First Measurement of the Hubble Constant from a Dark Standard Siren using the Dark Energy Survey Galaxies and the LIGO/Virgo Binary–Black-hole Merger GW170814

Unlike most extragalactic distance observables, mergers of neutron star and black hole binary systems are absolute distance indicators. Often referred to as "standard sirens," they emit gravitational waves (GWs) from which the luminosity distance can be inferred without relying on any calibration with respect to another source: the rate of change in frequency gives the system's size and thus the intrinsic amplitude, which is compared against the observed signal amplitude to obtain the distance to the source. If redshifts are associated with those sirens (in the simplest case, the host galaxy is identified and its redshift is obtained via spectroscopic follow up), a measurement of the present rate of expansion of the universe H₀ can be achieved via the distance–redshift relation. The use of GW sources as cosmological probes was first proposed by Schutz (1986), and recently revisited in several works (e.g., Holz & Hughes 2005).

For dark energy research, the possibility of measuring H₀ directly and independently from other methods is of great interest. Local measurements obtained from SN Ia and other distance indicators, as well as the predicted value inferred from the cosmic microwave background (CMB) at z ∼ 1100, have achieved remarkable precision of 1%–2.5% (e.g., Planck Collaboration et al. 2018; Riess et al. 2018). They disagree, however, by more than 3σ and interpreting this tension as evidence for beyond-ΛCDM dark energy or new physics at the early universe requires new measurements of great precision and accuracy (Freedman 2017; Mörtsell & Dhawan 2018). Those measurements are one of the greatest challenges faced by current experiments in cosmology because the observables are subject to correlated systematic effects arising from their complex astrophysics. As estimates become more precise, this challenge becomes more severe and the need for novel independent methods becomes more pressing. Those methods, however, are few and hard to come by. One possibility is standard sirens, which remained elusive for almost 30 yr, until the detection of the first GW event (GW150914; Abbott et al. 2016). The first standard siren-based H₀ measurement (Abbott et al. 2017a) came with the discovery of the binary–neutron-star (BNS) merger GW170817 (Abbott et al. 2017) and its associated electromagnetic counterpart (Arcavi et al. 2017; Coulter et al. 2017; LIGO Scientific Collaboration et al. 2017; Lipunov et al. 2017; Soares-Santos et al. 2017; Tanvir et al. 2017; Valenti et al. 2017). Several studies have developed methodologies to infer cosmological parameters from standard sirens and establish their constraining power (Schutz 1986; Holz & Hughes 2005; MacLeod & Hogan 2008; Nissanke et al. 2010, 2013; Del Pozzo 2012; Nishizawa 2017; Chen et al. 2018; Feeney et al. 2019; Mortlock et al. 2018; Vitale & Chen 2018). Chen et al. (2018) predicted that we will be able to constrain H₀ with 2% precision within 5 yr with standard sirens detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO)/Virgo, while Nair et al. (2018) predicted a ∼7% measurement with just 25 binary–black-hole (BBH) events from the Einstein telescope.

Anticipating that the LIGO/Virgo Collaboration (LVC) network of GW detectors would eventually achieve sensitivity sufficient to enable standard siren-based measurements, the Dark Energy Survey (DES) collaboration and external collaborators launched in 2015 the DES gravitational waves (DESGW) program. DESGW uses the Dark Energy Camera (DECam) to search for optical emission associated with LVC-detected mergers and pursues cosmological measurements with standard sirens. In particular, the multi-messenger shared discovery of the neutron-star merger GW170817, and of its optical kilonova, resulted in a measurement of H₀ (Abbott et al. 2017a) that inaugurated the era of siren-based cosmology. We have also performed the most comprehensive searches for optical emission to black hole events, including GW150914 (Soares-Santos et al. 2016), GW151226 (Cowperthwaite et al. 2016), and GW170814 (Doctor et al. 2018). These events are expected to be dark, although the possibility of optical emission has yet to be observationally excluded.

Dark sirens can also be used for cosmology using a statistical method, as first proposed in Schutz (1986). Provided a catalog of potential host galaxies within the event localization region, their redshifts will contribute in a probabilistic way to the measurement of H₀, depending on the galaxies' distance and sky position. This approach has been developed within a Bayesian framework by Del Pozzo (2012) and Chen et al. (2018) and implemented in Fishbach et al. (2019) using GW170817, which produced results consistent with the first measurement (Abbott et al. 2017a) where the identified host galaxy, NGC 4993 (e.g., Palmese et al. 2017), was used. Eventually, a large sample of events will enable precise cosmological measurements using the dark siren approach.

