The effects of host galaxy properties on merging compact binaries detectable by LIGO
Cosmological simulations of galaxy formation can produce present-day galaxies with a large range of assembly and star formation histories. A detailed study of the metallicity evolution and star formation history of such simulations can assist in predicting LIGO-detectable compact object binary mergers. Recent simulations of compact binary evolution suggest the compact object merger rate depends sensitively on the progenitor’s metallicity. Rare low-metallicity star formation during galaxy assembly can produce more detected compact binaries than typical star formation. Using detailed simulations of galaxy and chemical evolution, we determine how sensitively the compact binary populations of galaxies with similar present-day appearance depend on the details of their assembly. We also demonstrate by concrete example the extent to which dwarf galaxies overabundantly produce compact binary mergers, particularly binary black holes, relative to more massive galaxies. We discuss the implications for transient multimessenger astronomy with compact binary sources.
keywords:black hole physics – gravitational waves – galaxies: evolution
Gravitational waves have been detected from coalescing black hole binaries (The LIGO Scientific Collaboration and the Virgo Collaboration, 2016c, a). Over the next few years, ground-based gravitational wave detectors like LIGO and Virgo should detect the gravitational wave signal from many more similar merging compact binaries (The LIGO Scientific Collaboration and the Virgo Collaboration, 2016a, b; Belczynski et al., 2016), as well as binary neutron stars and black hole-neutron star binaries (Abadie et al (The LIGO-Virgo Scientific Collaboration), 2010; Dominik et al., 2015). The host galaxies of gravitational wave sources will be identified, either directly or statistically. If the event is a merger of at least one neutron star, it is expected to be accompanied by detectable electromagnetic radiation via a number of mechanisms (see Fernández & Metzger, 2016, and references therein) in addition to the strong gravitational wave signal. A multimessenger detection will pin down the sky position and therefore approximate birthplace of each merging binary (Nissanke et al., 2013). Even in the absence of well-identified electromagnetic counterparts, host galaxy information is still available from gravitational wave localization alone (Abbott et al., 2016; Singer et al., 2016). As GW detector networks increase in number and sensitivity, these localizations will allow statistical and, eventually, unique identification of host galaxies directly, even without associated electromagnetic emission. As with supernovae and GRBs, these host galaxy associations are expected to tightly constrain models for compact binary formation; see, for comparison, Maoz et al. (2011), Guetta & Piran (2007), Berger (2014), and references therein.
The host galaxies of distant short GRBs have already been extensively investigated, with the associations being used to draw preliminary conclusions about their progenitors (Berger, 2014). Unlike GRBs, detected gravitational wave sources will be limited by the range of LIGO to the local universe; for example, binary neutron star sources should be closer than . Due to their proximity, each host galaxy can be explored at great depth and detail via position-resolved spectroscopy, enabling detailed position-resolved star-formation and chemical evolution histories (see,e.g. Kotulla et al., 2009; Canning et al., 2014; Pérez et al., 2013; González Delgado et al., 2015). However, unlike short GRBs and supernovae (SN), present-day compact binary populations can depend sensitively on rare low metallicity star formation. In this work, we assess by concrete example the extent to which detailed analysis of individual galaxies’ assembly histories will be essential in investigating key physical questions about the origin of compact binary mergers.
This paper is organized as follows. In §2, we describe detailed hydrodynamical simulations of several galaxies, including four of Milky Way-mass and two dwarfs. Though the four Milky Way-like galaxies are morphologically similar at , their star formation and chemical evolution history have subtle differences due to their distinctive merger histories. To demonstrate the practical impact of these differences as well as that of halo mass, in §3, we introduce a simple, metallicity-dependent phenomenological model to calculate the present-day rate and mass distribution of compact binary mergers from a galaxy’s known history. In §4, we use this model to investigate the compact binary coalescence rate dependence on each galaxy’s assembly history and mass. In § 5 we discuss the implications of our study for the interpretation of host galaxy associations identified via transient multmiessenger astronomy, in the short and long term. We summarize our results in § 6.
