Eccentric mergers of black holes with spinning neutron stars
aa r X i v : . [ a s t r o - ph . H E ] J un Draft version October 23, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
ECCENTRIC MERGERS OF BLACK HOLES WITH SPINNING NEUTRON STARS
William E. East , Vasileios Paschalidis , and Frans Pretorius Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, SLAC National Accelerator Laboratory, Menlo Park, CA94025, USA Department of Physics, Princeton University, Princeton, NJ 08544, USA
Draft version October 23, 2018
ABSTRACTWe study dynamical capture binary black hole–neutron star (BH–NS) mergers focusing on theeffects of the neutron star spin. These events may arise in dense stellar regions, such as globularclusters, where the majority of neutron stars are expected to be rapidly rotating. We initialize theBH–NS systems with positions and velocities corresponding to marginally unbound Newtonian orbits,and evolve them using general-relativistic hydrodynamical simulations. We find that even moderatespins can significantly increase the amount of mass in unbound material. In some of the more extremecases, there can be up to a third of a solar mass in unbound matter. Similarly, large amounts oftidally stripped material can remain bound and eventually accrete onto the BH—as much as a tenthof a solar mass in some cases. These simulations demonstrate that it is important to treat neutronstar spin in order to make reliable predictions of the gravitational wave and electromagnetic transientsignals accompanying these sources.
Subject headings: black hole physics—gamma-ray burst: general—gravitation—gravitational waves—stars: neutron INTRODUCTION
Next generation ground-based gravitational wave(GW) detectors such as aLIGO (Abramovici et al.1992) are expected to reach design sensitivity withinthe next few years. Among their most promis-ing sources are mergers of compact objects (COs),including black hole–neutron star (BH–NS) bina-ries. BH–NS mergers are also proposed short-hard gamma-ray burst (sGRB) engines (e.g. Meszaros(2006)), and may power other electromagnetic (EM)transients either preceding (Hansen & Lyutikov 2001;McWilliams & Levin 2011; Paschalidis et al. 2013) orfollowing (Metzger & Berger 2012) the merger. TheseEM counterparts to GWs could be observed by currentand future wide-field telescopes such as PTF (Rau 2009)and LSST (LSST Dark Energy Science Collaboration2012).Extracting maximum information from such “mul-timessenger” observations requires careful modeling ofBH–NS mergers. Several studies of quasicircular BH–NSinspirals using numerical relativity simulations have beenperformed, see, e.g., Chawla et al. (2010); Etienne et al.(2012); Kyutoku et al. (2013); Tanaka et al. (2014);Foucart et al. (2014). While quasicircular binaries maydominate the global rates of BH–NS encounters inthe Universe, recent calculations (Kocsis & Levin 2012;Lee et al. 2010; Samsing et al. 2014) suggest that indense stellar regions, such as galactic nuclei and globularclusters (GCs), CO binaries can form through dynami-cal capture and merge with non-negligible eccentricities.Compared to quasi-circular inspirals, these emit moreGW energy in the high luminosity, strong-field regime ofgeneral relativity, and small changes in the energy of thebinary at each pericenter passage can lead to relativelylarge changes in the time between GW bursts—the lead-ing order GW observable. Hence these systems couldbe excellent laboratories to test gravity and measure the internal structure of a NS (insofar as this affects the en-ergy of the orbit, e.g. tidal excitation of f-modes). Ratesof these events are highly uncertain, but have been es-timated to be up to ∼
