The dynamic ejecta of compact object mergers and eccentric collisions
TThe dynamic ejecta of compact ob ject mergers andeccentric collisions
S. Rosswog (cid:63) The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden
16 July 2018
ABSTRACT
Compact object mergers eject neutron-rich matter in a number of ways: by the dynam-ical ejection mediated by gravitational torques, as neutrino-driven winds and probablyalso a good fraction of the resulting accretion disc finally becomes unbound by a com-bination of viscous and nuclear processes. If compact binary mergers produce indeedgamma-ray bursts there should also be an interaction region where an ultra-relativisticoutflow interacts with the neutrino-driven wind and produces moderately relativisticejecta. Each type of ejecta has different physical properties and therefore plays a differ-ent role for nucleosynthesis and for the electromagnetic transients that go along withcompact object encounters. Here we focus on the dynamic ejecta and present resultsfor over 30 hydrodynamical simulations of both gravitational wave-driven mergers andparabolic encounters as they may occur in globular clusters. We find that mergers eject ∼
1% of a solar mass of extremely neutron-rich material. The exact amount as well asthe ejection velocity depends on the involved masses with asymmetric systems eject-ing more material at higher velocities. This material undergoes a robust r-process andboth ejecta amount and abundance pattern are consistent with neutron star merg-ers being a major source of the ”heavy” (
A >
Key words: neutron stars, black holes, hydrodynamics, nucleosynthesis, transients,gravitational waves
Even before the discovery of the first neutron star binaryPSR 1913+16 (Hulse & Taylor 1975) efforts were under-taken to estimate how much mass a compact binary mergerwould eject into space. In a semi-analytic model Lattimer &Schramm (1974) estimated that in a neutron star (ns) blackhole (bh) collision ∼
5% of the neutron star could becomeunbound. By estimating the rates of such encounters theyalready noted that the accumulated amount of ejecta wouldbe roughly comparable to the galactic r-process inventory. Itwas only more recently, that the potential of the ejected ma-terial to produce electromagnetic (EM) transients has beenappreciated (Li & Paczy´nski 1998; Kulkarni 2005; Rosswog2005; Metzger et al. 2010; Roberts et al. 2011; Goriely et al.2011; Metzger & Berger 2012; Kelley et al. 2012). EM tran-sients from compact binary mergers are nowadays thought (cid:63)
E-mail: [email protected] to be instrumental for maximizing the science returns fromthe advanced gravitational wave (GW) detector networks.In fact, EM transients may actually provide compelling evi-dence for the first direct GW detection and they may deliverinformation about the nature of the GW source and its as-tronomical environment.The matter required to produce such transients fromcompact binary mergers can be ejected in a number of ways,see Fig. 1. First, there are dynamic ejecta that are launchedimmediately at first contact by the interplay between hy-drodynamics and gravity. This type of ejecta is the mainfocus here. In addition, the merger remnant emits neutri-nos at rates of a few times 10 erg/s (Ruffert & Janka2001; Rosswog & Liebend¨orfer 2003; Sekiguchi et al. 2011)and this neutrino emission has been shown to drive strongbaryonic winds (Dessart et al. 2009). In fact, for as longas the central, hypermassive neutron star has not collapsedinto a black hole, this baryonic wind may actually representa serious danger for the emergence of the ultra-relativistic a r X i v : . [ a s t r o - ph . H E ] N ov eutrino-driven winds 〈 v 〉 ≈ ⇒ dynamic ejecta 〈 v 〉 ≈ Γ > 100interaction region jet-wind, Γ ~ few (?) Figure 1.
