Fast neutrino flavor conversion, ejecta properties, and nucleosynthesis in newly-formed hypermassive remnants of neutron-star mergers
Manu George, Meng-Ru Wu, Irene Tamborra, Ricard Ardevol-Pulpillo, Hans-Thomas Janka
FFast neutrino flavor conversion, ejecta properties, and nucleosynthesis innewly-formed hypermassive remnants of neutron-star mergers
Manu George, ∗ Meng-Ru Wu,
1, 2, 3, † Irene Tamborra, ‡ Ricard Ardevol-Pulpillo, § and Hans-Thomas Janka ¶ Institute of Physics, Academia Sinica, Taipei, 11529, Taiwan Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, 10617, Taiwan Physics Division, National Center for Theoretical Sciences, 30013 Hsinchu, Taiwan Niels Bohr International Academy and DARK, Niels Bohr Institute,University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen, Denmark Max-Planck-Institut f¨ur Astrophysik, Postfach 1317, 85741 Garching, Germany (Dated: November 16, 2020)Neutrinos emitted in the coalescence of two neutron stars affect the dynamics of the outflow ejectaand the nucleosynthesis of heavy elements. In this work, we analyze the neutrino emission propertiesand the conditions leading to the growth of flavor instabilities in merger remnants consisting of ahypermassive neutron star and an accretion disk during the first 10 ms after the merger. Theanalyses are based on hydrodynamical simulations that include a modeling of neutrino emissionand absorption effects via the “improved leakage-equilibration-absorption scheme” (ILEAS). Wealso examine the nucleosynthesis of the heavy elements via the rapid neutron-capture process ( r -process) inside the material ejected during this phase. The dominant emission of ¯ ν e over ν e from themerger remnant leads to favorable conditions for the occurrence of fast pairwise flavor conversionsof neutrinos, independent of the chosen equation of state or the mass ratio of the binary. Thenucleosynthesis outcome is very robust, ranging from the first to the third r -process peaks. Inparticular, more than 10 − M (cid:12) of strontium are produced in these early ejecta that may account forthe GW170817 kilonova observation. We find that the amount of ejecta containing free neutrons afterthe r -process freeze-out, which may power early-time UV emission, is reduced by roughly a factor of10 when compared to simulations that do not include weak interactions. Finally, the potential flavorequipartition between all neutrino flavors is mainly found to affect the nucleosynthesis outcome inthe polar ejecta within (cid:46) ◦ , by changing the amount of the produced iron-peak and first-peaknuclei, but it does not alter the lanthanide mass fraction therein. I. INTRODUCTION
Compact binary systems consisting of two neutronstars (NS) or a NS and a black hole (BH) can lose theirangular momentum through continuous emission of grav-itational waves (GW), eventually leading to the mergingof the compact objects. Such merger events have longbeen considered to be the sites producing short gamma-ray bursts (sGRB) and synthesizing heavy elementsvia the rapid neutron-capture process ( r -process) [1–3],which powers electromagnetic transients in optical andinfrared wavelengths, the so-called kilonovae [4–7].The first detected GW emission from a binary neu-tron star merger event by the LIGO and Virgo Col-laborations (GW170817) together with multi-wavelengthelectromagnetic observations have confirmed theoreticalpredictions [8–10]. Future observations, like the one ofGW170817, will be able to offer further opportunities toprecisely determine the population of binary NS systemsand the yet-uncertain rich physics involved in binary NSmergers, including the nuclear equation of state (EoS)and the properties of neutron-rich nuclei. In order toachieve these goals, solid theoretical modeling of mergersis needed without any doubt.The interaction of neutrinos with matter and their fla-vor conversions in the binary NS merger environment areamong the most uncertain theoretical aspects that can af-fect the observables. A copious amount of neutrinos and antineutrinos can be produced by the merger as matteris heated up to several tens of MeV due to the collisionof two NSs. Neutrinos play an important role in deter-mining the cooling of the merger remnant, changing thecomposition of the ejecta, and altering the r -process out-come and the kilonova emission properties.The early-time blue color of the GW170817 kilonovaand the recently inferred amount of strontium produc-tion [11] both suggest that the merger ejecta containsome less neutron-rich material with electron fractionper nucleon Y e (cid:38) .
3. On the other hand, numericalsimulations which include weak interactions of neutrinoswith nucleons all suggest that neutrino emission and ab-sorption have the effect to reduce the neutron-richnessof the outflow launched at different post-merger phases,preferably in the direction perpendicular to the mergerplane [12–20]. In particular, recent work suggests thatneutrino absorption can be responsible for increasing Y e even for the early-time dynamical ejecta in the polar di-rection [15, 16, 19, 21–23]. Meanwhile, the ν e ¯ ν e pair anni-hilation to e + e − pairs above the accretion disk, althoughit might not be the dominant driver, can also contributeto launch the sGRB jet [2, 24–27]Neutrinos additionally undergo flavor conversionsabove the merger remnant, altering the neutrino absorp-tion rates on nucleons as well as their pair-annhilationrates [28–34], thus possibly affecting the interpretationof the observed signals. In particular, Ref. [33] showed a r X i v : . [ a s t r o - ph . H E ] N ov that favorable conditions for the so-called “fast flavorconversion” [35–43] exist nearly everywhere above themerger remnant because of the disk geometry and theprotonization of the merger remnant in its effort to reacha new beta-equilibrium state for the high temperaturesproduced in the merger process. Fast pairwise conver-sions can give rise to rapid flavor oscillations of neutrinoswithin a length scale of ∼ ( G F | n ν e − n ¯ ν e | ) − ≈ O (1) cm.Subsequently, Ref. [34] adopted time-dependent neutrinoemission characteristics from simulations of merger rem-nants consisting of a central BH with an accretion diskand also found favorable conditions for fast flavor con-version. By assuming full flavor equilibration betweenall neutrino flavors, it was shown that the nucleosynthesisoutcome in the neutrino-driven outflow from the BH–diskremnant can be largely altered [34].In this work, we focus on the newly formed hypermas-sive remnants of NS mergers. In fact, in the case of ahypermassive NS, which might transiently exist in manybinary NS mergers, the surrounding torus-like equatorialbulge (“disk”) is exposed to strong neutrino irradiationfrom the massive core of the merger remnant. This isdifferent from the BH-torus configuration, where there isno such intense central neutrino source. Moreover, thetorus itself produces heavy-lepton neutrinos only withvery low luminosities, whereas the hypermassive NS ra-diates high luminosities also of the heavy-lepton neutri-nos. Both aspects make it necessary to investigate thequestion of fast flavor conversions for the case where thehypermassive NS with a surrounding disk/torus still ex-ists. To this purpose, we focus on the first (cid:39)
10 ms afterthe merger of two NSs, during which a central hyper-massive NS surrounded by an accretion disk forms. Byrelying on recent hydrodynamical simulations with twodifferent EoS and two different mass ratios for the bi-nary, developed in Refs. [23, 44] and available at [45], weexplore the neutrino emission properties, the conditionsfor the occurrence of fast flavor instabilities, and the ef-fects of neutrino absorption and flavor conversions on theneutron-richness of the ejecta as well as the nucleosyn-thesis outcome.The paper is organized as follows. In Sec. II, we in-troduce the merger remnant models and the neutrinoemission properties. In Sec. III, we outline the frame-work used for the linear stability analysis and presentour numerical results on the occurrence of fast flavor con-versions. We analyze the ejecta properties, the neutrinoabsorption effects on the evolution of Y e , and the impactof flavor equipartition in Sec. IV. We summarize our find-ings and discuss their implications in Sec. V. We adoptnatural units with (cid:126) = c = 1 for all equations throughoutthe paper. II. NEUTRINO EMISSION FROM BINARYNEUTRON STAR MERGERSA. Models of binary neutron star mergers
We consider models of binary NS mergers sim-ulated by a three-dimensional relativistic smoothedparticle hydrodynamics code that adopts confor-mal flatness conditions [46]. The code has re-cently been coupled to an approximate neutrinotransport scheme called “improved-leakage-equilibration-absorption scheme (ILEAS),” which is implementedon a three-dimensional (3D) Cartesian coordinate grid( x, y, z ) with the axis perpendicular to the merging planechosen as z − axis. ILEAS serves as an efficient transportmethod for multidimensional simulations; when com-pared to two-moment neutrino transport results for pro-toneutron stars and post-merger tori, it captures wellneutrino energy losses from the densest regions of the sys-tem as well as neutrino absorption in the free-streamingregime [23, 44].Our fiducial models discussed in this section are fromRef. [23] and simulate the mergers of two non-rotatingNSs with mass 1.35 M (cid:12) each, with the EoS of DD2 [47,48] and SFHo [49]. In addition, we consider in later sec-tions cases of unequal mass binaries consisting of twoNSs with 1.25 M (cid:12) and 1.45 M (cid:12) each, based on the samenumerical scheme of Refs. [23, 44]. We note here thatwe have taken all simulation data averaged over the az-imuthal angle. This is a fairly good assumption as themerger remnant quickly reaches an approximately axi-symmetric state after ∼ − . During this time, the centralobject is a hypermassive NS supported by differential ro-tation. The energy luminosity of ¯ ν e ( L ¯ ν e (cid:39) erg s − )is a factor of 2 or 3 larger than the one of ν e through-out the whole 10 ms, leading to continuous protonizationof the remnant. The energy luminosities of the heavy-lepton neutrino flavors, denoted by ν x (with ν x beingrepresentative of one species of heavy-lepton neutrinos),are ∼ × erg s − per species. The averaged energiesestimated by the leakage approximation show a clear hi-erarchy of (cid:104) E ν e (cid:105) < (cid:104) E ¯ ν e (cid:105) < (cid:104) E ν x (cid:105) , reflecting the orderingof the temperature at decoupling; neutrinos that decou-ple in the innermost region of the remnant have higheraverage energy (see below and Fig. 2). When comparingthe energy luminosity evolution of the models with DD2and SFHo EoS, one sees that the latter produces higherluminosities in all flavors. This is related to the fact thatthe SFHo EoS is softer than the DD2 EoS, which re-sults in a NS with smaller radius. Consequently, a more More precisely, the time is measured with respect to the firstminimum of the lapse function (see Ref. [23]). Lu m i no s i t y ( e r g / s ) DD2 e DD2 e DD2 x SFHo e SFHo e SFHo x M ean ene r g y ( l ea k age ) [ M e V ] DD2 e DD2 e DD2 x SFHo e SFHo e SFHo x FIG. 1. Time evolution of the neutrino energy luminosityand average energy for different species, ν e (in red), ¯ ν e (ingreen) and ν x (in blue) of the 1 .
