A magnetar origin for the kilonova ejecta in GW170817
DDraft version February 21, 2018
Preprint typeset using L A TEX style emulateapj v. 12/16/11
A MAGNETAR ORIGIN FOR THE KILONOVA EJECTA IN GW170817
Brian D. Metzger , Todd A. Thompson , Eliot Quataert Draft version February 21, 2018
ABSTRACTThe neutron star (NS) merger GW170817 was followed over several days by optical-wavelength(“blue”) kilonova (KN) emission likely powered by the radioactive decay of light r -process nucleisynthesized by ejecta with a low neutron abundance (electron fraction Y e ≈ . − . B ≈ − × G and lifetime t rem ∼ . − X La ≈ − , as advocated by some authors, but onlyif the mixing occurs after neutrons are consumed in the r -process on a timescale (cid:38) SOURCE OF THE BLUE KILONOVA EJECTA
The gravitational wave chirp from the binary neutronstar (NS) merger GW170817 (Abbott et al. 2017b) wasfollowed within seconds by a short burst of gamma-rays(Goldstein et al. 2017; Savchenko et al. 2017; Abbottet al. 2017a). Roughly half a day later, a luminous opti-cal counterpart was discovered in the galaxy NGC 4993at a distance of only ≈
40 Mpc (Coulter et al. 2017;Soares-Santos et al. 2017; Arcavi et al. 2017; D´ıaz et al.2017; Hu et al. 2017; Kilpatrick et al. 2017; Smartt et al.2017; Drout et al. 2017; Evans et al. 2017; Abbott et al.2017c; McCully et al. 2017; Buckley et al. 2017; Utsumiet al. 2017; Covino et al. 2017; Hu et al. 2017). The ob-served emission started out blue in color, with a feature-less thermal spectrum that peaked at UV/optical fre-quencies (e.g. Nicholl et al. 2017; McCully et al. 2017;Evans et al. 2017), before rapidly evolving over the courseof a few days to become dominated by emission with aspectral peak in the near-infrared (NIR) (Chornock et al.2017; Pian et al. 2017; Tanvir et al. 2017). Simultaneousoptical (e.g. Nicholl et al. 2017; Shappee et al. 2017) andNIR (Chornock et al. 2017) spectra around day 2.5 ap-pear to demonstrate the presence of distinct optical andNIR emission components (however, see Smartt et al.2017; Waxman et al. 2017 for an alternative interpreta-tion).The properties of the optical/NIR emission agreed re-markably well with those predicted for “kilonova” (KN) Department of Physics and Columbia Astrophysics Labora-tory, Columbia University, New York, NY 10027, USA. email:[email protected] Department of Astronomy and Center for Cosmology &Astro-Particle Physics, The Ohio State University, Columbus,Ohio 43210, USA Departments of Physics and Astronomy, Theoretical Astro-physics Center, UC Berkeley, Berkeley, CA 94720, USA emission powered by the radioactive decay of r -processnuclei (Li & Paczy´nski 1998; Metzger et al. 2010; Robertset al. 2011; Barnes & Kasen 2013; Tanaka & Hotokezaka2013; Grossman et al. 2014; Martin et al. 2015; Tanakaet al. 2017b; Wollaeger et al. 2017; Fontes et al. 2017);see Fern´andez & Metzger 2016, Metzger 2017 for re-views), a conclusion reached independently by severalgroups (e.g. Kasen et al. 2017; Drout et al. 2017; Tanakaet al. 2017a; Kasliwal et al. 2017; Murguia-Berthier et al.2017; Waxman et al. 2017). The early-time blue emis-sion is well-explained by radioactive material with a rel-atively low opacity (a “blue” KN; Metzger et al. 2010;Roberts et al. 2011), as would be expected if the outerejecta layers contain exclusively light r -process nucleisynthesized from matter with a relatively high electronfraction, Y e (cid:38) .
25 (Metzger & Fern´andez 2014). Onthe other hand, an upper bound of Y e (cid:46) . − .
35 isneeded to produce a radioactive decay rate consistentwith the smooth decline in the bolometric light curve(e.g. Lippuner & Roberts 2015; Rosswog et al. 2017).The late NIR is instead well-explained by radioactivematerial with high line opacity, consistent with the pres-ence of at least a moderate mass fraction X La (cid:38) − of lanthanide or actinide nuclei (a so-called “red” or“purple” KN; Kasen et al. 2013; Barnes & Kasen 2013;Tanaka & Hotokezaka 2013). Motivated by the theoret-ical expectation of distinct ejecta components with dif-ferent compositions and opacities (Metzger & Fern´andez2014; Perego et al. 2014), a two-zone (“red”+“blue”)KN model provides a reasonable fit to the photometricand spectroscopic data; these give best-fit values for theejecta masses and mean velocities of the blue and redcomponents of M blue ≈ × − M (cid:12) , v blue ≈ .