Sketch of the various mass loss mechanisms from a merger remnant (Γ denotes the Lorentz factor). In addition to the illustratedmechanisms there is also a contribution from the disc-disintegration that is expected to occur at late stages when nucleons recombineinto light nuclei/alpha particles and release a nuclear binding energy comparable to their gravitational binding energy. outflow that is required to produce a gamma-ray burst(GRB). If compact binary mergers indeed power short GRBsthis neutrino-driven wind should interact near the rotationaxis with the ultra-relativistic outflow (”jet”) producing theGRB. This interaction is expected to accelerate matter tosemi-relativistic speeds. In addition, at late stages of the discevolution, viscous heating and/or recombination of free nu-cleons into light nuclei/alpha particles ejects most of whatis left from the original accretion disc (Beloborodov 2008;Metzger et al. 2009; Lee et al. 2009). The ejecta of each ofthese channels have different properties, therefore their rolein nucleosynthesis and for the production of EM transientsneeds to be investigated separately for each channel.Recently, dynamical collisions/high-eccentricity mergers be-tween two compact objects have received a fair amount ofattention (O’Leary et al. 2009; Lee et al. 2010; Rosswoget al. 2012; East et al. 2012; Kocsis & Levin 2012). Theycould, for example, be promising GRB central engines andproduce repeated bursts of GWs, but recent work Rosswoget al. (2012) concluded that they can only occur at a mod-erate fraction of the nsns merger rate, otherwise they wouldcause an overproduction of galactic r-process material.Here we discuss the properties of the dynamic ejecta for alarge number of simulations of both mergers and dynami-cal collisions. For both types of encounters we consider nsnsand nsbh systems, the properties of these simulations aresummarized in Tab. 1.
The presented simulations are performed with a 3DSmoothed Particle Hydrodynamics (SPH) code, implemen-tation details can be found in the literature (Rosswog et al.2000; Rosswog 2005; Rosswog & Price 2007), for recent re-views of the SPH method consult, for example, Rosswog(2009) or Springel (2010). The neutron star matter is mod-eled with the Shen et al. equation of state (EOS; Shenet al. (1998a,b)). We apply an opacity-dependent, multi-flavor leakage scheme (Rosswog & Liebend¨orfer 2003) to ac-count for the change of the electron fraction and the coolingby neutrino emission. Black holes are here simply treatedas Newtonian point masses with absorbing boundaries atthe Schwarzschild radius. For the case of parabolic encoun-ters we parametrize the impact strength by the ratio β ≡ ( R + R ) /R per , where R i is the neutron star/Schwarzschildradius and R per is the separation at pericentre passage. Theperformed simulations and ejecta properties are summarizedin Tab. 1.We also show two examples to illustrate the hydrodynamicevolution. Fig. 2 shows volume renderings of the tempera-ture for a neutron star merger case (run 12), an example ofa (substantially more violent) collision between two neutronstars ( β = 2; run 27) is shown in Fig. 3 (the upper half ofmatter has been ”chopped off” to allow for a view insidethe remnant; the temperature scales are capped to enhancevisibility). he dynamic ejecta of compact object mergers and eccentric collisions Figure 2.
Merger of a 1.3 and a 1.4 M (cid:12) neutron star binary with initial tidal locking. Shown are volume renderings of the temperatureat t = 5.04, 6.30, 7.56 and 8.82 ms after simulation start. Double neutron star mergers have been known for some timeto dynamically eject interesting amounts of neutron-rich ma-terial (Rosswog et al. 1999). We consider binary neutronstar mergers as the most likely type of encounter and run13 (1.3 and 1.4 M (cid:12) , no initial spins) as our reference case.Parabolic collisions are interesting, but likely rare encoun-ters whose overall occurrence rate is restricted by their largeejecta masses, see below. Our reference nsns merger casedynamically ejects 1 . × − M (cid:12) , unequal mass cases ejectmore matter at larger velocities than equal mass cases of thesame total mass, see Tab. 1. For mass ratios q = m /m < m ej ( m , m ) = ( m + m ) (cid:18) A − Bη − C η /σ (cid:19) , (1)where A = 0 . B = 0 . C = 0 . σ = 0 . η = 1 − m m / ( m + m ) is the dimensionless mass asymmetry parameter. Collisionsof two neutron stars eject comparable, but slightly largeramounts than double neutron star mergers, typically a fewpercent . We find that collisions between neutron stars and Our run 27 has the highest numerical resolution with morethan 8 × SPH particles and is the most expensive of all oursimulations, therefore it was only run up to t= 9 ms. We consider tellar mass black holes, which, due to their larger captureradius, should dominate over nsns collisions by a factor of ∼ ∼ .
