Halo Retention and Evolution of Coalescing Compact Binaries in Cosmological Simulations of Structure Formation: Implications for Short Gamma-Ray Bursts
DD RAFT VERSION N OVEMBER
11, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
HALO RETENTION AND EVOLUTION OF COALESCING COMPACT BINARIES IN COSMOLOGICAL SIMULATIONSOF STRUCTURE FORMATION: IMPLICATIONS FOR SHORT GAMMA-RAY BURSTS M ARCEL Z EMP , E
NRICO R AMIREZ -R UIZ AND J ÜRG D IEMAND
Draft version November 11, 2018
ABSTRACTMerging compact binaries are the one source of gravitational radiation so far identified. Because short-periodsystems which will merge in less than a Hubble time have already been observed as binary pulsars, they areimportant both as gravitational wave sources for observatories such as LIGO but also as progenitors for shortgamma-ray bursts (SGRBs). The fact that these systems must have large systemic velocities implies that by thetime they merge, they will be far from their formation site. The locations of merging sites depend sensitivelyon the gravitational potential of the galaxy host, which until now has been assumed to be static. Here werefine such calculations to incorporate the temporal evolution of the host’s gravitational potential as well asthat of its nearby neighbors using cosmological simulations of structure formation. This results in merger sitedistributions that are more diffusively distributed with respect to their putative hosts, with locations extendingout to distances of a few Mpc for lighter halos. The degree of mixing between neighboring compact binarypopulations computed in this way is severely enhanced in environments with a high number density of galaxies.We find that SGRB redshift estimates based solely on the nearest galaxy in projection can be very inaccurate,if progenitor systems inhere large systematic kicks at birth.
Subject headings: gamma rays: bursts — stars: formation — cosmology: observations — galaxies: formation— methods: N-body simulations INTRODUCTION
The association of short gamma-ray bursts with both star-forming galaxies and with ellipticals dominated by old stellarpopulations (Berger et al. 2005; Bloom et al. 2006; Fox et al.2005; Gehrels et al. 2005; Prochaska et al. 2006; Berger 2009)suggested an analogy to type Ia supernovae, as it indicated aclass of progenitors with a wide distribution of delay timesbetween formation and explosion. Similarly, just as core-collapse supernovae are discovered almost exclusively in star-forming galaxies, so too are long GRBs (Woosley & Bloom2006). Indeed, a detailed census of the types of host galaxies,burst locations and redshifts could help decide between thevarious SGRB progenitor alternatives (e.g. Zheng & Ramirez-Ruiz 2007; Guetta & Piran 2005; Bloom & Prochaska 2006):If the progenitor lifetime is long and the systemic kick issmall, then the bursts should correspond spatially to the old-est populations in a given host galaxy. For early-type galax-ies, the distribution would most likely follow the light of thehost. A neutron star (NS) binary could take billions of years tospiral together, and could by then, if given a substantial kickvelocity on formation, merge far from its birth site (Fryer etal. 1999; Bloom et al. 1999; Belczynski et al. 2002; Bloom etal. 2002). The burst offsets would then most likely be largerfor smaller mass hosts.Double neutron star binaries, such as the famousPSR1913+16, will eventually coalesce, when gravitational ra-diation drives them together (Kalogera et al. 2007). Each su-pernova is thought to impart a substantial kick to the result-ing NS (Hansen & Phinney 1997). For systems that surviveboth supernovae explosions the center of mass of the rem-nant binary itself will receive a velocity boost on the order Department of Astronomy, University of Michigan, Ann Arbor, MI48109; [email protected] Department of Astronomy and Astrophysics, University of California,Santa Cruz, CA 95064; [email protected], [email protected] Hubble Fellow of a few hundred kilometers per second (Brandt & Podsiad-lowski 1995; Fryer & Kalogera 1997). As a result, NS bina-ries will be ejected from their birth sites. The exact distribu-tion of merger sites depends sensitively on the gravitationalpotential of the host, which until now has been assumed to bestatic. The potential of a realistic host galaxy is, however, notstatic. In fact, the gravitational potential of the host as well asthat of its nearby neighbors is expected to evolve dramaticallyfrom compact binary production until coalescence. In order toincorporate these effects self-consistently, in this
Letter , westudy the orbital evolution of compact binary systems usingcosmological simulations of structure formation. Our resultsprovide new insights into what happens when compact binarystars are ejected from their birth halos as a result of veloc-ity kicks, and what progenitor clues a distant observer mightuncover from the distribution of SGRB sites in and aroundgalaxies. COMPACT BINARIES IN COSMOLOGICAL SIMULATIONS
The focus of this work is to understand the retention andevolution of compact binaries in an evolving cosmologicalsimulation. To this end, we have performed a dark matteronly cosmological structure formation simulation. A 80 co-moving Mpc periodic box with a single mass resolution of m p = 1 . × M (cid:12) corresponding to 256 particles is initial-ized at a starting redshift of z = 22.4 (161 Myr). The parti-cles have a softening length of 16 kpc and we have used theWMAP 3-year cosmological parameters (Spergel et al. 2007)with Ω M , = 0 . Ω Λ , = 0 .