In this work, we measure H₀ using the GW event GW170814 (Abbott et al. 2017b) as a dark siren. GW170814 resulted from the inspiral and merger of a BBH system at a luminosity distance of ${540}_{-210}^{+130}\,\mathrm{Mpc}$ (median value with 90% credible interval). The masses of the black holes were ${30.5}_{-3.0}^{+5.7}$ and ${25.3}_{-4.2}^{+2.8}\,{M}_{\odot }$, respectively. GW170814 is the first BBH detected by a triple network (including LIGO Hanford and Livingston, plus Virgo), and it has the smallest localization volume of any of the BBH events detected by LVC thus far. Therefore, the number of potential host galaxies is lower compared to other events, making GW170814 the most appropriate event for this measurement. Additionally, the event localization region falls within the DES footprint, making DES galaxy catalogs a prime sample for measurement of H₀. With this one event, our goal is to provide a proof of principle measurement, addressing the challenges that are specific to the dark siren method, and establishing its potential to yield precision cosmology results in the near future.

A key component of the measurement is crafting the appropriate galaxy catalog: completeness, as well as precise and accurate photometric redshifts (photo-z's), throughout the entire volume probed are required. The overlap of GW170814's area with DES allows us to employ galaxy catalogs produced from the first three years of the survey (DES Y3; Abbott et al. 2018). This first dark siren measurement is a step toward incorporating this new cosmological probe into the portfolio of cosmic surveys for dark energy.

A detailed description of the data used in this analysis is provided in Section 2, followed by a description of our implementation of the method in Section 3. We present our results and discussion in Section 4, and our conclusions in Section 5. Throughout this Letter we assume a flat ΛCDM cosmology with Ω_m = 0.3 and H₀ values in the 20–140 km s⁻¹ Mpc⁻¹ range. All quoted error bars represent the 68% confidence level (CL), unless otherwise stated.

2.1. The LVC Sky Map

The sky map used in this work is the publicly available LALInference map (LIGO Scientific Collaboration & Virgo Collaboration 2017),²³⁰ provided in HEALPix (Górski et al. 2005) pixels. The luminosity distance probability distribution is approximated with a Gaussian in each pixel. The region of interest, enclosing 90% of the localization probability, is 61.66 deg². The projected sky map and the distribution of luminosity distance mean values from the LVC distance likelihood in each pixel within the region of interest are shown in Figure 1. The probability peak is located at R.A., decl. = (47523, −44856). At the peak location, the luminosity distance is 504.7 Mpc and the Gaussian width is 91.9 Mpc. Using the limiting values of our H₀ prior range ([20,140] km s⁻¹ Mpc⁻¹) we can convert the 90% and 99.7% distance range into a redshift range (0.02 < z < 0.26 and z < 0.3, respectively) for this analysis.

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2.2. The DES Galaxy Catalog

In order to estimate the posterior probability of H₀ given GW data d_GW from a single event detection, and electromagnetic (EM) data from a galaxy survey, we follow Chen et al. (2018). By applying Bayes' theorem, one can write the posterior as

$$\begin{eqnarray}&&p({H}_{0}| {d}_{\mathrm{GW}},{d}_{\mathrm{EM}})\propto p({d}_{\mathrm{GW}},{d}_{\mathrm{EM}}| {H}_{0})p({H}_{0}).\end{eqnarray} \tag{ 1 }$$

We assume that all cosmological parameters except for H₀ are fixed (flat ΛCDM cosmology with Ω_m = 0.3 and Ω_Λ = 0.7). We treat the joint GW and EM likelihood $p({d}_{\mathrm{GW}},{d}_{\mathrm{EM}}| {H}_{0})$ as the product of two individual likelihoods (as the processes involved in producing the data from the two experiments are independent) marginalized over all variables except for the true luminosity distance d_L and solid angle ${\hat{{\rm{\Omega }}}}_{\mathrm{GW}}$ of the GW source, and for the true host galaxy redshift z_i and solid angle ${\hat{{\rm{\Omega }}}}_{i}$. Note that the solid angles $\hat{{\rm{\Omega }}}$ are vectors with the angular position of the source/galaxy as direction, and they all subtend the same area (∼3 × 10⁻³ deg²) as the sky is pixelized with HEALPix maps in this work. If we assume that the event happened in one of the observed galaxies i, then ${\hat{{\rm{\Omega }}}}_{\mathrm{GW}}$ and ${\hat{{\rm{\Omega }}}}_{i}$ are related, and so are d_L and z_i through the cosmology (in this case, H₀). By marginalizing also over the choice of galaxy i, the joint marginal likelihood can be written as