15 M (cid:12) . Unless equation of state orrelativistic gravity effects dramatically modify these results,the overall rate of compact object collisions should thereforebe seriously constrained, otherwise r-process elements wouldbe substantially overproduced.
Approximately half of the elements heavier than iron areformed by rapid (in comparison to β -decays) neutron cap-ture reactions or “r-process” for short. The r-process produc-tion sites, however, are still matters of debate. The r-processelements observed in metal-poor stars (Sneden et al. 2008)point to at least two groups of r-process events. One occursrelatively frequently and produces predominantly lighter el-ements from strontium to silver (Cowan & Sneden 2006;Honda et al. 2006). It may actually be the result of a super-position of a number of different sources. The other one israrer and produces whenever it occurs the heaviest r-processelements (beyond Ba, Z = 56) in nearly exactly solar pro-portions. So far, there is no generally accepted explanationfor the robustness of this unique heavy r-process component.Traditionally supernovae were considered the most likelysource of r-process elements, but a number of recent inves-tigations has cast doubts over this view (e.g. Arcones et al.(2007); Roberts et al. (2010); Fischer et al. (2010); H¨udepohlet al. (2010)). The main contenders of supernovae in termsof r-process nucleosynthesis are compact binary mergers ofeither two neutron stars or a neutron star and a stellar-massblack hole (Lattimer & Schramm 1974, 1976; Eichler et al.1989; Freiburghaus et al. 1999).The matter that is ejected by double neutron star merg-ers shows a narrow distribution of electron fractions around Y e ≈ .
03. Collisions produce a slightly broader but stillvery neutron-rich distribution, see Fig. 11 in Rosswog et al.(2012). The latter occurs due to the larger temperaturesin collisions which allow positron captures to increase Y e .We have explored the nucleosynthesis within these ejecta(Korobkin et al. 2012) and found a very robust r-processnucleosynthesis which produces all the elements from thesecond to the third r-process peak in close-to-solar ratios.The extreme neutron richness makes the r-process path me-ander along the neutron drip line and, as a result, the finalabundance patterns are predominantly determined by nu-clear properties rather than by those of the merging astro-physical system. Consequently, all cases produce essentiallyidentical abundance patterns, see Fig. 4c in Korobkin et al.(2012). Substantial deviations from this pattern only occurfor trajectories that have initial Y e -values above ∼ it likely that the final ejecta amount is larger than the 0.009 M (cid:12) that we measure at the end of our simulation. To gauge the possible relevance of nsns mergers for the en-richment of the Cosmos with heavy elements, we take theejecta masses found in the simulations and make the (verystrong) assumption that the considered mergers are the onlysource of r-process elements. The occurrence rates that arerequired under these assumptions to reproduce the galacticr-process enrichment rate of ∼ − M (cid:12) yr − (Qian 2000)are plotted in Fig. 4. The quantity η is the dimensionlessmass asymmetry parameter η that was also used in Eq. (1).These required rates are compared to the 95% confidenceinterval for the estimated nsns merger rate that is based onthe observed binary neutron star population (Kalogera et al.2004). Thus, within the existing uncertainties, double neu-tron star mergers eject enough material to deliver a majorcontribution to the Galactic r-process record.Collisions, on the other hand, eject substantially largeramounts. nsbh collisions are expected to occur five timesmore frequently than nsns collisions Lee et al. (2010), there-fore an average collision ejects ∼ (5 × .