25 c and M red ≈ . M (cid:12) , v red ≈ . a r X i v : . [ a s t r o - ph . H E ] F e b Perego et al. 2017; Villar et al. 2017).Several groups have made the case that the data isalso consistent with a single ejecta component with arange of velocities and single low opacity (Smartt et al.2017; Tanaka et al. 2017a; Waxman et al. 2017). How-ever, the thermal NIR continuum requires a higher lineopacity in this wavelength range than supplied by light r -process nuclei (with exclusively d-shell valence electronshell structure), implicating the presence of some lan-thanides/actinide nuclei in the inner ejecta layers (Kasenet al. 2017). Synthesizing a small but non-zero lan-thanide mass fraction (e.g. X La ≈ − ) requires fine-tuning of the ejecta Y e distribution: the value of X La in-creases from (cid:46) − to (cid:38) . Y e centered at Y e ≈ .
25 (Tanaka et al. 2017b).Ejecta with a smoothly varying Y e outwards to highervelocities, with distinct lanthanide-rich and lanthanide-poor regions, therefore provides a more physical expla-nation for the observations (though we point out howdelayed mixing of the ejecta might provide a loophole tothe lanthanide fine-tuning argument in § (cid:38) . M (cid:12) exceeds that of the dynamicalejecta for any general relativistic (GR) NS merger simu-lation published to date; furthermore, the velocity of thered/purple KN ejecta, v red ≈ . v (cid:38) . − . ≈
40% of the initial mass of the torus will be un-bound over a timescale of ∼ v ≈ . (cid:38) . M (cid:12) , as neededto supply the M red (cid:38) . M (cid:12) of wind ejecta inferred forGW170817, requires a fairly stiff NS equation of state.For instance, Radice et al. (2017) find that producing atorus of sufficient mass translates into a lower limit onthe dimensionless NS tidal deformability parameter of˜Λ (cid:38) (cid:46)
800 ob-tained from the absence of detectable tidal losses on theinspiral gravitational waveform (Abbott et al. 2017b).This bound ˜Λ (cid:38)
400 translates into a rough lower limiton the radius of a 1.4 M (cid:12) NS of (cid:38)
12 km. The source of the less neutron-rich ejecta responsi-ble for the early blue KN is not so easily understood.Table 1 summarizes several possible origins, with theirsuccesses and shortcomings. While the high velocities v blue ≈ . − . Y e (cid:38) .
25) agree wellwith predictions for the shock-heated dynamical ejecta(Oechslin & Janka 2006; Wanajo et al. 2014; Gorielyet al. 2015; Sekiguchi et al. 2016; Radice et al. 2016),the large quantity M blue ≈ × − M (cid:12) is more chal-lenging to explain. Bauswein et al. (2013) perform asuite of equal-mass merger simulations for a range ofdifferent equations of states, finding M blue (cid:38) . M (cid:12) ofdynamical ejecta only in cases where the NS radius isvery small R ns (cid:46)
11 km (Nicholl et al. 2017), near thelower bound of R ns (cid:38) . Y e ejecta because a relativis-tic jet contributes negligible baryon mass. The jet en-ergy required to explain the kinetic energy of the blueKN ejecta M blue v / ≈ ergs furthermore exceedsthe beaming-corrected kinetic energies of cosmologicalshort gamma-ray bursts ( ≈ − ergs; Nakar 2007;Berger 2014) by a factor of ∼ − ≈ . − B ≈ − × Gcan naturally provide the blue radioactive ejecta whichlit up GW170817. NEUTRINO-IRRADIATED OUTFLOWS FROM THEHMNS REMNANT For equal-mass mergers, most of the dynamical ejecta is shock-heated matter with high- Y e from the collision and not low- Y e tidalmaterial. Physically, a smaller NS radius results in greater shock-heatedejecta because more compact stars (of a fixed gravitational mass)collide at higher velocities.
TABLE 1Potential Sources of the Fast Blue KN Ejecta in GW170817
Ejecta Type Quantity? Velocity? Electron Fraction? ReferencesTidal Tail Dynamical Maybe, if M /M (cid:46) . † (cid:88) Too Low e.g., 1, 2Shock-Heated Dynamical Maybe, if R ns (cid:46)
11 km ‡ (cid:88) (cid:88) if NS long-lived e.g., 3-5Accretion Disk Outflow (cid:88) if torus massive Too Low (cid:88) if NS long-lived e.g., 6-9HMNS Neutrino-Driven Wind
Too Low Too Low Too High? e.g., 11, 12Magnetized HMNS Wind (cid:88) if NS long-lived (cid:88) (cid:88) e.g., 12,13 † where here M , M are the individual NS masses (see Dietrich et al. 2017; Dietrich & Ujevic 2017; Gao et al. 2017). ‡ However, a smallNS radius may be in tension with the creation of a large accretion disk needed to produce the red KN ejecta (Radice et al. 2017). (1)Rosswog et al. 1999; (2) Hotokezaka et al. 2013; (3) Bauswein et al. 2013; (4) Sekiguchi et al. 2016; (5) Radice et al. 2016; (6) Fern´andez& Metzger 2013; (7) Perego et al. 2014; (8) Just et al. 2015; (9) Siegel & Metzger 2017b; (10) Dessart et al. 2009; (11) Perego et al. 2014;(12) Metzger et al. 2008b; (13) Metzger et al. 2008c
The end product of a NS-NS merger is typically aHMNS remnant , which is supported against gravita-tional collapse by its rapid and differential rotation(e.g. Shibata & Taniguchi 2006; Hanauske et al. 2017).Once its differential rotation has been removed (e.g. bygravitational waves or internal “viscosity” resulting fromvarious MHD instabilities) the HMNS collapses into ablack hole; however, the timescale for this process, andthus the remnant lifetime t rem , is challenging to pre-dict theoretically due to uncertainties in the supranucleardensity equation of state and due to difficulties in nu-merically resolving all of the relevant physical processesover sufficiently long times (e.g. Siegel et al. 2013; Radice2017; Shibata & Kiuchi 2017; Shibata et al. 2017).As shown below, the mass-loss rate of the HMNS rem-nant over its first several seconds of cooling is so highas to preclude the formation of an ultra-relativistic jet(e.g. Metzger et al. 2008b; Murguia-Berthier et al. 2016).Thus, if the gamma-rays observed in coincidence withGW170817 (Goldstein et al. 2017; Savchenko et al. 2017;Abbott et al. 2017a) are in some way associated with anoff-axis − but otherwise typical − short GRB jet, then theformation of a black hole must have occurred prior tothe arrival of the gamma-rays, setting an upper limit of t rem (cid:46) . §
4, the velocity of the magnetized HMNSwind could grow to become mildly relativistic over theneutrino cooling timescale of the remnant of a few sec-onds (Metzger et al. 2008b), in which case the gamma-rays could have been produced by the relativistic shockbreak-out created by internal collisions within the HMNSwind itself.