35 + 1 . M (cid:12) NS-NS mergersimulation, with DD2 (solid lines) and SFHo (dashed lines)EoS. violent collision during the merging leads to higher tem-peratures, and correspondingly higher neutrino emissionrates, when the SFHo EoS was adopted. This gives riseto a faster protonization of the remnant.Comparing Fig. 1 to Fig. 2 of Ref. [34], where the latterdisplays the neutrino emission properties for a BH rem-nant, one can see that the neutrino emission properties ofthe electron-flavor neutrinos are comparable in the twoscenarios. However, the non-electron-flavor neutrinos aremore abundant in the models investigated in this workand have average energies higher than the electron-flavorneutrinos. In addition, the neutrino energy luminositiesin the case with the BH accretion disk quickly decreaseafter (cid:39)
20 ms (see Fig. 2 of Ref. [34]). Although we onlyfocus on the first 10 ms after the coalescence, the neu-trino energy luminosity reaches a plateau in the modelswhere a hypermassive NS forms.The first three rows in Fig. 2 and Fig. 3 show thebaryon density, temperature, and electron fraction pro-files in the half x − z plane for x > ν e , ¯ ν e , and ν x emission surfaces. The emissionsurface for a given neutrino species ν α ( ν e , ¯ ν e , or ν x ) isdefined by a surface where the energy-averaged opticaldepth is τ ν α = 2 / Y e (cid:46) . ∼ −
60 km. Both ν e and ¯ ν e decouple at locations where the matter density isapproximately between 10 − g cm − and the tem-perature is ∼ ν e emission surfaces generallysit inside the ones of ν e during this period, independentlyof the adopted EoS.The size of the neutrino emission surfaces slightly ex-pands as the remnant evolves, due to the settling of thepost-merger object and the redistribution of matter withhigh angular momentum toward the equatorial plane,where the disk formation process proceeds. Moreover,as the remnant keeps protonizing, Y e inside the neutrinosurfaces gradually increases with time. The thick disk ofthe remnant in the model with the softer SFHo EoS pro-tonizes faster as discussed above, and thus has higher Y e inside the disk when compared to the profiles with DD2EoS. Note that in the polar region close to the z -axis, ahigh Y e (cid:38) . ν e and ¯ ν e luminosities and averageenergies become smaller.In the bottom panels of both Fig. 2 and Fig. 3, weshow the ratio of the difference of the number densitiesof ¯ ν e and ν e to the sum of the ¯ ν e and ν e densities, i.e.,( n ¯ ν e − n ν e ) / ( n ¯ ν e + n ¯ ν e ). Once again, as the remnant isprotonizing and emitting more ¯ ν e than ν e , nearly anylocation above the ν e surface in both models has this ra-tio larger than zero during the entire first 10 ms. Theonly exception is represented by the small patches in thepolar region at 7.5 and 10 ms for the model with DD2EoS. These patches are a consequence of the neutron-ization that takes place locally around the poles of thehigh-density core of the merger remnant in the DD2 case.Because the stiff EoS prevents the merger core from fur-ther contraction, the polar regions cool quickly, and thedensity just inside the neutrinospheres increases by grav-itational settling, forcing the neutrinospheres to move in-ward to smaller radii. This explains the more pronouncedpolar trough of the neutrinospheres in the DD2 modelcompared to the SFHo merger. Striving for a new beta-equilibrium state, now at lower temperature, the plasmabegins to neutronize again, radiating more electron neu-trinos than antineutrinos in both polar directions. Thisleads to the excess of ν e relative to ¯ ν e outside the neu-trinospheres, visible as the two blue patches in the twobottom right panels of Fig. 2. Correspondingly, ν e cap-tures dominate ¯ ν e captures in this region and the polaroutflow becomes more and more proton-rich (red regionsof Y e > . z -axis in the right panels of thethird row of Fig. 2). The same trends are visible in the FIG. 2. Hydrodynamic and neutrino properties from the 1 .
35 + 1 . M (cid:12) NS-NS merger remnant simulation with DD2 EoS inthe ( x, z ) plane for the time snapshot taken at 2.5, 5, 7.5, and 10 ms after the coalescence (from left to right columns). Thefirst, second and third rows show the baryon mass density ρ , temperature T , the electron number fraction Y e . The fourth rowdisplays the ratio ( n ¯ ν e − n ν e ) / ( n ¯ ν e + n ν e ) . A value of this ratio above (below) 0 implies larger n ¯ ν e ( n ν e ) locally. Also shownwith solid lines are the contours of the ν e (red), ¯ ν e (green), and ν x (blue) emission surfaces. SFHo simulation (Fig. 3), though less extreme and lessrapidly evolving than in the DD2 run.
B. Neutrino number densities on their emissionsurfaces
The inner regions of the merger remnant are denseenough to trap neutrinos. This allows us to define a neu-trino emission surface for each species ν α above which ν α can approximately free-stream. As we will use the prop-erties of ν e and ¯ ν e on their respective surfaces to con-struct their angular distributions outside the ν e surfacein Sec. III, we discuss below the time evolution and thedependence on the adopted EoS of the neutrino densitieson their emission surfaces.For any point x inside the simulation domain, the op-tical depth along a specific path γ to another point y that a neutrino with an energy E traverses is given by τ ν α ( E, x , γ ) = (cid:90) yx λ − ν α ( E, x (cid:48) ) ds, (1)where x (cid:48) is a point, ds is the differential segment along γ , and λ ν α ( E, x (cid:48) ( s )) is the corresponding mean-free-pathat x (cid:48) . For each species α , we determine the positionof the neutrino decoupling surface in the same way asin Ref. [23], i.e. for every point x , the minimum of thespectral-averaged (cid:104) τ ν α ( x , i ) (cid:105) is computed along the sixdifferent directions ( i ∈ ( ± x, ± y, ± z )) through the edgeof the simulation domain. The neutrino decoupling sur-face is then defined by the location corresponding to (cid:104) τ ν α ( x , i ) (cid:105) = 2 / ν e , ¯ ν e , and ν x are the onesshown in Figs. 2 and 3.Figure 4 shows the number densities of ν e , ¯ ν e , and ν x at their respective emission surfaces as functions of x for different snapshots. Note that the ν e and ¯ ν e numberdensities are computed by using Fermi-Dirac distributionfunctions with temperature and chemical potential ex-tracted at each location on the neutrino surfaces, consis-tently with Ref. [23]. For ν x , we rescale the number den-sity according to the procedure described in Appendix Ato account for the trapping effect between the energy-surfaces and the emission surfaces, which is known toconsiderably reduce the ν x luminosity when compared tothe analogous values directly estimated through the localemission (see, e.g., [50]). The top panels show the neu-trino density corresponding to the DD2 EoS, while thebottom panels display the same quantities for the SFHoEoS. As discussed in Sec. II A, the softer SFHo EoS leadsto a generally higher temperature in the merger remnant;as a consequence, the ¯ ν e luminosity (Fig. 1) and numberdensity on the emission surface are higher than the oneobtained in the model with DD2 EoS. Both n ν e and n ¯ ν e are larger in a region close to the pole where the temper-ature is higher (see Figs. 2 and 3). Of relevance to theoccurrence of fast flavor conversions is the fact that the¯ ν e emission is a factor of 2–3 larger than the one of ν e across the whole emission surface; it remains quite stablethroughout the simulated evolution until 10 ms after theplunge. The only exception is the snapshot at 7.5 msfor the model with DD2 EoS, which shows a dip in the¯ ν e number density around x (cid:39)
10 km. This is becausethe enhanced deleptonization above the poles of the high-density core (described in Sec. II A) leads to a short, tran-sient excess of ν e over ¯ ν e near the neutrinospheres in thenorthern hemisphere (see Fig. 2). The effect is somewhatpathological and unusual, also because it is considerablyless strongly developed in the southern hemisphere. No-tably, comparing Fig. 4 with the bottom panel of Fig. 1of Ref. [34], one can see that the neutrino-antineutrinoasymmetry is more pronounced in the present modelsthan in the BH remnant case. III. FLAVOR INSTABILITY
In Sec. III A we first briefly introduce the theoret-ical formalism, viz., the dispersion relation (DR) ap-proach [38], widely used in the literature to investi-gate the occurrence of neutrino flavor conversions. InSec. III B we look for the conditions leading to flavor in-stabilities using the simulation data introduced in Sec. II.We then apply the DR formalism to investigate the oc-currence of flavor conversions above the neutrino emis-sion surfaces in our merger remnant models in Sec. III C.
A. Dispersion relation formalism
We adopt the density matrix formalism to describethe statistical properties of the neutrino dense gas in-corporating flavor mixing [51]. For a given density ma-trix (cid:37) ( p , x , t ), its diagonal elements in the flavor basis, (cid:37) αα , record the phase-space distributions f ν α of a givenneutrino flavor ν α at the space-time location ( t, x ) andwith momentum p . The off-diagonal terms (cid:37) αβ carrythe information about the neutrino mixing (neutrino fla-vor correlations). In the absence of any mixing, i.e., allneutrinos are in their flavor eigenstates, the off-diagonalelements vanish.Neglecting general-relativistic effects and collisions ofneutrinos with matter, the space-time evolution of thedensity matrix (cid:37) ( p , x , t ) is governed by a Liouville equa-tion ∂ t (cid:37) ( p , x , t ) + v p · ∇ (cid:37) ( p , x , t ) = − i [Ω( p , x , t ) , (cid:37) ( p , x , t )] , (2)where Ω is the Hamiltonian that accounts for the flavoroscillations of neutrinos. On the left hand side of Eq. (2),the first term takes care of the explicit time dependenceof (cid:37) and the second term takes into account the neutrinopropagation with velocity v p (cid:39) p / | p | for ultrarelativisticneutrinos. The Hamiltonian matrix Ω on the right handside can be decomposed asΩ( p , x , t ) = Ω vac + Ω MSW + Ω νν , (3) FIG. 3. Same as Fig. 2, but for the simulation with SFHo EoS. x ( km )0246 n ν α ( c m − ) DD2 . ms ν e ¯ ν e ν x x ( km) DD2 ms ν e ¯ ν e ν x x ( km )0246 DD2 . ms ν e ¯ ν e ν x x ( km )0246 DD2 ms ν e ¯ ν e ν x x ( km )0246 n ν α ( c m − ) SFHo . ms ν e ¯ ν e ν x x ( km) SFHo ms ν e ¯ ν e ν x x ( km )0246 SFHo . ms ν e ¯ ν e ν x x ( km )0246 SFHo ms ν e ¯ ν e ν x FIG. 4. Number density of ν e (red solid curves), ¯ ν e (green dash-dotted curves), and ν x (blue dash lines) on their respectiveemission surfaces in the northern hemisphere for the 1 .