2 Cosmological simulations
2.1 Simulating galaxy evolution
To thoroughly study the significance of low metallicity star formation, we examine cosmological smoothed particle hydrodynamics (SPH) -body simulations of Milky Way-like galaxies with GASOLINE (Stadel, 2001; Wadsley et al., 2004). These simulations allow us to analyze both spatially and temporally resolved star formation, and determine the metallicity history of compact object progenitors.
We selected our simulated regions of interest from a volume of
uniform resolution, and resampled the region at very high
resolution using the volume renormalization technique (Katz &
This technique allows us to follow the detailed physical processes
involved in galaxy evolution in our selected region while still
including large-scale torques from cosmic structure. Our cosmological parameters are , , , h = 0.73,
et al., 2007).
where the star formation efficiency parameter is set to 0.1 such
that our galaxies match the observed Kennicutt-Schmidt law
(Kennicutt, 1989); X is the molecular hydrogen fraction of the gas particle; and are the star and gas
We model supernova feedback using the blastwave formalism described in McKee & Ostriker (1977) and implemented in our simulations as in Stinson et al. (2006). Each supernova releases erg into the surrounding gas with a radius determined by the blastwave equations. These particles are not allowed to cool for the duration of the blastwave, mimicking the adiabatic expansion phase of a supernova explosion. Previous works have found that this set of parameters results in realistic galaxies which obey a number of observed relations such as the mass-metallicity relation (Brooks et al., 2007; Christensen et al., 2016), the Tully-Fisher relation (Christensen et al., 2016), and the size-luminosity relation (Brooks et al., 2011), as well as reproduce the detailed characteristics of bulgeless dwarf galaxies (Governato et al., 2010, 2012), low-mass disk galaxies with bulges (Christensen et al., 2014a), and the Milky Way (Guedes et al., 2011).
Metals are created in supernova explosions and deposited directly to the gas within the blast radius. Stellar masses are converted to ages as described by Raiteri et al. (1996), and stars more massive than 8 M are able to undergo a Type II supernova. For Type II supernovae, iron and oxygen are produced according to the analytic fits used in Raiteri et al. (1996) using the yields from Woosley & Weaver (1995):
Feedback from Type Ia supernovae also follows Raiteri et al. (1996). Each supernova produces iron and oxygen Thielemann et al. (1986). Metal production from stellar winds is also included; we implement stellar wind feedback based on Kennicutt et al. (1994) and the returned mass fraction is derived using a function by Weidemann (1987). The returned gas has the same metallicity as the star particle.
Also included in our simulations is a scheme for turbulent metal diffusion (Shen et al., 2010). Once created, metals diffuse through the surrounding gas, according to
where the diffusion parameter is given by
and is the SPH smoothing length, is the trace-free shear tensor, and is a dimensionless constant which we set to a conservative value of 0.03. Combined with infall, this procedure produces a range of metallicities within each galaxy.
We do not include specific prescriptions for metal distribution based on initial metallicity (such as for Population III stars) or variations in IMF. We cannot thus discuss Population III contributions to the gravitational wave background; however, studies by Hartwig et al. (2016a) and Dvorkin et al. (2016) suggest that this contribution is fairly negligible. We have shown that our scheme for metal production and distribution produces galaxies which match the mass-metallicity relation at (Brooks et al., 2007) as well as in the local universe (Christensen et al., 2016). At higher redshifts, there is a very large spread in the metal distributions of damped Lyman alpha systems (Dvorkin et al., 2015); manifestly, other features in the galaxy evolutionary history play a role in its present day metallicity. Recently Hunt et al. (2016a, b) has demonstrated a relationship between of the mass, metallicity, and star formation rate, which demonstrates an evolutionary relationship between these quantities. As we will discuss in future work, we have verified that our evolutionary prescriptions are also qualitatively consistent with this relation.
We identify individual galaxies using the halo finder (Gill et al., 2004; Knollmann & Knebe, 2009), which identifies haloes based on an overdensity criterion for a flat universe (Gross, 1997). In each simulation, we are focusing on the stars which make up the primary (i.e. most massive) galaxy within the zoomed-in high resolution region at .
2.2 Milky-Way-like galaxies with distinct histories
The evolution of a galaxy, in terms of its stellar mass and metallicity evolution, depends strongly on its interaction history. Galaxies which appear similar at the present day may have had drastically different histories, which may result in differences in compact object merger rates. To investigate whether galaxy history affects the compact binary event rate, we have chosen four simulations which are morphologically similar at (see Figure 1) but differ strongly in their merger histories.