Standard (unmagnetized) neutrino-driven wind
One source of post-dynamical ejecta is a neutrino-driven wind from the hot NS remnant (Dessart et al.2009; Metzger & Fern´andez 2014; Perego et al. 2014;Martin et al. 2015), qualitatively similar to that expectedfrom the hot proto-NS created by the core collapse of amassive star (Duncan et al. 1986; Qian & Woosley 1996).The steady-state mass-loss rate due to neutrino heat-ing from an unmagnetized NS is approximately given by GW170817 could in principle have instead produced a long-lived supra-massive NS remnant, which was still temporarily sup-ported against gravitational collapse by its solid body rotation evenonce differential rotation was removed; however, the prodigious ro-tational energy which must be deposited into its surroundings inorder to collapse in this case would have been observationally con-spicuous and thus is disfavored (Margalit & Metzger 2017; Granotet al. 2017; Pooley et al. 2017; Margutti et al. 2017; Ma et al. 2017). (Qian & Woosley 1996; Thompson et al. 2001)˙ M ν (cid:39) × − M (cid:12) s − (cid:18) L ν × ergs s − (cid:19) / (cid:16) (cid:15) ν
15 MeV (cid:17) / (cid:18) M ns . M (cid:12) (cid:19) − (cid:18) R ns
15 km (cid:19) / , (1)where we have combined the contributions of electronneutrinos and antineutrinos to the heating into a singleproduct of the neutrino luminosity L ν and mean neutrinoenergy (cid:15) ν defined by L ν (cid:15) ν ≡ L ν e | (cid:15) ν e | + L ¯ ν e | (cid:15) ¯ ν e | . Thefiducial values used above are motivated by axisymmetrichydrodynamical simulations of the post-merger remnantincluding neutrino transport by Dessart et al. (2009),who find L ν ≈ × ergs s − on timescales of t (cid:46) (cid:15) ν ≈ −
17 MeV. In agreement with the above,Dessart et al. (2009) found ˙ M ≈ − − − M (cid:12) s − over the first t ≈ −
100 ms of evolution.Absent magnetic fields, the wind is accelerated entirelyby thermal pressure and its asymptotic velocity is ap-proximately given by (Thompson et al. 2001) v ν ≈ .