$$\begin{eqnarray}&&\begin{array}{l}p\left({d}_{\mathrm{GW}},{d}_{\mathrm{EM}}| \left\{{z}_{j},{\hat{{\rm{\Omega }}}}_{j}\right\},{H}_{0}\right)\\ \quad \propto \ \sum _{i}{w}_{i}\int {\text{}}{{dd}}_{L}\,{\text{}}d{\hat{{\rm{\Omega }}}}_{\mathrm{GW}}\,p\left({d}_{\mathrm{GW}}| {d}_{L},{\hat{{\rm{\Omega }}}}_{\mathrm{GW}}\right)\\ \quad \times \ p\left({d}_{\mathrm{EM}}| \left\{{z}_{j},{\hat{{\rm{\Omega }}}}_{j}\right\}\right){\delta }_{D}({d}_{L}-{d}_{L}({z}_{i},{H}_{0})){\delta }_{D}\left({\hat{{\rm{\Omega }}}}_{\mathrm{GW}}-{\hat{{\rm{\Omega }}}}_{i}\right),\end{array}\end{eqnarray} \tag{ 2 }$$

where ${\delta }_{D}$ is the Dirac delta function, w_i are weights that represent the relative probability that different galaxies host a GW source, and $\{{z}_{j},{\hat{{\rm{\Omega }}}}_{j}\}$ represents all the galaxies' redshift and solid angle. These weights could be based on some galaxy properties, such as luminosity or star formation rate, but here we assume they are uniform across all galaxies given our lack of knowledge of GW host galaxy properties.

We also need to marginalize over the galaxies' redshifts and sky positions, with a reasonable choice of prior p(z_i, Ω_i). If one assumes that the galaxies are uniformly distributed in comoving volume V, and volume-limited within V_max,

$$\begin{eqnarray}&&p({z}_{i},{\hat{{\rm{\Omega }}}}_{i})\,{\text{}}{{dz}}_{i}\,{\text{}}d{\hat{{\rm{\Omega }}}}_{i}\propto \displaystyle \frac{1}{{V}_{\max }}\displaystyle \frac{{\text{}}{d}^{2}V}{{\text{}}{{dz}}_{i}{\text{}}d{\hat{{\rm{\Omega }}}}_{i}}{\text{}}{{dz}}_{i}\,{\text{}}d{\hat{{\rm{\Omega }}}}_{i}\propto \displaystyle \frac{1}{{V}_{\max }}\displaystyle \frac{{r}^{2}({z}_{i})}{H({z}_{i})}{\text{}}{{dz}}_{i}\,{\text{}}d{\hat{{\rm{\Omega }}}}_{i},\end{eqnarray} \tag{ 3 }$$

where r is the comoving distance to the galaxy. While this assumption holds on average over sufficiently large volumes, it is possible that future precision cosmology analyses will require taking into account the real clustering of galaxies in this formalism.

Assuming that we precisely know the galaxies' positions $\{{\hat{{\rm{\Omega }}}}_{j}\}$ (which is realistic especially in the limit in which spatial probabilities are considered within HEALPix pixels), we can integrate over the galaxies' positions as delta functions about the observed values. The marginal EM likelihood reduces to $p({d}_{\mathrm{EM}}| \{{z}_{j}\})$, which we approximate for simplicity by a product of Gaussian distributions, ${ \mathcal N }$, for each galaxy, centered around the observed redshift values z_obs,i with a width given by the redshift's uncertainty σ_z,i for each galaxy i:

$$\begin{eqnarray}&&p({d}_{\mathrm{EM}}| \{{z}_{j}\})=\displaystyle \prod _{i}p({z}_{\mathrm{obs},i}| {z}_{i})=\displaystyle \prod _{i}{ \mathcal N }({z}_{\mathrm{obs},i},{\sigma }_{z,i};{z}_{i}).\end{eqnarray} \tag{ 4 }$$

