the maximum posterior value with the minimal-width 68.3% credible interval). The distance quoted here differs from that in other studies3, because here we assume that the optical counterpart represents the true sky location of the gravitational-wave source instead of marginalizing over a range of potential sky locations. The uncertainty of approximately 15% is due to a combination of statistical measurement error from the noise in the detectors, instrumental calibration uncertainties3 and a geometrical factor that depends on the correlation of distance with inclination angle. The gravitational-wave measurement is consistent with the distance to NGC 4993 measured using the Tully–Fisher relation19, 25, dTF = 41.1 ± 5.8 Mpc.

The measurement of the gravitational-wave polarization is crucial for inferring the binary inclination. This inclination, ι, is defined as the angle between the line-of-sight vector from the source to the detector and the orbital-angular-momentum vector of the binary system. For electromagnetic phenomena it is typically not possible to tell whether a system is orbiting clockwise or anticlockwise (or, equivalently, face-on or face-off), and sources are therefore usually characterized by a viewing angle defined as min(ι, 180° − ι), with ι in the range [0°, 180°]. By contrast, gravitational-wave measurements can identify the sense of the rotation, and so ι ranges from 0° (anticlockwise) to 180° (clockwise). Previous gravitational-wave detections by the Laser Interferometer Gravitational-wave Observatory (LIGO) had large uncertainties in luminosity distance and inclination23 because the two LIGO detectors that were involved are nearly co-aligned, preventing a precise polarization measurement. In the present case, owing to the addition of the Virgo detector, the cosine of the inclination can be constrained at 68.3% (1σ) confidence to the range [−1.00, −0.81], corresponding to inclination angles in the range [144°, 180°]. This inclination range implies that the plane of the binary orbit is almost, but not quite, perpendicular to our line of sight to the source (ι ≈ 180°), which is consistent with the observation of a coincident γ-ray burst4, 5, 6. We report inferences on cosι because our prior for it is flat, so the posterior is proportional to the marginal likelihood for it from the gravitational-wave observations.

Electromagnetic follow-up observations of the gravitational-wave sky-localization region7 discovered an optical transient8, 9, 10, 11, 12, 13 in close proximity to the galaxy NGC 4993. The location of the transient was previously observed by the Distance Less Than 40 Mpc (DLT40) survey on 27.99 July 2017 universal time (ut) and no sources were found10. We estimate the probability of a random chance association between the optical counterpart and NGC 4993 to be 0.004% (Methods). In what follows we assume that the optical counterpart is associated with GW170817, and that this source resides in NGC 4993.

To compute H0 we need to estimate the background Hubble flow velocity at the position of NGC 4993. In the traditional electromagnetic calibration of the cosmic ‘distance ladder’19, this step is commonly carried out using secondary distance indicator information, such as the Tully–Fisher relation25, which enables the background Hubble flow velocity in the local Universe to be inferred by scaling back from more distant secondary indicators calibrated in quiet Hubble flow. We do not adopt this approach here, however, to preserve more fully the independence of our results from the electromagnetic distance ladder. Instead we estimate the Hubble flow velocity at the position of NGC 4993 by correcting for local peculiar motions.

NGC 4993 is part of a collection of galaxies, ESO 508, which has a center-of-mass recession velocity relative to the frame of the cosmic microwave background (CMB)26 of27 3,327 ± 72 km s−1. We correct the group velocity by 310 km s−1 owing to the coherent bulk flow28, 29 towards the Great Attractor (Methods). The standard error on our estimate of the peculiar velocity is 69 km s−1, but recognizing that this value may be sensitive to details of the bulk flow motion that have been imperfectly modelled, in our subsequent analysis we adopt a more conservative estimate29 of 150 km s−1 for the uncertainty on the peculiar velocity at the location of NGC 4993 and fold this into our estimate of the uncertainty on vH. From this, we obtain a Hubble velocity vH = 3,017 ± 166 km s−1.

Once the distance and Hubble-velocity distributions have been determined from the gravitational-wave and electromagnetic data, respectively, we can constrain the value of the Hubble constant. The measurement of the distance is strongly correlated with the measurement of the inclination of the orbital plane of the binary. The analysis of the gravitational-wave data also depends on other parameters describing the source, such as the masses of the components23. Here we treat the uncertainty in these other variables by marginalizing over the posterior distribution on system parameters3, with the exception of the position of the system on the sky, which is taken to be fixed at the location of the optical counterpart.

We carry out a Bayesian analysis to infer a posterior distribution on H0 and inclination, marginalized over uncertainties in the recessional and peculiar velocities (Methods). In Fig. 1 we show the marginal posterior for H0. The maximum a posteriori value with the minimal 68.3% credible interval is . Our estimate agrees well with state-of-the-art determinations of this quantity, including CMB measurements from Planck20 (67.74 ± 0.46 km s−1 Mpc−1; ‘TT, TE, EE + lowP + lensing + ext’) and type Ia supernova measurements from SHoES21 (73.24 ± 1.74 km s−1 Mpc−1), and with baryon acoustic oscillations measurements from SDSS30, strong lensing measurements from H0LiCOW31, high-angular-multipole CMB measurements from SPT32 and Cepheid measurements from the Hubble Space Telescope key project19. Our measurement is an independent determination of H0. The close agreement indicates that, although each method may be affected by different systematic uncertainties, we see no evidence at present for a systematic difference between gravitational-wave-based estimates and established electromagnetic-based estimates. As has been much remarked on, the Planck and SHoES results are inconsistent at a level greater than about 3σ. Our measurement does not resolve this inconsistency, being broadly consistent with both.

Figure 1: GW170817 measurement of H0.
GW170817 measurement of H0.

The marginalized posterior density for H0, p(H0 | GW170817), is shown by the blue curve. Constraints at 1σ (darker shading) and 2σ (lighter shading) from Planck20 and SHoES21 are shown in green and orange, respectively. The maximum a posteriori value and minimal 68.3% credible interval from this posterior density function is . The 68.3% (1σ) and 95.4% (2σ) minimal credible intervals are indicated by dashed and dotted lines, respectively.

One of the main sources of uncertainty in our measurement of H0 is due to the degeneracy between distance and inclination in the gravitational-wave measurements. A face-on or face-off binary far away has a similar gravitational-wave amplitude to that of an edge-on binary closer in. This relationship is captured in Fig. 2, which shows posterior contours in the H0–cosι parameter space.

Figure 2: Inference on H0 and inclination.
Inference on H0 and inclination.

The posterior density of H0 and cosι from the joint gravitational-wave–electromagnetic analysis are shown as blue contours. Shading levels are drawn at every 5% credible level, with the 68.3% (1σ; solid) and 95.4% (2σ; dashed) contours in black. Values of H0 and 1σ and 2σ error bands are also displayed from Planck20 and SHoES21. Inclination angles near 180° (cosι = −1) indicate that the orbital angular momentum is antiparallel to the direction from the source to the detector.

The posterior in Fig. 1 results from the vertical projection of Fig. 2, marginalizing out uncertainties in cosι to derive constraints on H0. Alternatively, it is possible to project horizontally, and thereby marginalize out H0 to derive constraints on cosι. If instead of deriving H0 we take the existing constraints20, 21 on H0 independently as priors, we are able to improve our constraints on cosι, as shown in Fig. 3 Assuming the Planck value for H0, the minimal 68.3% credible interval for cosι is [−1.00, −0.92] (corresponding to an inclination angle in the range [157°, 177°]). Assuming the SHoES value of H0, it is [−0.97, −0.85] (corresponding to an inclination angle in the range [148°, 166°]). We note that the face-off ι = 180° orientation for the SHoES result is just outside the 90% confidence range. It will be particularly interesting to compare these constraints to those from modelling7 of the short γ-ray burst, afterglow and optical counterpart associated with GW170817.

Figure 3: Constraints on the inclination angle of GW170817.
Constraints on the inclination angle of GW170817.

The posterior density on cosι (p(cosι)) is shown for various assumptions about the prior distribution of H0. The analysis of the joint gravitational-wave and electromagnetic data with a 1/H0 prior density gives the blue curve; using values of H0 from Planck20 and SHoES21 as a prior on H0 gives the green and red curves, respectively. Choosing a narrow prior on H0 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% (1σ) credible intervals are indicated by dashed lines. Because our prior on inclination is flat on cosι, the densities in this plot are proportional to the marginalized likelihood for cosι.

We have presented a standard siren determination of the Hubble constant, using a combination of a distance estimate from gravitational-wave observations and a Hubble velocity estimate from electromagnetic observations. Our measurement does not use a ‘distance ladder’ and makes no prior assumptions about H0. We find , which is consistent with existing measurements20, 21. This first gravitational-wave–electromagnetic multi-messenger event demonstrates the potential for cosmological inference from gravitational-wave standard sirens. We expect that additional multi-messenger binary neutron-star events will be detected in the coming years, and combining subsequent independent measurements of H0 from these future standard sirens will lead to an era of precision gravitational-wave cosmology.

Methods

Probability of optical counterpart association with NGC 4993

We calculate the probability that an NGC 4993-like galaxy (or brighter) is misidentified as the host by asking how often the centre of one or more such galaxies falls by random chance within a given angular radius θ of the counterpart. Assuming Poisson counting statistics this probability is given by P = 1 − exp[−πθ2S(<m)] where S(<m) is the surface density of galaxies with apparent magnitude equal to or brighter than m. From the local galaxy sample distribution in the infrared (K-band) apparent magnitude33 we obtain S(<K) = 0.68 × 10(0.64(K − 10.0) − 0.7) per square degree. As suggested previously34, we set θ equal to twice the half-light radius of the galaxy, for which we use diameter of NGC 4993 of about 1.1 arcmin, as measured in the near-infrared band (the predominant emission band for early-type galaxies). Using K = 9.2 mag taken from the 2MASS survey35 for NGC 4993, we find the probability of random chance association is P = 0.004%.

Finding the Hubble velocity of NGC 4993

In previous electromagnetic determinations of the cosmic ‘distance ladder’, the Hubble flow velocity of the local calibrating galaxies has generally been estimated using redshift-independent secondary galaxy distance indicators, such as the Tully–Fisher relation or type Ia supernovae, calibrated with more distant samples that can be assumed to sit in quiet Hubble flow19. We do not adopt this approach for NGC 4993, however, so that our inference of the Hubble constant is fully independent of the electromagnetic distance scale. Instead we estimate the Hubble flow velocity at the position of NGC 4993 by correcting its measured recessional velocity for local peculiar motions.

NGC 4993 resides in a group of galaxies whose center-of-mass recession velocity relative to the CMB frame26 is27 3,327 ± 72 km s−1. We assume that all of the galaxies in the group are at the same distance and therefore have the same Hubble flow velocity, which we assign to be the Hubble velocity of GW170817. This assumption is accurate to within 1% given that the radius of the group is approximately 0.4 Mpc. To calculate the Hubble flow velocity of the group, we correct its measured recessional velocity by the peculiar velocity caused by the local gravitational field. This is a large correction28, 29; typical peculiar velocities are 300 km s−1, equivalent to about 10% of the total recessional velocity at a distance of 40 Mpc.

We use the 6dF galaxy redshift survey peculiar velocity map28, 36, which used more than 8,000 Fundamental Plane galaxies to map the peculiar velocity field in the southern hemisphere out to redshift z ≈ 0.055. We weight the peculiar velocity corrections from this catalogue with a Gaussian kernel centered on the sky position of NGC 4993 and with a width of 8h−1 Mpc; the kernel width is independent of H0 and is equivalent to a width of 800 km s−1 in velocity space, typical of the widths used in the catalogue itself. There are ten galaxies in the 6dF peculiar velocity catalogue within one kernel width of NGC 4993. In the CMB frame26, the weighted radial component of the peculiar velocity and associated uncertainty is 〈vp〉 = 310 ± 69 km s−1.

We verified the robustness of this peculiar velocity correction by comparing it with the velocity field reconstructed from the 2MASS redshift survey29, 37. This exploits the linear relationship between the peculiar velocity and mass density fields smoothed on scales larger than about 8h−1 Mpc, and the constant of proportionality can be determined by comparison with radial peculiar velocities of individual galaxies estimated from, for example, Tully–Fisher and type Ia supernovae distances. Using these reconstructed peculiar velocities, which have a larger associated uncertainty29 of 150 km s−1, at the position of NGC 4993 we find a Hubble velocity in the CMB frame of vH = 3,047 km s−1—in excellent agreement with the result derived using 6dF. We adopt this larger uncertainty on the peculiar velocity correction in recognition that the peculiar velocity estimated from the 6dF data may represent an imperfect model of the true bulk flow at the location of NGC 4993. For our inference of the Hubble constant we therefore use a Hubble velocity vH = 3,017 ± 166 km s−1 with 68.3% uncertainty.

Finally, we emphasize again the independence of our Hubble-constant inference from the electromagnetic distance scale, but note the consistency of our gravitational-wave distance estimate to NGC 4993 with the Tully–Fisher distance estimate derived by scaling back the Tully–Fisher relation calibrated with more distant galaxies in quiet Hubble flow25. This consistency also strongly supports the robustness of our estimate for the Hubble velocity of NGC 4993.