12 c (cid:18) L ν × ergs s − (cid:19) . , (2)The asymptotic electron fraction in the wind is set bythe competition between the weak interactions ν e + n → p + e − and ¯ ν e + p → n + e + ; its equilibrium value isapproximately given by (Qian et al. 1993) Y e,ν (cid:39) (cid:18) L ¯ ν e L ν e (cid:15) ¯ ν e −
2∆ + 1 . /(cid:15) ¯ ν e (cid:15) ν e + 2∆ + 1 . /(cid:15) ν e (cid:19) − ≈ . − . , (3)where ∆ ≡ ( m n − m p ) c is the neutron-proton mass dif-ference. This equilibrium is achieved in the wind be-cause the gravitational binding energy of a nucleon onthe surface of the HMNS of GM ns m p /R ns ≈
200 MeVgreatly exceeds the mean neutrino energy (cid:15) ν ; each nu-cleon must therefore necessarily absorb several neutrinosin the process of escaping to infinity and the outflowis protonized as compared to the much lower value of Y e (cid:46) . Y e,ν is given as anrange because the difference between the spectra of elec-tron neutrinos and antineutrinos from the cooling mergerremnant which enters the expression for Y e,ν depends onthe detailed transport processes in this environment andare thus theoretically uncertain (e.g. Roberts et al. 2012; Fig. 1.—
Schematic diagram of the neutrino-irradiated wind froma magnetized HMNS. Neutrinos from the HMNS heat matter in anarrow layer above the HMNS surface, feeding baryons onto openmagnetic field lines at a rate which is substantially enhanced bymagneto-centrifugal forces from the purely neutrino-driven mass-loss rate (e.g. Thompson et al. 2004; Metzger et al. 2007). Mag-netic forces also accelerate the wind to a higher asymptotic velocity v ≈ v B ≈ . − . v (cid:46) . ∝ σ / ∝ B / / ˙ M / may increaseby a factor of ∼ M subsides, or its magnetic field B is amplified, resulting ininternal shocks on a radial scale R sh ∼ vt rem ∼ ( t rem / Mart´ınez-Pinedo et al. 2012 for recent work in the corecollapse context).The electron fraction of an unmagnetized PNS wind issufficiently high Y e (cid:38) . − . r -process nuclei with the lowopacities needed to produce blue KN emission. However,the quantity ˙ M ν t rem (cid:46) − M (cid:12) and velocity v ν ∼ . Y e ≈ Y e,ν (cid:38) . Y e can be unbound by neutrino heating of the surroundingaccretion disk (e.g. Metzger & Fern´andez 2014; Peregoet al. 2014; Martin et al. 2015), but the velocity of thismaterial (cid:46) . Magnetized, neutrino-heated wind
A standard neutrino-heated wind cannot explain theobserved properties of the blue KN, but the prospectsare better if the merger remnant possesses a strong mag-netic field. Due to the large orbital angular momentumof the initial binary, the remnant is necessarily rotating close to its mass-shedding limit, with a rotation period P = 2 π/ Ω ≈ . − (cid:38) G by several instabilities (e.g. Kelvin-Helmholtz,magneto-rotational) which tap into the free energy avail-able in differential rotation (e.g. Price & Rosswog 2006;Siegel et al. 2013; Zrake & MacFadyen 2013; Kiuchi et al.2015). As a part of this process, and the longer-termMHD evolution of its internal magnetic field (e.g. Braith-waite 2007), the rapidly-spinning remnant could acquirea large-scale surface field, though its strength is likely tobe weaker than the small-scale field.In the presence of rapid rotation and a strong or-dered magnetic field, magneto-centrifugal forces accel-erate matter outwards from the HMNS along the openfield lines in addition to the thermal pressure from neu-trino heating (Fig. 1). A magnetic field thus enhances themass loss rate and velocity of the HMNS wind (Thomp-son et al. 2004; Metzger et al. 2007), in addition to reduc-ing its electron fraction as compared to the equilibriumvalue obtain when the flow comes into equilibrium withthe neutrinos, Y e,ν (e.g. Metzger et al. 2008c).A key property quantifying the dynamical importanceof the magnetic field is the wind magnetization σ = Φ Ω ˙ M tot c = B R f open Ω ˙ M c , (4)where Φ M = f open BR is the open magnetic flux persteradian leaving the NS surface, B is the average sur-face magnetic field strength, f open is the fraction ofthe NS surface threaded by open magnetic field lines,˙ M tot = f open ˙ M is the total mass loss rate, and ˙ M isthe wind mass loss rate when f open = 1 limit (which ingeneral will be substantially enhanced from the purelyneutrino-driven value estimated in eq. 1). In what followswe assume the split-monopole magnetic field structure( f open = 1), which is a reasonable approximation if themagnetosphere is continuously “torn open” by latitudinaldifferential rotation (Siegel et al. 2014), neutrino heatingof the atmosphere in the closed-zone region (Thompson2003; Komissarov & Barkov 2007; Thompson & ud-Doula2017), and by the compression of the nominally closedfield zone by the ram pressure of the surrounding accre-tion disk (Parfrey et al. 2016). However, our results canalso be applied to the case f open (cid:28)
1, as would charac-terize a more complex magnetic field structure, providedthat the ratio B / ˙ M ∝ f − can be scaled-up accord-ingly to obtain the same value of σ needed by observa-tions.Upon reaching the fast magnetosonic surface (outsideof the light cylinder), the outflow achieves a radial four-velocity vγ (cid:39) cσ / (Michel 1969). Winds with σ (cid:29) γ (cid:29) σ / (cid:46) γ ≤ σ , dependingon how efficiently additional magnetic energy initiallycarried out by Poynting flux is converted into kineticenergy outside of the fast surface. By contrast, windswith σ < v B (cid:39) √ cσ / = √ (cid:18) B R Ω ˙ M (cid:19) / ≈ . (cid:18) B G (cid:19) / (cid:32) ˙ M . M (cid:12) s − (cid:33) − / (cid:18) P (cid:19) − / , (5)where in the final line we have taken R ns = 15 km andthe factor √ σ (or, equivalently,asymptotic four-velocity; top axis) and ˙ M from asuite of steady-state, one-dimensional, neutrino-heated,magneto-centrifugal wind solutions calculated by Met-zger et al. (2008c) for an assumed neutrino luminosity L ν ≈ . × ergs s − , similar to that from the hotpost-merger remnant at early times ∼ . − B =10 , , G (denoted by different colors, from leftto right) and several rotation rates Ω = 6000 , , − ( P = 1 . , . , .