100 yr − Gpc − . To realize thisrich potential to learn about the Universe from eccentricmergers, it is irrelevant what their rates are comparedto quasi-circular inspiral, only that eccentric mergers oc-cur frequently enough that some events could be observ-able by aLIGO within its lifetime. However, new detec-tion pipelines would be needed that are better adaptedto the repeated-burst nature of eccentric GW mergersfor aLIGO to efficiently detect them (Tai et al. 2014).For more discussion of rates, distinguishing features, anddetection issues for eccentric encounters, see East et al.(2013) and references therein.Motivated by the above, Stephens et al. (2011);East et al. (2012a) performed fully general-relativistichydrodynamical (GR-HD) simulations of dynamical-capture BH–NS mergers. These studies explored the ef-fects of impact parameter, BH spin, and NS equationof state (EOS) on GW emission and post-merger BHdisk and ejecta masses. Here, we expand upon this workby including the effects of NS spin. To date the onlysimulations including spinning NSs focused on quasicir-cular NS–NS mergers, e.g. Tichy (2011); Bernuzzi et al.(2014), demonstrating that even moderate spins can af-fect the dynamics.NS spin has two main effects: (1) it modifies the star’sstructure, making it less gravitationally bound; (2) itchanges the orbital dynamics, e.g., by shifting the effec-tive innermost stable orbit (ISO). This can impact notonly the GWs from CO mergers, but also the amountof matter forming the BH accretion disk that putativelypowers a sGRB, and the amount of unbound matter thatpowers other EM transients, such as kilonovae. Theremay also be effects on pre-merger EM signals since theNS spin determines the light-cylinder radius, and hence East, Paschalidis & Pretoriusthe orbital separation at which unipolar induction turnson.Spin effects on the NS structure cannot be neglected ifthe NS spin period P is O (ms). Furthermore, for com-parable mass BH–NSs near the tidal disruption radius,NS spin effects on the orbit will be non-negligible when P is similar to the BH–NS encounter timescale (Tichy2011). For example, a BH–NS eccentric encounter withmass ratio q = M BH /M NS = 4 (as studied here) neara periapse of r p = 10 M has an interaction timescaleof t int ≃ ( r p /M ) / ∼ . M NS / . M ⊙ )ms ( M is thesystem’s total mass, and we use geometric units with G = c = 1 throughout).NSs in field BH–NS binaries may not commonly have P = O (ms) near merger. However, there are two reasonsto think that the opposite may hold for dynamical cap-ture BH–NS mergers occurring in GCs: the pulsar spinperiod distribution in Galactic GCs peaks in the mil-liseconds, and millisecond pulsars (MSPs) have longerinferred magnetic dipole spin-down timescales.Of the 144 currently known pulsars in Galactic GCs, ∼
83% have periods less than 10 ms, ∼
55% less than 5ms, and ∼
12% have periods less than 2.5 ms . This setincludes PSR-J1748-2446ad—the fastest-spinning pul-sar known, with P = 1 .
396 ms (Hessels et al. 2006).The theoretical explanation for this skew toward shortperiods is that GCs favor the formation of low-massX-ray binaries (LMXB) (Verbunt & Hut 1987), whichare thought to spin up the NS to ms periods throughmass and angular momentum transfer (Alpar et al. 1982;Radhakrishnan & Srinivasan 1982).Assuming that pulsar spin-down is predominantly dueto magnetic dipole emission, both the magnetic fieldstrength ( B ) and spin-down timescale ( t sd ) can be com-puted from observations of P and its time derivative ˙ P .For B the relation is (Bhattacharya & van den Heuvel1991) B ∼ . × G " P . P − / , which for known GC MSPs with ˙ P > B ∼ —10 G. Observations of X-ray os-cillations of accretion-powered MSPs in LMXBs, andpulsar recycling theory imply B in the range 3 × —3 × G (Lamb & Yu 2005). For t sd the expressionis (Zhang & M´esz´aros 2001) t sd ∼ I g cm (cid:18) B × G (cid:19) − (1) (cid:18) P . (cid:19) (cid:18) R NS