762 and H = 73 km s − Mpc − , σ = 0 .
74 and n s = 0 . η D = 0 .
03 (Zempet al. 2007). a r X i v : . [ a s t r o - ph . C O ] O c t Zemp, Ramirez-Ruiz & DiemandFirst, we evolve the initial conditions until redshift z = 1.60(4.24 Gyr). At this time we find all the halos in our sim-ulation with a friends-of-friends method (Davis et al. 1985)and select all those with a minimum of 200 particles of whichthere are 2461. This criterion corresponds to a halo mass of2 . × M (cid:12) . Second, we populate each of these selectedhalos with 2000 massless tracer particles which are placedat the centre of each halo. Each tracer particle is meant torepresent a compact binary system, which, on average, formsaround the peak of the star formation epoch (Madau et al.1996). The velocity distribution of the tracer particles is as-sumed to be isotropic and to have a Maxwell-Boltzmann dis-tribution with a mean speed of ¯ v = 360 km s − and a disper-sion of σ = 150 km s − . This is consistent with the magni-tude of the natal kicks required to explain the observed pa-rameters of binary neutron star systems – only when kickshave magnitudes exceeding 200 km s − can the progenitor or-bits be sufficiently wide to accommodate evolved helium starsand still produce the small separations measured in these sys-tems (Brandt & Podsiadlowski 1995; Fryer & Kalogera 1997).Third, we weight each tracer particle by w i ≡ m i / m max where m i is the mass of the halo where the tracer particle with in-dex i initially starts and m max is the mass of the most massivehalo at redshift z = 1.60. This is done in order to account forthe contribution of a given halo to the total number of com-pact binaries produced at z = 1.60 under the assumption that itscales with the mass content in each halo. Finally, we evolvethe cosmological cube together with the tracer particle popu-lations until redshift z = 0 (13.8 Gyr).To explore the ability of individual halos in retaining theirown birth compact binary population, one requires to accu-rately follow not only the location of the tracer particles butalso the fate of the individual halos as they evolve and expe-rienced a substantial metamorphosis. To this end, we havemarked the particles with the highest phase space density ineach of the 2461 halos that have been populated with tracerparticles. By following these marked particles, we can thenaccurately track the location of the halos over time. Thesehigh phase space density particles are optimal for tracking thehalo positions since they stay at the centre of the halo and areonly minimally affected by tidal effects. Even when a halo be-comes tidally disrupted, the centre of the debris of these highphase space density particles still provides a good represen-tation of where the halo would be if it would not have beendisrupted. THE COSMOLOGICAL COMPACT BINARY MERGING SITES
We now turn to an examination of the cosmological distri-bution of the compact binary systems, which is done here byfollowing the massless tracer particle populations over time.Herefore, we picked out by eye three halos, each in a differ-ent environment (field, group and cluster). Figure 1 showsthe probability density function of finding tracer particles as afunction of distance from a given halo at three different snap-shots in time. The red lines show the radial probability densityfunction for all tracer particles originating in the particularhalo while the blue lines show the same function for tracersbelonging to all other halos.Figure 1 is self-explanatory. In the field environment, thedistribution is dominated out to a distance of a few Mpc by itsown tracer particles at all cosmological times. The tracer par-ticle population injected at z = 1.60 (4.24 Gyr) is observed tobe rather extended ∼