Summary of the model

Given observed data from a set of gravitational-wave detectors, xGW, parameter estimation is used to generate a posterior on the parameters that determine the waveform of the gravitational-wave signal. Parameters are inferred within a Bayesian framework38 by comparing strain measurements3 in the two LIGO detectors and the Virgo detector with the gravitational waveforms expected from the inspiral of two point masses39 under general relativity. We use algorithms for removing short-lived detector noise artefacts3, 40 and use approximate point-particle waveform models39, 41, 42. We have verified that the systematic changes in the results presented here from incorporating non-point-mass (tidal) effects43, 44 and from different data processing methods are much smaller than the statistical uncertainties in the measurement of H0 and the orbital inclination angle of the binary.

From this analysis we can obtain the parameter estimation likelihood of the observed gravitational-wave data, marginalized over all parameters that characterize the gravitational-wave signal except d and cosι:

The other waveform parameters are denoted by λ, with p(λ) denoting the corresponding prior.

Given perfect knowledge of the Hubble flow velocity of the gravitational-wave source vH, this posterior distribution can be readily converted into a posterior on cosι and H0 = vH/d:

where pd(d) and pι(cosι) are the prior distributions on distance and inclination. For the Hubble velocity vH = 3,017 km s−1, the maximum a posteriori distance from the gravitational-wave measurement of 43.8 Mpc corresponds to H0 = 68.9 km s−1 Mpc−1, so this procedure would be expected to generate a posterior on H0 that peaks close to that value.

Although the above analysis is conceptually straightforward, it makes several assumptions. In practice, the Hubble flow velocity cannot be determined exactly and must be corrected for uncertain peculiar velocities. This correction does not explicitly set a prior on H0, but instead inherits a prior from the usual pd(d) ∝ d2 prior used in gravitational-wave parameter estimation. In addition, the logic in this model is that a redshift has been obtained first and the distance is then measured using gravitational waves. Because gravitational-wave detectors cannot be pointed, we cannot target particular galaxies or redshifts for gravitational-wave sources. In practice, we wait for a gravitational-wave event to trigger the analysis and this introduces potential selection effects that we must consider. We see below that the simple analysis described above does give results that are consistent with a more careful analysis for this first detection. However, the simple analysis cannot be readily extended to include second and subsequent detections, so we now describe a more general framework that does not suffer from these limitations.

We suppose that we have observed a gravitational-wave event, which generated data xGW in our detectors, and that we have also measured a recessional velocity for the host vr and the peculiar velocity field 〈vp〉 in the vicinity of the host. These observations are statistically independent and so the combined likelihood is

The quantity p(vr | d, vp, H0) is the likelihood of the recessional velocity measurement, which we model as

where N[μ, σ2](x) is the normal (Gaussian) probability density with mean μ and standard deviation σ evaluated at x. The measured recessional velocity vr = 3,327 km s−1, with uncertainty , is the mean velocity and standard error for the members of the group hosting NGC 4993 taken from 2MASS27, corrected to the CMB frame26. We take a similar Gaussian likelihood for the measured peculiar velocity 〈vp〉 = 310 km s−1, with uncertainty :

From the likelihood in equation (2) we derive the posterior

where p(H0), p(d), p(vp) and p(cosι) are the parameter prior probabilities. Our standard analysis assumes a volumetric prior, p(d) ∝ d2, on the Hubble distance, but we explore sensitivity to this choice below. We take a flat-in-log(H0) prior, p(H0) ∝ 1/H0, and impose a flat (that is, isotropic) prior on cosι and a flat prior on vp for vp ∈ [−1,000, 1,000] km s−1. These priors characterize our beliefs about the cosmological population of gravitational-wave events and their hosts before we make any additional measurements or account for selection biases. The full statistical model is summarized graphically in Extended Data Fig. 1. This model with these priors is our canonical analysis.

In equation (3), the term Ns(H0) encodes selection effects23, 45, 46. These arise because of the finite sensitivity of our detectors. Although all events in the Universe generate a response in the detector, we will be able to identify, and hence use, only signals that generate a response of sufficiently high amplitude. The decision about whether to include an event in the analysis is a property of the data only, in this case {xGW, vr, 〈vp〉}, but the fact that we condition our analysis on a signal being detected, that is, the data exceeding these thresholds, means that the likelihood must be renormalized to become the likelihood for detected events. This is the role of

where the integral is over the full prior ranges of the parameters {d, vp, cosι, λ} and over datasets that would be selected for inclusion in the analysis (that is, that exceed the specified thresholds). If the integral was over all datasets then it would evaluate to 1, but because the range is restricted there can be a non-trivial dependence on parameters characterizing the population of sources, in this case H0.

In our analysis, there are in principle selection effects in both the gravitational-wave data and the electromagnetic data. However, around the time of detection of GW170817, the LIGO–Virgo detector network had a detection horizon of approximately 190 Mpc for binary neutron-star events3, within which electromagnetic measurements are largely complete. For example, the counterpart associated with GW170817 had a brightness of about 17 mag in the I band at 40 Mpc (refs 8, 9, 10, 11, 12, 13); this source would be about 22 mag at 400 Mpc, and therefore still detectable by survey telescopes such as DECam well beyond the gravitational-wave horizon. Even the dimmest theoretical light curves for kilonovae are expected to peak at about 22.5 mag at the LIGO–Virgo horizon47. We therefore expect that gravitational-wave selection effects are dominant and ignore electromagnetic selection effects. The fact that the fraction of binary neutron-star events that will have observed kilonova counterparts is presently unknown does not modify these conclusions, because we can restrict our analysis to only gravitational-wave events with kilonova counterparts.

For the gravitational-wave data, the decision about whether or not to analyse an event is determined largely by the signal-to-noise ratio ρ of the event. A reasonable model for the selection process is a cut in signal-to-noise ratio; that is, events with ρ > ρ* are analysed48. In that model, the integral over xGW in equation (4) can be replaced by an integral over signal-to-noise ratio from ρ* to ∞, and p(xGW | d, cosι, λ) replaced by p(ρ | d, cosι, λ) in the integrand. This distribution depends on the noise properties of the operating detectors and on the intrinsic strain amplitude of the source. The former are clearly independent of the population parameters, whereas the latter scales as a function of the source parameters divided by the luminosity distance. The dependence on source parameters is on redshifted parameters, which introduces an explicit redshift dependence. However, within the approximately 190-Mpc horizon redshift corrections are at most about 5%, and the Hubble constant measurement is a weak function of these, meaning that the overall effect is even smaller. At present, whether or not a particular event in the population ends up being analysed can therefore be regarded as a function of d only. When gravitational-wave selection effects dominate, only the terms in equation (4) arising from the gravitational-wave measurement matter. Because these are a function of d only and we set a prior on d, there is no explicit H0 dependence in these terms. Hence, Ns(H0) is a constant and can be ignored. This would not be the case if we set a prior on the redshifts of potential sources instead of their distances, because then changes in H0 would modify the range of detectable redshifts. As the LIGO–Virgo detectors improve in sensitivity, the redshift dependence in the gravitational-wave selection effects will become more important, as will electromagnetic selection effects. However, at that point we will also have to consider deviations in the cosmological model from the simple Hubble flow described in equation (1).

Marginalizing equation (3) over d, vp and cosι then yields

The posterior computed in this way is shown in Fig. 1 and has a maximum a posteriori value and minimal 68.3% credible interval of   . The posterior mean is 78 km s−1 Mpc−1 and the standard deviation is 15 km s−1 Mpc−1. Various other summary statistics are given in Extended Data Table 1.

Robustness to prior specification

Our canonical analysis uses a uniform volumetric prior on distance, p(d) ∝ d2. The distribution of galaxies is not completely uniform owing to clustering, so we explore sensitivity to this prior choice. We are free to place priors on any two of the three variables {d, H0, z}, where z = H0d/c is the Hubble flow redshift of NGC 4993. A choice of prior for two of these variables induces a prior on the third that may or may not correspond to a natural choice for that parameter. A prior on z could be obtained from galaxy catalogue observations49, but must be corrected for incompleteness. When setting a prior on H0 and z, the posterior becomes

but now

When gravitational-wave selection effects dominate, the integral is effectively

which has an H0 dependence, unless p(z) takes a special, H0-dependent form, p(z) = f(z/H0)/H0. However, if the redshift prior is volumetric, p(z) ∝ z2, then the selection-effect term is proportional to , which cancels a similar correction to the likelihood and gives a posterior on H0 that is identical to the canonical analysis.

For a single event, any choice of prior can be mapped to our canonical analysis with a different prior on H0. For any reasonable prior choices on d or z, we would expect to gradually lose sensitivity to the particular prior choice as further observed events are added to the analysis. However, to illustrate the uncertainty that comes from the prior choice for this first event, we compare in Extended Data Fig. 2 and Extended Data Table 1 the results from the canonical prior choice p(d) ∝ d2 to those from two other choices: using a flat prior on z, and assuming a velocity correction due to the peculiar velocity of NGC 4993 that is a Gaussian with width 250 km s−1. (To do the first of these, the posterior samples from gravitational-wave parameter estimation have to be re-weighted, because they are generated with the d2 prior used in the canonical analysis. We first ‘undo’ the default prior before applying the desired new prior.)

The choice of a flat prior on z is motivated by the simple model described above, in which we imagine first making a redshift measurement for the host and then use that as a prior for analysing the gravitational-wave data. Setting priors on distance and redshift, the simple analysis gives the same result as the canonical analysis, but now we set a prior on redshift and H0 and obtain a different result. This is to be expected because we are making different assumptions about the underlying population, and it arises for similar reasons as the different biases in peculiar velocity measurements based on redshift-selected or distance-selected samples50. As can be seen in Extended Data Table 1, the results change by less than 1σ, as measured by the statistical error of the canonical analysis.

By increasing the uncertainty in the peculiar velocity prior, we test the assumptions in our canonical analysis that (1) NGC 4993 is a member of the nearby group of galaxies, and (2) that this group has a center-of-mass velocity close to the Hubble flow. The results in Extended Data Table 1 summarize changes in the values of H0 and in the error bars.

We conclude that the effect of a reasonable change to the prior is small relative to the statistical uncertainties for this event.

Incorporating additional constraints on H 0

By including previous measurements20, 21 of H0 we can constrain the orbital inclination more precisely. We do this by setting the H0 prior in equation (3) to , where for ShoES21 and , and for Planck20 and . The posterior on cosι is then

This posterior is shown in Fig. 3.

Data and code availability

The publicly available codes and data can be found at the LIGO Open Science Center (https://losc.ligo.org).

References

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Acknowledgements

We acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. We acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. We acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, the Department of Science and Technology, India, the Science and Engineering Research Board (SERB), India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigación, the Vicepresidència i Conselleria d’Innovació, Recerca i Turisme and the Conselleria d’Educació i Universitat del Govern de les Illes Balears, the Conselleria d’Educació, Investigació, Cultura i Esport de la Generalitat Valenciana, the National Science Centre of Poland, the Swiss National Science Foundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research, Development and Innovation Office Hungary (NKFI), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, the Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, Innovations, and Communications, the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), the Research Grants Council of Hong Kong, the National Natural Science Foundation of China (NSFC), the Leverhulme Trust, the Research Corporation, the Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. We acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources. This paper has been assigned the document number LIGO-P1700296. We thank the University of Copenhagen, DARK Cosmology Centre, and the Niels Bohr International Academy for hosting D.A.C., R.J.F., A.M.B., E. Ramirez-Ruiz and M.R.S. during the discovery of GW170817/SSS17a. R.J.F., A.M.B., E. Ramirez-Ruiz and D.E.H. were participating in the Kavli Summer Program in Astrophysics, ‘Astrophysics with gravitational wave detections’. This program was supported by the the Kavli Foundation, Danish National Research Foundation, the Niels Bohr International Academy, and the DARK Cosmology Centre. The UCSC group is supported in part by NSF grant AST–1518052, the Gordon & Betty Moore Foundation, the Heising-Simons Foundation, generous donations from many individuals through a UCSC Giving Day grant, and from fellowships from the Alfred P. Sloan Foundation (R.J.F.), the David and Lucile Packard Foundation (R.J.F. and E. Ramirez-Ruiz) and the Niels Bohr Professorship from the DNRF (E. Ramirez-Ruiz). A.M.B. acknowledges support from a UCMEXUS-CONACYT Doctoral Fellowship. Support for this work was provided by NASA through Hubble Fellowship grants HST–HF–51348.001 and HST–HF–51373.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5–26555. The Berger Time-Domain Group at Harvard is supported in part by the NSF through grants AST-1411763 and AST-1714498, and by NASA through grants NNX15AE50G and NNX16AC22G. Funding for the DES Projects has been provided by the DOE and NSF (USA), MEC/MICINN/MINECO (Spain), STFC (UK), HEFCE (UK). NCSA (UIUC), KICP (U. Chicago), CCAPP (Ohio State), MIFPA (Texas A&M), CNPQ, FAPERJ, FINEP (Brazil), DFG (Germany) and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne Lab, UC Santa Cruz, University of Cambridge, CIEMAT-Madrid, University of Chicago, University College London, DES-Brazil Consortium, University of Edinburgh, ETH Zürich, Fermilab, University of Illinois, ICE (IEEC-CSIC), IFAE Barcelona, Lawrence Berkeley Lab, LMU München and the associated Excellence Cluster Universe, University of Michigan, NOAO, University of Nottingham, Ohio State University, University of Pennsylvania, University of Portsmouth, SLAC National Lab, Stanford University, University of Sussex, Texas A&M University and the OzDES Membership Consortium. Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The DES Data Management System is supported by the NSF under grant numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-88861, FPA2015-68048, and Centro de Excelencia SEV-2012-0234, SEV-2016-0597 and MDM-2015-0509. Research leading to these results has received funding from the ERC under the European Union’s Seventh Framework Programme including grants ERC 240672, 291329 and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. This manuscript has been authored by Fermi Research Alliance, LLC under contract number DE-AC02-07CH11359 with the US Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. D.J.S. acknowledges support for the DLT40 programme from NSF grant AST-1517649. Support for I. Arcavi was provided by NASA through the Einstein Fellowship Program, grant PF6-170148. G. Hosseinzadeh, D.A.H. and C. McCully are supported by NSF grant AST-1313484. D. Poznanski acknowledges support by Israel Science Foundation grant 541/17. VINROUGE is an European Southern Observatory Large Survey (id: 0198.D-2010). MASTER acknowledges the Lomonosov MSU Development Programme and the Russian Federation Ministry of Education and Science. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA.