The simulation h277 is a Milky Way analog with a quiescent merger history. It experiences its last major merger at , after which a small number of minor interactions permeate its life. This simulation has been shown to emulate several Milky Way properties, including stellar dynamics (Loebman et al., 2012; Loebman et al., 2014; Kassin et al., 2014), baryon fraction (Munshi et al., 2013), and satellite properties (Zolotov et al., 2012; Brooks & Zolotov, 2014). It has a virial mass of , stellar mass , and maximum circular velocity km s.
The simulation h258, on the other hand, has a much more active merger history. At there is a 1:1 merger event; a gas disc rapidly reforms following the collision (see Governato et al. (2009)), resulting in a massive galaxy at which looks remarkably similar to the Milky Way and to the other simulation, h277. Prior to the merger, each of the four progenitor galaxies actually experiences its own additional major merger events around . The combination of the series of major mergers, plus a number of minor interactions and flybys, gives a stark contrast to the relatively quiescent history of h277. At , h258 has a virial mass of , stellar mass , and maximum circular velocity km s.
We include two additional Milky Way simulations with similar properties, which have evolutionary histories that fall in between the extremes of the two described above. The galaxy h239 has a total virial mass of , stellar mass , and maximum circular velocity km s. The galaxy h285 has a total virial mass of , stellar mass , and maximum circular velocity km s. These galaxies are also described in Bellovary et al. (2014); Sloane et al. (2016).
Due to the differences in merger histories, the star formation histories and metallicity
evolution of h258 and h277 also differ at early times. Figure
2 shows the star formation history (left panel) and metallicity evolution (right panel) of h277 (black) and h258 (red).
We wish to point out that these simulations do not include the effects of supermassive black holes (SMBHs). These galaxies are at the mass where feedback from SMBH accretion is thought to affect star formation, and adding these effects may add additional scatter to the stellar and metal evolution of each galaxy, which could alter the binary black hole merger history as well.
2.3 Dwarf galaxies
We have also employed the results of detailed simulations for two dwarf galaxies: h603 and h516. The simulation of h603 consists of a low-mass disc galaxy (qualitatively similar to M33). It has a virial mass of , stellar mass of , and maximum circular velocity of 111 km s. The structure and star formation of this galaxy has been extensively studied by Christensen et al. (2014a). We also include a bulgeless dwarf galaxy, h516, which has a disc with irregularly distributed star formation, with a virial mass of , stellar mass , and maximum circular velocity of 65 km s. Images of these galaxies are shown in Figure 3, and we show their star formation history and metallicity evolution in Figure 4. Note that these galaxies have quite different masses, and are not meant to be directly comparable. The more massive h603 has a much more active star formation history and an overall increasing metallicity with time, whereas the less massive h516 is characterized by small bursts of star formation and a fairly flat metallicity evolution, perhaps due to its substantial outflows.
3 Detection-weighted compact binary formation
Our goal in this work is to estimate the ratio of compact binaries that should be merging, at present, in the four simulated Milky-Way analog galaxies described above as well as the dwarfs.
To explore plausible binary detection scenarios, we adopt a parametrized formalism for binary evolution and event detection in an individual galaxy, motivated by the detailed studies of (O’Shaughnessy et al., 2008, (hereafter PSG)) and O’Shaughnessy et al. (2010, (hereafter PSE)); similar approaches have been used by Lamberts et al. (2016) and others. Since prior population synthesis investigations extend relatively smoothly to very metallicity, we do not introduce a distinct, special group of low-metallicity Population III stars.
Binary evolution calculations suggest the binary compact object formation rate depends sensitively on the assumed metallicity, in conjunction with other parameters (see, e.g. Belczynski et al., 2010a; O’Shaughnessy et al., 2012a; Belczynski et al., 2016, and references therein). Gravitational wave detectors are also far more sensitive to massive compact binaries, which are preferentially formed in low metallicity environments (O’Shaughnessy et al., 2010; Dominik et al., 2015). As a result, low metallicity environments can be overwhelmingly efficient factories for detectable black hole binaries (Dominik et al., 2015; Belczynski et al., 2016). For this reason, our estimates for compact binary coalescence rates must account for how often different star-forming conditions occur; how often compact binaries that can coalesce now can derive from each environment; and how often LIGO will detect compact binaries with different masses, all other things being equal.