10 Mpc. This is because this field halo, whose mass at z = 1.60 was 2 . × M (cid:12) , was unable toeffectively retain most of its own tracer particles. This is alsothe case for the host halo belonging to the group environment,whose central mass at z = 1.60 was 2 . × M (cid:12) . However,in this more crowded environment, the close proximity of theneighboring halos allows foreign tracer particles to pollute thecentral regions of the host halo. In the cluster environment,only very few tracer particles are able to escape the deep halopotential well where they were born (Niino & Totani 2008),whose mass at z = 1.60 was 5 . × M (cid:12) . The few unboundparticles are still effectively retained by the cluster’s potential.As a result of the high merger activity in such cluster environ-ments, the mixing of the various tracer populations increasesdramatically with time. At z = 0, for example, the probabil-ity of finding a foreign tracer is equal or higher at all radialdistances than finding one originating from the massive cen-tral halo, whose mass at z = 0 is now 7 . × M (cid:12) . Thisclearly indicates, that in a high density environment with a lotof merger activity there is a high degree of tracer mixing and,as a result, the closest galaxy at the time of merging is likelynot to be the one where the compact binary system originatedfrom.The ability of a halo to retain its birth population of tracerparticles is further illustrated in Figure 2 where we plot thedensity field at z = 0 (left column) of the three halo environ-ments shown in Figure 1 together with the distribution of theparticle tracers that originate from the selected halo (right col-umn). We see that in the cluster environment, the tracer par-ticle population stays compact. In this crowded environment,the many accreted subhaloes contribute significantly to thepollution of the tracer particle population in the central clus-ter region as shown in Figure 1. In the small mass field halo,the tracer particles spread over many Mpc in distance. Giventhat there are not many other halos in the immediate neigh-bourhood, the tracer particle pollution is negligible. This is,however, not the case for the selected halo in the group en-vironment which despite having a mass similar to that of thefield halo at z = 1.60, experiences a substantial degree of tracerparticle mixing from the other group members.Now the question arises over whether the compact binarywas born in the galaxy it is closest to at the time of merger?If SGRB are triggered by compact binary formation, then themerging site can be deduced by the afterglow location. Wecan answer this by following the population of compact bi-naries as the cosmological simulation evolves. At any giventime we can calculate the weighted fraction of tracer particlesthat are still closest to the halo they started at redshift z = 1.60given by f ≡ (cid:80) N co k w k / (cid:80) N tot i w i , where N tot = 2461 × k sum-mation runs over all N co tracers that are still closest to theiroriginal halo. In Figure 3, we plot this fraction as a functionof the environment mass containing the tracer particle popu-lation.The environment of a tracer particle is defined by the mostmassive halo we find at a given time that contains the tracerparticle. We define that a tracer particle is contained within ahalo if they are within a sphere of radius d = 2 s from its centreand where s is given by s ≡ (cid:16)(cid:80) k =1 x k , max − x k , min (cid:17) and x k , max respectively x k , min are the maximum/minimum coordinate inthe k th dimension of any particle in the halo. The fraction f is not very sensitive to the detailed definition of environmentused here since for example the definition d = s results in aalo Retention and Evolution of Coalescing Compact Binaries 3qualitatively similar plot.Figure 3 highlights the importance of environment on com-pact binary retention. It shows that in environments (cid:46) M (cid:12) around 95% of all weighted tracers at all cosmo-logical times are still closest to their halo where they origi-nate from. For more massive environments, this ceases to betrue. For example, in environments (cid:38) M (cid:12) , the fractionof binaries found closest to their birth halo severely decreaseswith time, reaching 45% at redshift z = 0. This implies thatin more than half the cases the merger event would not takeplace closest to its birth galaxy site if occurring within a clus-ter environment. DISCUSSION