10 km (cid:19) − , where the NS moment of inertia is I . Even neglecting thepossibility of magnetic field decay, e.g. a pulsar with amagnetic field of 3 × G and initial P = 2 . P to double. Given the longspin-down timescale of MSPs and the results of Lee et al.(2010), which suggest that in GCs there could be 40 BH–NS collisions per Gyr per Milky Way-equivalent galaxy, it is at least conceivable that some of these eccentric BH–NS collisions take place with millisecond NSs.With this motivation, here we focus on eccentric BH–NS mergers (with initial conditions corresponding to amarginally unbound Newtonian orbit) and explore NSspin effects. We show that even moderate spins cansignificantly impact the outcome, both in terms of theGWs, and amounts of tidally stripped bound and un-bound matter. The remainder of the paper is as follows:in Sec. 2 we describe our initial data and numerical meth-ods. In Sec. 3 we present our simulation results anddiscuss the impact of NS spin on gravitational and EMsignatures. We summarize in Sec. 4 and discuss futurework. NUMERICAL APPROACH
We perform GR-HD simulations of BHs merging withrotating NSs using the code of East et al. (2012b). Thefield equations are solved in the generalized-harmonicformulation, using finite differences, while the hydrody-namics are evolved using the same high-resolution shock-capturing techniques as in East et al. (2012a).To construct initial data, we solve the constraint equa-tions using the code of East et al. (2012c), specifying thefree-data as a superposition of a non-spinning BH with anequilibrium, uniformly rotating NS, which we generateusing the code of Cook et al. (1994a,b). For the NS EOS,we adopt the HB piece-wise polytrope from Read et al.(2009), and include a thermal component P th = 0 . ǫ th ρ allowing for shock heating.Fixing the NS gravitational mass to 1 . M ⊙ , we con-sider NSs with dimensionless spins a NS = J/M = 0,0.1, 0.2, 0.3, 0.4, 0.5, and 0.756, having correspond-ing compactions (mass-to-equatorial-radius) C = 0 . .
12. The rangesof
T / | W | (kinetic-to-gravitational-potential-energy ra-tio) and P in our spinning NS models are [0 . , . . , .
00] ms. The fastest spinning NS consideredhas a polar-to-equatorial-radius ratio of r po /r eq = 0 . r po /r eq = 0 . r p /M ∈ [5 , q = 4. The two COs are ini-tially placed at a separation of d = 50 M ( ∼ r p . For this initialstudy, we only consider cases where the spin is alignedor anti-aligned with the orbital angular momentum (thelatter indicated by a NS < points, and finest-level resolution with approxi-mately 75 (130) points covering the (non-spinning) NS(BH) diameter, respectively. For r p /M = 6, a NS = 0 . / / × the reso-lution, to establish convergence and estimate truncationerror. In Fig. 1 we demonstrate the convergence in theGW emission. RESULTS AND DISCUSSION
Simple estimates
During eccentric encounters between NSs and BHs, forNS tidal disruption to form a substantial disk and un-ynamical Capture Mergers of BHs with spinning NSs 3 R e ( C ) × M t−r (ms) −1.0−0.50.00.51.0 ∆ R e ( C ) × M Fig. 1.—
Convergence of the GW emission for the r p /M = 6, a NS = 0 .
