The binary–host connection: astrophysics of gravitational wave binaries from their host galaxy properties

The first gravitational-wave (GW) detection of a binary neutron star (BNS), GW170817, detected by advanced LIGO (Aasi et al., 2015) and Virgo (Acernese et al., 2015), ushered in the era of GW multi-messenger astronomy (Abbott et al., 2017a, b). GW170817 was observed in a broad swath of the electromagnetic spectrum, including as a short gamma-ray burst (sGRB), X-ray/radio afterglow, and optical kilonova (Abbott et al., 2017; Margutti et al., 2017; Alexander et al., 2017; Coulter et al., 2017; Soares-Santos et al., 2017; Abbott et al., 2017b).

The formation and evolutionary history of BNS systems are not well constrained (see e.g. Belczynski et al., 2018). These systems are usually characterized by a delay time between the initial formation of the binary and its eventual merger. The distribution of these delay times is expected to follow the distribution of the major axes of their orbits  (Peters, 1964), and in the case of massive O/B stars that collapse to form compact objects binaries, a power-law distribution $dN/da\propto a^{\beta}$ is assumed (Sana et al., 2012; Kobulnicky et al., 2014). The merger time delay distribution is therefore also expected to follow a power-law distribution, $dN/dt\propto t^{\alpha}$, with some minimum time delay $t_{d}$. In general binary neutron stars are expected to have $\alpha=-1$, but if the binary goes through a common envelope phase the power-law dependence can be steeper and closer to $t^{-1.5}$ (Dominik et al., 2012; Belczynski et al., 2018; Safarzadeh & Berger, 2019).

Within the next few years the network of GW detectors are likely to provide a statistical sample of tens to hundreds of BNS detections (Abbott et al., 2018). We expect a substantial fraction of these BNS events to have electromagnetic counterparts and identified host galaxies. Statistical studies of the properties of the host galaxies will provide a new window into understanding these systems. For example a recent study by Safarzadeh & Berger (2019) proposes to use the stellar masses of BNS host galaxies to infer the time-delay distribution of neutron star mergers. In particular, they forecast the constraints on the minimum delay time $t_{d}$ and the slope $\alpha$ of the time-delay distribution that will be possible with future events. They find that it will take $\mathcal{O}(1,000)$ GW detections with identified host galaxies to constrain the parameter space of time-delay models. With third-generation GW detectors, such as Einstein telescope and Cosmic Explorer, the redshift distribution of detected events alone will provide tight constraints on the star-formation rate/time-delay distributions, without additional information from the host galaxies (Vitale et al., 2019; Safarzadeh et al., 2019). In the meantime, it is instructive to explore the complete range of host galaxy properties that potentially correlate with binary evolution. In this work, we explore how the properties of galaxies that host BNS mergers depend on the BNS merger timescales. We show how a full range of galaxy observables can be used to constrain details of BNS evolution.

In addition to stellar mass, there are other host galaxy observables that contain information about the evolution of BNS systems through cosmic time. The rate of BNS mergers in a given galaxy is a convolution of the galaxy’s entire history of star formation over its lifetime and the delay time between formation and merger. Galaxies reside in the centers of dark matter halos, and their evolutionary history is tied to the evolution of the dark matter halo in the cosmic web (for a detailed review of the galaxy–halo connection see Wechsler & Tinker, 2018). Even at a fixed stellar mass, for example, star-forming and quiescent galaxies have significantly different evolutionary histories, affected by the environments of their parent dark matter halos. Adding information about the star-formation rate of a BNS host can therefore provide important insights into the underlying formation mechanism. Recent work by Artale et al. (2019a) uses a population synthesis model for BNS mergers coupled with a hydrodynamic galaxy simulation to predict host galaxy properties, with a focus on stellar mass and star-formation rate. Their results suggest that while the BNS merger rate correlates most strongly with a galaxy’s stellar mass, it also depends on the star-formation rate of the galaxy.