79 ms; bottom to top) in therange expected for the post-merger remnant.The strong magnetic field increases both the kineticenergy and mass-loss rate of the wind. ˙ M is increasedby a factor of (cid:38) − B ∼ − G ascompared to the unmagnetized value given in eq. 1. Atfixed B , ˙ M also rapidly increases with faster rotation,while the outflow velocity slightly decreases for larger Ωbecause of the v B ∝ ˙ M − / dependence.The additional magneto-centrifugal acceleration re-duces the time matter spends in the neutrino-heated re-gion and reduces the final electron fraction Y e of the out-flow compared to the neutrino-driven equilibrium value Y e,ν (eq. 3), as marked next to each solution in Fig. 2.While a relatively weak magnetic field (10 G) and slowrotation results in a value Y e ≈ Y e,ν (cid:39) .
46 similar to theunmagnetized case, the more strongly-magnetized andrapidly-rotating cases have Y e (cid:28) Y e,ν . In these cases themagnetic field accelerates matter away from the NS sur-face so rapidly that electron neutrinos have insufficienttime to convert the initially neutron-rich composition atthe electron-degenerate base of the wind back into onewith a nearly equal number of neutrons and protons bymuch larger radii (where the r -process itself takes place).Magneto-centrifugal enhancement of ˙ M is cruciallytied to the conditions required for Y e (cid:28) Y e,ν , as both arerelated to the timescale matter has to absorb neutrinosnear the base of the wind. In the limit that the magneticfield dominates the wind dynamics in the neutrino heat-ing region, an outflow which is sufficiently neutron-rich( Y e (cid:46) .
25) to synthesize lathanide nuclei is necessar-ily accompanied by a minimum mass loss rate (Metzger This result can be understood to order-of-magnitude by notingthat v B ≈ R A Ω, where R A is the Alfv´en radius at which B / π ≈ ρv /
2, where v and ρ = ˙ M/ πvr are the velocity and density ofthe wind at radius r (Thompson et al. 2004). et al. 2008c; their eq. 20)˙ M blue ≈ (cid:18) GM ns m p R ns (cid:15) ν (cid:19) ˙ M ν ≈ . M (cid:12) s − × (cid:18) L ν × ergs s − (cid:19) / (cid:16) (cid:15) ν
15 MeV (cid:17) / (cid:18) M ns . M (cid:12) (cid:19) − . (6)The factor ( GM ns m p /R ns (cid:15) ν ) accounts for the additionalenergy per nucleon supplied which must be by the mag-netic acceleration, above the normal value from neutrinoheating acting alone, in order to obtain Y e (cid:46) Y e,ν . Thenumerically-calibrated pre-factor of 20 is that needed toreduce Y e further to (cid:46) .
25. Thus, one can place a strictupper limit on the quantity of blue KN ejecta ( Y e (cid:38) . M maxblue ∼ ˙ M blue t rem ∼ − ( t rem / . M (cid:12) , (7)where we have taken L ν ≈ ergs s − as theroughly constant neutrino luminosity of the remnant ontimescales of t rem (cid:46) Y e integrated across the full open mag-netosphere (Vlasov et al. 2014, 2017). Nevertheless, thewind velocity and composition do show moderate varia-tion with polar latitude θ of the outflow launching point;for instance, Vlasov et al. (2014) found that for P ≈ L ν ≈ × ergs s − , Y e varied from ≈ ≈ θ increased from (cid:46) .
35 to ≈ . ≈
20% and ≈
80% of the total mass loss,respectively).
Application to the blue KN of GW170817
On the timescale t (cid:46) t rem (cid:46) (cid:46) t rem , producing the observed quantity of ejecta M blue ≈ × − M (cid:12) (e.g. Cowperthwaite et al. 2017; Nicholl et al.2017; Villar et al. 2017; Perego et al. 2017) requires anaverage wind mass loss rate˙ M ≈ × − ( t rem / − M (cid:12) s − (8)According to eq. 5, explaining the velocity of the ejecta v blue ≈ . − . v B requires a wind magnetization σ ≈ . − . − , R = 15km) B ≈ − × ( t rem / − / G , (9) Y e = 0.28 0.32 0.42 0.41 0.26 Y e = 0.19 Y e = 0.42 0.44 0.46 G 10 G 10 G GRB 170817A
GW170817
Models from Metzger et al. 2008
Fig. 2.—
Mass loss rate and magnetization (equivalently, asymptotic four-velocity βγ , where β = v/c where v is the wind velocity; topaxis) from the steady-state, one-dimensional, neutrino-heated magneto-centrifugal wind solutions calculated by Metzger et al. (2008c). Thesolutions shown were calculated for a neutrino luminosity L ν = L ν e + L ¯ ν e ≈ . × ergs s − and mean neutrino energies (cid:15) ν e = 11 MeV, (cid:15) ¯ ν e = 14 MeV, similar to those from the HMNS remnant on timescales (cid:46) t rem required to produce the total blue ejecta mass M blue ≈ × − M (cid:12) of GW170817 given a constant mass loss rate˙ M shown on the left axis. Each square shows a distinct steady-state solution, calculated for a different values of the surface magnetic fieldstrength ( B = 10 , , G, denoted by blue, red, and black colors, respectively) and for three rotation rates (Ω = 6000 , , − , from bottom to top) in the range necessary for a rapidly-spinning HMNS. The asymptotic electron fraction of the wind is also markednext to each solution; this value is sufficiently high Y e (cid:38) .