15 + 0 . / ∼ . (cid:12) per event, about an order of magnitude more than thetypical merger case. We can obtain a robust upper limiton the collision rate if we make the extreme assumptionthat collisions are the only producers of r-process and thatno other event contributes. Under this extreme assumptiontheir occurrence rate would be about 10% of the nsns mergerrate. The rate realized in nature may actually be well belowthis value. The electromagnetic transients that go along with a com-pact binary merger have recently attracted much interest(Li & Paczy´nski 1998; Kulkarni 2005; Rosswog 2005;Metzger et al. 2010; Roberts et al. 2011; Goriely et al.2011; Metzger & Berger 2012; Kelley et al. 2012). Suchtransients can provide information on the distance, on thetype of and the position with respect to the host galaxy,on its metallicity and on the ambient matter densities. Inother words EM transients help to place a compact binarycoalescence into an astrophysical context. After havingbeen operational intermittently during the last decade theLIGO and VIRGO detectors are currently being upgraded(Abbott et al. 2009; Sengupta et al. 2010). By about 2016they should reach their new design sensitivities which are10-15 times higher than those of the initial instruments,so that the accessible volume increases by more thanthree orders of magnitude. This will push the detectionhorizons for nsns mergers out to a few hundred Mpc andto nearly a Gpc for nsbh mergers (Abadie et al. 2010).The first detections are expected to be near threshold andaccompanying EM signals could substantially boost theconfidence in a candidate event and thus effectively increasethe instrument sensitivities (Kochanek & Piran 1993;Hughes & Holz 2003; Dalal et al. 2006; Arun et al. 2009).Rather than relying on accidental coincident EM and GWdetections one could increase the detection rate by eitherfollowing a GW candidate event by target-of-opportunitysearches for EM transients or by scanning through archivaldata based on EM triggers (e.g. Kochanek & Piran (1993);Mohanty (2005); Mandel & O’Shaughnessy (2010); Nakar he dynamic ejecta of compact object mergers and eccentric collisions Figure 3.
Collision of a 1.3 and a 1.4 M (cid:12) neutron star with an impact strength of β = 2. Shown are volume renderings of the temperature(at t = 1.49, 3.83, 6.27 and 8.32 ms after simulation start), only matter below the orbital plane is shown. & Piran (2011); Metzger & Berger (2012)). The most luminous expected EM transients are shortGamma-ray bursts (sGRBs; Paczynski (1986); Eichler et al.(1989); Narayan et al. (1992); Piran (2004); Nakar (2007);Lee & Ramirez-Ruiz (2007). The physical mechanisms be-hind launching such a burst are still far from being settled,it seems, however, that the ultra-relativistic outflows thatproduce the bursts are collimated into half-opening anglesof ∼ ◦ (Fong et al. 2012), consistent with theoretical expectations (Rosswog & Ramirez-Ruiz 2003; Aloy et al.2005). As discussed previously, the emerging neutrino-driven winds pose a serious threat to the emergence ofan ultra-relativistic outflow and therefore not every nsnsmerger may actually be able to produce a sGRB. In otherwords, the detected sGRB rate may possibly be only a smallfraction of the true nsns merger rate, R sGRB = f b f p R nsns ,where f b is the beaming fraction and f p the fraction ofnsns mergers that is not choked by baryonic pollution (e.g.through neutrino-driven winds). Cases where a GW signalis detected but no GRB might then be used as trigger onthose EM transients that are less beamed such such as able 1. Overview over the performed simulations, the superscript + indicates that the primary is a blackhole. Unless otherwise noted, neutron stars have zero initial spin. Binary mergers
Run m [M (cid:12) ] m [M (cid:12) ] N SPH [10 ] t end [ms] m ej [10 − M (cid:12) ] (cid:104) v (cid:105) [c] comment1 1.0 1.0 1.0 15.3 0 .
76 0.102 1.2 1.0 1.0 15.3 2 . . . > . > . . . . . > . . . . . . . . . . . . . + . + . Parabolic collisions
Run m [M (cid:12) ] m [M (cid:12) ] N SPH [10 ] t end [ms] m ej [10 − M (cid:12) ] (cid:104) v (cid:105) [c] comment26 1.4 1.3 2.7 21.2 6 . β = 127 1.4 1.3 8.0 9.0 0 . β = 228 1.4 1.3 2.7 13.2 3 . β = 529 3.0 + . β = 130 5.0 + . β = 131 10.0 + . β = 1 ”orphan afterglows” or macronovae, see below. ”Macronovae” are radioactively powered transients thatemerge from the decaying ejecta of compact object mergersLi & Paczy´nski (1998). In contrast to GRBs, they should be”isotropic” in the sense that they are visible from all sides,although the ejecta distribution suggests a viewing angle de-pendence, see Figs. 1 and 2 in Piran et al. 2012. Macronovaeshare some similarities with supernovae, in particular, with-out late-time energy injection from radioactive decays they would be hardly detectable at all. The ejecta compositionof a macronova is unique and very different from any typeof supernova. While the latter produce elements up to theiron group near Z = 26, the dynamic ejecta of neutron starmergers consist entirely of r-process elements up to the thirdpeak near Z ≈
90, see above, and should thus leave a dis-tinctive imprint on the observable electromagnetic display.Given the expected complexity of the involved physics, themodels that exist to date are still rather basic. They relyon estimates for the ejected mass and its velocity distri-bution (or alternatively dm/dv ), which can be straightfor-wardly extracted from hydrodynamics simulations. Via nu-clear network calculations along hydrodynamic trajectories he dynamic ejecta of compact object mergers and eccentric collisions Figure 4.