The marginal GW likelihood $p({d}_{\mathrm{GW}}| {d}_{L},{\rm{\Omega }})$ can be computed as prescribed in Singer et al. (2016):

$$\begin{eqnarray}&&p({d}_{\mathrm{GW}}| {d}_{L},\hat{{\rm{\Omega }}})\propto p(\hat{{\rm{\Omega }}})\displaystyle \frac{1}{\sqrt{2\pi }\sigma (\hat{{\rm{\Omega }}})}\exp \left[-\displaystyle \frac{{\left({d}_{L}-\mu (\hat{{\rm{\Omega }}})\right)}^{2}}{2{\sigma }^{2}(\hat{{\rm{\Omega }}})}\right]N(\hat{{\rm{\Omega }}}),\end{eqnarray} \tag{ 5 }$$

where the position probability, location, normalization, and scale (PROB $p(\hat{{\rm{\Omega }}})$, DISTMU μ, DISTNORM N, and DISTSTD σ, respectively) of the luminosity distance at each position are provided in the sky map.

We now consider the selection effects of GW events and galaxies introduced by the experiments' sensitivities and detection pipelines. We follow the approach of Chen et al. (2018) and Mandel et al. (2019), and include a ${[\beta ({H}_{0})]}^{-1}$ factor that normalizes the likelihood over all possible GW and EM data. Given that our galaxy catalog is volume-limited out to larger distances than the maximum observable distance for the GW events, this term reduces to

$$\begin{eqnarray}&&\beta ({H}_{0})=\displaystyle \frac{V[{d}_{L,\mathrm{GW}}^{\max }({H}_{0})]}{{V}_{\max }({H}_{0})},\end{eqnarray} \tag{ 6 }$$

where $V[{d}_{L,\mathrm{GW}}^{\max }({H}_{0})]$ is the maximum observable volume for the GW events considered.

Finally, Equation (1) becomes

$$\begin{eqnarray}&&\begin{array}{l}p({H}_{0}| {d}_{\mathrm{GW}},{d}_{\mathrm{EM}})\propto \displaystyle \frac{p({H}_{0})}{V[{d}_{L,\mathrm{GW}}^{\max }({H}_{0})]}\sum _{i}\displaystyle \frac{1}{{{ \mathcal Z }}_{i}}\\ \quad \times \,\int {\text{}}{{dz}}_{i}\,p({d}_{\mathrm{GW}}| {d}_{L}({z}_{i},{H}_{0}),{\hat{{\rm{\Omega }}}}_{i})p({d}_{\mathrm{EM}}| {z}_{i})\displaystyle \frac{{r}^{2}({z}_{i})}{H({z}_{i})},\end{array}\end{eqnarray} \tag{ 7 }$$

where ${{ \mathcal Z }}_{i}=\int p({d}_{\mathrm{EM}}| {z}_{i}){r}^{2}({z}_{i})/H({z}_{i})\,{\text{}}{{dz}}_{i}$ are evidence terms that arise from integrating out the other galaxy redshifts in each term of the sum. This formalism can be extended to combine data {d_GW,j} and d_EM from a sample of multiple events j, assuming that the GW events are independent and that the galaxy catalog is fixed for all events:

$$\begin{eqnarray}&&\begin{array}{l}p({H}_{0}| \{{d}_{\mathrm{GW},j}\},{d}_{\mathrm{EM}})\propto p({H}_{0})\int {\text{}}{d}^{N}{z}_{k}{\text{}}{d}^{N}{\hat{{\rm{\Omega }}}}_{k}p({z}_{k},{\hat{{\rm{\Omega }}}}_{k})\\ \qquad \times \,p({d}_{{EM}}| \{{z}_{k},{\hat{{\rm{\Omega }}}}_{k}\})\left[\displaystyle \prod _{j}p({d}_{{GW},j}| \{{z}_{k},{\hat{{\rm{\Omega }}}}_{k}\})\right].\end{array}\end{eqnarray} \tag{ 8 }$$

In the following, we assume a flat prior on H₀ within [20,140]  km s⁻¹ Mpc⁻¹, unless otherwise stated. This is a very broad prior, covering a range that is much larger than current estimates of H₀. This choice was made as a compromise between the following aspects: (i) a result that is mostly informed by the LVC and DES data rather than by external constraints, (ii) a result that can be compared with the first standard siren estimate, and (iii) a complete galaxy sample that contains most of the stellar mass within the localization volume, to minimize the chance of missing the real host galaxy. As explained in more detail in Section 4, the redshift cut is related to the H₀ prior range, and in order to explore higher values of H₀, one needs to include higher redshift galaxies, and make a higher luminosity cut to preserve the volume-limited sample.