25 to avoid significant lanthanide production for ˙ M (cid:46) ˙ M blue (eq. 6; solid blackline). A magnetar remnant with B ∼ − × G, Ω ≈ ≈ . t rem ≈ . − v blue ≈ . M blue ≈ × − M (cid:12) , and composition Y e ≈ . − . or B ∼ − × G for t rem ∼ . − B = 10 G and 10 G solutions in Fig. 2shows that winds with mass-loss rates corresponding to t rem (cid:46) Y e ≈ . − . THE FIRST FEW HOURS
Following its discovery at t ≈
11 hours, the first fewdays of optical emission following GW170817 is well-explained by KN emission powered by the decay of heavy r -process nuclei. This agreement is independent of theprecise origin of the ejecta because, by this late time,most of the initial thermal energy released during theejection process on timescales t (cid:46) ∼ t . However, different sources ofblue KN ejecta will make quantitatively distinct predic-tions for the emission at earlier times, within the firstfew hours after the merger. Though not available forGW170817, such early observations may be possible forfuture GW-detected mergers, such as those which occurabove the North American continent at night (e.g. Kasli-wal & Nissanke 2014). Early UV follow-up would also bepossible with a dedicated wide-field satellite, such as theproposed ULTRASAT mission (e.g. Waxman et al. 2017)A key distinguishing feature of different ejecta sourcesis the timescale over which the mass loss occurs. Dynam-ical ejecta emerges almost immediately, within (cid:46) − t ∼ . − ∼ ∆ t · v blue ∼ − cm which greatly exceed those of the centralengine (cid:46) −
100 km (e.g. Beloborodov 2014).As the HMNS cools following the merger, approx-imately over its Kelvin-Helmholtz diffusion timescale∆ t ∼ ≈ ≈ v B ∝ ˙ M − / by a factor of ∼ . v B ∝ B / . The rising wind ve-locity will result in the development of internal shocks,heating the ejecta as discussed above.A crude but illustrative estimate of the time evolutionof the wind velocity is shown in Fig. 4, separately fora case in which the HMNS magnetic field is held con-stant in time, and when the field is assumed to growexponentially on a timescale of ≈ . M ∝ L / ν (cid:15) / ν (eq. 1), where L ν ( t ) and (cid:15) ν ( t ) are takenfrom the proto-NS cooling calculations of Pons et al.(1999) (which should qualitatively capture the coolingevolution of the post-merger remnant). In the case oftemporally-strengthening field, the internal shocks in themagnetar wind could grow to trans-relativistic velocities γβ (cid:38) L bol ≈ ergs s − measured at t ≈
11 hours (see Appendix fordetails) yet do not overproduce the luminosity at 1.5days (at which time the slower inner layers which pro-duce the red/purple KN are beginning to contribute).Solid black lines show models for ejecta for different as-sumptions about the time t = 0 . , . , t ≥ t , the only heating is by the decay of r -process nuclei). As discussed above, this timescale canbe roughly associated with the timescale ∆ t over which asignificant fraction of the mass loss is occurring, e.g. theHMNS lifetime t rem in the case of a magnetar wind orthe viscous timescale in the case of a jet or accretion disk Heating at large radii might also be possible in rare instancesby collision of the ejecta with a companion star in an evolved triplesystem (Chang & Murray 2018). outflow (e.g. Fern´andez & Metzger 2013). Fig. 3 showsthat the luminosity at one hour post-merger is ∼ − t ∼ . − t (cid:46) .
01 s).Additional thermal energy could be deposited into theexpanding matter also by the passage of a relativisticjet through the blue ejecta, creating an expanding tailof high velocity shock-heated matter (e.g. Gottlieb et al.2018, 2017; Bromberg et al. 2017; Kasliwal et al. 2017;Piro & Kollmeier 2017). However, reasonable constraintscan be placed on the magnitude of this effect basedon the observed kinetic energies of on-axis cosmologi-cal short duration gamma-ray bursts. The isotropic ki-netic energies of short GRB jets as inferred from theirnon-thermal afterglows are typically E iso , K ≈ − ergs (Nakar 2007; Berger 2014; Fong et al. 2015). Thelocal ( z = 0) rate of binary NS mergers as measured byAdvanced LIGO after GW170817 is R BNS = 1540 +3200 − Gpc − yr − , while the observed rate of short GRBs is R SGRB ≈ − − yr − (Wanderman & Piran 2015).This places an upper limit on the beaming fraction of theemission of f b (cid:46) .