Author information

Affiliations

  1. LIGO, California Institute of Technology, Pasadena, California 91125, USA.

    • B. P. Abbott,
    • R. Abbott,
    • R. X. Adhikari,
    • A. Ananyeva,
    • S. B. Anderson,
    • S. Appert,
    • K. Arai,
    • M. C. Araya,
    • J. C. Barayoga,
    • B. C. Barish,
    • B. K. Berger,
    • G. Billingsley,
    • S. Biscans,
    • J. K. Blackburn,
    • C. D. Blair,
    • R. Bork,
    • A. F. Brooks,
    • S. Brunett,
    • C. Cahillane,
    • T. A. Callister,
    • C. B. Cepeda,
    • M. W. Coughlin,
    • P. Couvares,
    • D. C. Coyne,
    • P. Ehrens,
    • J. Eichholz,
    • T. Etzel,
    • J. Feicht,
    • E. M. Fries,
    • S. E. Gossan,
    • K. E. Gushwa,
    • E. K. Gustafson,
    • A. W. Heptonstall,
    • M. Isi,
    • B. Kamai,
    • J. B. Kanner,
    • V. Kondrashov,
    • W. Z. Korth,
    • D. B. Kozak,
    • A. Lazzarini,
    • A. Markowitz,
    • E. Maros,
    • T. J. Massinger,
    • F. Matichard,
    • G. McIntyre,
    • J. McIver,
    • S. Meshkov,
    • L. Nevin,
    • M. Pedraza,
    • A. Perreca,
    • E. A. Quintero,
    • D. H. Reitze,
    • N. A. Robertson,
    • J. G. Rollins,
    • S. Sachdev,
    • E. J. Sanchez,
    • L. E. Sanchez,
    • P. Schmidt,
    • R. J. E. Smith,
    • R. Taylor,
    • C. I. Torrie,
    • R. Tso,
    • A. L. Urban,
    • G. Vajente,
    • S. Vass,
    • G. Venugopalan,
    • A. R. Wade,
    • L. Wallace,
    • A. J. Weinstein,
    • S. E. Whitcomb,
    • R. D. Williams,
    • J. L. Willis,
    • C. C. Wipf,
    • S. Xiao,
    • H. Yamamoto,
    • L. Zhang,
    • M. E. Zucker &
    • J. Zweizig
  2. Louisiana State University, Baton Rouge, Louisiana 70803, USA.

    • T. D. Abbott,
    • C. Austin,
    • C. C. Buchanan,
    • T. R. Corbitt,
    • J. Cripe,
    • T. J. Cullen,
    • J. A. Giaime,
    • G. González,
    • T. Hardwick,
    • W. W. Johnson,
    • M. Kasprzack &
    • G. Valdes
  3. Università di Salerno, Fisciano, I-84084 Salerno, Italy.

    • F. Acernese,
    • F. Barone &
    • R. Romano
  4. INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy.

    • F. Acernese,
    • F. Barone,
    • E. Calloni,
    • M. De Laurentis,
    • R. De Rosa,
    • L. Di Fiore,
    • T. Di Girolamo,
    • F. Garufi,
    • A. Grado,
    • L. Milano &
    • R. Romano
  5. University of Florida, Gainesville, Florida 32611, USA.

    • K. Ackley,
    • I. Bartos,
    • C. R. Billman,
    • H.-P. Cheng,
    • H. Chia,
    • G. Ciani,
    • C. F. Da Silva Costa,
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    • D. B. Tanner,
    • J. Trinastic,
    • B. F. Whiting &
    • M. Yazback
  6. OzGrav, School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia.

    • K. Ackley,
    • S. Biscoveanu,
    • B. Goncharov,
    • P. D. Lasky,
    • Y. Levin,
    • L. McNeill,
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    • R. J. E. Smith,
    • C. Talbot,
    • E. Thrane,
    • C. Whittle &
    • X. J. Zhu
  7. LIGO Livingston Observatory, Livingston, Louisiana 70754, USA.

    • C. Adams,
    • S. M. Aston,
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    • J. Birch,
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    • D. Sellers,
    • B. Smith,
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    • M. Thomas,
    • K. A. Thorne &
    • G. Traylor
  8. Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France.

    • T. Adams,
    • R. Bonnand,
    • D. Buskulic,
    • M. Ducrot,
    • D. Estevez,
    • V. Germain,
    • R. Gouaty,
    • N. Letendre,
    • F. Marion,
    • A. Masserot,
    • B. Mours,
    • L. Rolland,
    • D. Verkindt,
    • M. Was &
    • M. Yvert
  9. University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy.

    • P. Addesso,
    • E. Mejuto-Villa,
    • V. Pierro,
    • I. M. Pinto &
    • M. Principe
  10. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany.

    • V. B. Adya,
    • C. Affeldt,
    • B. Allen,
    • G. Ashton,
    • C. Aulbert,
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    • M. Mehmet,
    • Arunava Mukherjee,
    • M. Nery,
    • A. B. Nielsen,
    • A. Nitz,
    • A. Noack,
    • F. Ohme,
    • P. Oppermann,
    • M. A. Papa,
    • A. Post,
    • M. Prijatelj,
    • O. Puncken,
    • S. Rieger,
    • A. Rüdiger,
    • F. Salemi,
    • J. Schmidt,
    • E. Schreiber,
    • D. Schuette,
    • B. W. Schulte,
    • B. F. Schutz,
    • A. Singh,
    • M. Steinke,
    • D. Steinmeyer,
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    • F. Thies,
    • S. Walsh,
    • L.-W. Wei,
    • M. Weinert,
    • P. Weßels,
    • J. Westerweck,
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    • M. H. Wimmer,
    • W. Winkler,
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    • J. Woehler,
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    • S. J. Zhu
  11. The University of Mississippi, University, Mississippi 38677, USA.

    • M. Afrough,
    • M. Cavaglià,
    • C. Cocchieri,
    • K. L. Dooley &
    • K. Mogushi
  12. NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.

    • B. Agarwal,
    • G. Allen,
    • D. George,
    • E. A. Huerta,
    • M. Katolik,
    • A. J. Kemball,
    • C. Markakis,
    • W. Ren,
    • P. M. Ricker,
    • E. Seidel &
    • E. K. Wessel
  13. University of Cambridge, Cambridge CB2 1TN, UK.

    • M. Agathos,
    • A. J. K. Chua &
    • C. J. Moore
  14. Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands.

    • K. Agatsuma,
    • M. K. M. Bader,
    • A. Bertolini,
    • B. A. Boom,
    • H. J. Bulten,
    • S. Caudill,
    • Archisman Ghosh,
    • S. Ghosh,
    • R. J. G. Jonker,
    • S. Koley,
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    • J. F. J. van den Brand,
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  15. LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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    • L. Barsotti,
    • S. Biscans,
    • A. Buikema,
    • N. Demos,
    • F. Donovan,
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    • F. Matichard,
    • N. Mavalvala,
    • L. McCuller,
    • J. Miller,
    • R. Mittleman,
    • S. R. P. Mohapatra,
    • D. H. Shoemaker,
    • M. Tse,
    • S. Vitale,
    • R. Weiss,
    • Hang Yu,
    • Haocun Yu &
    • M. E. Zucker
  16. Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil.

    • O. D. Aguiar,
    • M. Constancio Jr.,
    • C. A. Costa,
    • E. C. Ferreira,
    • M. A. Okada &
    • A. D. Silva
  17. Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy.

    • L. Aiello,
    • M. Branchesi,
    • E. Coccia,
    • M. De Laurentis,
    • V. Fafone,
    • O. Halim,
    • J. Harms,
    • I. Khan,
    • M. Lorenzini,
    • V. Sequino,
    • A. Singhal,
    • S. Tiwari &
    • G. Wang
  18. INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy.

    • L. Aiello,
    • M. Branchesi,
    • E. Coccia,
    • O. Halim,
    • J. Harms &
    • M. Lorenzini
  19. Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India.

    • A. Ain,
    • S. Bose,
    • S. Dhurandhar,
    • B. U. Gadre,
    • S. G. Gaonkar,
    • S. Mitra,
    • N. Mukund,
    • A. Parida,
    • J. Prasad,
    • T. Souradeep &
    • J. Suresh
  20. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.

    • P. Ajith,
    • Abhirup Ghosh,
    • Archisman Ghosh,
    • B. R. Iyer &
    • S. Kumar
  21. University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA.

    • B. Allen,
    • W. G. Anderson,
    • P. R. Brady,
    • P. Brockill,
    • S. Caudill,
    • D. Chatterjee,
    • J. D. E. Creighton,
    • T. P. Downes,
    • S. Ghosh,
    • C. Horst,
    • S. J. Kapadia,
    • S. Kwang,
    • X. Liu,
    • I. Magaña Hernandez,
    • M. Manske,
    • R. A. Mercer,
    • D. Mukherjee,
    • M. A. Papa,
    • M. Poe,
    • T. Prestegard,
    • H. Qi,
    • L. Sadeghian,
    • A. Sheperd,
    • X. Siemens,
    • J. A. Sonnenberg,
    • K. Ueno,
    • A. D. Viets &
    • S. Walsh
  22. Leibniz Universität Hannover, D-30167 Hannover, Germany.

    • B. Allen,
    • P. Aufmuth,
    • A. Bisht,
    • S. L. Danilishin,
    • K. Danzmann,
    • M. Heurs,
    • S. Kaufer,
    • H. Lück,
    • D. Schuette,
    • A. Singh,
    • H. Vahlbruch,
    • L.-W. Wei,
    • B. Willke &
    • H. Wittel
  23. Università di Pisa, I-56127 Pisa, Italy.

    • A. Allocca,
    • A. Basti,
    • G. Cerretani,
    • W. Del Pozzo,
    • A. Di Lieto,
    • F. Di Renzo,
    • I. Ferrante,
    • F. Fidecaro,
    • J. M. Gonzalez Castro,
    • R. Passaquieti,
    • R. Poggiani,
    • M. Razzano &
    • M. Tonelli
  24. INFN, Sezione di Pisa, I-56127 Pisa, Italy.

    • A. Allocca,
    • A. Basti,
    • M. Bitossi,
    • V. Boschi,
    • C. Bradaschia,
    • G. Cella,
    • G. Cerretani,
    • W. Del Pozzo,
    • A. Di Lieto,
    • F. Di Renzo,
    • I. Ferrante,
    • F. Fidecaro,
    • F. Frasconi,
    • A. Gennai,
    • A. Giazotto,
    • J. M. Gonzalez Castro,
    • G. Losurdo,
    • A. Moggi,
    • F. Paoletti,
    • R. Passaquieti,
    • D. Passuello,
    • B. Patricelli,
    • R. Poggiani,
    • M. Razzano,
    • M. Tonelli &
    • L. Trozzo
  25. OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia.

    • P. A. Altin,
    • J. H. Chow,
    • P. W. F. Forsyth,
    • N. Kijbunchoo,
    • G. L. Mansell,
    • M. Manske,
    • D. E. McClelland,
    • D. J. McManus,
    • T. McRae,
    • T. T. Nguyen,
    • D. S. Rabeling,
    • S. M. Scott,
    • D. A. Shaddock,
    • B. J. J. Slagmolen,
    • R. L. Ward,
    • K. Wette &
    • M. J. Yap
  26. Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France.

    • A. Amato,
    • G. Cagnoli,
    • J. Degallaix,
    • C. De Rossi,
    • V. Dolique,
    • R. Flaminio,
    • M. Granata,
    • D. Hofman,
    • C. Michel,
    • R. Pedurand,
    • L. Pinard &
    • B. Sassolas
  27. SUPA, University of the West of Scotland, Paisley PA1 2BE, UK.