Relevance for cosmic r-process inventory. Shown is the event rate that is, based on the simulation results, required to reproducethe galactic r-process enrichment rate, ˙ M r , gal , for a given mass asymmetry parameter η . For each value of η the required rate (square)is calculated as ˙ M r , gal /m ej , sim , where m ej , sim is the ejecta mass found in the simulations. For comparison, the expected 95% confidenceinterval for the nsns merger rate as derived from observations (Kalogera et al. 2004) is shown. Within the existing uncertainties, theejecta masses are consistent with nsns mergers being major production sites of r-process material. one can extract the nuclear energy injection rate, ˙ (cid:15) , whichshows little sensitivity to the exact details (Metzger et al.2010; Korobkin et al. 2012). The latter authors find that˙ (cid:15) ( t ) = 2 × erggs (cid:16) − π arctan t − . . (cid:17) . × (cid:16) (cid:15) th . (cid:17) (2)provides a good fit to the results of the network calculations.Here (cid:15) th is the fraction of energy that is injected as thermalradiation. The last ingredient of existing models is anaverage value for the opacity κ . The opacity value is crucialsince it determines the diffusion time which, in turn, setsthe time of peak emission. In existing models this value hasbeen taken as 0.1 cm /g which is characteristic of the lineexpansion opacity from iron group elements (e.g. Kasen &Woosley (2007)).With these assumptions one finds that a macronova result-ing from a 2 × (cid:12) nsns merger peaks after ≈ . L peak ≈ × erg/s (Piran et al. 2012). Nearlyall other nsns and nsbh cases, both mergers and collisions,deliver larger ejecta masses and velocities and thereforeproduce larger luminosities (up to ∼ erg/s) at slightlylater times ( t peak < Z = 57 − It is important to realize that compact object merger ejectacan contain a kinetic energy that is comparable to a super-nova. For example, the ejecta of a typical nsns merger (1.3& 1.4 M (cid:12) ) contain 2 × erg. The more extreme, butprobably rare collision cases can even contain up to 10 erg of kinetic energy (Rosswog et al. 2012). The decelera-tion of this sub-/mildly relativistic material drives a strongshock into the ambient medium. Shocks with similar prop-erties have been observed in late stages of GRB afterglowsand in the early phases of some supernovae. In both circum-stances they produce bright radio emission. The ejecta ofcompact object encounters are sprayed with a distributionf velocities into the surroundings, for typical nsns mergersthe average velocity is close to 0.1c. Asymmetric mergers( q (cid:54) = 1) deliver average velocities up to 0.18c, but how of-ten these higher-velocity cases occur depends on their notso well-known mass distribution. Collisions yield substan-tially larger average velocities (up to 0.28c, see Tab. 1) witha high velocity tail reaching close to the speed of light. Thehighest of these velocities, however, need to be interpretedwith care since the simulations are essentially Newtonian.Nevertheless, it is a robust result that dynamical collisionsproduce substantially larger ejecta velocities, therefore theirradio signals are brighter and peak earlier. It needs to be re-iterated, though, that collisions must be rare in comparisonto nsns mergers.With assumptions similar to those successfully applied inGRB afterglows, i.e. constant internal energy fractions be-hind the shock in electrons, (cid:15) e = 0 .