35 + 1 . M (cid:12) merger models with DD2 EoS (top panels) and SFHoEoS (bottom panels) at 2.5, 5, 7.5 and 10 ms post merger. Note that the ν x number density has been rescaled, see text andAppendix A for details. where the first term Ω vac takes into account flavor con-versions in vacuum. In a simplified two-flavor scenario,Ω vac = diag( ω v / , − ω v /
2) in the mass basis with ω v =( m − m ) / E being the vacuum oscillation frequency ofthe neutrinos with energy E .The second term on the right hand side of Eq. (3) em-bodies the effects of neutrino coherent forward scatteringwith electrons and nucleons. In the flavor basis, this termcan be expressed asΩ MSW = ( √ G F n e )diag(1 , , (4)where n e is the net electron number density. The lastterm in Eq. (3) is the effective Hamiltonian due to the ν – ν interaction. For a neutrino traveling with momentum p , Ω νν is given byΩ νν = √ G F (cid:90) d q (2 π ) (1 − v p · v q )( (cid:37) ( q , x , t ) − ¯ (cid:37) ( q , x , t )) , (5)where ¯ (cid:37) is the corresponding density matrix for antineu-trinos. The presence of (1 − v p · v q ) in Eq. (5) leadsto multi-angle effects, i.e., neutrinos propagating in dif-ferent directions experience different Ω νν . The equationof motion for antineutrinos can be obtained in a similarfashion, by replacing ω v by − ω v in Ω vac .We focus on a simplified system that deals with twoneutrino flavors. Under this assumption, both the den-sity matrix (cid:37) and the Hamiltonian Ω are 2 × (cid:37) = [( f ν e + f ν x ) + ( f ν e − f ν x ) ξ ] / (cid:37) = − [( f ¯ ν e + f ¯ ν x ) + ( f ¯ ν e − f ¯ ν x ) ξ ∗ ] / ξ is a matrix defined as ξ = (cid:18) s SS ∗ − s (cid:19) , (6)where − ≤ s ≤ | s | + | S | =1. In the absence ofany flavor correlation S = 0. Furthermore, as in previ-ous work that studied the fast neutrino flavor conversion,we omit the vacuum oscillation term in the following dis-cussion as ω v marginally affects the linear regime [52–54]. With these assumptions and introducing the met-ric tensor η µν = diag(1 , − , − , −
1) and for anycontra-variant vector A µ , A µ = η µν A ν , we can recast theHamiltonian defined in Eq. (3) into the following formΩ = v µ λ µ σ (cid:90) d Γ (cid:48) v µ v (cid:48) µ ξ ( v (cid:48) ) g ( v (cid:48) ) , (7)where v = (sin θ cos φ, sin θ sin φ, cos θ ) with velocity v µ = (1 , v ), d Γ = sin θdθdφ and λ µ = √ G F n e (1 , v m )with v m being the vector of the fluid velocity of the back-ground matter. Since the rate of pairwise conversion ismuch faster than any other inverse time scale involved inthe problem, we treat the background matter as station-ary and homogeneous: λ µ v µ = λ .The quantity g ( v ) is related to the angular distributionof the neutrino ELN angular distribution g ( v ) = √ G F ( Φ ν e − Φ ¯ ν e ) , (8)where Φ ν α = dn ν α /d Γ . To study the growth of S inthe linear regime, we treat the flavor correlation S as aperturbation and neglect all terms of O ( S ) or higher.Taking S ( t, x ) = Q ( ω, k ) e − i ( ωt − k · x ) , the EoM becomes v µ ¯ λ µ Q ( ω, k ) = − (cid:90) d Γ (cid:48) v µ v (cid:48) µ g ( v (cid:48) ) Q ( ω, k ) . (9)In the above Eq. (9) we have introduced the four vec-tor ¯ λ µ = ( ω − λ − (cid:15) , k − (cid:15) ), (cid:15) ≡ (cid:82) d Γ g ( v ) and (cid:15) ≡ (cid:82) d Γ v g ( v ). Inspecting Eq. (9), one can make theansatz Q ( ω, k ) = v µ a µ /v µ ¯ λ µ , with a µ being the coeffi-cients of eigenfunction solutions. Thus, Eq. (9) becomes v µ Π µν a ν = 0 , (10)where we have used the definitionΠ µν ≡ η µν + (cid:90) d Γ g ( v ) v µ v ν v σ ¯ λ σ . (11)The EoM defined in Eq. (10) holds for any v µ . Thus,we have the condition Π µν a ν = 0. Eigenfunctions of thelatter have non-trivial solution only if Π µν satisfies thecondition det[Π µν ( ω, k )] = 0 . (12)Equation (12) is the DR in flavor space. The solutionsof the DR have been classified into several types [39, 41].If ω is real for real values of k , a perturbation in S onlypropagates without growing or damping, i.e., it stays inthe linear regime, meaning that no significant flavor con-version occurs. On the other hand, an imaginary solu-tion of ω with Im( ω ) > | S | grows exponentially with time, leading to significantflavor conversion. Rigorous studies have been carriedout to understand the characteristics of the above DRwith respect to the ELN angular distribution of neutri-nos [38, 39, 41]. It was shown that in the presence of acrossing in the ELN distribution, the DR will yield com-plex ω solutions for real k , leading to temporal instabili-ties. In the following, we examine the ELN distributionsabove the merger remnants and the corresponding flavorinstabilities. B. Neutrino electron lepton number angulardistribution
To construct the ELN distribution above the mergerremnant, we follow a method similar to the one adoptedin Ref. [34]. First, we assume that both ν e and ¯ ν e freelypropagate outside their respective emission surfaces de-fined in Sec. II B. Second, we approximate their forward-peaked angular distributions at each point on the emis-sion surfaces as Φ ν e , ¯ ν e ( θ n ) = n ν e , ¯ ν e π (1 + cos θ n ) , (13) where θ n is the angle with respect to the normal direc-tion of the location on the emission surface. Ignoringthe minor effect of GR bending, we can then ray-tracethe neutrino intensities from the emission surfaces to ob-tain their angular distributions at any location above thesurfaces.Figures 5 and 6 show the obtained ELN distributionsas a function of the local angular variables θ (angle withrespect to the z -axis) and φ (angle with respect to the x -axis on the x - y plane) at selected locations above the ν e surface at 2.5, 5, 7.5 and 10 ms after the coalescence,for the 1 .
35 + 1 . M (cid:12) merger models with DD2 andSFHo EoS, respectively. Here we only show the sign ofthe ELN distribution to highlight the crossing. The blueshade represents the region where the net ELN is positivewhile the red region corresponds to negative ELN. Thetop panel shows the ELN distribution at a representativepoint on the z axis and the middle and bottom panelsshow the ELN distributions at near-center and outer re-gions above the ν e surface. Note here that Figs. 5 and6 only show the ELN distribution for φ/π ≥ ν e , ¯ ν e (cos θ, φ ) = Φ ν e , ¯ ν e (cos θ, − φ ).The angular coverage of the ν e and ¯ ν e fluxes at a point( x, z ) is determined by the geometry of the ν e and ¯ ν e emission surfaces. On the other hand, the ELN angu-lar distribution is determined by the combination of theemission surface geometries and their respective emissionproperties, including the relative strength of ν e and ¯ ν e and the angular dependence of the emission. For exam-ple, the ELN angular distribution at any point on the z axis above the emission surface is independent of φ , re-flecting the (assumed) rotational symmetry of the mergerremnants about the z axis. As we move away from the z axis, the ELN distribution becomes dependent on φ (sec-ond and third panels). For both EoS, the angular cov-erage in θ slightly increases with time for a given ( x, z ),caused by the expansion of the emission surfaces. Thisis different from what was found in Ref. [34] where thecentral remnant is a BH for which the size of the ν e / ¯ ν e emitting torus surfaces shrinks with time. As ¯ ν e are moreabundant than ν e in most parts of the emission regionduring the first 10 ms (see Fig. 4), the overall shapes ofthe ELN crossings are qualitatively similar. The only ex-ception is represented by the snapshot at 7.5 ms for thecase with DD2 EoS, for which the inner region above themerger remnant shows a double ELN crossing structure,see the left and middle panels in the third row. This isrelated to the dip of the ¯ ν e density on the ¯ ν e surface at ∼
10 km discussed in Sec. II B. Also, the ELN angulardistribution in Fig. 6 is more extended toward θ = 0 com-pared to Fig. 5, resulting from slightly larger radii of theneutrino emission surfaces in the SFHo model. For thesimulations adopting 1 .
25 + 1 . M (cid:12) binaries, we havesimilarly checked the ELN distributions during the sametime snapshots for both EoS. Unsurprisingly, ELN cross-ings appear at all times as those shown here. FIG. 5. Neutrino electron lepton number angular crossings at different positions ( x, z ) = (0 , , (10 , , (40 ,
25) km and times t = 2 . , , . ,
10 ms, above the remnant for the 1 .
35 + 1 . M (cid:12) model with DD2 EoS. The red (blue) shaded region representsthe region where Φ ν e − Φ ¯ ν e > ν e − Φ ¯ ν e < .
35 + 1 . M (cid:12) simulation with SFHo EoS. C. Flavor instabilities for fast pairwise conversion
After obtaining the ELN distributions above the neu-trino emitting surface, we numerically solve the DR[Eq. (12)] starting from the outer neutrino surface to in- spect whether solutions containing non-zero Im( ω ) for agiven k can be found . As the ELN distributions above Note that the positive and negative Im( ω ) solutions always ap-pear together.
30 20 10 0 100.00.51.0 | I m () | ( c m ) DD2 Symmetry preserving
DD2 Symmetry breaking k ( cm ) | I m () | ( c m ) SFHo Symmetry preserving k ( cm ) SFHo Symmetry breaking
FIG. 7. Solutions of | Im( ω ) | obtained from the DR [Eq. (12)] for k = (0 , , k ) at the location ( x, z ) = (10 ,
25) km above themerger remnant for different times. The top (bottom) panels show the results for the 1 .
35 + 1 . M (cid:12) model with the DD2(SFHo) EoS, while the left (right) panels show the symmetry-preserving (symmetry-breaking) solutions.