    • S. V. Angelova,
    • J. Devenson,
    • S. Macfoy,
    • G. Rutins &
    • D. J. Vine
  28. LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, F-91898 Orsay, France.

    • S. Antier,
    • N. Arnaud,
    • I. Belahcene,
    • M. A. Bizouard,
    • V. Brisson,
    • J. Casanueva Diaz,
    • F. Cavalier,
    • D. Cohen,
    • M. Davier,
    • V. Frey,
    • P. Gruning,
    • P. Hello,
    • D. Huet,
    • A. Lartaux-Vollard,
    • N. Leroy &
    • F. Robinet
  29. California State University Fullerton, Fullerton, California 92831, USA.

    • J. S. Areeda,
    • A. Avila-Alvarez,
    • T. J. Cullen,
    • G. Lovelace,
    • J. Read,
    • J. R. Smith &
    • M. Walker
  30. European Gravitational Observatory (EGO), I-56021 Cascina, Italy.

    • N. Arnaud,
    • G. Ballardin,
    • M. Bitossi,
    • V. Boschi,
    • A. Bozzi,
    • F. Carbognani,
    • R. Cavalieri,
    • A. Chiummo,
    • S. Cortese,
    • E. Cuoco,
    • V. Dattilo,
    • C. De Rossi,
    • F. Ferrini,
    • I. Fiori,
    • E. Genin,
    • M. Gosselin,
    • G. Hemming,
    • D. Hoak,
    • M. Mantovani,
    • M. Mohan,
    • F. Nocera,
    • A. Paoli,
    • A. Pasqualetti,
    • G. Pillant,
    • P. Popolizio,
    • P. Ruggi,
    • L. Salconi,
    • D. Sentenac,
    • B. L. Swinkels,
    • F. Travasso &
    • T. Zelenova
  31. Chennai Mathematical Institute, Chennai 603103, India.

    • K. G. Arun
  32. Università di Roma Tor Vergata, I-00133 Roma, Italy.

    • S. Ascenzi,
    • C. Casentini,
    • V. Fafone,
    • D. Lumaca,
    • I. Nardecchia &
    • V. Sequino
  33. INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy.

    • S. Ascenzi,
    • C. Casentini,
    • E. Cesarini,
    • S. D’Antonio,
    • V. Fafone,
    • I. Khan,
    • D. Lumaca,
    • Y. Minenkov,
    • I. Nardecchia,
    • A. Rocchi &
    • V. Sequino
  34. Universität Hamburg, D-22761 Hamburg, Germany.

    • M. Ast,
    • L. Kleybolte,
    • M. Korobko,
    • A. Pal-Singh,
    • A. Sawadsky,
    • R. Schnabel,
    • A. Schönbeck,
    • J. Steinlechner &
    • S. Steinlechner
  35. INFN, Sezione di Roma, I-00185 Roma, Italy.

    • P. Astone,
    • A. Colla,
    • S. Di Pace,
    • I. Di Palma,
    • S. Frasca,
    • G. Intini,
    • P. Leaci,
    • E. Majorana,
    • S. Mastrogiovanni,
    • A. L. Miller,
    • L. Naticchioni,
    • C. Palomba,
    • O. J. Piccinni,
    • P. Puppo,
    • P. Rapagnani,
    • F. Ricci &
    • A. Singhal
  36. Cardiff University, Cardiff CF24 3AA, UK.

    • D. V. Atallah,
    • I. Dorrington,
    • S. Fairhurst,
    • E. J. Fauchon-Jones,
    • M. Fays,
    • S. Gomes,
    • E. Z. Hamilton,
    • M. D. Hannam,
    • P. Hopkins,
    • C. V. Kalaghatgi,
    • C. Kent,
    • L. T. London,
    • R. Macas,
    • D. M. Macleod,
    • A. W. Muir,
    • C. North,
    • L. K. Nuttall,
    • F. Pannarale,
    • V. Predoi,
    • B. S. Sathyaprakash,
    • B. F. Schutz,
    • P. J. Sutton,
    • V. Tiwari &
    • S. A. Usman
  37. Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA.

    • K. AultONeal,
    • S. Gaudio,
    • K. Gill,
    • E. M. Gretarsson,
    • B. Hughey,
    • M. Muratore,
    • J. W. W. Pratt,
    • S. G. Schwalbe,
    • K. Staats,
    • M. J. Szczepańczyk &
    • M. Zanolin
  38. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany.

    • S. Babak,
    • A. Bohe,
    • A. Buonanno,
    • V. Dergachev,
    • H.-B. Eggenstein,
    • S. Grunewald,
    • I. W. Harry,
    • B. D. Lackey,
    • G. D. Meadors,
    • J. Ming,
    • S. Ossokine,
    • M. A. Papa,
    • H. P. Pfeiffer,
    • S. Privitera,
    • M. Pürrer,
    • V. Raymond,
    • L. Shao,
    • A. Singh,
    • A. Taracchini,
    • S. Walsh &
    • S. J. Zhu
  39. APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France.

    • P. Bacon,
    • M. Barsuglia,
    • Y. Bouffanais,
    • C. Buy,
    • E. Capocasa,
    • E. Chassande-Mottin,
    • D. Fiorucci,
    • E. K. Porter &
    • D. Steer
  40. Korea Institute of Science and Technology Information, Daejeon 34141, South Korea.

    • S. Bae &
    • G. Kang
  41. West Virginia University, Morgantown, West Virginia 26506, USA.

    • P. T. Baker,
    • B. D. Cheeseboro,
    • Z. B. Etienne,
    • T. D. Knowles,
    • A. Lenon &
    • S. T. McWilliams
  42. Università di Perugia, I-06123 Perugia, Italy.

    • F. Baldaccini,
    • L. Gammaitoni &
    • H. Vocca
  43. INFN, Sezione di Perugia, I-06123 Perugia, Italy.

    • F. Baldaccini,
    • M. Bawaj,
    • F. Marchesoni,
    • M. Punturo,
    • F. Travasso &
    • H. Vocca
  44. Syracuse University, Syracuse, New York 13244, USA.

    • S. W. Ballmer,
    • S. Bhagwat,
    • C. Biwer,
    • D. A. Brown,
    • D. Davis,
    • S. De,
    • H. Fair,
    • D. Finstad,
    • R. P. Fisher,
    • J. E. Lord,
    • F. Magaña-Sandoval,
    • L. Magaña Zertuche,
    • E. A. Muñiz,
    • L. Pekowsky,
    • S. D. Reyes,
    • J. R. Sanders,
    • P. R. Saulson,
    • D. C. Vander-Hyde &
    • T. Vo
  45. University of Minnesota, Minneapolis, Minnesota 55455, USA.

    • S. Banagiri,
    • M. Fitz-Axen,
    • V. Mandic,
    • A. Matas,
    • P. M. Meyers &
    • R. Ormiston
  46. SUPA, University of Glasgow, Glasgow G12 8QQ, UK.

    • S. E. Barclay,
    • B. Barr,
    • J. C. Bayley,
    • A. S. Bell,
    • M. Chan,
    • A. Cumming,
    • L. Cunningham,
    • L. E. H. Datrier,
    • R. Douglas,
    • P. Dupej,
    • M. Fletcher,
    • H. Gabbard,
    • C. Graef,
    • A. Grant,
    • G. Hammond,
    • M. J. Hart,
    • K. Haughian,
    • M. Hendry,
    • I. S. Heng,
    • J. Hennig,
    • S. Hild,
    • J. Hough,
    • E. A. Houston,
    • S. H. Huttner,
    • H. N. Isa,
    • R. Jones,
    • D. Keitel,
    • S. Leavey,
    • K. Lee,
    • V. Mangano,
    • I. W. Martin,
    • M. Masso-Reid,
    • C. Messenger,
    • P. G. Murray,
    • G. Newton,
    • D. Pascucci,
    • B. L. Pearlstone,
    • M. Phelps,
    • M. Pitkin,
    • J. Powell,
    • N. A. Robertson,
    • R. Robie,
    • S. Rowan,
    • J. Scott,
    • B. Sorazu,
    • A. P. Spencer,
    • J. Steinlechner,
    • K. A. Strain,
    • S. C. Tait,
    • K. Toland,
    • Z. Tornasi,
    • A. A. van Veggel,
    • J. Veitch,
    • D. Williams,
    • G. Woan,
    • J. L. Wright &
    • T. Zhang
  47. LIGO Hanford Observatory, Richland, Washington 99352, USA.

    • D. Barker,
    • J. Bartlett,
    • J. C. Batch,
    • R. M. Blair,
    • F. Clara,
    • J. C. Driggers,
    • S. E. Dwyer,
    • B. Gateley,
    • C. Gray,
    • J. Hanks,
    • K. Izumi,
    • K. Kawabe,
    • P. J. King,
    • J. S. Kissel,
    • M. Landry,
    • R. McCarthy,
    • G. Mendell,
    • E. L. Merilh,
    • D. Moraru,
    • G. Moreno,
    • J. Oberling,
    • C. J. Perez,
    • M. Pirello,
    • F. J. Raab,
    • H. Radkins,
    • C. L. Romel,
    • K. Ryan,
    • T. Sadecki,
    • V. Sandberg,
    • R. L. Savage,
    • T. J. Shaffer,
    • D. Sigg,
    • A. Strunk,
    • P. Thomas,
    • C. Vorvick,
    • J. Warner,
    • B. Weaver &
    • J. Worden
  48. Caltech CaRT, Pasadena, California 91125, USA.

    • K. Barkett,
    • J. Blackman,
    • Y. Chen,
    • Y. Ma,
    • B. Pang,
    • M. Scheel &
    • V. Varma
  49. Wigner RCP, RMKI, Konkoly Thege Miklós út 29-33, H-1121 Budapest, Hungary.

    • D. Barta &
    • M. Vasúth
  50. Columbia University, New York, New York 10027, USA.

    • I. Bartos,
    • K. R. Corley,
    • S. T. Countryman,
    • T. Di Girolamo,
    • M. Factourovich,
    • S. Márka,
    • Z. Márka,
    • L. Matone &
    • A. Staley
  51. Stanford University, Stanford, California 94305, USA.

    • R. Bassiri,
    • E. Bonilla,
    • R. L. Byer,
    • C. E. Cirelli,
    • D. DeBra,
    • M. M. Fejer,
    • B. Lantz,
    • A. S. Markosyan &
    • B. Shapiro
  52. Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy.

    • M. Bawaj &
    • F. Marchesoni
  53. Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy.

    • M. Bazzan,
    • G. Ciani &
    • M. Vardaro
  54. INFN, Sezione di Padova, I-35131 Padova, Italy.

    • M. Bazzan,
    • G. Ciani,
    • L. Conti,
    • C. Lazzaro,
    • M. Vardaro,
    • G. Vedovato &
    • J.-P. Zendri
  55. Institute of Physics, Eötvös University, Pázmány P. s. 1/A, Budapest 1117, Hungary.

    • B. Bécsy,
    • G. Dálya,
    • Z. Frei &
    • P. Raffai
  56. Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716 Warsaw, Poland.

    • M. Bejger,
    • D. Rosińska &
    • M. Sieniawska
  57. Rochester Institute of Technology, Rochester, New York 14623, USA.

    • J. J. Bero,
    • J. Healy,
    • J. Lange,
    • C. O. Lousto,
    • R. O’Shaughnessy,
    • M. Rizzo,
    • J. T. Whelan,
    • J. Wofford,
    • D. M. Wysocki &
    • Y.-H. Zhang
  58. University of Birmingham, Birmingham B15 2TT, UK.

    • C. P. L. Berry,
    • S. J. Cooper,
    • W. Del Pozzo,
    • M. Dovale álvarez,
    • W. M. Farr,
    • A. Freise,
    • S. M. Gaebel,
    • A. C. Green,
    • H. Miao,
    • H. Middleton,
    • C. M. Mow-Lowry,
    • S. P. Stevenson,
    • D. J. Stops,
    • E. G. Thomas,
    • D. Töyrä,
    • A. Vecchio,
    • S. Vinciguerra &
    • H. Wang
  59. INFN, Sezione di Genova, I-16146 Genova, Italy.

    • D. Bersanetti,
    • M. Canepa,
    • A. Chincarini,
    • A. Cirone,
    • S. Farinon,
    • G. Gemme,
    • L. Rei &
    • F. Sorrentino
  60. RRCAT, Indore MP 452013, India.

    • R. Bhandare,
    • I. Dave,
    • J. George,
    • S. A. Pai,
    • B. C. Pant,
    • S. Raja &
    • C. Rajan
  61. Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia.

    • I. A. Bilenko,
    • M. L. Gorodetsky,
    • F. Y. Khalili,
    • V. P. Mitrofanov,
    • L. G. Prokhorov,
    • S. E. Strigin &
    • S. P. Vyatchanin
  62. SUPA, University of Strathclyde, Glasgow G1 1XQ, UK.

    • R. Birney,
    • S. Jawahar,
    • N. A. Lockerbie,
    • S. Reid &
    • K. V. Tokmakov
  63. The Pennsylvania State University, University Park, Pennsylvania 16802, USA.