02, which in turn implies a beaming-corrected GRB jet energy of (cid:46) ergs which is 2 ordersof magnitude smaller than the measured kinetic energyof the blue KN ejecta of ∼ ergs. Thus, unless thejet cocoon contains (cid:38) −
100 times more energy than istypical of the ultra-relativistic GRB itself, cocoon heat-ing contributes insignificantly to the early-time opticalemission. This argument would not be valid if cosmolog-ical short GRBs do not originate from NS-NS mergers.The early KN emission can also be enhanced due tothe radioactive decay of free neutrons in the outermostlayers of the ejecta (Metzger et al. 2015; see also Kulkarni2005). Free neutrons may be present in the outermost ∼
1% of the ejecta if these layers are expanding suffi-ciently rapidly for neutron-capture reactions to freeze-out prior to completion of the r -process (as occurs ona timescale of ∼ τ n ≈
10 min-utes, as compared to a typical r -process isotope ( τ ∼ r -process heat-ing during the first several hours of emission. Figure 3shows that the presence of free neutrons in the outermost ∼ − − − M (cid:12) of the expanding material can mim-ick to some extent the effects of a long heating timescale t rem (cid:38) . − DISCUSSION
While the presence of luminous optical (blue) KNemission from the first NS merger was not a surprise(e.g. Metzger et al. 2010), the large ejecta mass, highvelocity, and relatively neutron-poor composition arein tension with traditionally-considered ejecta sources(Table 1). Instead, we have proposed that the blueKN ejecta in GW170817 originates from the neutrino-irradiated, magneto-centrifugally-driven outflow froma temporarily-stable rapidly-rotating HMNS remnant(Fig. 1). Fig. 2 shows that such a millisecondmagnetar wind can simultaneously explain the largeejecta mass (due to magneto-centrifugal enhancement of
Fig. 3.—
Bolometric light curve of the blue KN emission duringthe first few hours after the merger, calculated for several modelswhich reproduce the measured luminosity L bol ≈ ergs s − ofGW170817 at t ≈
11 hours (blue uncertainty bar; e.g. Cowperth-waite et al. 2017; Arcavi et al. 2017; Drout et al. 2017). Black solidlines show models for different assumptions about the timescale t = 0 . , . , t ≥ t , the heating is solelydue to r -process radioactivity). A small value of t (cid:46) .
01 s cor-responds to a dynamical ejecta origin with no additional heating,while a large value of t (cid:38) . − ≈ t . We have assumed KN param-eters (see Appendix): β = 3, v = 0 . c , M tot = 0 . M (cid:12) , κ = 0 . g − (except for the t = 1 s case, for which M tot = 0 . M (cid:12) ).Red dashed lines show models with t = 0 .
01 s in which the outer10 − M (cid:12) or 10 − M (cid:12) of the ejecta contain free neutrons instead of r -process nuclei (Metzger et al. 2015), showing how the enhancedluminosity from neutron decay (the “neutron precursor”) is degen-erate with large thermalization times. the neutrino-driven mass-loss), high velocity (magneto-centrifugal enhancement of the wind acceleration), andelectron fraction (from moderate, but not excessive, neu-trino irradiation near the wind launching point), givenonly two free parameters: the surface magnetic fieldstrength B ∼ − × G and HMNS lifetime t rem ∼ . − given its large-scale magnetic field B , t A = R ns v A ≈ . (cid:18) B G (cid:19) − s (10)where v A = B/ √ πρ is the Alfv´en velocity and ρ ≈ M ns / (4 πR ) is the mean density of the NS. Interest-ingly, the value of t A for values of B ∼ − × G In detail, the timescale to establish solid body can slightlyexceed t A (e.g., Charbonneau & MacGregor 1992). B = constant = 2x10 G G R B A Fig. 4.—
Time evolution of the 4-velocity γβ of the hyper-massivemagnetar wind, calculated assuming that the wind mass-loss rateevolves as ˙ M ∝ L / ν (cid:15) / ν , where the cooling evolution of the neu-trino luminosity L ν ( t ) and mean neutrino energy (cid:15) ν ( t ) are takenfrom the 2 . M (cid:12) proto-NS model of Pons et al. (1999). We sep-arately show a case in which the magnetic field strength is heldconstant in time at B ≈ × G (black solid line) and one inwhich the field strength grows exponentially on a timescale of 0 .
5s (dashed blue line). In both cases the wind velocity over the first ∼ . − ∼ . − . γβ (cid:38)
1) by the onset of GRB 170817A, in which caserelativistic break-out of internal shocks within the wind (Nakar &Sari 2012) could serve as a potential origin for the gamma-rays. we find are needed to explain the blue KN is similar tothe HMNS collapse time t rem ≈ . − t rem ), which (for fixed B ) would reduce thequantity of the blue KN ejecta from the magnetar wind( M blue ∝ t rem ). On the other hand, if t A (eq. 10) alsoplays a role in the collapse time, then a merger remnantof total mass otherwise similar to that in GW170817,but with a stronger magnetic field B , will produce botha higher KN ejecta velocity v B ∝ B / and a shorter life-time t rem ∝ B − ∝ v − / ; the latter may correlate alsowith the timescale of the observed gamma-ray burst, as-suming it is powered by an ultra-relativistic jet which isgenerated soon after black hole formation.Although disk outflows provide a satisfactory expla-nation for the slower, red KN ejecta (e.g. Siegel & Met-zger 2017b), it is important to address whether the latteralso be explained by a magnetar wind with time-evolvingproperties. If the magnetic field of the HMNS remnantwere to grow in time, then Fig. 2 shows that Y e will de-crease and ˙ M will increase (for fixed Ω), although thedecaying neutrino luminosity as the remnant cools willcounter the latter. If Y e were to decrease in time, thiswould be consistent with the observed late emergenceof red/purple KN ejecta ( Y e (cid:46) .