80 60 40 20 0 20012 | I m () | ( c m ) ) DD2 Symmetry preserving (0, 25)(10, 25)(40, 25) 5 0 5 10 15 20 25 300.000.250.500.75
DD2 Symmetry breaking (0, 25)(10, 25)(40, 25)80 60 40 20 0 k ( cm ) | I m () | ( c m ) SFHo Symmetry preserving (0, 25)(10, 25)(40, 25) 5 0 5 10 15 20 25 k ( cm ) SFHo Symmetry breaking (0, 25)(10, 25)(40, 25)
FIG. 8. Solutions of | Im( ω ) | obtained from the DR [Eq. (12)] for k = (0 , , k ) at 5 ms for different locations labeled by thecoordinates ( x, z ) expressed in km. The top (bottom) panels show the results for the 1 .
35 + 1 . M (cid:12) model with the DD2(SFHo) EoS, while the left (right) panels show the symmetry-preserving (symmetry-breaking) solutions. φ → − φ , one can obtaintwo different solutions that correspond to the reflectionsymmetry-preserving and symmetry-breaking cases [33].We show the obtained | Im( ω ) | as a function of k z ,taking k x = k y = 0, at different times for a locationat ( x, z ) = (10 ,
25) km above the emitting surfaces inFig. 7 and the solutions for different locations corre-sponding to the ELN crossing shown in Fig. 8 at 5 ms.The top (bottom) panels are for cases with DD2 (SFHo)EoS while the left (right) panels show the symmetry-preserving (symmetry-breaking) solutions.Flavor instabilities with growth rate of O (1) cm − ex-ist at all locations at all times for a large range of k z .The symmetry preserving solution of the DR has twobranches while the symmetry breaking solution has onlyone branch, similar to what was found in Ref. [33]. Com-paring the results for the models with DD2 and SHFoEoS, the growth rate of the flavor instability is generallylarger in the latter, as the neutrino emission is strongerwith the SHFo EoS. The shape of the solutions is ratherstable over time for the case with SFHo EoS. On theother hand, the model with DD2 EoS shows a somewhatstronger time-dependence. In particular, the range of k z that leads to non-zero | Im( ω ) | as well as the value of | Im( ω ) | both decrease at the snapshot of 7.5 ms, when thedouble crossing shape of the ELN appears (see Fig. 5).By comparing the solutions at different locations forthe t = 5 ms snapshot, Fig. 8 shows that | Im( ω ) | is largercloser to the z -axis for both the symmetry-preserving andsymmetry-breaking solutions. This, again, is caused bythe fact that Φ ν e and Φ ¯ ν e are largest in this region (seeFig. 4).As shown in Figs. 7 and 8, the symmetry-breaking so-lutions at all times and all locations contain non-zero | Im( ω ) | for the mode k = 0. We further show in Fig. 9the contour plot of | Im( ω ) | above the neutrino surfacefor this mode. The plots in this figure clearly show thatgrowth rates of the instability of ∼ O (1) cm − exist ev-erywhere above the remnant at all times. The regioncloser to the z -axis just above the emission surface hasthe maximal growth rates. Moving away from the sur-face, the neutrino flux is suppressed by the geometriceffects and the magnitude of the instability decreases inall cases. For the sake of comparison with the existingliterature, we find | Im( ω ) /µ | ∼ O (10 − ) for all cases ex-amined here; this value of the growth rate is similar al-beit a bit smaller than the ones reported in Refs. [34, 55].The growth rates | Im( ω ) /µ | are generally larger towardthe middle region above the ν e surface, in agreement withthe findings of Ref. [33, 34]. This is due to the relativestrength of the positive vs. negative ELN strength, in theproximity of crossings between the ν e and ¯ ν e angular dis-tributions [56]. For a system that is more dominated by ν e or ¯ ν e , i.e., where the positive ELN distribution dom-inates the negative parts or the other way around, oneexpects that the value of | Im( ω ) /µ | is smaller than in amore balanced system with similar positive and negative parts of the ELN distribution (see e.g., Ref. [41]). Look-ing at the ELN crossing pattern shown in Figs. 5 and 6,the locations above the middle part of the remnant havelarge angular area of g ( v ) > ν e and ¯ ν e surfaces (see Fig. 2 and 3). This,in turn, enhances the corresponding values of | Im( ω ) /µ | relative to the ones in the inner region closer to the z -axis.Likewise, when comparing the values of | Im( ω ) /µ | tothe ones shown in Ref. [34], the more dominant ¯ ν e emis-sion relative to ν e here, together with the smaller sepa-ration of their emission surfaces, results in smaller valuesof | Im( ω ) /µ | .On the other hand, while Ref. [34] showed that the re-gion where the flavor instability exists shrinks on a timescale of ∼ O (10) ms as the BH-disk remnant evolves,the instability region found here remains stable withinthe examined 10 ms of post-merger evolution. This canhave important consequences for the growth of the insta-bilities and seems to favor the eventual development offlavor conversions in the non-linear regime. The effect ofadvection hindering the growth of the flavor instabilitiesfor systems with non-sustained and fluctuating unstableconditions shown by Ref. [56] may therefore not happenabove the merger remnant, as shown in Ref. [55]. In thecase of the models with unequal mass binaries, due tothe similar ELN crossing features, we find unstable re-gions above the merger remnant disk and growth ratesvery similar to the symmetric models (results not shownhere).We here focus on the diagnostics of flavor instabilities,but do not distinguish whether they belong to the con-vective or absolute type (see Refs. [41, 57]). This wouldrequire solving the full dispersion relation for the com-plete ( ω, k ) space. IV. MERGER EJECTA ANDNUCLEOSYNTHESIS OF THE HEAVYELEMENTS
In this section, we first analyze the properties of thematerial ejected during the first (cid:39)
10 ms post merger, ex-amine how neutrino absorption affects the evolution of Y e of the outflow material, and discuss the nucleosynthesisoutcome in the absence of neutrino flavor conversion inSec. IV A. In Sec. IV B, we further explore the potentialeffect of fast flavor conversion on the neutrino absorp-tion rates and the outcome of nucleosynthesis of in theseejecta. A. Ejecta properties and nucleosynthesis
The dynamical ejecta masses extracted at 10 ms post-merger for the 1 .
35 + 1 . M (cid:12) merger simulations are ∼ . × − M (cid:12) and 3 . × − M (cid:12) with the DD2 andSFHo EoS, represented by 783 and 1263 tracer particles,respectively. For the 1 . . M (cid:12) merger cases, the dy-2 FIG. 9. Contour plots showing | Im( ω ) | above the ν e surface for k = 0 at t = 2 .
5, 5 .
0, 7 . . .
35 + 1 . M (cid:12) model. The top (bottom) panels are based on the model with the DD2 (SFHo) EoS. The red and greensolid lines represent the locations of ¯ ν e and ν e emission surfaces, respectively. M e j / M e j , t o t t ( r = 100km)(ms)(a) 00.050.10.150.2 30 60 90 120 150 θ ej(degree)(b) 00.050.10.150.2 0 0.2 0.4 0.6 0.8( v r /c )( r = 100km)(c) 00.020.040.060.080.10.120.140.160 0.1 0.2 0.3 0.4 0.5 0.6 Y ( no osc ) e ( r = 100km)(d)(e) DD2 (f) DD2 (g) SFHo (h) SFHo Y (no osc) e DD2SFHo0 30 60 90 120 150 180 θ ej (degree)0246810 t ( r = k m )( m s ) θ ej (degree)00.10.20.30.40.50.60.70.8 ( v r / c )( r = k m ) θ ej (degree)0246810 t ( r = k m )( m s ) θ ej (degree)00.10.20.30.40.50.60.70.8 ( v r / c )( r = k m ) FIG. 10. Histograms of the ejecta mass fraction when the ejecta reach r = 100 km at t ( r = 100 km), [panel (a)], θ ej [panel (b)],radial velocity v r at r = 100 km, and Y e at r = 100 km without flavor conversions for the simulations with 1 .
35 + 1 . M (cid:12) NSbinaries. Panel (e) [(g)] and (f) [(h)] show the distributions of each tracer particle in the t ( r = 100) km– θ ej and ( v r /c )– θ ej planeswith the DD2 (SFHo) EoS. The color coding of each tracer particle indicates its Y e value at r = 100 km without consideringflavor conversions. namical ejecta masses are ∼ . × − M (cid:12) (DD2) and8 . × − M (cid:12) (SFHo), represented by 1290 and 4398tracer particles. In computing the evolution of Y e for agiven tracer particle, we first post-process the neutrinoemission data from Ref. [23] to calculate the absorption rates of ν e and ¯ ν e on neutrons and protons, λ ν e and λ ν e (the superscript 0 here denotes the case where any neu-trino flavor conversion is omitted), as detailed in Appen-dices A and B. These rates are then combined with thenuclear reaction network used in Refs. [58, 59] to com-3pute the nucleosynthesis yields in the merger ejecta. Foreach tracer particle, we begin the network calculation ei-ther at a location where T = 50 GK or just outside thedisk with height of 25 km and radius of 55 km to makesure that it is outside the ν e emission surface. The initialnuclear abundances are calculated by using the nuclearstatistical equilibrium (NSE) condition. For T >
10 GK,we only compute the weak reaction rates to track the Y e evolution while assuming NSE at each moment to obtainthe abundances. When T ≤
10 GK, we instead followthe full evolution of all nuclear species and include thefeedback due to the nuclear energy release on the ejectatemperature following Ref. [60].In Fig. 10, we show the distributions of the ejectamass for the 1 .
35 + 1 . M (cid:12) models as a function ofthe time when the ejecta reach the radius r = 100 km at t ( r = 100 km) in panel (a), the angle θ ej (relative to the z -axis) when they leave the simulation domain in panel(b), and the radial velocity v r at r = 100 km in panel(c). We also show, in panel (d), the distributions of Y e forthe ejecta at r = 100 km, in the absence of flavor mixing.Additionally, panels (e) and (g) [(f) and (h)] show thedistributions of each tracer particle in the plane spannedby t ( r = 100 km) [ v r ( r = 100) km] and θ ej with the cor-responding Y e at 100 km labeled in color for the DD2 andSHFo EoS, respectively. These plots show that, indepen-dently of the adopted EoS, most of the material is ejectedwithin the first ∼ Y e (cid:46) .
3, within ∼ ◦ away from the mid-plane. The ejecta launched in thesecond episode [ t ( r = 100 km) (cid:39) − Y e (cid:39) .