    • S. Biscoveanu,
    • S. J. Chamberlin,
    • A. Gupta,
    • C. Hanna,
    • R. M. Magee,
    • D. Meacher,
    • C. Messick,
    • A. E. Pace,
    • B. S. Sathyaprakash &
    • J. Z. Wang
  64. OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia.

    • C. D. Blair,
    • D. G. Blair,
    • X. Chen,
    • Q. Chu,
    • S. Chung,
    • D. M. Coward,
    • E. J. Howell,
    • L. Ju,
    • J. Liu,
    • M. A. Page,
    • L. Wen &
    • C. Zhao
  65. Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands.

    • S. Bloemen,
    • P. Canizares,
    • S. Ghosh,
    • P. Groot,
    • T. Hinderer,
    • G. Nelemans,
    • D. Nichols,
    • S. Nissanke,
    • P. Schmidt &
    • A. R. Williamson
  66. Artemis, Université Côte d’Azur, Observatoire Côte d’Azur, CNRS, CS 34229, F-06304 Nice Cedex 4, France.

    • M. Boer,
    • G. Bogaert,
    • A. Brillet,
    • N. Christensen,
    • F. Cleva,
    • J.-P. Coulon,
    • J.-D. Fournier,
    • H. Heitmann,
    • A. Hreibi,
    • F. Kéfélian,
    • N. Man,
    • L. Martellini,
    • M. Merzougui,
    • O. Minazzoli,
    • M. Pichot,
    • T. Regimbau &
    • J.-Y. Vinet
  67. Institut FOTON, CNRS, Université de Rennes 1, F-35042 Rennes, France.

    • F. Bondu
  68. Washington State University, Pullman, Washington 99164, USA.

    • S. Bose,
    • B. R. Hall &
    • N. Mazumder
  69. University of Oregon, Eugene, Oregon 97403, USA.

    • J. E. Brau,
    • R. Frey,
    • S. Karki,
    • J. R. Palamos,
    • R. Quitzow-James,
    • V. J. Roma,
    • P. Schale,
    • R. M. S. Schofield &
    • D. Talukder
  70. Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris, France.

    • T. Briant,
    • S. Chua,
    • P.-F. Cohadon,
    • S. Deléglise,
    • A. Heidmann,
    • J.-M. Isac,
    • T. Jacqmin &
    • R. Metzdorff
  71. Carleton College, Northfield, Minnesota 55057, USA.

    • J. E. Broida,
    • N. Christensen,
    • M. W. Coughlin,
    • M. C. Edwards &
    • J. D. Tasson
  72. OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia.

    • D. D. Brown,
    • H. Cao,
    • M. R. Ganija,
    • W. Kim,
    • E. J. King,
    • J. Munch,
    • D. J. Ottaway &
    • P. J. Veitch
  73. Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland.

    • T. Bulik &
    • I. Kowalska
  74. VU University Amsterdam, 1081 HV Amsterdam, The Netherlands.

    • H. J. Bulten &
    • J. F. J. van den Brand
  75. University of Maryland, College Park, Maryland 20742, USA.

    • A. Buonanno,
    • M. Cho,
    • P. Shawhan &
    • C. C. Yancey
  76. Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

    • L. Cadonati,
    • J. Calderón Bustillo,
    • J. A. Clark,
    • E. E. Cowan,
    • B. Day,
    • S. S. Forsyth,
    • S. Ghonge,
    • K. Jani,
    • S. J. Kimbrell,
    • K. Napier,
    • D. M. Shoemaker &
    • K. Siellez
  77. Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France.

    • G. Cagnoli
  78. Università di Napoli ‘Federico II’, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy.

    • E. Calloni,
    • R. De Rosa,
    • T. Di Girolamo,
    • F. Garufi &
    • L. Milano
  79. NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.

    • J. B. Camp,
    • T. Dal Canton,
    • N. Gehrels &
    • L. P. Singer
  80. Dipartimento di Fisica, Università degli Studi di Genova, I-16146 Genova, Italy.

    • M. Canepa &
    • A. Cirone
  81. RESCEU, University of Tokyo, Tokyo 113-0033, Japan.

    • K. C. Cannon,
    • L. Tsukada &
    • D. Tsuna
  82. Tsinghua University, Beijing 100084, China.

    • J. Cao,
    • Z. Du,
    • X. Fan &
    • X. Guo
  83. Texas Tech University, Lubbock, Texas 79409, USA.

    • S. Caride,
    • A. Corsi,
    • R. Coyne,
    • R. Inta,
    • B. J. Owen &
    • B. Rajbhandari
  84. Kenyon College, Gambier, Ohio 43022, USA.

    • M. F. Carney,
    • T. Chmiel,
    • C. Fee,
    • D. Moffa,
    • L. E. Wade &
    • M. Wade
  85. Departamento de Astronomía y Astrofísica, Universitat de València, E-46100 Burjassot, Spain.

    • P. Cerdá-Durán,
    • J. A. Font,
    • N. Sanchis-Gual &
    • A. Torres-Forné
  86. Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, I-00184 Roma, Italy.

    • E. Cesarini
  87. National Tsing Hua University, Hsinchu City, 30013 Taiwan, China.

    • S. Chao,
    • L. Kuo,
    • Howard Pan &
    • Huang-Wei Pan
  88. Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia.

    • P. Charlton
  89. Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, Illinois 60208, USA.

    • E. Chase,
    • S. B. Coughlin,
    • V. Kalogera,
    • B. B. Miller,
    • C. Pankow,
    • L. M. Perri,
    • L. M. Sampson,
    • J. Scheuer,
    • M. S. Shahriar,
    • M. Zevin,
    • M. Zhou &
    • Z. Zhou
  90. Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada.

    • K. Chatziioannou,
    • H. Fong,
    • C.-J. Haster,
    • P. Kumar,
    • H. P. Pfeiffer &
    • A. B. Zimmerman
  91. University of Chicago, Chicago, Illinois 60637, USA.

    • H. Y. Chen,
    • Z. Doctor,
    • B. Farr,
    • M. Fishbach &
    • D. E. Holz
  92. Pusan National University, Busan 46241, South Korea.

    • H. S. Cho,
    • Y.-M. Kim &
    • C. H. Lee
  93. The Chinese University of Hong Kong, Shatin, Hong Kong.

    • A. K. W. Chung,
    • O. A. Hannuksela,
    • K. Kim,
    • K. H. Lai,
    • T. G. F. Li,
    • R. K. L. Lo,
    • K. K. Y. Ng,
    • P. T. H. Pang,
    • Y. F. Wang &
    • K. W. K. Wong
  94. INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy.

    • R. Ciolfi
  95. INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Italy.

    • R. Ciolfi,
    • M. Di Giovanni,
    • M. Leonardi,
    • A. Perreca,
    • G. A. Prodi,
    • S. Tiwari &
    • M. C. Tringali
  96. OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia.

    • P. Clearwater,
    • A. Melatos &
    • L. Sun
  97. Università di Roma ‘La Sapienza’, I-00185 Roma, Italy.

    • A. Colla,
    • S. Di Pace,
    • I. Di Palma,
    • S. Frasca,
    • G. Intini,
    • P. Leaci,
    • S. Mastrogiovanni,
    • A. L. Miller,
    • L. Naticchioni,
    • O. J. Piccinni,
    • P. Rapagnani &
    • F. Ricci
  98. Université Libre de Bruxelles, 1050 Brussels, Belgium.

    • C. G. Collette &
    • J. Watchi
  99. Sonoma State University, Rohnert Park, California 94928, USA.

    • L. R. Cominsky
  100. Departamento de Matemáticas, Universitat de València, E-46100 Burjassot, Spain.

    • I. Cordero-Carrión &
    • A. Marquina
  101. Montana State University, Bozeman, Montana 59717, USA.

    • N. Cornish &
    • M. Millhouse
  102. Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain.

    • P. B. Covas,
    • C. Garcia-Quiros,
    • S. Husa,
    • F. Jiménez-Forteza,
    • M. Oliver,
    • G. Pratten,
    • A. Ramos-Buades &
    • A. M. Sintes
  103. The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA.

    • T. D. Creighton,
    • M. C. Díaz,
    • S. R. Morriss,
    • S. Mukherjee,
    • V. Quetschke,
    • M. Rakhmanov,
    • K. E. Ramirez,
    • J. D. Romano,
    • R. Stone,
    • D. Tuyenbayev &
    • W. H. Wang
  104. Bellevue College, Bellevue, Washington 98007, USA.

    • S. G. Crowder
  105. Institute for Plasma Research, Bhat, Gandhinagar 382428, India.

    • A. Dasgupta,
    • M. K. Gupta,
    • Z. Khan,
    • R. Kumar,
    • A. K. Srivastava &
    • S. Sunil
  106. The University of Sheffield, Sheffield S10 2TN, UK.

    • E. J. Daw,
    • T. B. Edo,
    • R. Kennedy &
    • E. Massera
  107. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy.

    • R. De Pietri
  108. INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy.

    • R. De Pietri
  109. California State University, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA.

    • R. DeSalvo,
    • L. Glover,
    • S. D. Linker,
    • M. C. Milovich-Goff,
    • J. Neilson,
    • G. D. O’Dea &
    • M. B. Shaner
  110. Università di Trento, Dipartimento di Fisica, I-38123 Povo, Italy.

    • M. Di Giovanni,
    • M. Leonardi,
    • A. Perreca,
    • G. A. Prodi &
    • M. C. Tringali
  111. Montclair State University, Montclair, New Jersey 07043, USA.

    • M. Favata &
    • R. M. Martin
  112. National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan.

    • R. Flaminio
  113. Observatori Astronòmic, Universitat de València, E-46980 Paterna, Spain.

    • J. A. Font
  114. School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, UK.

    • J. R. Gair
  115. University and Institute of Advanced Research, Koba Institutional Area, Gandhinagar Gujarat 382007, India.

    • G. Gaur
  116. IISER-TVM, CET Campus, Trivandrum Kerala 695016, India.

    • V. Gayathri,
    • A. Pai &
    • M. Saleem
  117. University of Szeged, Dóm tér 9, 6720 Szeged, Hungary.

    • L. Gergely &
    • M. Tápai
  118. University of Michigan, Ann Arbor, Michigan 48109, USA.

    • E. Goetz,
    • R. Gustafson,
    • A. Neunzert,
    • K. Riles &
    • O. Sauter
  119. Tata Institute of Fundamental Research, Mumbai 400005, India.

    • A. Gopakumar &
    • C. S. Unnikrishnan
  120. INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy.

    • A. Grado
  121. Università degli Studi di Urbino ‘Carlo Bo’, I-61029 Urbino, Italy.

    • G. Greco,
    • G. M. Guidi,
    • F. Martelli,
    • M. Montani,
    • F. Piergiovanni,
    • G. Stratta,
    • F. Vetrano &
    • A. Viceré
  122. INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy.

    • G. Greco,
    • G. M. Guidi,
    • F. Martelli,
    • M. Montani,
    • F. Piergiovanni,
    • G. Stratta,
    • F. Vetrano,
    • A. Viceré &
    • G. Wang
  123. Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.

    • M. Haney
  124. American University, Washington DC 20016, USA.

    • G. M. Harry,
    • M. Kinley-Hanlon &
    • J. M. Newport
  125. University of Białystok, 15-424 Białystok, Poland.

    • P. Jaranowski
  126. University of Southampton, Southampton SO17 1BJ, UK.

    • D. I. Jones
  127. University of Washington Bothell, 18115 Campus Way NE, Bothell, Washington 98011, USA.

    • J. S. Key
  128. Institute of Applied Physics, Nizhny Novgorod 603950, Russia.

    • E. A. Khazanov,
    • O. Palashov &
    • A. Sergeev
  129. Korea Astronomy and Space Science Institute, Daejeon 34055, South Korea.

    • Chunglee Kim
  130. Inje University Gimhae, South Gyeongsang 50834, South Korea.

    • J. C. Kim &
    • H. W. Lee
  131. National Institute for Mathematical Sciences, Daejeon 34047, South Korea.

    • W. S. Kim,
    • J. J. Oh,
    • S. H. Oh &
    • E. J. Son
  132. NCBJ, 05-400 Świerk-Otwock, Poland.

    • A. Królak,
    • A. Kutynia &
    • A. Zadrożny
  133. Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland.

    • A. Królak &
    • M. Patil
  134. Hillsdale College, Hillsdale, Michigan 49242, USA.

    • R. N. Lang
  135. Hanyang University, Seoul 04763, South Korea.

    • H. K. Lee
  136. Seoul National University, Seoul 08826, South Korea.

    • H. M. Lee
  137. NASA Marshall Space Flight Center, Huntsville, Alabama 35811, USA.

    • T. B. Littenberg,
    • J. Page,
    • A. A. Shah &
    • J. A. Taylor
  138. ESPCI, CNRS, F-75005 Paris, France.

    • V. Loriette &
    • I. Maksimovic
  139. Southern University and A&M College, Baton Rouge, Louisiana 70813, USA.

    • S. C. McGuire
  140. College of William and Mary, Williamsburg, Virginia 23187, USA.