756 case. The top panel shows the real part of the ℓ = m =2 mode of the Newman–Penrose scalar Ψ at three resolutions, andthe bottom panel the differences in this quantity with resolution,scaled assuming second-order convergence. bind a non-negligible amount of matter, it must occuroutside the ISO radius ( r ISO = 4 M BH for a marginallyunbound test particle about a non-spinning BH). In addi-tion to shifting the effective ISO, spin makes the NS lessself-bound, and thus alters the tidal disruption radius.Equating the sum of the tidal and centrifugal accelera-tions to the gravitational acceleration on the NS surfaceyields r t M BH ∼ q − / C − (cid:18) − ( a NS /a ms ) (cid:19) / , (2)where we replaced the NS angular frequency with Ω = J/I = a NS M /I , and let I = 2 f M NS R /
5, with f anorder-unity constant that depends on the NS structure.Here, a ms = (4 f / C ) / ≃ . f / . C/ . − / isthe mass-shedding limit spin parameter. Equation (2)shows that the closer a NS is to a ms , the larger the tidaldisruption radius. It also suggests that for sufficientlyfast rotators, the tidal disruption radius can be outsidethe ISO even for large q , something which is not truefor non-spinning NSs unless the BH has near-extremalspin. Additionally, as the prograde NS spin increases,the effective ISO decreases. Therefore, we expect moremassive disks and more unbound material following tidaldisruption outside the ISO with increasing a NS . Dynamics and Gravitational Waves
For the cases considered here, those with r p ≤ . r p ≥ . r p /M = 6, 7, and 8; see also Table 1. Near the critical r p — below (above) where a merger (fly-by) occurs —there are large differences in the dynamics that have anoticeable impact on the GW signal and tidally strippedmatter. This is evident here with the r p /M = 7 case,where there is either partial tidal disruption followed by amerger on a second encounter (for a NS = 0 . t−r (ms) −5−4−3−2−101234 R e ( C ) × M NS =−0.40a NS =0.00a NS =0.10a NS =0.20a NS =0.40a NS =0.768 10 12 14 16 18 t−r (ms) −4−3−2−101234 R e ( C ) × M a NS =−0.40a NS =0.00a NS =0.20 a NS =0.40a NS =0.50a NS =0.76 t−r (ms) −6−4−202468 R e ( C ) × M NS =0.00a NS =0.20a NS =0.40a NS =0.76 Fig. 2.—
Plots of the real part of the l = m = 2 mode of thescalar Ψ . The top and middle panels show GWs from simulationswith r p /M = 6 and 7, respectively. The bottom panel plots theGWs for r p /M = 8 fly-by cases. a NS = 0 . , .
5, as well as the bottom-right panel of Fig. 4where it can be seen that the NS for a NS = 0 . ∼
10% ( ∼ a NS for r p /M = 7. The a NS = 0 .
756 NS is the least East, Paschalidis & Pretoriusbound and for this case complete tidal disruption occurson the initial encounter. As the NS is tidally stretched,GW emission effectively shuts off (middle panel Fig. 2),and matter begins to accrete onto the BH (bottom panelof Fig. 4). For the next two lower spins, the materialis more tightly bound, and only partial disruption oc-curs, with some of the material promptly accreting ontothe BH. However, as the NS spin decreases, the effectiveISO radius increases, and for a NS . . a NS = 0 . r p /M = 7 the a NS = 0 .
756 case is com-pletely disrupted, while some of the lower spin cases arepartially disrupted, r p /M = 8 , a NS = 0 .
756 should alsobe disrupted, given how close this spin is to the break upvalue. That this does not happen shows that this crudeestimate significantly underestimates the self-binding ofhigh spin stars.
Post-merger Matter Distribution
In Table 1 we list the amount of bound and unboundmass exterior to the BH shortly following merger. For r p /M = 5 , a NS , with the notable exception of a NS = 0 . , r p /M =6. By contrast, near the critical impact parameter( r p /M = 7) there is over an order of magnitude vari-ation in bound material as a function of NS spin.The amount of bound rest-mass that forms a BH accre-tion disk is 0 . . M ⊙ in our set. If these disks powersGRBs on timescales of ∼ . ∼ . . M ⊙ s − , i.e., consistent with magneto-hydrodynamic BH–NS studies (Paschalidis et al. 2014).Assuming a 1% conversion efficiency of accretion powerto jet luminosity, these accretion rates imply luminosi-ties of 10 –10 erg s − —consistent with characteristicsGRB luminosities.The top two panels in Fig. 4 show plots of the asymp-totic velocity distribution of the unbound matter for r p /M = 6 ,