4. After that, neutrino irradiation continues topower the mass ejection along the polar direction with Y e reaching ∼ .
5. In terms of the ejecta kinematics, be-cause of the weak interactions, it is clear that Y e can beraised up to 0 . − . v r /c ∼ . − . r = 100 km, evenaround the equatorial plane, and reach ∼ . v r /c (cid:38) . Y e distribution [panel (d)]for both models shows that Y e ( r = 100 km) is slightlylarger for the DD2 EoS model than for the SFHo EoSone. This reflects the higher ¯ ν e luminosity obtained inthe SHFo EoS model (see Fig. 1) leading to larger ¯ ν e ab-sorption rates on protons; hence, Y e is raised less for thebulk of the ejecta. The high Y e tail extends to values (cid:38) . (cid:46) . Y e ejecta than in theDD2 model [see panel (f)], different from the main bulkof the ejecta. This is because these ejecta are mainlydriven during the early post-merger phase. During thisearly phase, positron capture is responsible for raising Y e in the ejecta, rather than neutrino absorption. Thus, inthe model with SFHo EoS, the higher post-merger tem-perature of the remnant due to the more violent mergerleads to relatively higher Y e material in the early fastejecta.We show in Fig. 11 the same quantities as in Fig. 10,but for the models with 1 .
25 + 1 . M (cid:12) mass binaries.Qualitatively, the features are similar to the ones de-scribed above, but they are quantitatively different. Forinstance, the division between different episodes of massejection is less clear, in particular for the SHFo EoS model[see panel (a)]. On average, most of the ejecta havehigher velocities, peaked at ∼ . c [see panel (c), (f)and (h)]. Moreover, a larger fraction of the ejecta haslower Y e (cid:46) .
2, despite the fact that similarly wide dis-tributions of 0 . (cid:46) Y e (cid:46) . r abundance pattern [61]. Due to thewide-spread Y e distribution ranging from 0 . − . r -process peaks at A (cid:39)
90, 130, and195 are in relatively good agreement with the solar abun-dance pattern. The difference of the high Y e componentdiscussed above only results in abundance variations at A (cid:39) −
80. In particular, we compute the amount ofstrontium present at the time of a day, which is of rele-vance to the potential identification in the spectral anal-ysis of the GW170817 kilonova [11]. The total amountof strontium is (cid:39) . × − M (cid:12) and (cid:39) . × − M (cid:12) for the DD2 and SFHo EoS models with equal mass bi-naries. For the asymmetric merger models, the corre-sponding amount of strontium is (cid:39) . × − M (cid:12) and3 . × − M (cid:12) , respectively. These results are consistentwith the findings of Ref. [11].References [22, 60, 62, 63] found that some mergerejecta have low Y e and fast expansion time scale to allowfor a neutron-rich freeze-out during the r -process nucle-osynthesis. A potentially thin layer of “neutron-skin” atthe outskirts of the ejecta may possibly power an early-time UV emission at ∼ hours post-merger due to theradioactive heating of neutron decay [7, 62]. We findthat the amount of free neutrons at the end of the r -process, for equal-mass binaries, is (cid:39) . × − M (cid:12) and6 . × − M (cid:12) with the DD2 and SFHo EoS, respectively.These numbers are roughly a factor of 10 smaller thanwhat was found in Ref. [60], which analyzed simulationtrajectories without including the weak interactions. Thereduction of the amount of free neutrons at the end ofthe r -process is related to the high post-merger temper-ature effect raising Y e even for the early fast ejecta. Forthe unequal mass binaries, the corresponding amount offree neutrons is (cid:39) . × − M (cid:12) and 3 . × − M (cid:12) for4 M e j / M e j , t o t t ( r = 100km)(ms)(a) 00.050.10.150.2 30 60 90 120 150 θ ej(degree)(b) 00.050.10.150.2 0 0.2 0.4 0.6 0.8( v r /c )( r = 100km)(c) 00.020.040.060.080.10.120.140.160 0.1 0.2 0.3 0.4 0.5 0.6 Y ( no osc ) e ( r = 100km)(d)(e) DD2 (f) DD2 (g) SFHo (h) SFHo Y (no osc) e DD2SFHo0 30 60 90 120 150 180 θ ej (degree)0246810 t ( r = k m )( m s ) θ ej (degree)00.10.20.30.40.50.60.70.8 ( v r / c )( r = k m ) θ ej (degree)0246810 t ( r = k m )( m s ) θ ej (degree)00.10.20.30.40.50.60.70.8 ( v r / c )( r = k m ) FIG. 11. Same as Fig. 10, but for the 1 .
25 + 1 . M (cid:12) models. -7-6-5-4-3-2 40 60 80 100 120 140 160 180 200 220 l og [ Y ( A ) ] mass number, A DD2, 1 .
35 + 1 . M ⊙ SFHo, 1 .
35 + 1 . M ⊙ DD2, 1 .
25 + 1 . M ⊙ SFHo, 1 .
25 + 1 . M ⊙ FIG. 12. Nucleosynthesis yields, Y ( A ), as a function of thenuclear mass number A at the time of 1 Gyr for all NS mergermodels investigated in this work. the DD2 EoS model and for the SFHo model. A future(non)identification of this component may shed light onthe role of weak interactions in the post-merger environ-ments. B. Impact of flavor equipartition on Y e andnucleosynthesis Following previous work [34, 64], we assume thatfast flavor conversions lead to conditions close to flavorequipartition for neutrinos and antineutrinos. The as- sumption of flavor equilibration is an extreme ansatz, es-pecially in the light of the findings of Ref. [55], which,however, relied on a simplified model of a relic mergerdisk. Moreover, this simple assumption does not pre-serve the total electron neutrino lepton number, which isa strictly conserved quantity in the case of pairwise fla-vor conversions. Nevertheless, our extreme assumptionfor the flavor ratio is useful to explore the largest pos-sible impact that flavor conversions might have on thenucleosynthesis of the heavy elements. The correspond-ing neutrino absorption rates can be approximated by λ osc ν e = 13 λ ν e + 23 λ ν x , (14) λ osc¯ ν e = 13 λ ν e + 23 λ ¯ ν x , (15)where λ ν x and λ ¯ ν x are the neutrino absorption rates onfree nucleons assuming that all ν x and ¯ ν x are convertedto ν e and ¯ ν e , as detailed in Appendices A and B. Wethen perform the same nucleosynthesis calculations as inSec. IV A for all tracer particles in all the merger modelsby replacing λ ν e and λ ν e by λ osc ν e and λ osc¯ ν e . Below, we onlyfocus on the findings for the models with equal mass anddifferent EoS because the results obtained in the unequalmass binaries are qualitatively the same, independent ofthe EoS.We show in Fig. 13 the comparison of the ratio of λ ν e /λ ¯ ν e evaluated at r = 100 km for all tracer particlesfor the cases with and without flavor equipartition. Thecorresponding values of λ ¯ ν e are also shown. These figureshighlight that the neutrino absorption rates are orders ofmagnitudes larger in the polar region than close to the5 log [ λ ν e / (s − )](a) EoS: DD2 log [ λ osc ¯ ν e / (s − )](b) EoS: DD2log [ λ ν e / (s − )](c) EoS: SFHo log [ λ osc ¯ ν e / (s − )](d) EoS: SFHo0 20 40 60 80 100 120 140 160 180 θ ej (degree)00.20.40.60.811.21.4 λ ν e / λ ν e θ ej (degree)00.20.40.60.811.21.4 λ o s c ν e / λ o s c ¯ ν e θ ej (degree)00.20.40.60.811.21.4 λ ν e / λ ν e θ ej (degree)00.20.40.60.811.21.4 λ o s c ν e / λ o s c ¯ ν e FIG. 13. Distribution of the ratios of the ν e absorption rates on neutrons, λ ν e , to the ¯ ν e absorption rates on protons, λ ¯ ν e , asa function of θ ej for all tracer particles at r = 100 km in the 1 .
35 + 1 . M (cid:12) models. Panels (a) and (c) are without flavorconversions, while panels (b) and (d) include flavor equipartition. The color of each point indicates the absolute rate of λ ¯ ν e . equator. For the case without neutrino flavor equipar-tition, nearly all tracer particles have λ ν e /λ ν e (cid:46)
1, re-flecting the stronger ¯ ν e flux emitted from its surface.With flavor equipartition, the nearly equal contributionof the converted ν x and ¯ ν x significantly changes the ra-tio λ osc ν e /λ osc¯ ν e for both EoS. For the case with DD2 EoS,most of the trajectories with θ ej (cid:46) ◦ or θ ej (cid:38) ◦ have λ osc ν e /λ osc¯ ν e (cid:38)
1. On the other hand, the values of λ osc ν e /λ osc¯ ν e scatter around 1 for the model with SFHo EoS.The large change in λ ν e /λ ¯ ν e strongly affects the Y e distribution of the ejecta. Figures 14(a) and 15(a) show∆ Y e ≡ Y (osc) e − Y (no osc) e calculated at r = 100 km foreach tracer particles as a function of the corresponding θ ej , where Y (osc) e and Y (no osc) e are the Y e values with andwithout flavor equipartition. These results show that theflavor equipartition can significantly increase Y e of theejecta up to ∼ .
15 for θ ej < ◦ or θ ej > ◦ closerto the polar directions. In particular, the increase of Y e due to flavor equipartition for these ejecta is more pro-nounced with Y (no osc) e (cid:39) . − .
4. For the ejecta with Y (no osc) e (cid:46) . Y (no osc) e (cid:39) . Y e is less affected. Thisis because the ejecta with Y (no osc) e (cid:46) . Y e either with or withoutflavor conversion. On the other hand, for the ejecta with Y (no osc) e (cid:39) . λ ν e /λ ¯ ν e (cid:39) ◦ ≤ θ ej ≤ ◦ closer to the disk mid-plane, Y e is barely influenced byflavor equipartition because of the low neutrino absorp- tion rates (see Fig. 13).Figures 14(b)-(d) and 15(b)-(d) further show the com-parison of the Y e distribution for the cases with and with-out flavor conversion, for the ejecta classified into threegroups according to θ ej : the polar ejecta with 60 ◦ < | θ ej − ◦ | ≤ ◦ , the middle ejecta with 30 ◦ < | θ ej − ◦ | ≤ ◦ ,and the equatorial ejecta with 0 ◦ ≤ | θ ej − ◦ | ≤ ◦ .Flavor equipartition influences the Y e distribution of thepolar ejecta by shifting the peak from ∼ . ∼ . Y e peak in the DD2 (SFHo) model is re-lated to the larger (smaller) values of λ osc ν e /λ osc¯ ν e shown inFig. 13. For the middle ejecta, a fraction of ejecta orig-inally with 0 . (cid:46) Y (no osc) e (cid:46) . Y (osc) e (cid:39) . − . Y e (cid:46) . Y e distribution is only affectednegligibly, as expected.The impact of flavor equipartition in the neutrino-driven ejecta studied in Ref. [34] is to lower Y e (see Fig. 11therein), while Y e increases in the models investigated inthis work, as discussed above. The main difference isthat flavor equipartition leads to a larger reduction of λ ν e and λ ¯ ν e in the BH–torus case, due to the vanishinglysmall ν x fluxes. Moreover, a significant part of the ejectain the BH–torus case is ejected on timescales of severaltens of milliseconds during which the neutrino luminosi-ties decrease substantially (see Figs. 2 and 8 in Ref. [34]);this leads to much smaller neutrino absorption rates even6 Y (no osc) e (a) EoS: DD2 012345678 0 0.1 0.2 0.3 0.4 0.5 0.6 M e j ( − M ⊙ ) Y e ( r = 100 km)(b) polar ejecta (60 ◦ < | θ ej − ◦ | ≤ ◦ )0246810120 0.1 0.2 0.3 0.4 0.5 0.6 M e j ( − M ⊙ ) Y e ( r = 100 km)(c) middle ejecta (30 ◦ < | θ ej − ◦ | ≤ ◦ ) 05101520250 0.1 0.2 0.3 0.4 0.5 0.6 M e j ( − M ⊙ ) Y e ( r = 100 km)(d) equatorial ejecta (0 ◦ < | θ ej − ◦ | ≤ ◦ )0 20 40 60 80 100 120 140 160 180 θ ej (degree)-0.0200.020.040.060.080.10.120.140.160.18 ∆ Y e ( r = k m ) Y ( no osc ) e Y ( osc ) e Y ( no osc ) e Y ( osc ) e Y ( no osc ) e Y ( osc ) e FIG. 14. Impact of neutrino flavor equipartition on the ejecta Y e for the 1 .