    • E. E. Mikhailov &
    • M. Zhang
  141. Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco.

    • O. Minazzoli
  142. Indian Institute of Technology Madras, Chennai 600036, India.

    • C. Mishra
  143. IISER-Kolkata, Mohanpur, West Bengal 741252, India.

    • R. K. Nayak &
    • A. Samajdar
  144. Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA.

    • G. H. Ogin
  145. Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India.

    • A. Pai
  146. Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.

    • B. Patricelli
  147. Université de Lyon, F-69361 Lyon, France.

    • R. Pedurand
  148. Hobart and William Smith Colleges, Geneva, New York 14456, USA.

    • S. Penn &
    • S. V. Tewari
  149. OzGrav, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia.

    • J. Powell &
    • S. P. Stevenson
  150. Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland.

    • D. Rosińska
  151. University of Washington, Seattle, Washington 98195, USA.

    • M. P. Ross &
    • K. Venkateswara
  152. King’s College London, University of London, London WC2R 2LS, UK.

    • M. Sakellariadou
  153. Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India.

    • A. S. Sengupta
  154. Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India.

    • S. Somala
  155. International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil.

    • R. Sturani
  156. Andrews University, Berrien Springs, Michigan 49104, USA.

    • T. Z. Summerscales
  157. Università di Siena, I-53100 Siena, Italy.

    • L. Trozzo
  158. Trinity University, San Antonio, Texas 78212, USA.

    • D. Ugolini
  159. Abilene Christian University, Abilene, Texas 79699, USA.

    • J. L. Willis
  160. Colorado State University, Fort Collins, Colorado 80523, USA.

    • L. Yang
  161. Department of Astronomy and Astrophysics, University of California, Santa Cruz, California 95064, USA.

    • R. J. Foley,
    • D. A. Coulter,
    • C. D. Kilpatrick,
    • A. Murguia-Berthier,
    • Y.-C. Pan,
    • J. X. Prochaska,
    • E. Ramirez-Ruiz,
    • C. Rojas-Bravo &
    • M. R. Siebert
  162. The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, California 91101, USA.

    • M. R. Drout,
    • B. F. Madore,
    • A. L. Piro,
    • B. J. Shappee &
    • J. D. Simon
  163. Hubble and Carnegie-Dunlap Fellow.

    • M. R. Drout
  164. Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.

    • D. Kasen
  165. Departments of Physics and Astronomy, University of California, Berkeley, California 94720, USA.

    • D. Kasen
  166. Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.

    • E. Ramirez-Ruiz
  167. Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, Maryland 21218, USA.

    • A. Rest
  168. Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA.

    • B. J. Shappee
  169. Hubble and Carnegie-Princeton Fellow.

    • B. J. Shappee
  170. Departamento de Física y Astronomía, Universidad de La Serena, La Serena, Chile.

    • N. Ulloa
  171. Fermi National Accelerator Laboratory, PO Box 500, Batavia, Illinois 60510, USA

    • J. Annis,
    • M. Soares-Santos,
    • H. T. Diehl,
    • J. Frieman,
    • S. Allam,
    • R. E. Butler,
    • A. Drlica-Wagner,
    • D. A. Finley,
    • K. Herner,
    • T. S. Li,
    • H. Lin,
    • J. Marriner,
    • A. Stebbins,
    • W. Wester,
    • B. Yanny,
    • E. Buckley-Geer,
    • J. Estrada,
    • B. Flaugher,
    • G. Gutierrez,
    • S. Kent,
    • R. Kron,
    • N. Kuropatkin,
    • E. Neilsen,
    • B. Nord,
    • V. Scarpine,
    • D. L. Tucker &
    • Y. Zhang
  172. Department of Physics, Brandeis University, Waltham, Massachusetts, USA

    • M. Soares-Santos
  173. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

    • D. Brout,
    • M. Sako,
    • L. F. Secco,
    • C. B. D’Andrea,
    • B. Jain &
    • M. March
  174. Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA

    • D. Scolnic,
    • J. Frieman,
    • R. Kessler,
    • S. Kent &
    • R. Kron
  175. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA

    • E. Berger,
    • K. D. Alexander,
    • P. Cowperthwaite &
    • M. Nicholl
  176. Department of Physics, University of Surrey, Guildford GU2 7XH, UK

    • E. Balbinot
  177. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA

    • P. Blanchard,
    • T. Eftekhari,
    • V. A. Villar &
    • P. K. G. Williams
  178. Department of Astronomy, Indiana University, 727 East Third Street, Bloomington, Indiana 47405, USA

    • R. E. Butler
  179. Astrophysical Institute, Department of Physics and Astronomy, 251B Clippinger Lab, Ohio University, Athens, Ohio 45701, USA

    • R. Chornock
  180. George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA

    • E. R. Cook,
    • J. L. Marshall,
    • M. Sauseda &
    • D. L. DePoy
  181. LSST, 933 North Cherry Avenue, Tucson, Arizona 85721, USA

    • E. R. Cook &
    • K. Bechtol
  182. Hubble and Carnegie-Dunlap Fellow

    • M. R. Drout
  183. The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, California 91101, USA

    • M. R. Drout
  184. Institut d’Astrophysique de Paris (UMR7095: CNRS and UPMC), 98 bis Bd Arago, F-75014 Paris, France

    • F. Durret
  185. Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA

    • W. Fong
  186. Hubble Fellow

    • W. Fong
  187. Center for Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87544

    • C. L. Fryer
  188. Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain

    • J. García-Bellido
  189. SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

    • M. S. S. Gill,
    • D. L. Burke,
    • D. Gruen,
    • A. Roodman &
    • E. S. Rykoff
  190. Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, Illinois 61801, USA

    • R. A. Gruendl &
    • M. Carrasco Kind
  191. National Center for Supercomputing Applications, 1205 West Clark Street, Urbana, Illinois 61801, USA

    • R. A. Gruendl,
    • C. Hanna,
    • F. Paz-Chinchón,
    • M. Carrasco Kind &
    • M. W. G. Johnson
  192. Department of Physics and Astronomy and Astrophysics,The Pennsylvania State University, University Park, Pennsylvania 16802, USA

    • C. Hanna
  193. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

    • W. Hartley,
    • A. Palmese,
    • F. B. Abdalla,
    • A. Benoit-Lévy,
    • D. Brooks,
    • W. G. Hartley &
    • O. Lahav
  194. Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 16, CH-8093 Zurich, Switzerland

    • W. Hartley &
    • W. G. Hartley
  195. Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

    • D. Huterer,
    • D. W. Gerdes,
    • C. J. Miller,
    • M. Schubnell &
    • G. Tarle
  196. Departments of Physics and Astronomy, and Theoretical Astrophysics Center, University of California, Berkeley, California 94720-7300, USA

    • D. Kasen
  197. Observatòrio do Valongo, Universidade Federal do Rio de Janeiro, Ladeira do Pedro Antônio 43, Rio de Janeiro, RJ 20080-090, Brazil

    • P. A. A. Lopes &
    • A. C. C. Lourenço
  198. Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA

    • R. Margutti
  199. National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, Arizona 85719, USA

    • T. Matheson
  200. Departamento de Astronomonía, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile

    • G. E. Medina &
    • R. R. Muñoz
  201. Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA

    • B. D. Metzger
  202. Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA

    • J. Muir
  203. Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA

    • P. Nugent,
    • D. A. Goldstein &
    • R. C. Thomas
  204. Department of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley, California 94720-3411, USA

    • E. Quataert
  205. Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-8160, USA

    • D. J. Schlegel
  206. Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, Arizona 85721, USA

    • N. Smith
  207. Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas SP 13083-859, Brazil

    • F. Sobreira
  208. Laboratório Interinstitucional de e-Astronomia — LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil

    • F. Sobreira,
    • A. Carnero Rosell,
    • L. N. da Costa,
    • M. Lima,
    • M. A. G. Maia &
    • R. L. C. Ogando
  209. Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, Casilla 603, La Serena, Chile

    • A. K. Vivas,
    • A. Zenteno,
    • T. M. C. Abbott,
    • R. C. Smith &
    • A. R. Walker
  210. Department of Physics and Electronics, Rhodes University, PO Box 94, Grahamstown 6140, South Africa.

    • F. B. Abdalla
  211. CNRS, UMR 7095, Institut d’Astrophysique de Paris, F-75014 Paris, France

    • A. Benoit-Lévy &
    • E. Bertin
  212. Sorbonne Universités, UPMC Université Paris 06, UMR 7095, Institut d’Astrophysique de Paris, F-75014 Paris, France

    • A. Benoit-Lévy &
    • E. Bertin
  213. Jodrell Bank Center for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

    • S. L. Bridle
  214. Kavli Institute for Particle Astrophysics and Cosmology, PO Box 2450, Stanford University, Stanford, California 94305, USA

    • D. L. Burke,
    • C. E. Cunha,
    • C. Davis,
    • D. Gruen,
    • E. Krause,
    • A. Roodman &
    • E. S. Rykoff
  215. Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil

    • A. Carnero Rosell,
    • L. N. da Costa,
    • M. A. G. Maia &
    • R. L. C. Ogando
  216. Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, Spain

    • J. Carretero,
    • E. Fernandez &
    • R. Miquel
  217. Institute of Space Sciences, IEEC-CSIC, Campus UAB, Carrer de Can Magrans, 08193 Barcelona, Spain

    • F. J. Castander,
    • P. Fosalba &
    • E. Gaztanaga
  218. Department of Physics, IIT Hyderabad, Kandi, Telangana 502285, India

    • S. Desai
  219. Excellence Cluster Universe, Boltzmannstrasse 2, 85748 Garching, Germany

    • J. P. Dietrich &
    • J. Weller
  220. Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstrasse 1, 81679 Munich, Germany

    • J. P. Dietrich
  221. Department of Astronomy, University of Michigan, Ann Arbor, Michigan 48109, USA

    • D. W. Gerdes &
    • C. J. Miller
  222. Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

    • T. Giannantonio
  223. Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

    • T. Giannantonio
  224. Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians Universität München, Scheinerstrasse 1, 81679 München, Germany

    • T. Giannantonio &
    • J. Weller
  225. Department of Astronomy, University of California, Berkeley, 501 Campbell Hall, Berkeley, California 94720, USA

    • D. A. Goldstein
  226. Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, Ohio 43210, USA

    • K. Honscheid &
    • M. A. Troxel
  227. Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA

    • K. Honscheid &
    • M. A. Troxel
  228. Astronomy Department, University of Washington, Box 351580, Seattle, Washington 98195, USA

    • D. J. James
  229. Santa Cruz Institute for Particle Physics, Santa Cruz, California 95064, USA

    • T. Jeltema
  230. Australian Astronomical Observatory, North Ryde, New South Wales 2113, Australia

    • K. Kuehn
  231. Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA

    • S. Kuhlmann &
    • V. Vikram
  232. Departamento de Física Matemática, Instituto de Física, Universidade de São Paulo, CP 66318, São Paulo, SP 05314-970, Brazil

    • M. Lima
  233. Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain

    • R. Miquel
  234. Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA

    • A. A. Plazas
  235. Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton BN1 9QH, UK

    • A. K. Romer
  236. Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain

    • E. Sanchez &
    • I. Sevilla-Noarbe
  237. School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK

    • M. Smith
  238. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

    • E. Suchyta
  239. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK

    • D. Thomas
  240. Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse, 85748 Garching, Germany

    • J. Weller
  241. Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA.

    • J. B. Haislip,
    • V. V. Kouprianov &
    • D. E. Reichart
  242. Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Ave, Tucson, Arizona 85719, USA.

    • L. Tartaglia &
    • D. J. Sand
  243. Department of Physics, University of California, 1 Shields Avenue, Davis, California 95616-5270, USA.

    • L. Tartaglia,
    • S. Valenti &
    • S. Yang
  244. Department of Physics and Astronomy, University of Padova, Via 8 Febbraio, 2-35122 Padova, Italy.

    • S. Yang
  245. INAF Osservatorio Astronomico di Padova, Vicolo della Osservatorio 5, I-35122 Padova, Italy.

    • S. Yang
  246. Department of Physics, University of California, Santa Barbara, California 93106-9530, USA.

    • Iair Arcavi,
    • Griffin Hosseinzadeh,
    • D. Andrew Howell,
    • Curtis McCully &
    • Sergiy Vasylyev
  247. Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, California 93117-5575, USA.

    • Iair Arcavi,
    • Griffin Hosseinzadeh,
    • D. Andrew Howell,
    • Curtis McCully &
    • Sergiy Vasylyev
  248. School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.

    • Dovi Poznanski
  249. Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK.

    • N. R. Tanvir,
    • P. A. Evans,
    • P. O’Brien,
    • J. P. Osborne,
    • S. Rosetti &
    • K. Wiersema
  250. Department of Physics, University of Warwick, Coventry CV4 7AL, UK.

    • A. J. Levan,
    • J. Lyman,
    • D. T. H. Steeghs,
    • K. Ulaczyk &
    • K. Wiersema
  251. DARK, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark.

    • J. Hjorth,
    • J. P. U. Fynbo,
    • B. Milvang-Jensen &
    • D. Watson
  252. Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada, Spain.