Before the detailed modeling of light curves was used toconstrain the nature of supernovae progenitors, the location ofsupernovae in and around galaxies provided important cluesto the nature of the progenitors. Similarly, in the absence ofsupernova-like features (e.g. Hjorth et al. 2005a), detailed ob-servations of the astrophysics of individual host galaxies maythus be essential before stringent constraints on the identityof SGRB progenitors can be placed (e.g. Zheng & Ramirez-Ruiz 2007; Fox et al. 2005).Even with a handful of SGRBs detected to date, it has be-come apparent that short and long events are not drawn fromthe same parent stellar population (Nakar 2007). In contrastto long GRBs, the galaxies associated with SGRBs exhibit awide range of star-formation rates, morphologies and metal-licities (Berger 2009). They are also often found in older andlower-redshift galaxies and, in a few cases, with large ( (cid:38) − in order to explain theobserved parameters of double neutron star systems; Fryer &Kalogera 1997) whose properties do not vary with the initialbinary separation.Two important predictions stand out. First, the merger sitedistributions computed in this way are more diffusively lo-cated with respect to their putative hosts. In a field environ-ment, for example, the distribution of merging sites can ex-tend out to a distance of a few Mpc. This is more severe forthose host galaxy halos that were unable to effectively retainmost of its own compact binary population at birth. Second,the degree of mixing between neighboring compact binarypopulations depends on galactic environment. In a cluster,for example, the mixing of the various compact binary pop-ulations is severe as a result of the high merger activity andincreases dramatically with time. At z = 0, in a cluster envi-ronment, the probability of finding a foreign coalescing com-pact binary system is equal or higher at all radial distancesthan finding one originating from the massive central halo. Asa result, the closest galaxy at the time of binary coalescenceand possibly SGRB occurrence may not to be the one wherethe compact binary system originated from.Of course, our basic model is rather simple since we assumea single epoch of star formation and a simple star formationrecipe. Also different distributions of kick velocities shouldbe considered. We do not expect that our qualitative resultswill change dramatically as our first, more general, results in-dicate.It is evident form the discussion above that assuming alarge (already evolved) host galaxy at the time of compactbinary formation thus severely overestimates the binary re-tention fraction and the concentration of their merging sitedistribution. This implies that SGRB redshift estimates basedsolely on the nearest galaxy in projection can be very inac-curate, if progenitor systems inhere large systematic kicks atbirth. Interpretations on the nature of the SGRB progenitorusing the stellar and mass properties of the nearest galaxy inprojection as established by the afterglow location must there-fore be regarded with suspicion. Finally, it should be notedthat a direct comparison with model predictions is still im-peded by the possibility of an ambient density bias (Bloomet al. 2006; Lee et al. 2005) where SGRBs are more likely tobe found in denser gas regions and , as a result, we could bemissing a population of bursts with large systematic kicks.We thank J. Bloom, S. Faber, C. Fryer, V.Kalogera, R.O’Shaughnessy and X. Prochaska for useful discussions.M.Z. is supported by NSF grant AST-0708087. We fur-ther acknowledge support from Swift: NASA NNX08AN88G(E.R.), NSF: 0521566, and the David and Lucile PackardFoundation (E.R.). 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The dash-dotted red lines show the radial probability density function for all tracer particles formed in the particular halo while thesolid blue lines show the same function for tracers belonging to all other halos. Note how the bound and unbound tracers of local origin (dash-dot/red) give riseto bimodal distributions in the field and group environments, while all of them remain bound in cluster environment. Zemp, Ramirez-Ruiz & Diemand F IG . 2.— The tracer particle populations as a function of environment in the local universe. The dark matter density field at z = 0 (top row) of the three haloenvironments shown in Figure 1 are plotted together with the distribution of the particle tracers that originate from the selected central halo (bottom row). Theside length of each panel is 10 Mpc. alo Retention and Evolution of Coalescing Compact Binaries 7 F IG . 3.— The weighted fraction ff