25) following the ear-lier blue KN ejecta ( Y e (cid:38) . §
3, wouldgive rise to powerful internal shocks. This interactionwould cause a redistribution of the radial velocity strati-fication and might lead to mixing of the high- and low- Y e material (see below). We conclude that a time-evolvingmagnetar wind could in principle supply both the blueand red KN ejecta, though detailed numerical modelingof the magnetized outflow including neutrino transportfrom the remnant will be needed to confirm this ideaquantitatively.We have discussed ways to observationally disentan-gle different sources for the ejecta based on the first fewhours of the KN (Fig. 3). In particular, the KN lumi-nosity will be substantially higher at these early timesif the ejecta is re-heated above its launching point byinternal shocks. The latter is generally expected forany long-lived ejecta source, e.g. a magnetar of lifetime t rem (cid:38) . − ∼ X La ≈ − (e.g. Tanaka et al. 2017b; Smartt et al. 2017;Waxman et al. 2017). However, as already discussed, en-dowing the ejecta with a low but non-zero lanthanideabundance appears to require fine tuning of the Y e dis-tribution to be tightly peaked around Y e ≈ .
25 (see alsoTanaka et al. 2017b).One loophole to creating a homogeneous low- X La com-position would be to mix separate ejecta componentswith vastly different lanthanide abundances, e.g. com-bine 1% of the mass with Y e (cid:46) .
25 and X La ≈ . (cid:38)
99% that was lanthanide-free( Y e (cid:38) . such mixing wouldneed to occur after the r -process is complete, i.e. afterfree neutrons are captured into nuclei on a timescale of t capture ∼ s after ejection . While such late-time mix-ing would not be consistent with a dynamical origin forthe ejecta, it could result naturally if the engine lifetimewas indeed t rem (cid:38) . − ∼ t capture , as predicted fora long-lived magnetar. As already discussed, the mod-erate rise in the magnetar outflow velocity, even over itsshort lifetime, will indeed produce internal shocks withinthe ejecta (Metzger et al. 2008b) that would also en-able mixing. Moderate variations in Y e are also expectedwith polar latitude in the wind (Vlasov et al. 2014) aswell as in time, both secularly as the HMNS cools and onshorter timescales due to periodic magnetic reconnectionevents instigated by opening of closed magnetic field linesby differential rotation and neutrino heating (Thompson2003). BDM is supported by NASA through the ATPprogram, grant numbers NNX16AB30G andNNX17AK43G. EQ was supported in part by a Si-mons Investigator Award from the Simons Foundationand the Gordon and Betty Moore Foundation throughGrant GBMF5076. We thank Niccolo Bucciantini forprevious collaborations and many useful discussions onthis topic. APPENDIX: LAYERED KILONOVA MODEL
Multi-velocity semi-analytic one-dimensional kilonovamodels have been considered in several previous works(e.g. Piran et al. 2013; Metzger 2017; Waxman et al.2017). Following the merger and any subsequent shockheating, e.g. by the GRB jet, the radial velocity struc-ture of the ejecta ultimately approaches homologous ex-pansion (e.g. Rosswog et al. 2014). We approximate thedistribution of mass with velocity greater than a value v as a power-law of index β , M v = M ( v/v ) − β , v (cid:38) v (11)where M is the total mass, v is the minimum ( ∼ av-erage) velocity. The thermal energy of each mass shellevolves as a function of time t after the merger accordingto dE v dt = − E v t − E v t d,v + t lc,v + ˙ Q v , (12)where the first term accounts for PdV losses, the secondterm is the radiative luminosity, where t d = 3 M v κ πcvt (13)is the photon diffusion time through layer v and t lc , v =( v/c ) t is the light crossing time. We have modeled theopacity produced by r -process lines as a grey opacityof value κ . Tanaka et al. (2017b) show that bolometricluminosities are reasonably well-produced for κ = 0 . g − for light r -process nuclei (lanthanide-free, Y e (cid:38) .
25) and κ = 10 cm g − (full lanthanide-fraction, Y e (cid:46) . r -process nuclei is reasonably approx-imated by (Metzger et al. 2010; Roberts et al. 2011)˙ Q v = (cid:15) th,v M v ˙ Q ,v ( t/ − . , (14)where the normalization depends on both the thermal-ization efficiency (cid:15) th , v of the decay products and the over-all normalization ˙ Q ,v of the specific radioactive energyloss rate at 1 day. The thermalization efficiency varieswith the density of the mass shell, with a high valueat early times ≈ . − . Q ,v depends on the nucleosyn-thesis products and varies with Y e from ≈ . × ergsg − s − at low Y e (cid:46) . ≈ − × ergs g − s − at higher Y e . In what follows we take ˙ Q ,v = 2 × ergs g − s − .In some cases we also include radioactive heating fromfree neutrons (decay timescale τ n ≈
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