    • Z. Cano,
    • A. de Ugarte-Postigo &
    • C. C. Thöne
  253. Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK.

    • C. Copperwheat &
    • D. A. Perley
  254. Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK.

    • C. González-Fernández,
    • M. Irwin &
    • R. McMahon
  255. Max-Planck-Institut für extraterrestrische Physik, 85740 Garching, Giessenbachstrasse 1, Germany.

    • J. Greiner
  256. Birmingham Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK.

    • I. Mandel
  257. INAF, Institute of Space Astrophysics and Cosmic Physics, Via Gobetti 101, I-40129 Bologna, Italy.

    • E. Pian &
    • E. Palazzi
  258. School of Physics and Astronomy, and Monash Centre for Astrophysics, Monash University, Clayton, Victoria 3800, Australia.

    • E. Rol
  259. The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden.

    • S. Rosswog
  260. Anton Pannekoek Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.

    • A. Rowlinson
  261. ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands.

    • A. Rowlinson
  262. Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 76100 Rehovot, Israel.

    • S. Schulze
  263. M. V. Lomonosov Moscow State University, Physics Department, Leninskie gory, GSP-1, Moscow 119991, Russia.

    • V. M. Lipunov,
    • V. G. Kornilov &
    • D. Vlasenko
  264. M. V. Lomonosov Moscow State University, Sternberg Astronomical Institute, Universitetsky pr., 13, Moscow 119234, Russia.

    • V. M. Lipunov,
    • E. Gorbovskoy,
    • V. G. Kornilov,
    • N. Tyurina,
    • P. Balanutsa,
    • D. Vlasenko,
    • I. Gorbunov &
    • O. Gress
  265. Observatorio Astronomico Felix Aguilar (OAFA), National University of San Juan, San Juan, Argentina.

    • R. Podesta
  266. Instituto de Ciencias Astronomicas,de la Tierra y del Espacio (ICATE), San Juan, Argentina.

    • H. Levato &
    • C. Saffe
  267. South African Astrophysical Observatory, PO Box 9, 7935 Observatory, Cape Town, South Africa.

    • D. A. H. Buckley
  268. Irkutsk State University, Applied Physics Institute, 20 Gagarin boulevard, 664003 Irkutsk, Russia.

    • N. M. Budnev &
    • O. Gress
  269. Blagoveschensk State Pedagogical University, Lenin street 104, Amur Region, Blagoveschensk 675000, Russia.

    • V. Yurkov
  270. Instituto de Astrofacuteisica de Canarias Via Lactea, E-38205La Laguna, Spain.

    • R. Rebolo &
    • M. Serra-Ricart

Consortia

  1. The LIGO Scientific Collaboration and The Virgo Collaboration

    • B. P. Abbott,
    • R. Abbott,
    • T. D. Abbott,
    • F. Acernese,
    • K. Ackley,
    • C. Adams,
    • T. Adams,
    • P. Addesso,
    • R. X. Adhikari,
    • V. B. Adya,
    • C. Affeldt,
    • M. Afrough,
    • B. Agarwal,
    • M. Agathos,
    • K. Agatsuma,
    • N. Aggarwal,
    • O. D. Aguiar,
    • L. Aiello,
    • A. Ain,
    • P. Ajith,
    • B. Allen,
    • G. Allen,
    • A. Allocca,
    • P. A. Altin,
    • A. Amato,
    • A. Ananyeva,
    • S. B. Anderson,
    • W. G. Anderson,
    • S. V. Angelova,
    • S. Antier,
    • S. Appert,
    • K. Arai,
    • M. C. Araya,
    • J. S. Areeda,
    • N. Arnaud,
    • K. G. Arun,
    • S. Ascenzi,
    • G. Ashton,
    • M. Ast,
    • S. M. Aston,
    • P. Astone,
    • D. V. Atallah,
    • P. Aufmuth,
    • C. Aulbert,
    • K. AultONeal,
    • C. Austin,
    • A. Avila-Alvarez,
    • S. Babak,
    • P. Bacon,
    • M. K. M. Bader,
    • S. Bae,
    • P. T. Baker,
    • F. Baldaccini,
    • G. Ballardin,
    • S. W. Ballmer,
    • S. Banagiri,
    • J. C. Barayoga,
    • S. E. Barclay,
    • B. C. Barish,
    • D. Barker,
    • K. Barkett,
    • F. Barone,
    • B. Barr,
    • L. Barsotti,
    • M. Barsuglia,
    • D. Barta,
    • J. Bartlett,
    • I. Bartos,
    • R. Bassiri,
    • A. Basti,
    • J. C. Batch,
    • M. Bawaj,
    • J. C. Bayley,
    • M. Bazzan,
    • B. Bécsy,
    • C. Beer,
    • M. Bejger,
    • I. Belahcene,
    • A. S. Bell,
    • B. K. Berger,
    • G. Bergmann,
    • J. J. Bero,
    • C. P. L. Berry,
    • D. Bersanetti,
    • A. Bertolini,
    • J. Betzwieser,
    • S. Bhagwat,
    • R. Bhandare,
    • I. A. Bilenko,
    • G. Billingsley,
    • C. R. Billman,
    • J. Birch,
    • R. Birney,
    • O. Birnholtz,
    • S. Biscans,
    • S. Biscoveanu,
    • A. Bisht,
    • M. Bitossi,
    • C. Biwer,
    • M. A. Bizouard,
    • J. K. Blackburn,
    • J. Blackman,
    • C. D. Blair,
    • D. G. Blair,
    • R. M. Blair,
    • S. Bloemen,
    • O. Bock,
    • N. Bode,
    • M. Boer,
    • G. Bogaert,
    • A. Bohe,
    • F. Bondu,
    • E. Bonilla,
    • R. Bonnand,
    • B. A. Boom,
    • R. Bork,
    • V. Boschi,
    • S. Bose,
    • K. Bossie,
    • Y. Bouffanais,
    • A. Bozzi,
    • C. Bradaschia,
    • P. R. Brady,
    • M. Branchesi,
    • J. E. Brau,
    • T. Briant,
    • A. Brillet,
    • M. Brinkmann,
    • V. Brisson,
    • P. Brockill,
    • J. E. Broida,
    • A. F. Brooks,
    • D. A. Brown,
    • D. D. Brown,
    • S. Brunett,
    • C. C. Buchanan,
    • A. Buikema,
    • T. Bulik,
    • H. J. Bulten,
    • A. Buonanno,
    • D. Buskulic,
    • C. Buy,
    • R. L. Byer,
    • M. Cabero,
    • L. Cadonati,
    • G. Cagnoli,
    • C. Cahillane,
    • J. Calderón Bustillo,
    • T. A. Callister,
    • E. Calloni,
    • J. B. Camp,
    • M. Canepa,
    • P. Canizares,
    • K. C. Cannon,
    • H. Cao,
    • J. Cao,
    • C. D. Capano,
    • E. Capocasa,
    • F. Carbognani,
    • S. Caride,
    • M. F. Carney,
    • J. Casanueva Diaz,
    • C. Casentini,
    • S. Caudill,
    • M. Cavaglià,
    • F. Cavalier,
    • R. Cavalieri,
    • G. Cella,
    • C. B. Cepeda,
    • P. Cerdá-Durán,
    • G. Cerretani,
    • E. Cesarini,
    • S. J. Chamberlin,
    • M. Chan,
    • S. Chao,
    • P. Charlton,
    • E. Chase,
    • E. Chassande-Mottin,
    • D. Chatterjee,
    • K. Chatziioannou,
    • B. D. Cheeseboro,
    • H. Y. Chen,
    • X. Chen,
    • Y. Chen,
    • H.-P. Cheng,
    • H. Chia,
    • A. Chincarini,
    • A. Chiummo,
    • T. Chmiel,
    • H. S. Cho,
    • M. Cho,
    • J. H. Chow,
    • N. Christensen,
    • Q. Chu,
    • A. J. K. Chua,
    • S. Chua,
    • A. K. W. Chung,
    • S. Chung,
    • G. Ciani,
    • R. Ciolfi,
    • C. E. Cirelli,
    • A. Cirone,
    • F. Clara,
    • J. A. Clark,
    • P. Clearwater,
    • F. Cleva,
    • C. Cocchieri,
    • E. Coccia,
    • P.-F. Cohadon,
    • D. Cohen,
    • A. Colla,
    • C. G. Collette,
    • L. R. Cominsky,
    • M. Constancio Jr.,
    • L. Conti,
    • S. J. Cooper,
    • P. Corban,
    • T. R. Corbitt,
    • I. Cordero-Carrión,
    • K. R. Corley,
    • N. Cornish,
    • A. Corsi,
    • S. Cortese,
    • C. A. Costa,
    • M. W. Coughlin,
    • S. B. Coughlin,
    • J.-P. Coulon,
    • S. T. Countryman,
    • P. Couvares,
    • P. B. Covas,
    • E. E. Cowan,
    • D. M. Coward,
    • M. J. Cowart,
    • D. C. Coyne,
    • R. Coyne,
    • J. D. E. Creighton,
    • T. D. Creighton,
    • J. Cripe,
    • S. G. Crowder,
    • T. J. Cullen,
    • A. Cumming,
    • L. Cunningham,
    • E. Cuoco,
    • T. Dal Canton,
    • G. Dálya,
    • S. L. Danilishin,
    • S. D’Antonio,
    • K. Danzmann,
    • A. Dasgupta,
    • C. F. Da Silva Costa,
    • L. E. H. Datrier,
    • V. Dattilo,
    • I. Dave,
    • M. Davier,
    • D. Davis,
    • E. J. Daw,
    • B. Day,
    • S. De,
    • D. DeBra,
    • J. Degallaix,
    • M. De Laurentis,
    • S. Deléglise,
    • W. Del Pozzo,
    • N. Demos,
    • T. Denker,
    • T. Dent,
    • R. De Pietri,
    • V. Dergachev,
    • R. De Rosa,
    • R. T. DeRosa,
    • C. De Rossi,
    • R. DeSalvo,
    • O. de Varona,
    • J. Devenson,
    • S. Dhurandhar,
    • M. C. Díaz,
    • L. Di Fiore,
    • M. Di Giovanni,
    • T. Di Girolamo,
    • A. Di Lieto,
    • S. Di Pace,
    • I. Di Palma,
    • F. Di Renzo,
    • Z. Doctor,
    • V. Dolique,
    • F. Donovan,
    • K. L. Dooley,
    • S. Doravari,
    • I. Dorrington,
    • R. Douglas,
    • M. Dovale álvarez,
    • T. P. Downes,
    • M. Drago,
    • C. Dreissigacker,
    • J. C. Driggers,
    • Z. Du,
    • M. Ducrot,
    • P. Dupej,
    • S. E. Dwyer,
    • T. B. Edo,
    • M. C. Edwards,
    • A. Effler,
    • H.-B. Eggenstein,
    • P. Ehrens,
    • J. Eichholz,
    • S. S. Eikenberry,
    • R. A. Eisenstein,
    • R. C. Essick,
    • D. Estevez,
    • Z. B. Etienne,
    • T. Etzel,
    • M. Evans,
    • T. M. Evans,
    • M. Factourovich,
    • V. Fafone,
    • H. Fair,
    • S. Fairhurst,
    • X. Fan,
    • S. Farinon,
    • B. Farr,
    • W. M. Farr,
    • E. J. Fauchon-Jones,
    • M. Favata,
    • M. Fays,
    • C. Fee,
    • H. Fehrmann,
    • J. Feicht,
    • M. M. Fejer,
    • A. Fernandez-Galiana,
    • I. Ferrante,
    • E. C. Ferreira,
    • F. Ferrini,
    • F. Fidecaro,
    • D. Finstad,
    • I. Fiori,
    • D. Fiorucci,
    • M. Fishbach,
    • R. P. Fisher,
    • M. Fitz-Axen,
    • R. Flaminio,
    • M. Fletcher,
    • H. Fong,
    • J. A. Font,
    • P. W. F. Forsyth,
    • S. S. Forsyth,
    • J.-D. Fournier,
    • S. Frasca,
    • F. Frasconi,
    • Z. Frei,
    • A. Freise,
    • R. Frey,
    • V. Frey,
    • E. M. Fries,
    • P. Fritschel,
    • V. V. Frolov,
    • P. Fulda,
    • M. Fyffe,
    • H. Gabbard,
    • B. U. Gadre,
    • S. M. Gaebel,
    • J. R. Gair,
    • L. Gammaitoni,
    • M. R. Ganija,
    • S. G. Gaonkar,
    • C. Garcia-Quiros,
    • F. Garufi,
    • B. Gateley,
    • S. Gaudio,
    • G. Gaur,
    • V. Gayathri,
    • N. Gehrels,
    • G. Gemme,
    • E. Genin,
    • A. Gennai,
    • D. George,
    • J. George,
    • L. Gergely,
    • V. Germain,
    • S. Ghonge,
    • Abhirup Ghosh,
    • Archisman Ghosh,
    • S. Ghosh,
    • J. A. Giaime,
    • K. D. Giardina,
    • A. Giazotto,
    • K. Gill,
    • L. Glover,
    • E. Goetz,
    • R. Goetz,
    • S. Gomes,
    • B. Goncharov,
    • G. González,
    • J. M. Gonzalez Castro,
    • A. Gopakumar,
    • M. L. Gorodetsky,
    • S. E. Gossan,
    • M. Gosselin,
    • R. Gouaty,
    • A. Grado,
    • C. Graef,
    • M. Granata,
    • A. Grant,
    • S. Gras,
    • C. Gray,
    • G. Greco,
    • A. C. Green,
    • E. M. Gretarsson,
    • P. Groot,
    • H. Grote,
    • S. Grunewald,
    • P. Gruning,
    • G. M. Guidi,
    • X. Guo,
    • A. Gupta,
    • M. K. Gupta,
    • K. E. Gushwa,
    • E. K. Gustafson,
    • R. Gustafson,
    • O. Halim,
    • B. R. Hall,
    • E. D. Hall,
    • E. Z. Hamilton,
    • G. Hammond,
    • M. Haney,
    • M. M. Hanke,
    • J. Hanks,
    • C. Hanna,
    • M. D. Hannam,
    • O. A. Hannuksela,
    • J. Hanson,
    • T. Hardwick,
    • J. Harms,
    • G. M. Harry,
    • I. W. Harry,
    • M. J. Hart,
    • C.-J. Haster,
    • K. Haughian,
    • J. Healy,
    • A. Heidmann,
    • M. C. Heintze,
    • H. Heitmann,
    • P. Hello,
    • G. Hemming,
    • M. Hendry,
    • I. S. Heng,
    • J. Hennig,
    • A. W. Heptonstall,
    • M. Heurs,
    • S. Hild,
    • T. Hinderer,
    • D. Hoak,
    • D. Hofman,
    • K. Holt,
    • D. E. Holz,
    • P. Hopkins,
    • C. Horst,
    • J. Hough,
    • E. A. Houston,
    • E. J. Howell,
    • A. Hreibi,
    • Y. M. Hu,
    • E. A. Huerta,
    • D. Huet,
    • B. Hughey,
    • S. Husa,
    • S. H. Huttner,
    • T. Huynh-Dinh,
    • N. Indik,
    • R. Inta,
    • G. Intini,
    • H. N. Isa,
    • J.-M. Isac,
    • M. Isi,
    • B. R. Iyer,
    • K. Izumi,
    • T. Jacqmin,
    • K. Jani,
    • P. Jaranowski,
    • S. Jawahar,
    • F. Jiménez-Forteza,
    • W. W. Johnson,
    • D. I. Jones,
    • R. Jones,
    • R. J. G. Jonker,
    • L. Ju,
    • J. Junker,
    • C. V. Kalaghatgi,
    • V. Kalogera,
    • B. Kamai,
    • S. Kandhasamy,
    • G. Kang,
    • J. B. Kanner,
    • S. J. Kapadia,
    • S. Karki,
    • K. S. Karvinen,
    • M. Kasprzack,
    • M. Katolik,
    • E. Katsavounidis,
    • W. Katzman,
    • S. Kaufer,
    • K. Kawabe,
    • F. Kéfélian,
    • D. Keitel,
    • A. J. Kemball,
    • R. Kennedy,
    • C. Kent,
    • J. S. Key,
    • F. Y. Khalili,
    • I. Khan,
    • S. Khan,
    • Z. Khan,
    • E. A. Khazanov,
    • N. Kijbunchoo,
    • Chunglee Kim,
    • J. C. Kim,
    • K. Kim,
    • W. Kim,
    • W. S. Kim,
    • Y.-M. Kim,
    • S. J. Kimbrell,
    • E. J. King,
    • P. J. King,
    • M. Kinley-Hanlon,
    • R. Kirchhoff,
    • J. S. Kissel,
    • L. Kleybolte,
    • S. Klimenko,
    • T. D. Knowles,
    • P. Koch,
    • S. M. Koehlenbeck,
    • S. Koley,
    • V. Kondrashov,
    • A. Kontos,
    • M. Korobko,
    • W. Z. Korth,
    • I. Kowalska,
    • D. B. Kozak,
    • C. Krämer,
    • V. Kringel,
    • B. Krishnan,
    • A. Królak,
    • G. Kuehn,
    • P. Kumar,
    • R. Kumar,
    • S. Kumar,
    • L. Kuo,
    • A. Kutynia,
    • S. Kwang,
    • B. D. Lackey,
    • K. H. Lai,
    • M. Landry,
    • R. N. Lang,
    • J. Lange,
    • B. Lantz,
    • R. K. Lanza,
    • A. Lartaux-Vollard,
    • P. D. Lasky,
    • M. Laxen,
    • A. Lazzarini,
    • C. Lazzaro,
    • P. Leaci,
    • S. Leavey,
    • C. H. Lee,
    • H. K. Lee,
    • H. M. Lee,
    • H. W. Lee,
    • K. Lee,
    • J. Lehmann,
    • A. Lenon,
    • M. Leonardi,
    • N. Leroy,
    • N. Letendre,
    • Y. Levin,
    • T. G. F. Li,
    • S. D. Linker,
    • T. B. Littenberg,
    • J. Liu,
    • X. Liu,
    • R. K. L. Lo,
    • N. A. Lockerbie,
    • L. T. London,
    • J. E. Lord,
    • M. Lorenzini,
    • V. Loriette,
    • M. Lormand,
    • G. Losurdo,
    • J. D. Lough,
    • C. O. Lousto,
    • G. Lovelace,
    • H. Lück,
    • D. Lumaca,
    • A. P. Lundgren,
    • R. Lynch,
    • Y. Ma,
    • R. Macas,
    • S. Macfoy,
    • B. Machenschalk,
    • M. MacInnis,
    • D. M. Macleod,
    • I. Magaña Hernandez,
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  2. The 1M2H Collaboration