35 + 1 . M (cid:12) model with DD2 EoS. Panel (a)shows the distribution ∆ Y e = Y (osc) e − Y (no osc) e , at r = 100 km, as a function of θ ej for all tracer particles. The color barrepresents Y e without flavor conversions. Panels (b)–(d) show the histograms of the ejecta mass distributions as functions of Y e at r = 100 km, for the polar, middle, and equatorial ejecta, respectively. without assuming neutrino flavor equipartition. As aconsequence, since the ejecta start out as neutron-richmaterial, a largely reduced Y e for the neutrino-drivenoutflow was found in the BH–torus model of Ref. [34].We show in Fig. 16 the impact of flavor equiparti-tion on the abundance distribution for the polar ejecta(60 ◦ ≤ | θ ej − ◦ | ≤ ◦ ) for the 1 .
35 + 1 . M (cid:12) modelwith both EoSs. Since flavor equipartition mainly shiftsthe distribution of high Y e (cid:38) . A = 56 nuclei is enhanced by a factor of ∼ ∼ a factorof 2 for the SHFo model. Since the polar ejecta contributeup to ∼
10% to the total ejecta mass considered here, theoverall modifications induced by flavor equipartition onthe total abundance yields are relatively small. For in-stance, the change of the produced amount of strontiumat the time of a day and the amount of free neutrons atthe end of the r -process is at the level of ∼ V. SUMMARY AND DISCUSSION
In this work, we have examined the neutrino emissionproperties and the conditions for the occurrence of fastneutrino flavor conversions during the first 10 ms afterthe coalescence of symmetric (1 . . M (cid:12) ) and asym-metric (1 .
25 + 1 . M (cid:12) ) NS binaries, during which theremnant consists of a hypermassive NS surrounded by anaccretion disk. We have also performed detailed analysesregarding the properties of the material ejected duringthis phase and nucleosynthesis calculations for cases withand without neutrino flavor mixing. Our study is basedon the outputs from the general-relativistic simulationswith approximate neutrino transport, performed withtwo different EoS (DD2 and SHFo) based on Refs. [23, 44]and available at [45].Flavor instabilities that may lead to fast pairwise fla-vor conversions occur throughout the whole investigatedpost-merger evolution, independent of the adopted EoSor the mass ratio of the binary. This is a direct conse-quence of the ¯ ν e emission dominating over the ν e one dueto the protonization of the merger remnant, which leadsto crossings in the neutrino ELN angular distributionseverywhere above the neutrino emitting surfaces. Our7 Y (no osc) e (a) EoS: SFHo 012345678 0 0.1 0.2 0.3 0.4 0.5 0.6 M e j ( − M ⊙ ) Y e ( r = 100 km)(b) polar ejecta (60 ◦ < | θ ej − ◦ | ≤ ◦ )0246810121416180 0.1 0.2 0.3 0.4 0.5 0.6 M e j ( − M ⊙ ) Y e ( r = 100 km)(c) middle ejecta (30 ◦ < | θ ej − ◦ | ≤ ◦ ) 0510152025300 0.1 0.2 0.3 0.4 0.5 0.6 M e j ( − M ⊙ ) Y e ( r = 100 km)(d) equatorial ejecta (0 ◦ < | θ ej − ◦ | ≤ ◦ )0 20 40 60 80 100 120 140 160 180 θ ej (degree)-0.0200.020.040.060.080.10.120.140.160.18 ∆ Y e ( r = k m ) Y ( no osc ) e Y ( osc ) e Y ( no osc ) e Y ( osc ) e Y ( no osc ) e Y ( osc ) e FIG. 15. Same as Fig. 14, but for the 1 .
35 + 1 . M (cid:12) model with SHFo EoS. results thus confirm the earlier conclusions of Ref. [33],which adopted a simple toy-model for the neutrino emis-sion characteristics and emission surface geometry. How-ever, in contrast to the results obtained in Ref. [34],which showed that the region where flavor instabilitiesexist shrinks on a time scale of ∼ O (10) ms as the BH–disk remnant evolves, the flavor unstable regions reportedhere remain quite stable within the examined 10 ms ofpost-merger evolution. Since Refs. [13, 18] reported dom-inating emission of ¯ ν e over ν e on time scales longer than O (100) ms for a hypermassive NS accretion disk system,we expect that the flavor instabilities found in this papermay be sustained for even longer duration and affect thenucleosynthesis in the disk winds.As for the ejecta properties and the nucleosynthesisoutcome, the ejecta contain a wide Y e distribution upto 0.5 due to the effect of weak interactions includingneutrino absorption, allowing for the formation of heavyelements in all three r -process peaks. In particular, a fewtimes 10 − M (cid:12) of strontium are synthesized in the ejectain all models, consistent with the amount inferred fromthe GW170817 kilonova observation [11]. We also findthat the amount of free neutrons left after the r -processfreeze-out is roughly a factor of 10 smaller than the oneobtained in simulations without taking into account theeffect of weak interactions. This has implications for theprediction of the early-time UV emission that may be powered by the decay of free neutrons [62].By relying on the extreme ansatz that fast pairwiseconversions lead to flavor equilibration, we find that fla-vor mixing of neutrinos mostly affects the polar ejectawithin ∼ ◦ by changing the peak Y e from ∼ . ∼ .
5. The dominant effect is thus to reduce the firstpeak abundances while enhancing the iron peak abun-dances. This result quantifies the most extreme impactof neutrino flavor conversions on the nucleosynthesis inthe early-time ejecta; most likely, the effect due to neu-trino flavor conversions should be between our exploredtwo cases with and without oscillations. Note that wehave only examined the flavor instability above the neu-trino emitting surfaces. Beyond that, future work inves-tigating the occurrence of unstable conditions inside theneutrino-trapping regime, along the lines of recent workdone in the context of core-collapse supernovae [65–71],should be carried out. Potential effects due to the pres-ence of turbulence [72] may also play a role in post-mergerenvironments.Multidimensional numerical simulations tracking theflavor evolution in the presence of fast pairwise conver-sions (see, e.g., Refs. [54–56, 73–76]), including the col-lisional term in the equations of motion, are essentialto draw robust conclusions on the role of neutrino fla-vor conversion for the outcome of nucleosynthesis in theejecta and the corresponding kilonova observables.8 -8-7-6-5-4-3-2 40 60 80 100 120 140 160 180 200 220 l og [ Y ( A ) ] mass number, A (a) EoS: DD2, polar ejecta only-8-7-6-5-4-3-2 40 60 80 100 120 140 160 180 200 220 l og [ Y ( A ) ] mass number, A (b) EoS: SFHo, polar ejecta onlyoscno osc.oscno osc. FIG. 16. Nucleosynthesis outcome in the polar ejecta for thecases with and without flavor equipartition for the 1 .
35 +1 . M (cid:12) model with DD2 EoS (a) and for the SHFo EoSmodel (b). ACKNOWLEDGMENTS
MG and MRW acknowledge support from the Ministryof Science and Technology, Taiwan under Grant No. 107-2119-M-001-038, No. 108-2112-M-001-010, No. 109-2112-M-001-004, the Academia Sinica under project numberAS-CDA-109-M11, and the Physics Division of NationalCenter for Theoretical Sciences. IT acknowledges sup-port from the Villum Foundation (Project No. 13164),the Danmarks Frie Forskningsfonds (Project No. 8049-00038B), the Knud Højgaard Foundation. At Garch-ing, funding by the European Research Council throughgrant ERC-AdG No. 341157-COCO2CASA and by theDeutsche Forschungsgemeinschaft (DFG, German Re-search Foundation) through grants SFB-1258 “Neutrinosand Dark Matter in Astro- and Particle Physics (NDM)”and under Germany’s Excellence Strategy through Ex-cellence Cluster ORIGINS (EXC 2094)—390783311 is ac-knowledged.