7. As anticipated (see Sec. (3.1)), the generaltrend is that increasing a NS increases both the amountand average asymptotic velocity of unbound material.This is also seen in Table 1 where we list these quanti-ties for all cases. The bottom-left panel of Fig. 4 alsodemonstrates that including spin increases the amountof unbound material by an order of magnitude or morefor the cases considered.The increase in total rest-mass M , u and velocity v ofthe unbound material with increasing a NS can stronglyimpact potential kilonovae signatures from such mergers.These arise when neutron-rich ejecta produce heavy el-ements through the r-process than then undergo fission,emitting photons (Li & Paczynski 1998; Kulkarni 2005).Recently Barnes & Kasen (2013) have shown that theopacities in r-process ejecta will likely be dominated bylanthanides, giving rise times of t peak ≈ . M , u / − M ⊙ ) / ( v/ . c ) − / dwith peak luminosities of L ≈ × (cid:18) M , u − M ⊙ (cid:19) / (cid:16) v . c (cid:17) / erg s − (3) for typical values found here. In some cases, opacitiesan order of magnitude lower than those used above maybe justified (Metzger et al. 2015). Using Eq. (3) we esti-mate the luminosity from potential kilonovae in Table 1.Apart from the fact that NS spin can make the differencein whether there will be a kilonova at all for r p /M = 5,for r p /M = 6 and r p /M = 7 spin affects L by an orderof magnitude in our set. For r p /M = 6 even a moder-ate a NS = 0 . L by a factor of 4 compared to a NS = 0. Barnes & Kasen (2013) predict that a kilonovaluminosity of ∼ erg s − corresponds to an r-bandmagnitude of 23.5 mag at 200 Mpc (near the edge of theaLIGO volume), above the planned LSST survey sensi-tivity of 24.5 mag. Thus, differences in luminosity byfactors of a few could be discernible.Ejecta will also sweep the interstellar medium (ISM)producing radio waves. These will peak on timescales ofweeks with brightness (Nakar & Piran 2011) F ( ν obs ) ≈ . E kin / erg)( n / . − ) / (4)( v/ . c ) / ( ν obs / GHz) − / ( d/
100 Mpc) − mJyfor an observation frequency ν obs at a distance d ,and using n ∼ . − as the density for GCcores (Rosswog et al. 2013). Estimating the kinetic en-ergy and the mass-averaged velocity in the ejecta, weshow F ( ν obs ) via Eq. (4) in Table 1. For r p /M = 6( r p /M = 7) F ( ν obs ) varies by 3 (2) orders of magnitudeover our set of spins.Finally, it has been suggested that ejecta from merg-ers involving NSs may make a non-negligible contri-bution to the overall abundance of r-process elements(Lattimer & Schramm 1974; Rosswog et al. 1998). Inparticular, dynamical-capture binaries, which can formand merge on shorter timescales, may be favoredover field binaries in explaining abundances in carbon-enhanced metal-poor stars (Ramirez-Ruiz et al. 2014).The average galactic production of these elements isestimated to be ∼ − M ⊙ yr − (Qian 2000). Mak-ing the limiting assumption that all r-process mate-rial comes from extreme BH-NS mergers cases like the r p = 7, a NS = 0 .
76 with M , u ≈ . M ⊙ caps theseextreme events at 3 × − yr − per galaxy (sim-ilar to predicted rates for primordial BH–NS merg-ers (Abadie et al. 2010)). CONCLUSIONS
We have demonstrated using GR-HD simulations ofdynamical capture BH–NS mergers that even moderatevalues of NS spin can significantly increase the mean ve-locity and amount of unbound material (to as much as0 . M ⊙ for extreme spins). This could lead to signifi-cantly brighter transients, including kilonovae a factorof a few brighter, and radio wave emission from inter-action with the ISM an order of magnitude or morebrighter. For comparison, simulations of quasicircularBH–NS mergers with nonspinning NSs typically findejecta velocities ∼ . . c , comparable, though some-what smaller than found here, but only find similaramounts of ejected material for cases with smaller mass-ratios and/or high BH spin (Kyutoku et al. 2015). Wealso find that the NS spin can alter the amount of boundmatter that, following tidal disruption, remains to forman accretion disk that may power a sGRB. Dependingynamical Capture Mergers of BHs with spinning NSs 5 gm cm − gm cm − Fig. 3.—
Equatorial density snapshots. Top row ( r p /M = 7 , a NS = 0 .