1, and in magnetic field, (cid:15) B = 0 .
1, and electrons being accelerated into a power lawdistribution with index p = 2 .
5, one can estimate the re-sulting radio emission (for a detailed description see Piranet al. (2012)). At 1.4 GHz the radio signal that emergesfrom a typical nsns merger at the detection horizon of ad-vanced LIGO (300 Mpc) remains on a level of ∼ µ Jy forseveral years, provided that it occurs in an environment sim-ilar to the one of the observed Galactic nsns systems wherethe density is of order 1 cm − . Asymmetric q (cid:54) = 1 mergersand in particular collisions with their larger ejecta veloci-ties and masses produce brighter and longer lasting radioflares (Piran et al. 2012; Rosswog et al. 2012). The ambientmatter density is a major uncertainty for the detectability,though. Neutron star binary systems that receive a kick atbirth could easily travel out of the galactic plane and mergewhere densities are substantially lower (Fryer et al. 1999;Bloom et al. 1999; Rosswog et al. 2003; Belczynski et al.2006; Fong et al. 2010). The transients from the dynamicejecta of such cases would be very hard to detect.Due to their velocities of ∼ . We have briefly summarized the ways in which a compactbinary encounter ejects neutron-rich matter into its sur-roundings. Our focus was on the dynamic ejecta, launchedby hydrodynamic effects and gravitational torques, and ontheir implications for nucleosynthesis and EM transients going along with a compact binary encounter.nsns mergers eject close to one percent of a solar mass withan extremely low electron fraction, Y e ≈ .
03. The exactamount of ejecta and their velocities depend on both thetotal mass and the mass ratio of the binary system. Ourreference system, the merger of a 1.3 and 1.4 M (cid:12) binarysystem, ejects 1 . × − M (cid:12) at an average velocity of0.12c. Robust r-process within the ejecta produces elementsin close-to-solar proportions from the second to the thirdr-process peak. This abundance pattern is extremely robustand essentially the same for all investigated cases, seeKorobkin et al. (2012). The ejected amounts are consistentwith nsns mergers being a major source of heavy r-process.A question that needs further investigation, though, iswhether/under which conditions this is consistent withgalactic chemical evolution. Earlier work (Argast et al.2004) concluded that neutron star mergers could not bethe major source of r-process, but all existing studies foundthat the conditions in merger ejecta are very favorable forr-process isotopes to be forged in close-to-solar proportions(Freiburghaus et al. 1999; Goriely et al. 2011; Robertset al. 2011; Korobkin et al. 2012) and this discrepancyremains to be understood. Dynamical collisions as they areexpected to occur, for example, in the cores of globularclusters, eject substantially larger amounts of matter andthe overproduction of r-process material by collisions canonly be avoided if they are rare in comparison to nsnsmergers (less, possibly much less, than 10%).We have also discussed the implications for macronovae,radioactively powered, fast EM transients and for the radioflares that are produced when the ejecta share their kineticenergy with the ambient medium.The presented amounts of ejecta and their velocities arenumerically converged and very robust. They may depend,however, on the employed physics. In particular, they maybe affected by general relativistic and possibly nuclearequation of state effects. We suspect that such effects maychange the ejecta masses at maximum by a factor of afew, therefore, the conclusions with respect to the role ofmergers as r-process production sites should be robust. Thesensitivity to GR and nuclear equation of state effects willbe explored in future studies. Acknowledgements
It is a pleasure to acknowledge insightful discussions withA. Arcones, E. Berger, A. MacFadyen, O. Korobkin, B.Metzger, E. Nakar, T. Piran, E. Ramirez-Ruiz, F.-K. Thiele-mann and I. Zalamea. Special thanks to E. Gafton whohelped preparing Fig.1. This work was supported by DFGgrant RO-3399, AOBJ- 584282. The simulations were per-formed on the facilities of the H¨ochstleistungsrechenzentrumNord (HLRN), we used SPLASH developed by D. Price tovisualize the hydrodynamics simulations.Movies from our hydrodynamic simulations and ejectatrajectories can be downloaded from:http://compact-merger.astro.su.se/
REFERENCES