A blinded analysis has been performed when estimating the H₀ posterior from the data to avoid confirmation bias. The values of the Hubble constant have been randomly displaced by an unknown amount, and we unblinded after our pipeline was able to reliably reproduce the input cosmology on simulation tests.

We apply the described methodology to the DES galaxies' redshifts and the GW170814 LIGO/Virgo sky map to produce a posterior distribution for the Hubble constant. We find that changes in the H₀ estimate and its uncertainty between using the corrected DNF photo-z's or the ANNz2 outputs are below the percent level. This agreement is expected, because the two methods produce redshift distributions that are consistent with similar uncertainties. We also add a 0.001 systematic redshift error in quadrature (corresponding to a typical peculiar velocity of $\sim 300\,\mathrm{km}\,{{\rm{s}}}^{-1}$). The effect of this correction on the posterior is negligible because only a few percent of the galaxies have a spectroscopic redshift, and the effect of peculiar velocities on the remaining galaxies is more than an order of magnitude below their typical photo-z error.

Our maximum a posteriori estimate of the Hubble constant is ${H}_{0}={75}_{-32}^{+40}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ using a flat prior between 20 and 140 km s⁻¹ Mpc⁻¹. The full posterior distribution is shown in Figure 2, and Table 1 summarizes our findings. The presence of a main, though broad, peak, is expected given the large-scale structure seen in the observed volume.

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Table 1.  Hubble Constant Estimate from this Work

Prior	H0	$+{\sigma }_{{H}_{0}}$	$-{\sigma }_{{H}_{0}}$	${\sigma }_{{H}_{0}}/{H}_{0}$	${\sigma }_{{H}_{0}}/{H}_{0}$ prior
[20,140]	75	40	32	47.8%	54.3%

Note. All H₀ values and errors are in km s⁻¹ Mpc⁻¹. The uncertainty from the flat prior only is derived by assuming the same H₀ maximum found in the analysis. Quoted uncertainties represent 68% confidence level around the maximum of the posterior, and they are statistical only. The last column quantity (${\sigma }_{{H}_{0}}/{H}_{0}$ prior) corresponds to 68% times the prior width divided by H₀.

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As described in Section 2.1, the galaxy sample used in these results is selected as described in Section 2, and covers the LIGO/Virgo 90% credible localization volume. The distance cut is translated into a redshift cut (made on the mean photo-z value of each galaxy) for a given H₀ prior. This cut ensures that the galaxy catalog is as complete as possible throughout the whole redshift range of interest for the cosmological parameters used, and includes the fainter galaxies observable for a volume-limited sample defined as in Section 2. In fact, in order to include more distant galaxies, the luminosity cut needs to be brighter to ensure that the sample is still volume limited, with the risk of missing the true host galaxy. We have explored the impact of the redshift cut on the H₀ posterior, while keeping the angular selection to be within the 90% credible localization area. The effect of including galaxies out to 99.7% of the distance localization (corresponding to z ≲ 0.3) is most pronounced at high H₀ values, as shown by the shaded red region in Figure 2. With this less restrictive cut, the credible region shifts to ${H}_{0}={77}_{-33}^{+41}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$, showing a ∼2% change of the maximum. The effect described here arises from tens of thousand of galaxies at the higher redshifts included with the more relaxed distance cut and the ansatz of Gaussianity of the luminosity distance posterior. In fact, these galaxies contribute with a non-negligible probability to the posterior because of the high d_L tail shown in the bottom-right panel of Figure 1, and they contribute more significantly at high H₀ values. This few percent effect is insignificant at the current levels of precision, but will need to be explored in the future using a more realistic luminosity distance posterior.