5) from left to right: the NS survives the first encounter (firstand second panels), it is completely tidally disrupted during the second encounter (third panel), the bulk of the matter outside the BHis unbound (fourth panel). Bottom row ( r p /M = 7 , a NS = 0 .
2) from left to right: the NS is tidally disrupted during the first encounter(first panel), a tidal tail forms ejecting some matter to infinity (second panel), an accretion disk develops outside the BH (third and fourthpanels). The scale can be inferred from the size of the BH ( R BH ∼
16 km). v ∞ /c -5 -4 -3 -2 M ( v < v ∞ < v ) ( M (cid:2) ) a NS =⊙0.40a NS =0.00a NS =0.10a NS =0.20a NS =0.40a NS =0.76Low res.High res. v ∞ /c -4 -3 -2 -1 M ( v < v ∞ < v ) ( M (cid:2) ) a NS =⊙0.40a NS =0.00a NS =0.20a NS =0.30a NS =0.40a NS =0.50a NS =0.76 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 a NS -5 -4 -3 -2 -1 M , u ( M ⊙ ) r p =5.0r p =6.0r p =7.0 time (ms) M ( t ) / M ( t = ) a NS =−0.40a NS =0.00a NS =0.20a NS =0.30a NS =0.40a NS =0.50a NS =0.75 Fig. 4.—
Top: distribution of the asymptotic velocity of unbound rest-mass, binned in increments of 0 . c , and computed ≈
10 mspost-merger for r p /M = 6 (left) and r p /M = 7 (right) and various spins. Bottom: total unbound mass as a function of NS spin (left) andrest-mass outside the BH versus time for r p /M = 7 and various spins (right). Note that for the lowest point in the bottom-left panel, nounbound matter was found in the simulation (indicated by an arrow). East, Paschalidis & Pretorius r p a NS J ADM M E GW M × b J GW M × c M ,b d M ,u e < v ∞ > f E kin ,
51 g L
41 h F ν i a BH j k TABLE 1Summary of simulations followed through merger.
For r p /M ≥ . r p after the first encounter, as expected. To within the estimated 20% truncationerror inferred from the r p = 6 case resolution study, we see no variation with spin. However, even a small variation in the energy emission at fly-bycould result in a significant change in the time to the subsequent close encounter in a highly eccentric binary. Thus, higher resolution studies wouldbe needed to ascertain the effect of spin on the GW signal for r p /M ≥ . a ADM angular momentum. b Total energy emitted in GWs through the r = 100 M surface. c Total angular momentum emitted in GWs. d Bound rest mass outside the BH ∼
10 ms post-merger in percent of M ⊙ . e Unbound rest mass in percent of M ⊙ . f Rest-mass averaged asymptotic velocity of unbound material. g Kinetic energy of ejecta in units of 10 erg. h Kilonovae bolometric luminosity in units of 10 erg s − using Eq. (3). i Specific brightness from ejecta interaction with ISM in units of mJy using Eq. (4). j Remnant BH dimensionless spin. k Values in parentheses are Richardson extrapolated values using all three resolutions. ynamical Capture Mergers of BHs with spinning NSs 7on the impact parameter and NS spin, these mergers canproduce accretion disks of up to a tenth of a solar mass.We find that near the critical impact parameter the NSspin influences the orbital dynamics to a sufficient extentto affect whether a merger or fly-by occurs, with a cor-responding large effect on the GW emission. At a firstglance this variability might seem exceedingly rare, re-quiring a finely tuned impact parameter. However, sincethe primary source of this sensitivity to binary parame-ters arises because the pericenter gets close to the regionof unstable orbits, which exists for all eccentricities, notmerely the initially hyperbolic case considered here, onecan speculate that the last few encounters for any casewhere non-negligible orbital eccentricity remains will besubject to this sensitivity. Likewise, the variability as-sociated with EM counterparts could also be present fora larger range of initial impact parameters. Future sim-ulations of multi-burst events will be needed to addressthis speculation. At the other end of the spectrum, somefraction of dynamical-capture binaries that form at largerinitial separations will circularize prior to merger due toGW emission; the results found here thus also motivatethe