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  7. The MASTER Collaboration

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    • O. Gress,
    • V. Yurkov,
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    • M. Serra-Ricart

Contributions

All authors contributed to the work presented in this paper.

Competing financial interests

The authors declare no competing financial interests.

Reviewer Information Nature thanks N. Suntzeff and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Author details

    Extended data figures and tables

    Extended Data Figures

    1. Extended Data Figure 1: Graphical model illustrating the statistical relationships between the data and parameters. (55 KB)

      Open circles indicate parameters that require a prior; filled circles describe measured data, which are conditioned on in the analysis. Here we assume that we have measurements of the gravitational-wave data xGW, a recessional velocity (that is, redshift) vr, and the mean peculiar velocity in the neighborhood of NGC 4993 〈vp〉. 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 gravitational-wave data p(xGW | d, cosι) depends on the distance and inclination of the source (and additional parameters, here marginalized out).

    2. Extended Data Figure 2: Using different assumptions compared to our canonical analysis. (139 KB)

      The posterior distribution on H0 discussed in the main text is shown in black, the alternative flat prior on z (discussed in Methods) gives the distribution shown in blue, and the increased uncertainty (250 km s−1) applied to our peculiar velocity measurement (also discussed in Methods) is shown in pink. Minimal 68.3% (1σ) credible intervals are shown by dashed lines.

    Extended Data Tables

    1. Extended Data Table 1: Summary of constraints on the Hubble constant, binary inclination and distance (171 KB)

    Comments

    1. Report this comment #70849

      Xinhang Shen said:

      Please be aware that the theory LIGO uses to make its calculations is completely wrong!

      Einstein's relativity theory has already been disproved both logically and experimentally (see "Challenge to the special theory of relativity", March 1, 2016 on Physics Essays and a press release "Special Theory of Relativity Has Been Disproved Theoretically" on Eurekalert website: https://www.eurekalert.org/pub_releases/2016-03/ngpi-tst030116.php ). The problem of Einstein's relativity is that it has redefined time and space through Lorentz Transformation. The newly defined time is no longer the physical time measured with physical clocks, which can be easily demonstrated by the following thought experiment of candle clocks:

      There are a series of vertically standing candles with the same burning rate and moving at different constant horizontal velocities in an inertial reference frame of (x, y, z, t) where x, y, z, t are relativistic positions and time. At any moment t of relativistic time, all candles have the same height H in the reference frame of (x, y, z, t) and the height has been calibrated to physical time as physical clocks. Therefore, we have the simultaneous events of the observation measured in both relativistic time and physical time in the frame of (x, y, z, t): (Candle1, x1, y1, H, t), (candle2, x2, y2, H, t), ?, (CandleN, xN, yN, H, t). When these events are observed on anther horizontally moving inertial reference frame (x', y', z', t'), according to special relativity, these events in the reference frame of (x', y', z', t') can be obtained through Lorentz Transformation: (Candle1, x'1, y'1, H, t'1), (Candle2, x'2, y'2, H, t'2), ? , (CandleN, x'N, y'N, H, t'N) where t'1, t'2, ?, and t'N are relativistic times of the events in the frame of (x', y', z', t'). It is seen that these events have different relativistic times after Lorentz Transformation in the frame of (x', y', z', t'), i.e., they are no longer simultaneous measured with relativistic time in the frame of (x', y', z', t'), but the heights of the candles remain the same because the vertical heights here do not experience any Lorentz contraction. Since the heights of the candles are the measures of the physical time, we can see these events still have the same physical time, i.e., they are still simultaneous measured with the physical time. Therefore, the physical time is invariant of inertial reference frames, which is different from relativistic time. As relativistic time is no longer the physical time we measure with physical devices, the des cription of special relativity is irrelevant to the physical world.

      Now let's have a look at the symmetric twin paradox. Two twins made separate space travels in the same velocity and acceleration relative to the earth all the time during their entire trips but in opposite directions. According to special relativity, each twin should find the other twin?s clock ticking more slowly than his own clock during the entire trip due to the relative velocity between them because acceleration did not have any effect on kinematic time dilation in special relativity. But when they came back to the earth, they found their clocks had exact the same time because of symmetry. Thus, there is a contradiction which has disproved special relativity. This thought experiment demonstrates that relativistic time is not our physical time and can never be materialized on physical clocks.

      Now let's look at clocks on the GPS satellites which is thought as one of the strong evidences of Einstein's relativity. Many physicists claim that clocks on the GPS satellites are corrected according to both special relativity and general relativity. This is not true because the corrections of the atomic clocks on the GPS satellites are absolute changes of the clocks (i.e. the same observed in all reference frames), none of which is relative to a specific observer as claimed by special relativity. After all corrections, the clocks are synchronized not only relative to the ground clocks but also relative to each other, i.e., time is absolute and special relativity is wrong.

      This is a fact as shown on Wikipedia. But some people still argue that the clocks on the GPS satellites are only synchronized in the earth centered inertial reference frame, and are not synchronized in the reference frames of the GPS satellites. If it were true, then the time difference between a clock on a GPS satellite and a clock on the ground observed in the satellite reference frame would monotonically grow due to their relative velocity while the same clocks observed on the earth centered reference frame were still synchronized. If you corrected the clock on the satellite when the difference became significant, the correction would break the synchronization of the clocks observed in the earth centered frame. That is, there is no way to make such a correction without breaking the synchronization of the clocks observed in the earth centered frame. Therefore, it is wrong to think that the clocks are not synchronized in the satellite frame.

      Hefele-Keating experiment is also considered as another evidence of relativistic effects. It is clear that all the differences of the clocks after flights in Hefele-Keating experiment were absolute (i.e., they were the same no matter whether you observe them on the earth, on the moon or on the space station). But according to relativity, if the clocks were observed on the earth, the two clocks after flights had experienced the equivalent paths of same velocity and same distance in same elevation, and thus should generate the same kinematic time dilation and the same gravitational time dilation, directly contradicting the experimental result. Therefore, the differences of the clocks were nothing to do with the velocities relative to each other or relative to the earth as claimed by relativists, but were the result of the velocities relative to one medium which seems fully dragged by the earth on its surface but partially dragged on the altitude of the airplanes. It is wrong to interpret the differences of the displayed times of the clocks as the results of relativistic effects.

      Experiments show that electrons will emit photons when they are "moving", but ?moving? is relative. All electrons on the earth can be considered "moving" when you observe them on a rocket. According to special relativity, you should see them emit photons. Why in a rocket frame don't you see the electrons emit photons? It is because special relativity is wrong. It is not the velocity relative to the observer which makes an electron emit photons, but it is the velocity relative to ?something? makes an electron emit photons. This ?something? is aether, the existence of which has been proved in the above paper. Photons are waves of aether which is a compressible viscous fluid filling up the entire visible part of the universe, though its viscosity is very very small. It is the velocity relative to aether makes an electron emit photons, just as a boat on a water generates waves only when it moves relative to the water.

      The increase of the lives of muons in particle accelerators or going through the atmosphere are the effects of aether caused by their velocities relative to aether, which are absolute changes and the same observed in all reference frames, nothing to do with relativity.

      All so-called proofs of relativistic effects are just misinterpretations of experiments and observations without exception, and all what relativity describes is irrelevant to physical phenomena, including the speed of light which in special relativity is constant in all inertial reference frames, but which in real physical world still follows Newton's velocity addition formula (see the paper).

      That is, time is absolute and space is 3D Euclidean. There is nothing called spacetime continuum in nature, not to mention the ripples of spacetime.

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