To characterize how much more likely LIGO will detect coalescing binaries with different masses, we use a common and
naive estimate for the volume to which advanced LIGO is sensitive (see,e.g., O’Shaughnessy et al., 2010):
where . This expression depends explicitly on an assumed and metallicity-dependent mass distribution for compact object mergers, through the characteristic chirp mass . We calibrate our metallicity-dependent mass distributions to metallicity-dependent binary evolution calculations presented in Dominik et al. (2012) and Dominik et al. (2015). For neutron stars, we adopt a fiducial neutron star mass of at all metallicities. For BH-NS binaries, we adopt a highly simplified model: the black hole masses are uniformly drawn from to the maximum black hole mass allowed by isolated stellar evolution, as reported in prior work (see,e.g. Belczynski et al., 2016, and references therein). In agreement with much more detailed prior work Dominik et al. (2015), this simplified model yields typical chirp masses for BH-NS binaries that vary slightly as decreases, from a lower limit of near solar metallicity to an upper limit of in low-metallicity environments. Not least because the average chirp mass for BH-NS simply cannot vary dramatically, given the functional form of , our results for the BH-NS coalescence rate per unit galaxy mass do not depend sensitively on the choice of black hole mass distribution. Finally, for binary black holes, we assume comparable-mass binaries form (), with the distribution of component masses chosen to be between and and zero otherwise, adopting a fiducial exponent ; see, e.g., Dominik et al. (2013). For binary black holes, this means the detection-weighted mass distribution  depends weakly on mass [. In our simple model, the total and chirp mass distributions are qualitatively consistent with detailed binary evolution calculations (Dominik et al., 2013).
To characterize the frequency of different star-forming conditions, we use our cosmological simulations of Milky Way-like galaxies, which provide each galaxy’s star formation rate and metallicity distribution over time (see Eqn. 9).
To characterize how often compact binaries form and coalesce, we use the ansatz adopted in PSE and
PSG: for a star-forming parcel of mass the number of binaries born at time which
are coalescing now is , where is an overall efficiency per unit mass and is
a metallicity-dependent delay time distribution.
with and (see, e.g.O’Shaughnessy et al. (2012a), BD2010). For the purposes of illustration, we adopt a concrete scale factor , a typical value suitable for neutron star compact binaries (see PSG, PSE, and BD2010). To calibrate the exponent, based on Tables 2 and 3 of Dominik et al. (2012) (model B), for binary black holes and black hole-neutron star binaries, we adopt , while for binary neutron stars we adopt ; see, e.g., their Table 1 and Figures 5-7. This choice of exponent provides an extremely conservative assessment of the impact of low Z (see,e.g., O’Shaughnessy et al., 2012b; Belczynski et al., 2016). For binaries containing neutron stars, for simplicity and without loss of generality we adopt the universal delay time distribution
PSG and PSE show this distribution is a reasonable approximation to compact binary delay
Therefore, up to an irrelevant overall scale factor, the present-day detection-weighted coalescence rate of binary compact objects formed by within two similar galaxies can be calculated via
4 Compact object binary formation rate
Our four Milky Way-like galaxies have extremely similar star formation histories and metallicity evolution, particularly at late
However, at early times, the h258 galaxy forms stars for at a lower characteristic metallicity
to the h277 galaxy (). In this regime, the formation efficiency and sensitive volume
can depend sensitively on mass; for example, for binary black holes, the ratio of .
The close agreement between the two galaxies’ binary black hole populations, determined by the anticorrelation between star formation rate and metallicity, may be a single example of a broad trend. This anticorrelation could cause galaxies with similar present-day properties to always have similar present-day binary black hole populations, regardless of their detailed assembly histories. If low metallicity star formation makes up a small fraction of the total stellar mass, which is the case for each Milky Way-like galaxy we study here, then the quantity must differ by about an order of magnitude for the binary black hole merger rates to differ strongly. Such a scenario is possible if we alter our conservative choice of the exponent in the function, but nonetheless is rather unlikely that galaxies in this mass range will undergo drastically different early evolution. The effects described here are well within the scatter around the mass-metallicity relation. Marginally different realizations of these histories can easily produce factors of order unity difference in galaxies with otherwise indistinguishable present-day properties.