Our result agrees well (as expected, due to the large uncertainty) with the latest CMB estimate of the Hubble constant by the Planck Collaboration (67.36 ± 0.54 km s⁻¹ Mpc⁻¹ from TT,TE,EE+lowP+lensing; Planck Collaboration et al. 2018), and with results using distance ladder methods by ShoES (73.52 ± 1.62 km s⁻¹ Mpc⁻¹; Riess et al. 2016) and by DES (67.77 ± 1.30 km s⁻¹ Mpc⁻¹ from SN+BAO; Macaulay et al. 2019).

For the bright standard siren measurement using GW170817 and its electromagnetic counterpart, Abbott et al. (2017a) found ${H}_{0}={70.0}_{-8.0}^{+12.0}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ at 68% credible interval. Without an EM counterpart leading to a unique host galaxy redshift, we would have recovered a broader H₀ posterior because we average over all possible host galaxies in the localization volume. For example, Fishbach et al. (2019) applied the statistical standard siren method to GW170817 and found a larger uncertainty than the counterpart standard siren result: ${H}_{0}={76}_{-23}^{+48}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ for a uniform prior over the range [10,220] km s⁻¹ Mpc⁻¹. For a BBH standard siren measurement, as in this work, the combination of the larger localization volume (implying a significantly greater number of potential host galaxies) and the large photometric redshift uncertainty for each galaxy results in an even broader H₀ posterior. Therefore, while applying the statistical standard siren method to GW170817 yields a 68% credible region on H₀ comprising 34% of the prior range (Fishbach et al. 2019), in this work we obtain a 68% credible region on H₀ that is 60% of the prior range. We note that the prior used in Fishbach et al. (2018) is 1.75 times broader than the prior used in this work; if we adopt the same broader prior of [10,220] for our analysis of GW170814, we find ${H}_{0}={78}_{-24}^{+96}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$. The dependence of the width of the H₀ posterior on the prior width is a consequence of the fact that the GW observation, which provides only a luminosity distance estimate, is consistent with arbitrarily large H₀'s, if there are galaxies at sufficiently large redshifts. If the galaxy catalog extends to some redshift, z_max, the posterior would fall off around H₀ ≈ cz_max/d_L, where d_L is the typical luminosity distance from the GW posterior. However, this fall off is artificial as there are galaxies at greater redshifts that are not included in the catalog. These may be accounted for using catalog incompleteness corrections. We chose the prior range for this analysis rather than a larger one such that we did not need to include such corrections, which simplifies the analysis. However, dark siren measurements will become particularly interesting when multiple events can be combined and this effect becomes irrelevant (Chen et al. 2018).

The analysis in Fishbach et al. (2019) for GW170817 used the Galaxy List for the Advanced Detector Era (GLADE) galaxy catalog (Dálya et al. 2018), and accounted for incompleteness at the distance of GW170817. GLADE becomes significantly incomplete at the distance to GW170814. As GW detectors improve in sensitivity, the majority of dark standard sirens will be detected at even greater distances and with larger localization volumes, well beyond the reach of spectroscopic galaxy catalogs. This highlights the need for reliable and complete photometric galaxy catalogs. Surveys such as DES, Pan-STARRS1 (Chambers et al. 2016), and the Large Synoptic Survey Telescope (LSST) are therefore likely to play an important role in future constraints from BBH standard sirens.

The assumption throughout this work is that even if the event occurred in a galaxy below our luminosity threshold, large-scale structure predicts that fainter galaxies follow the clustering pattern of the more luminous galaxies in our sample. We have verified in our simulations that a threshold up to 1 mag brighter than the limit used here to place events has a negligible impact over a sample of 100 events, provided that the catalog is volume limited for the range of redshifts relevant to the measurement.

Galaxies are biased tracers of the universe's dark matter, therefore some theories predict that the origin of the black holes involved in these GW events is primordial, constituting part or all of the dark matter (Bird et al. 2016; Clesse & García-Bellido 2017, 2018; García-Bellido 2017). In that case, GW events follow exactly the underlying dark matter distribution (presenting an unbiased tracer). Because of the stellar mass to dark matter halo connection (see Wechsler & Tinker 2018, and references therein) it is reasonable to weight galaxies by their stellar mass in Equation (2) as w_i ∝ M_⋆. The impact of this scaling with stellar mass or star formation rate has been explored in Fishbach et al. (2019). We find that the stellar mass weighting has a negligible effect on the posterior. This is due to the large volume analyzed (over which the stellar masses tend to be averaged out) and to the precision level of this measurement. In other theories, these black hole binaries are produced in very-low-metallicity galaxies (e.g., Cao et al. 2018; Mapelli et al. 2018), biased relative to the dark matter distribution differently than the luminous galaxies in our catalog. J. Annis et al. (2019, in preparation) explore the effect of the tracer bias assumptions on the H₀ posterior for future analyses aiming at precision measurements.