study of quasicircular mergers involving millisecondNSs.We have shown it is important to include spin to under-stand the full range of possible EM and GW outcomes in eccentric mergers. However, whether it will be possibleto perform parameter estimation from a putative multi-messenger event is a different question. Certainly in asingle burst event the degeneracies will be too strong to,for example, identify NS spin as the sole reason for anunusually bright counterpart. Multi-burst events can inprinciple lift much of the degeneracy, as information inthe timing of the bursts could significantly narrow theparameters of the progenitor binary. The range of viableNS EOSs, NS spin directions, and BH spins needs to besimulated, both to determine how these parameters af-fect the observable outcomes, and how they add to orlift degeneracies. GW detection rates and parameter es-timation also needs to be investigated within a realisticdata analysis framework including detector noise. All ofthese problems we leave for future studies. We also planto study the effect of spin in dynamical-capture NS–NSmergers.We are grateful to Stuart Shapiro for access to theequilibrium rotating NS code. This work was sup-ported by NSF grant PHY-1305682 and the SimonsFoundation. Computational resources were provided byXSEDE/TACC under grant TG-PHY100053 and the Or-bital cluster at Princeton University.ynamical Capture Mergers of BHs with spinning NSs 7on the impact parameter and NS spin, these mergers canproduce accretion disks of up to a tenth of a solar mass.We find that near the critical impact parameter the NSspin influences the orbital dynamics to a sufficient extentto affect whether a merger or fly-by occurs, with a cor-responding large effect on the GW emission. At a firstglance this variability might seem exceedingly rare, re-quiring a finely tuned impact parameter. However, sincethe primary source of this sensitivity to binary parame-ters arises because the pericenter gets close to the regionof unstable orbits, which exists for all eccentricities, notmerely the initially hyperbolic case considered here, onecan speculate that the last few encounters for any casewhere non-negligible orbital eccentricity remains will besubject to this sensitivity. Likewise, the variability as-sociated with EM counterparts could also be present fora larger range of initial impact parameters. Future sim-ulations of multi-burst events will be needed to addressthis speculation. At the other end of the spectrum, somefraction of dynamical-capture binaries that form at largerinitial separations will circularize prior to merger due toGW emission; the results found here thus also motivatethe study of quasicircular mergers involving millisecondNSs.We have shown it is important to include spin to under-stand the full range of possible EM and GW outcomes in eccentric mergers. However, whether it will be possibleto perform parameter estimation from a putative multi-messenger event is a different question. Certainly in asingle burst event the degeneracies will be too strong to,for example, identify NS spin as the sole reason for anunusually bright counterpart. Multi-burst events can inprinciple lift much of the degeneracy, as information inthe timing of the bursts could significantly narrow theparameters of the progenitor binary. The range of viableNS EOSs, NS spin directions, and BH spins needs to besimulated, both to determine how these parameters af-fect the observable outcomes, and how they add to orlift degeneracies. GW detection rates and parameter es-timation also needs to be investigated within a realisticdata analysis framework including detector noise. All ofthese problems we leave for future studies. We also planto study the effect of spin in dynamical-capture NS–NSmergers.We are grateful to Stuart Shapiro for access to theequilibrium rotating NS code. This work was sup-ported by NSF grant PHY-1305682 and the SimonsFoundation. Computational resources were provided byXSEDE/TACC under grant TG-PHY100053 and the Or-bital cluster at Princeton University.