More broadly, Table 1 shows the results of our calculations for the three types of compact binaries described above. These calculations show just how dramatically different the compact binary populations of galaxies with different present-day masses could be. The dwarf galaxies have an exceptionally large fraction of low-metallicity star formation in their history (Kirby et al., 2013) relative to the more massive galaxies. The precise details of their chemical evolution can modify their present-day binary black hole binary populations by factors of order a few, despite adopting the conservative choices described above for the dependence of rate on metallicity. The progenitors (and, if present, electromagnetic counterparts) of future binary black hole gravitational wave events are overall much more likely to be located in nearby dwarf galaxies with a large population of low metallicity stars.
To highlight how sensitively compact binaries depend on detailed evolutionary trajectories, Table 1 shows results for binary neutron stars. By our construction, no metallicity dependence is included in the present-day event rate for neutron stars. Thus, the differences in present-day state between these two galaxy population models arise solely and exclusively on the time distribution history of past star formation. In general, the present-day population depends often significantly (i.e., tens of percent) on the assembly history alone, even aside from any composition-dependent effects.
5 Implications for transient multimessenger astronomy
While a gravitational wave detection provides detailed information about merging objects (i.e. masses, spins, distance), we need further knowledge to understand the actual origins of the progenitors. Even when electromagnetic counterparts are available, the long delay times between binary formation and merger limit the prospects of examining the environment where the binary first formed. On the one hand, compact binaries are kicked by supernovae, moving substantially away from their birth position (Fong & Berger, 2013; Berger, 2014). On the other hand, particularly during the early epoch of galaxy formation, gas in galaxies is well-mixed: stars and adjacent gas generally do not have similar chemical composition. These mixing effects have been previously recognized as an obstacle to interpreting transient event spectra. For example, Pontzen et al. (2010) previously demonstrated that absorbing gas neighbouring transient events (there, long GRBs) would generally have high metallicity, even for low-metallicity progenitors. Pontzen et al. (2010) have previously used hydrodynamical simulations to demonstrate that observed ambient metallicities (there, using damped Lyman absorbers in the host) do not tightly constrain the metallicity distribution of the progenitor; see, e.g., their Fig 3. Thus, the metallicity of stars and gas adjacent to a specific merger event provides few direct, unambiguous clues to a compact binary merger’s progenitors.
Fortunately, with the advent of IFUs and position-resolved spectroscopy, observers can now probe the star formation history and metallicity of individual gas packets at different points in a galaxy. These highly-detailed probes will be essential tools to develop a comprehensive model of the galaxy’s merger and chemical evolution history. Obtaining the galaxy-wide evolutionary history can help us infer compact binary formation conditions by identifying the lowest-metallicity formation events using stellar archaeological techniques. These techniques have been applied with great success to other transient events. For example, in several cases the metallicity of gas neighbouring a long GRB (Modjaz et al. (2008); Levesque et al. (2010)) has been directly measured. The precise host offset can be compared to the distribution of light and star formation (Fong et al., 2010). Finally, on a host-by-host basis, the delay time between birth and merger has been constrained for short GRBs (Leibler & Berger, 2010) and SN Ia (Maoz et al., 2011); see, e.g., the review in Berger (2014).
Thus, despite the challenges involved in obtaining sufficient statistics, possibly requiring third-generation instruments to obtain sufficiently many associations, past experience suggests host galaxy associations will provide unique clues into the formation mechanism of compact binaries. Each host galaxy associates a merger to a unique star formation history and metallicity distribution. With many events, these associations can potentially determine the “response function” for compact binaries: how often star forming gas of a given metallicity evolves into merging compact binaries.
We examine the present-day populations of coalescing compact binaries in galaxies with different assembly histories. We combine detailed and state-of-the-art cosmological simulations of galaxies with a simple but robust phenomenological model for how compact binaries form from different environments. We demonstrate that galaxies which appear similar at but have differing merger histories will have somewhat different detection-weighted compact binary coalescence rates.