The mass of the parent halo can also in principle be probed by a variety of mass proxies, including X-ray measurements of the virial temperature of the gas or the velocity dispersion of the satellites or stars associated with it. The net amount of baryonic matter available for a galaxy to form stars is directly related to the depth of the potential of its parent dark matter halo, leading to a correlation between a galaxy’s luminosity and its halo mass. In general, high-mass halos tend to host more luminous galaxies (e.g. Kravtsov et al., 2004; Vale & Ostriker, 2004); however, it has been shown that the slope of the stellar mass-halo mass relation becomes significantly shallower at high halo masses (e.g. Behroozi et al., 2013; Wechsler & Tinker, 2018; Kravtsov et al., 2018), indicating that galaxies with the same stellar mass can exist in a range of halo masses. Considering that quenching of star formation and various astrophysical feedback processes that control stellar evolution in a galaxy vary as a function of the host halo potential (Silk & Rees, 1998; Croton et al., 2007; Bullock et al., 2000; Hopkins et al., 2012), this implies different evolutionary channels for galaxies with similar luminosities but different halo masses. Therefore, in principle, the host halo mass can provide complementary information to the stellar mass of a galaxy with regard to its growth history. Further, particularly at high stellar masses, where star formation appears to be quenched, the parent halo mass and environment provides additional information, independent from the star-formation rate, about the merger history of the galaxy itself.

A galaxy’s environment can provide additional information about the history of the galaxy. For example, galaxies that live in dense local environments like clusters or galaxy groups tend to be less star-forming and redder, while the fraction of blue, star-forming galaxies dominate the population in the field or low density environments (Balogh et al., 1997; Dressler, 1980; Dressler & Gunn, 1983). In principle, the large-scale environment of a galaxy can also play a role in its star-formation history. Since halos form hierarchically, assembling through mergers of smaller halos, the nature of halo mergers and their frequency are both dictated by the environment around the initial density peak. The halo’s merger history can also be expected to impact the history of the galaxy that resides within it. There are many ways to parameterize this environment; one relevant cosmological measure is the density of matter in the vicinity of a galaxy at different scales, which is often measured as an abundance or number density of galaxies in the neighbourhood of a target galaxy. This is an observable that is measurable in most galaxy surveys and can in principle be used to constrain delay time distributions of binary systems.

The galaxy in which a binary forms evolves in the time between formation and the binary’s eventual merger. Correlations between properties of the host galaxy at binary formation, and the properties of the host galaxy when the binary merges, can therefore, in principle, be washed out for sufficiently long delay times (Zevin et al., 2019). However, the evolution of the galaxy can be inferred by studying the properties of host galaxies extensively in the full cosmological context. In this paper we study a set of observational properties that contain information about the evolution of the galaxy through cosmic time. To study the distribution of galaxy properties we use the Universe machine simulations (Behroozi et al., 2018). These simulations populate dark matter halos in a cold dark matter (CDM), N-body simulation with galaxies. The connection between galaxies and their halos is based on a semi-empirical model that parameterizes the correlation between the star-formation rate of a galaxy and the properties of its parent halo including the potential well depth, redshift, and assembly history using an extensive set of observational constraints.

GW170817 was accompanied by an sGRB, and there there is thus evidence that (at least some) sGRBs are expected to be produced by neutron star mergers. Previous studies into the host galaxies of sGRBs (Berger et al., 2007; Leibler & Berger, 2010; Fong & Berger, 2013; Prochaska et al., 2006) have already provided important insights into the progenitors of BNS systems. A comparison between the host galaxy of GW170817 and the host galaxies of cosmological sGRBs was carried out in Fong et al. (2017). Furthermore, understanding the connection between binaries and their hosts provides novel cosmological probes, such as inferring the cosmic star-formation history of the Universe (Fishbach et al., 2018; Vitale et al., 2019). Characterizing the binary–host connection can also provide an understanding of the systematic uncertainties involved in measuring the Hubble constant from standard sirens (Schutz, 1986; Holz & Hughes, 2005; Dalal et al., 2006; Abbott et al., 2017), and similar studies have already been used to understand the connection between supernovae and their host galaxies (Brout et al., 2019).