Another assumption of our analysis that needs attention concerns the redshift likelihood. As anticipated above for the GW likelihood, this will not, in general, be well approximated by a Gaussian. In the future, we plan to explore the impact of realistic photometric redshift PDFs on the H₀ posterior, in order to enable precision cosmology with BBH events. An analysis with the full, asymmetric, GW likelihood will also be required. While an estimate of those effects is needed, tests on off-source lines of sight show that our constraint is likely not strongly impacted by the photo-z training sample or systematic failures.

In the past two LVC observing seasons, black hole mergers outnumbered neutron star events at a rate of approximately 10–1. Uncertainties on the expected detection rate are large, but conservative estimates predict ∼1 event per week for the upcoming observing campaign (scheduled to start in 2019 April). The majority of these events will have larger localization volumes than GW170814 (Chen & Holz 2016 estimated that ≲1% of BBHs will be localized to better than 10⁴ Mpc³), and hence provide poorer constraints than those reported here. However, given the high expected event rate for dark sirens, larger event samples will be available in the future. Chen et al. (2018) provided forecasts using a distribution of realistic localization area, finding that the dark siren method will reach ∼10% statistical precision on H₀ by 2026 from BBH mergers only, and 5%–10% precision from BNS mergers if none of them have EM counterparts.

In this Letter, we have performed the first measurement of the Hubble constant using a GW detection of a BBH merger as a dark standard siren and the DES galaxies as a sample of potential host galaxies. Our analysis was blinded to avoid confirmation bias. Our main results, discussed in Section 4, include a measurement of ${H}_{0}={75}_{-32}^{+40}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ for a flat prior within [20,140] km s⁻¹ Mpc⁻¹, which is consistent with previous measurements of H₀. The 68% confidence interval quoted here is 60% of the uniform prior range, and it depends on the width of the prior. For example, with a broader prior of [10,220] km s⁻¹ Mpc⁻¹, we find ${H}_{0}={78}_{-24}^{+96}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$. Albeit weak, this measurement is not uninformative and the method becomes more powerful when we combine large numbers of dark sirens (Chen et al. 2018).

Future dark siren measurements will require complete galaxy catalogs. A wide field galaxy catalog with a DES-like depth is currently available only for ∼one-eighth of the sky. However, DES can be complemented with other data sets taken with DECam (such as the Blanco Imaging of the Southern Sky, BLISS, and the Dark Energy Camera Legacy Survey (DECals)), to cover the whole Southern sky to a good depth (r ∼ 23.4, 5σ depth). An even deeper survey with more precise photo-z's, such as the LSST (LSST Dark Energy Science Collaboration 2012), would be of great value for further improving these constraints.

At the expected level of precision from hundreds of events (<10%), systematics will play an important role. In future work, we plan to incorporate systematic uncertainties in our simulated data studies, in order to prepare for precision cosmology analyses on real data. We anticipate that some of the main sources of systematics will be photo-z biases and catastrophic outliers, photo-z training sample sample variance, galaxy catalog cuts, and galaxy catalog completeness. In order to achieve the full potential of statistical standard siren cosmology, wide and deep galaxy surveys such as DES and LSST are necessary. Overall, our findings show that the synergy between GW black hole merger detections and new-generation large galaxy surveys will establish a new powerful probe for precision cosmology.

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 (University of 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 Nos. 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-2016-0588, SEV-2016-0597, and MDM-2015-0509. Research leading to these results has received funding from the ERC under the EU's 7th 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 No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.

The authors gratefully 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. The authors gratefully 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. The authors also gratefully 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 & 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 Paris Île-de-France Region, the National Research, Development and Innovation Office Hungary (NKFIH), 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. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS, and the State of Niedersachsen/Germany for provision of computational resources.