For binary black hole mergers in particular, we show that the present-day binary black hole coalescence rate for our two Milky-Way like galaxies is nearly identical, independent of their highly distinctive early-time formation histories. This result perhaps comes as somewhat of a surprise, considering the early differences in stellar and chemical evolution. Our calculations adopt the same framework as prior investigations, which demonstrated that black hole merger rates depend sensitively on low-metallicitiy environments (see,e.g. O’Shaughnessy et al., 2010; Dominik et al., 2013; Belczynski et al., 2016). More broadly, because compact binaries can merge long after they form, their host galaxy can evolve substantially in composition between birth and merger. Nonetheless, the apparent anticorrelation between the star formation rate and metallicity evolution of our galaxies has led to similar late-time populations, despite substantial differences early on. Further investigation is critical to assess whether this similarity is retained for more generic galaxy assembly histories and binary formation models. Now that we have introduced this method as a proof-of-concept here, it can be applied to large volume simulations, such as Illustris, EAGLE, or Romulus (Vogelsberger et al., 2014; Schaye et al., 2015; Tremmel et al., 2016), in order to examine large numbers of galaxies and thus obtain statistically significant results.
The detailed analysis of the compact binary populations formed through the assembly history of individual galaxies is complementary to the population-based approach reported in Lamberts et al. (2016). More broadly, our analysis reflects similar theoretical studies performed in the interpretation of, for example, long GRBs and their host galaxies. For example, Kocevski et al. (2009) demonstrated that a sufficiently strong bias towards low-metallicity star formation would predict most events in the local universe occur low-mass and dwarf galaxies. For less extreme metallicity biases, subsequent calculations by Niino (2011) demonstrated that the metallicity distribution within galaxies will usually lead to events in a wide range of host galaxies in the local universe.
In our investigation, we have neglected the impact of population III stars. Previous studies suggest the first generation of stars may contribute a small but nonzero fraction of detectable events, potentially with distinctively high black hole masses (Hartwig et al., 2016b; Sasaki et al., 2016; Kinugawa et al., 2014).
In short, in this work we have demonstrated that the confounding effects of host galaxy assembly history can in the near term complicate the interpretation of associations between GW sources and candidate host galaxies. However, given sufficient statistics, as will inevitably become available with next-generation GW instruments, combined with large-scale multiband followup, these confounding challenges can both be overcome and converged into opportunity. In the far future, with hundreds of thousands of thousands to millions of events per year in networks like Cosmic Voyager, Einstein Telescope, and DECIGO, GW measurements could even provide complementary statistical probes of the past history of galaxy assembly and evolution.
ROS acknowledges support from NSF award AST-1412449, via subcontract from the University of Wisconsin-Milwaukee, and PHY-1505629. JB acknowledges generous support from the Helen Gurley Brown Trust. A portion of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293.
- pubyear: 2016
- pagerange: The effects of host galaxy properties on merging compact binaries detectable by LIGO–LABEL:lastpage
- Since we are simulating individual galaxy environments rather than large populations of halos, the selection of cosmological parameters provides a negligible contribution to the variance in the overall evolutionary history of galaxies in our simulations.
- Gas particles start with a set mass and may gain mass from feedback and lose it to star formation. Each star particle, when formed, has of the progenitor mass of the forming gas particle. See Christensen et al. (2010) for a discussion of resolution issues in SPH simulations.
- We choose not to show galaxies h239 and h285 in our figures, as they fall in between the values bracketed by h258 and h277 and add confusion to the plots.
- For simplicity, in this calculation we neglect the effects of cosmology; strong field coalescence; and black hole spin; see Dominik et al. (2015), The LIGO Scientific Collaboration and the Virgo Collaboration (2016d), or The LIGO Scientific Collaboration and the Virgo Collaboration (2016b) for more details.
- For simplicity, we assume the mass and delay time distributions are uncorrelated. Figure A9 in PSG shows this approximation, while not strictly true, is an excellent approximation for merging BH-BH binaries at solar metallicity.
- Simulations suggest the delay time distribution varies from model to model and with mass. These variations have less impact on our results than the evolving metallicity distribution of star forming gas.
- Adopting a more extreme exponent for the metallicity dependence () only changes this ratio by of order .
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