Here we explore constraints on the time-delay distributions resulting from analyzing observable properties of the host galaxies to binary neutron star mergers. In particular we focus on the distributions of four observables: the stellar mass, specific star-formation rate, halo velocity dispersion (a proxy for halo mass), and the local density around the hosts of GW events. For a range of time-delay models, we forward model the distribution of host galaxy properties using a simulated galaxy catalog. In §2 we describe the simulations, and in §3 we describe our method and main results.

Given the star-formation history of a galaxy and an assumed distribution of delay times between formation and merger, we can calculate the merger rate, $\mathcal{R}$, at redshift $z_{f}$:

where $\Psi_{g}(t)$ is the star formation rate of the galaxy at time $t$, $dP/dt$ is the delay time distribution, and $\lambda$ is an efficiency factor. We consider a power-law distribution in merger times, such that $dP/dt\propto(t-t_{d})^{-\alpha}$, where $t_{d}$ is the minimum delay time below which no BNS system can merge. We use $t(z)$ to convert between redshift and time assuming Planck cosmology (Aghanim et al., 2018).

The star-formation history of a galaxy depends on the galaxy properties, such as its halo mass, stellar mass, and local environment. Therefore, the observed merger rate in the Universe at a given time is the convolution of the delay time distribution and the star formation rate, where the star formation rate depends on various galaxy properties.

To emulate the distribution of galaxy properties in a cosmological context we use the Universe Machine simulation. Universe Machine provides a galaxy catalog with galaxy stellar masses and star- formation histories extending from $z=0$ to $z=10$. We use the publicly available galaxy catalogs created using the Bolshoi–Planck simulation (Klypin et al., 2011), which is a dissipationless CDM-only $N$-body simulation of a $250$ Mpc $h^{-1}$ volume with $2048^{3}$ particles in a Planck Cosmology, $\Omega_{m}=0.307$, $h=0.7$.

To study the hosts of BNS events at $z=0$, we track the galaxy properties of every object in the catalog that has a halo mass greater than $1.35\times 10^{10}M_{\odot}h^{-1}$, corresponding to halos with more than 100 particles in the simulation. We use the merger trees from the Rockstar halo finder (Behroozi et al., 2013) to reconstruct the galaxies’ star formation histories across cosmic time. We use the main branch of the merger tree for every galaxy in the catalog, which tracks a galaxy’s most massive progenitors in time. The galaxy merger history is sampled at 164 log-spaced points between $z=0$ and $z=10$.

We focus on four observable properties of the galaxies: the stellar mass of the galaxy, $M_{\ast}$, the galaxy’s specific star-formation rate, sSFR ($SFR/M_{\ast}$), the velocity dispersion of the parent halo, $\sigma_{h}$, and the ratio of the local and large-scale density, $\Delta_{r}$. The stellar mass and specific star-formation rates are provided by the simulated galaxy catalog. We use the specific star-formation rate because it traces the strength of the current burst of star-formation with respect to the galaxy’s underlying stellar mass, it correlates strongly with the observed color and morphology of a galaxy. (Guzman et al., 1997; Brinchmann et al., 2004).

Meanwhile, we use the velocity dispersion of galaxies within the parent halo as an observable proxy for the total halo mass. This velocity dispersion is computed using the velocities of galaxies within a halo’s virial radius. For satellite galaxies (i.e., galaxies that reside in subhalos) we use the velocity dispersion of the parent halo in which the subhalo resides. For galaxies that reside in low mass halos, where a sufficient number of subhalos are not resolved, we use the mass of the halo to compute the velocity dispersion. To compute the local density around a given galaxy, we measure the number density of neighbouring galaxies as a function of their 3D radius from the given galaxy. We only include neighbouring galaxies with stellar masses larger than $M_{\ast}=10^{9}M_{\odot}h^{-1}$. We define the observable $\Delta_{r}$ as the ratio of density within $0.6$ Mpc$\,h^{-1}$ compared to the density within $5$ Mpc$\,h^{-1}$. The smaller scale is chosen to represent a galaxy’s local environment, sensitive to whether or not it exists as a part of a group or a cluster of galaxies, while the larger radius is representative of its large scale environment or neighbourhood beyond its own parent halo.