Appendix A: Computing the neutrino numberdensities from the simulation data
As the simulation outputs from Refs. [23, 44] did notdirectly store the ν e and ¯ ν e absorption rates on free nu-cleons along the ejecta trajectories, we compute the ratesin a post-processing fashion as follows. First, the simula-tions provide the local ν e and ¯ ν e energy luminosities andaverage energies at radii of 50 and 100 km as functions ofthe polar angle θ (with respect to the z -axis) for differentpost-merger time snapshots. This allows to compute the ν e and ¯ ν e number densities at these two radii. Then, at agiven time t , for any spatial coordinate x on a trajectorywith radius 50 km ≤ r ≤
100 km (with an angle θ ), wecompute the corresponding number densities of ν e and¯ ν e by linearly interpolating the logarithmic values of thedensities obtained above at r = 50 and 100 km. Once wehave the number densities of the ν e and ¯ ν e , the absorp-tion rates for 50 km ≤ r ≤
100 km can be computed usingEqs. (B1) and (B2) in Appendix. B. For r >
100 km, weextrapolate the rates assuming that they scale as r − : λ ν α ( r >
100 km) = λ ν α ( r = 100 km) × (cid:18)
100 km r (cid:19) , (A1)For r <
50 km, we take a different form of extrapolationto partly account for the finite-size emission geometry: λ ν α ( r < λ ν α ( r = 50km) × (A2) (cid:32) − (cid:112) − ( r /r ) − (cid:112) − ( r / (50km)) (cid:33) , with r = 25 km. We have checked that even simplytaking the 1 /r extrapolation for regions with r <
50 kmleads to nearly identical results to those obtained by usingEq. (A2).Figure 17 compares the Y e distribution at r = 100 km,obtained by the simulation of Ref. [23] to the one ob-tained by using the above neutrino absorption rates inthe nuclear reaction network described in Sec. IV A. Itshows that the Y e distributions agree with each otherreasonably well.For ν x , since the simulations do not store the energy lu-minosity and average energy in the bins at 50 and 100 km,we estimate the ν x number density and average energyalong each ejecta trajectory as follows. First, the loca-tions of the ν x surface and the associated temperaturesfor times between 2 . ≤ t ≤
10 ms are interpolated byusing the data provided at 2 . , , . t , a ν x number density on each point (cid:126)x ,˜ n ν x ( (cid:126)x ), at the emission surface following the Fermi-Diracdistribution with temperature T ( (cid:126)x i ) and zero chemicalpotential can be easily calculated. We then re-normalizethe total neutrino number luminosity emitted from the ν x surface to the value given by simulation data, L N,ν x = L ν x (cid:104) E ν x (cid:105) = 5 · ξ (cid:90) dS ˜ n ν x , (A3)9 M e j ( − M ⊙ ) Y e ( r = 100km)simulationpost-processing FIG. 17. Ejecta Y e histograms computed via post-processingand as from the simulations of Refs. [23, 44]. where L ν x and (cid:104) E ν x (cid:105) are the energy luminosity and meanenergy of ν x shown in Fig. 1, respectively. The quantity dS is the differential surface area on the ν x surface. Thefactor 5 /
12 accounts for the forward peaked angular pro-file of ν x emission consistent with Eq. (13), and ξ is thenormalization constant. Correspondingly, the rescaled ν x number density on their emission surface is given by n ν x ( (cid:126)x ) = ξ ˜ n ν x ( (cid:126)x ).We assume the ν x average energy at each location (cid:126)x on the emission surface to be (cid:104) E ν x (cid:105) ( (cid:126)x ) = 12 ( (cid:104) E ν x (cid:105) + 3 . T ( (cid:126)x )) , (A4)to partly account for the fact that the ν x - e ± scatterings,which can down-scatter ν x , was not included in the nu-merical simulations of Ref. [23]. Since the local temper-ature on the ν x emission surface within x (cid:46)
20 km isfound to be (cid:38) (cid:104) E ν x (cid:105) ( (cid:126)x ) at the outer edge of the emis-sion surface. We have additionally confirmed that adopt-ing a location independent average energy of ν x given by (cid:104) E ν x (cid:105) does not qualitatively change our results shown inthe main text.For t < . t = 2 . n ν x ( (cid:126)x, t ) and the averageenergy (cid:104) E ν x (cid:105) ( (cid:126)x, t ) in the following way n ν x ( (cid:126)x, t ) = n ν x ( (cid:126)x, t = 2 . (cid:18) L N,ν x ( t ) L N,ν x ( t = 2 . (cid:19) , (A5) (cid:104) E ν x (cid:105) ( (cid:126)x, t ) = (cid:104) E ν x (cid:105) ( (cid:126)x, t = 2 . (cid:18) (cid:104) E ν x (cid:105) ( t ) (cid:104) E ν x (cid:105) ( t = 2 . (cid:19) . (A6)Once we have the desired quantities on the emissionsurface for all times, we use the same ray-tracing tech- nique as in the main text to compute the ν x number den-sities for the locations crossed by the trajectories. Theabsorption rates of the converted ν x and ¯ ν x on nucleons, λ ν x and λ ¯ ν x , along all trajectories, are similarly com-puted as those of ν e and ¯ ν e given in Appendix B by re-placing the corresponding number densities, the averageenergies, and other higher energy moments. Appendix B: Computing the neutrino absorptionrates
In order to compute the evolution of Y e for the out-flows for the cases with and without flavor conversions,we first compute the number densities and average ener-gies of ν e , ¯ ν e and ν x (without flavor conversions) alongthe trajectories of all tracer particles by post-processingthe simulation data as detailed in Appendix A. For thecase without flavor conversions, we follow Ref. [77] tocalculate the ν e and ¯ ν e absorption on free nucleons: λ ν e = n ν e (cid:104) σ ν e (cid:105) , (B1) λ ν e = n ¯ ν e (cid:104) σ ¯ ν e (cid:105) , (B2)where (cid:104) σ ν e (cid:105) and (cid:104) σ ν e (cid:105) are the spectrally averaged absorp-tion cross-sections of ν e and ¯ ν e . By taking into accountthe recoil corrections and weak magnetism [78], the av-erage neutrino capture cross sections are approximatedby (cid:104) σ ν e (cid:105) (cid:39) k (cid:104) E ν e (cid:105) ε ν e (cid:34) (cid:18) ∆ ε ν e (cid:19) + a ν e (cid:18) ∆ ε ν e (cid:19) (cid:35) W ν e , (B3) (cid:104) σ ¯ ν e (cid:105) (cid:39) k (cid:104) E ¯ ν e (cid:105) ε ¯ ν e (cid:34) (cid:18) ∆ ε ¯ ν e (cid:19) + a ¯ ν e (cid:18) ∆ ε ¯ ν e (cid:19) (cid:35) W ¯ ν e , (B4)where k = 9 . × − cm / MeV , ε ν e , ¯ ν e = (cid:104) E ν e , ¯ ν e (cid:105) / (cid:104) E ν e , ¯ ν e (cid:105) , a ν e , ¯ ν e = (cid:104) E ν e , ¯ ν e (cid:105) / (cid:104) E ν e , ¯ ν e (cid:105) , and ∆ =( m n − m p ) = 1 .
293 MeV is the neutron-proton mass dif-ference. The weak-magnetism and recoil correction fac-tors W ν e , ¯ ν e are given by W ν e = (cid:20) . b ν e ε ν e M (cid:21) , (B5) W ¯ ν e = (cid:20) − . b ¯¯ ν e ε ¯ ν e M (cid:21) , (B6)where b ν e , ¯ ν e = (cid:104) E ν e , ¯ ν e (cid:105)(cid:104) E ν e , ¯ ν e (cid:105) / (cid:104) E ν e , ¯ ν e (cid:105) is the spectralshape factor for ν e (¯ ν e ) and M = 940 is roughly themass of a nucleon in MeV. Note that in deriving therates through the above equations, we have assumed zerochemical potentials for all neutrino species to computethe i -th neutrino energy moments (cid:104) E iν α (cid:105) .0 ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] ¶ [email protected][1] James M. Lattimer and David N. Schramm, “Black-hole-neutron-star collisions,” Astrophys. J. , L145–L147(1974).[2] David Eichler, Mario Livio, Tsvi Piran, andDavid N. Schramm, “Nucleosynthesis, Neutrino Burstsand Gamma-Rays from Coalescing Neutron Stars,” Na-ture , 126–128 (1989).[3] John J. Cowan, Christopher Sneden, James E.Lawler, Ani Aprahamian, Michael Wiescher, Karl-heinz Langanke, Gabriel Mart´ınez-Pinedo, andFriedrich-Karl Thielemann, “Origin of the Heaviest El-ements: the Rapid Neutron-Capture Process,” (2019),arXiv:1901.01410 [astro-ph.HE].[4] Li-Xin Li and Bohdan Paczynski, “Transient events fromneutron star mergers,” Astrophys. J. , L59 (1998),arXiv:astro-ph/9807272 [astro-ph].[5] Shrinivas R. Kulkarni, “Modeling supernova-like explo-sions associated with gamma-ray bursts with short dura-tions,” (2005), arXiv:astro-ph/0510256 [astro-ph].[6] B. D. Metzger, G. Mart´ınez-Pinedo, S. Darbha,E. Quataert, A. Arcones, D. Kasen, R. Thomas, P. Nu-gent, I. V. Panov, and N. T. Zinner, “Electromag-netic Counterparts of Compact Object Mergers Poweredby the Radioactive Decay of R-process Nuclei,” Mon.Not. Roy. Astron. Soc. , 2650 (2010), arXiv:1001.5029[astro-ph.HE].[7] Brian D. Metzger, “Kilonovae,” Living Rev. Rel. , 3(2017), arXiv:1610.09381 [astro-ph.HE].[8] Benjamin P. Abbott et al. (Virgo and LIGO ScientificCollaborations), “GW170817: Observation of Gravita-tional Waves from a Binary Neutron Star Inspiral,” Phys.Rev. Lett. , 161101 (2017), arXiv:1710.05832 [gr-qc].[9] Benjamin P. Abbott et al. (Fermi-GBM, INTEGRAL,Virgo and LIGO Scientific Collaborations), “Gravita-tional Waves and Gamma-Rays from a Binary NeutronStar Merger: GW170817 and GRB 170817A,” Astrophys.J. , L13 (2017), arXiv:1710.05834 [astro-ph.HE].