In the following sections we study the properties of the host galaxies to BNS mergers as a function of the time-delay model. We estimate the number of events needed to draw inferences about the evolutionary history of merging binaries.

We have used the Universe Machine galaxy evolution model to predict the formation and merger of binary neutron stars over cosmological time. This allows us to relate astrophysical properties of the evolution of binaries detected by gravitational-wave networks to observable properties of their host galaxies.

We estimate the rate of mergers for each galaxy at $z=0$ from merger-time models parameterized by the slope of the time-delay distribution, $\alpha$, and the minimum delay time, $t_{d}$, to make mock observations of GW events and study the properties of their hosts. Current generation gravitational-wave detectors, such as Advanced LIGO/Virgo and LIGO A+, are expected to detect tens to hundreds of BNS mergers with counterparts in the coming years. We show that the combination of events from current GW detectors with current and future galaxy surveys is a particularly promising avenue that will allow us to draw important inferences about the underlying astrophysical population of binaries. The main findings of our work are:

• (i)

  With a sample of $\mathcal{O}(10)$ host galaxies to GW events, it is possible to distinguish formation models that predominantly trace stellar mass, star formation rate, or parent halo mass from each other and from a random selection of galaxies (see Fig. 2). We note that with $\sim 30$ host galaxies it is possible to distinguish between halo-mass weighting and stellar-mass weighting, and thereby distinguish between associated formation channels of binary systems in globular clusters as opposed to galaxies.

• (ii)

  Using the distribution of observable galaxy properties (i.e. stellar mass, star formation rate, halo velocity dispersion, and local density) we find that with order of a few tens of events we can distinguish short and long delay times at $\gtrsim 3\sigma$ (see Fig. 6). For longer delay times, we find an inability to constrain the slope of the merger time distributions. Adding in the halo velocity dispersion information significantly improves the constraints over those obtained using only stellar mass and sSFR.

• (iii)

  In the context of our single existing GW counterpart event, GW17087, we find that the properties of the host NGC 4993 prefer a delay time that is longer than a Gyr (consistent with previous work; see Levan et al. 2017; Pan et al. 2017; Belczynski et al. 2018). This can be attributed to the fact that NGC 4993 has a lower than expected star-formation rate for its measured stellar mass. Using the current star-formation rate we find that NGC 4993 shows a preference for a delay time close to $8$ Gyr. Related to this is the inference that this host galaxy appears to be drawn from a stellar-mass weighted or a halo-mass weighted sample. We also note that, while in the literature NGC 4993 has been associated with a bound group of galaxies, the measured velocity dispersion of the galaxies in the group suggest that the estimated virial radius of the group may not be representative of its true halo mass. The galaxies in the purported group appear to favor a $10^{12}{M_{\odot}}h^{-1}$ halo, with NGC 4993 at its outskirts.

• (iv)

  In general we find that the probability of a galaxy hosting a merger today is a function of the delay time model, where BNSs with short delay times preferentially exist in star-forming galaxies that inhabit halos that are similar or lower in mass than the Milky Way, while mergers with longer delay times prefer more massive galaxies that on average populate groups or clusters and tend to be more clustered in space.

• (v)

  Follow up strategies to localize electromagnetic counterparts for gravitational wave events can be optimized by searching for transients around massive galaxy groups (see Fig. 9). While the clustering of events is related to the underlying delay-time distribution, we find that even for short delay times nearly $80\%$ of all events can be captured by searching within a few Mpc of halos of mass $M$ > $10^{12.5}M_{\odot}h^{-1}$. We also infer if transients are not found around the most massive objects in the Universe, this can be interpreted as favoring a model with short delay times. Although the study in this paper is limited to the low-redshift Universe, consisting of a $250^{3}$ Mpc³ $h^{-3}$ volume at $z=0$, we note that clustering of events is an important probe of the underlying population of binary systems and may also provide a potentially useful tool to optimize localization strategies for future surveys.

As galaxy surveys become more sophisticated, properties of galaxy hosts such as halo velocity dispersions and 3D clustering can be measured with greater accuracy using spectroscopic instruments like DESI and WFIRST (Aghamousa et al., 2016; Spergel et al., 2013). Moreover, photometric surveys like DES, HSC, and LSST (Abbott et al., 2005; Aihara et al., 2018; LSST Science Collaboration et al., 2009) can be used to measure clustering in projected space, which contains similar information about halo mass and environment. A systematic study of the properties of the host galaxies that include the properties of the parent halo and its spatial and temporal clustering as a function of delay-time models is a powerful tool to determine the underlying astrophysics of binary systems. In fact, we emphasize that folding in properties of the parent halo can provide important information to distinguish dynamical formation channels of binaries in dense stellar regions like globular clusters, the individual stars in these systems are not born as binaries and are not required to follow the power law delay time models.

While GW17087 is the first gravitational wave associated with the confirmed merger of a binary neutron star, other astrophysical phenomena like sGRBs are also expected to be sourced by mergers of BNSs; therefore a similar study of hosts of sGRBs can be used to constrain delay-time models. In fact, GRB150101B, an sGRB similar to GW17087 and conjectured to be associated with a neutron-star merger (Troja et al., 2018), also has a very low star-formation rate and a stellar mass similar to NGC4993 (Xie et al., 2016). Furthermore, in the scenarios where host galaxies can be identified, it will also be informative to study the distribution of other probes of the underlying formation mechanisms like offsets between the site of the merger and the host galaxy (Voss & Tauris, 2003; Perna & Belczynski, 2002; Belczynski et al., 2002; Zevin et al., 2019) in relation to the properties of the hosts. For example, Kelley et al. (2010) studied the distribution of binary events in the local universe by modelling natal velocity kicks that create such offsets in an N-body simulation. We also note that recent work has shown that a small fraction of BBH mergers (on order $\sim 1$ per year) can be localized well enough to allow the identification of a unique host galaxy, despite not having associated electromagnetic counterparts (Chen & Holz, 2016). Therefore a comprehensive follow up of the properties of the host galaxies, including its halo mass, environment along with its stellar mass and star-formation history can provide a window into the formation models of binary black hole systems as well. We note that Lamberts et al. (2016), Artale et al. (2019a) and Artale et al. (2019b) have made predictions regarding the host galaxy properties of BBH mergers from population synthesis models.

The advent of gravitational wave astronomy provides a new observational probe of the physics of binary systems; the formation of galaxies and their co-evolution with cosmological structure, on the other hand, has been studied extensively over the years both theoretically and observationally through simulations and large scale galaxy surveys. We show that in the unique opportunity where we can identify a host galaxy for a gravitational wave event, the distribution of host properties combined with knowledge of galaxy formation can provide important information about the evolution of binaries through time. In the absence of a electromagnetic counterpart an understanding of the binary-host connection can help localization strategies for probable host galaxies. We emphasize that further studies of the connection between binaries and their hosts through the history of the Universe in an exciting prospect that can lead to a better understanding of the cosmological and astrophysical information we can extract from gravitational wave sources.

We thank Tom Abel, Kirk Barrow, Peter Behroozi, Antonella Palmese, and Michael Zevin for useful discussions. This research made use of computational resources at SLAC National Accelerator Laboratory, a U.S. Department of Energy Office, as well as the Sherlock cluster at the Stanford Research Computing Center (SRCC); the authors thank support of the SLAC and SRCC teams. This research was conducted in part at the Kavli Institute for Theoretical Physics, supported by NSF grant PHY-1748958. MF and DEH were supported by NSF grant PHY-1708081. This work was partially supported by the Kavli Institute for Particle Physics and Cosmology at Stanford and SLAC and the Kavli Institute for Cosmological Physics at the University of Chicago through endowments from the Kavli Foundation. MF was supported by NSF Graduate Research Fellowship Program grant DGE-1746045. DEH also gratefully acknowledges support from the Marion and Stuart Rice Award.