[10] B. P. Abbott et al. (GROND, SALT Group, Oz-Grav, DFN, INTEGRAL, Virgo, Insight-Hxmt, MAXITeam, Fermi-LAT, J-GEM, RATIR, IceCube, CAAS-TRO, LWA, ePESSTO, GRAWITA, RIMAS, SKASouth Africa/MeerKAT, H.E.S.S., 1M2H Team, IKI-GWFollow-up, Fermi GBM, Pi of Sky, DWF (Deeper WiderFaster Program), Dark Energy Survey, MASTER, As-troSat Cadmium Zinc Telluride Imager Team, Swift,Pierre Auger, ASKAP, VINROUGE, JAGWAR, Chan-dra Team at McGill University, TTU-NRAO, GROWTH,AGILE Team, MWA, ATCA, AST3, TOROS, Pan-STARRS, NuSTAR, ATLAS Telescopes, BOOTES, Cal-techNRAO, LIGO Scientific, High Time Resolution Uni-verse Survey, Nordic Optical Telescope, Las CumbresObservatory Group, TZAC Consortium, LOFAR, IPN,DLT40, Texas Tech University, HAWC, ANTARES, KU,Dark Energy Camera GW-EM, CALET, Euro VLBITeam, and ALMA Collaborations), “Multi-messengerObservations of a Binary Neutron Star Merger,” As- trophys. J. , L12 (2017), arXiv:1710.05833 [astro-ph.HE].[11] Darach Watson et al., “Identification of strontium inthe merger of two neutron stars,” Nature , 497–500(2019), arXiv:1910.10510 [astro-ph.HE].[12] Shinya Wanajo, Yuichiro Sekiguchi, Nobuya Nishimura,Kenta Kiuchi, Koutarou Kyutoku, and Masaru Shibata,“Production of all the r -process nuclides in the dynamicalejecta of neutron star mergers,” Astrophys. J. , L39(2014), arXiv:1402.7317 [astro-ph.SR].[13] Albino Perego, Stephan Rosswog, Ruben M. Cabez´on,Oleg Korobkin, Roger K¨appeli, Almudena Arcones,and Matthias Liebend¨orfer, “Neutrino-driven winds fromneutron star merger remnants,” Mon. Not. Roy. As-tron. Soc. , 3134–3156 (2014), arXiv:1405.6730 [astro-ph.HE].[14] Rodrigo Fern´andez and Brian D. Metzger, “Delayed out-flows from black hole accretion tori following neutron starbinary coalescence,” Mon. Not. Roy. Astron. Soc. ,502 (2013), arXiv:1304.6720 [astro-ph.HE].[15] Yuichiro Sekiguchi, Kenta Kiuchi, Koutarou Kyutoku,and Masaru Shibata, “Dynamical mass ejection from bi-nary neutron star mergers: Radiation-hydrodynamicsstudy in general relativity,” Phys. Rev. D91 , 064059(2015), arXiv:1502.06660 [astro-ph.HE].[16] David Radice, Filippo Galeazzi, Jonas Lippuner, Luke F.Roberts, Christian D. Ott, and Luciano Rezzolla, “Dy-namical Mass Ejection from Binary Neutron Star Merg-ers,” Mon. Not. Roy. Astron. Soc. , 3255–3271 (2016),arXiv:1601.02426 [astro-ph.HE].[17] Francois Foucart, Evan O’Connor, Luke Roberts,Lawrence E. Kidder, Harald P. Pfeiffer, and Mark A.Scheel, “Impact of an improved neutrino energy esti-mate on outflows in neutron star merger simulations,”Phys. Rev. D , 123016 (2016), arXiv:1607.07450 [astro-ph.HE].[18] Sho Fujibayashi, Kenta Kiuchi, Nobuya Nishimura,Yuichiro Sekiguchi, and Masaru Shibata, “Mass Ejec-tion from the Remnant of a Binary Neutron Star Merger:Viscous-Radiation Hydrodynamics Study,” Astrophys. J. , 64 (2018), arXiv:1711.02093 [astro-ph.HE].[19] Jonah M. Miller, Benjamin R. Ryan, Joshua C. Do-lence, Adam Burrows, Christopher J. Fontes, Christo-pher L. Fryer, Oleg Korobkin, Jonas Lippuner,Matthew R. Mumpower, and Ryan T. Wollaeger,“Full Transport Model of GW170817-Like Disk Producesa Blue Kilonova,” Phys. Rev. D100 , 023008 (2019),arXiv:1905.07477 [astro-ph.HE].[20] Trevor Vincent, Francois Foucart, Matthew D. Duez,Roland Haas, Lawrence E. Kidder, Harald P. Pfeiffer,and Mark A. Scheel, “Unequal Mass Binary NeutronStar Simulations with Neutrino Transport: Ejecta andNeutrino Emission,” Phys. Rev. D , 044053 (2020),arXiv:1908.00655 [gr-qc].[21] S. Wanajo, “The rp-process in neutrino-driven winds,”Astrophys. J. , 1323–1340 (2006), arXiv:astro-ph/0602488.[22] S. Goriely, A. Bauswein, H.-T. Janka, S. Panebianco, J-L.Sida, J-F. Lemaˆıtre, S. Hilaire, and N. Dubray, “The r-process nucleosynthesis during the decompression of neu-tron star crust material,” J. Phys. Conf. Ser. , 012052 (2016).[23] Ricard Ardevol-Pulpillo, H.-Thomas Janka, OliverJust, and Andreas Bauswein, “Improved Leakage-Equilibration-Absorption Scheme (ILEAS) for NeutrinoPhysics in Compact Object Mergers,” Mon. Not. Roy.Astron. Soc. , 4754–4789 (2019), arXiv:1808.00006[astro-ph.HE].[24] Stan E. Woosley, “Gamma-ray bursts from stellar massaccretion disks around black holes,” Astrophys. J. ,273 (1993).[25] Maximillian Ruffert and H.-Thomas Janka, “Gamma-ray bursts from accreting black holes in neutron starmergers,” Astron. Astrophys. , 573–606 (1999),arXiv:astro-ph/9809280 [astro-ph].[26] Ivan Zalamea and Andrei M. Beloborodov, “Neu-trino heating near hyper-accreting black holes,” Mon.Not. Roy. Astron. Soc. , 2302–2308 (2011),arXiv:1003.0710 [astro-ph.HE].[27] Oliver Just, Martin Obergaulinger, H.-Thomas Janka,Andreas Bauswein, and Nicole Schwarz, “Neutron-star merger ejecta as obstacles to neutrino-powered jetsof gamma-ray bursts,” Astrophys. J. , L30 (2016),arXiv:1510.04288 [astro-ph.HE].[28] A. Malkus, J. P. Kneller, G. C. McLaughlin, and R. Sur-man, “Neutrino oscillations above black hole accretiondisks: disks with electron-flavor emission,” Phys. Rev. D86 , 085015 (2012), arXiv:1207.6648 [hep-ph].[29] A. Malkus, A. Friedland, and G. C. McLaughlin,“Matter-Neutrino Resonance Above Merging CompactObjects,” (2014), arXiv:1403.5797 [hep-ph].[30] Meng-Ru Wu, Huaiyu Duan, and Yong-Zhong Qian,“Physics of neutrino flavor transformation throughmatter-neutrino resonances,” Phys. Lett.
B752 , 89–94(2016), arXiv:1509.08975 [hep-ph].[31] Yong-Lin Zhu, Albino Perego, and Gail C. McLaughlin,“Matter Neutrino Resonance Transitions above a Neu-tron Star Merger Remnant,” Phys. Rev.
D94 , 105006(2016), arXiv:1607.04671 [hep-ph].[32] Maik Frensel, Meng-Ru Wu, Cristina Volpe, and AlbinoPerego, “Neutrino Flavor Evolution in Binary NeutronStar Merger Remnants,” Phys. Rev.
D95 , 023011 (2017),arXiv:1607.05938 [astro-ph.HE].[33] Meng-Ru Wu and Irene Tamborra, “Fast neu-trino conversions: Ubiquitous in compact binarymerger remnants,” Phys. Rev.
D95 , 103007 (2017),arXiv:1701.06580 [astro-ph.HE].[34] Meng-Ru Wu, Irene Tamborra, Oliver Just, and H.-Thomas Janka, “Imprints of neutrino-pair flavor con-versions on nucleosynthesis in ejecta from neutron-starmerger remnants,” Phys. Rev.
D96 , 123015 (2017),arXiv:1711.00477 [astro-ph.HE].[35] Raymond F. Sawyer, “Speed-up of neutrino transforma-tions in a supernova environment,” Phys. Rev.
D72 ,045003 (2005), arXiv:hep-ph/0503013 [hep-ph].[36] Raymond F. Sawyer, “Neutrino cloud instabilities justabove the neutrino sphere of a supernova,” Phys.Rev. Lett. , 081101 (2016), arXiv:1509.03323 [astro-ph.HE].[37] Basudeb Dasgupta, Alessandro Mirizzi, and ManibrataSen, “Fast neutrino flavor conversions near the super-nova core with realistic flavor-dependent angular dis-tributions,” JCAP , 019 (2017), arXiv:1609.00528[hep-ph]. [38] Ignacio Izaguirre, Georg G. Raffelt, and Irene Tamborra,“Fast Pairwise Conversion of Supernova Neutrinos: ADispersion-Relation Approach,” Phys. Rev. Lett. ,021101 (2017), arXiv:1610.01612 [hep-ph].[39] Francesco Capozzi, Basudeb Dasgupta, Eligio Lisi, An-tonio Marrone, and Alessandro Mirizzi, “Fast flavor con-versions of supernova neutrinos: Classifying instabilitiesvia dispersion relations,” Phys. Rev.
D96 , 043016 (2017),arXiv:1706.03360 [hep-ph].[40] Sajad Abbar and Huaiyu Duan, “Fast neutrino flavorconversion: roles of dense matter and spectrum cross-ing,” Phys. Rev.
D98 , 043014 (2018), arXiv:1712.07013[hep-ph].[41] Changhao Yi, Lei Ma, Joshua D. Martin, and HuaiyuDuan, “Dispersion relation of the fast neutrino oscillationwave,” Phys. Rev.
D99 , 063005 (2019), arXiv:1901.01546[hep-ph].[42] Francesco Capozzi, Georg G. Raffelt, and TobiasStirner, “Fast Neutrino Flavor Conversion: CollectiveMotion vs. Decoherence,” JCAP , 002 (2019),arXiv:1906.08794 [hep-ph].[43] Madhurima Chakraborty and Sovan Chakraborty,“Three flavor neutrino conversions in supernovae:slow & fast instabilities,” JCAP , 005 (2020),arXiv:1909.10420 [hep-ph].[44] Ricard Ardevol-Pulpillo, “A new scheme to treat neu-trino effects in neutron-star mergers: implementation,tests and applications,” (2018), PhD Thesis, Technis-che Universit¨at M¨unchen.[45] MPA Data Archive, .[46] Andreas Bauswein, Stephane Goriely, and H.-ThomasJanka, “Systematics of dynamical mass ejection, nucle-osynthesis, and radioactively powered electromagneticsignals from neutron-star mergers,” Astrophys. J. ,78 (2013), arXiv:1302.6530 [astro-ph.SR].[47] S. Typel, G. R¨opke, T. Klahn, D. Blaschke, and H. H.Wolter, “Composition and thermodynamics of nuclearmatter with light clusters,” Phys. Rev. C81 , 015803(2010), arXiv:0908.2344 [nucl-th].[48] Matthias Hempel, Tobias Fischer, J¨urgen Schaffner-Bielich, and Matthias Liebend¨orfer, “New Equationsof State in Simulations of Core-Collapse Supernovae,”Astrophys. J. , 70 (2012), arXiv:1108.0848 [astro-ph.HE].[49] Andrew W. Steiner, Matthias Hempel, and Tobias Fis-cher, “Core-collapse supernova equations of state basedon neutron star observations,” Astrophys. J. , 17(2013), arXiv:1207.2184 [astro-ph.SR].[50] H.-Thomas Janka, “When do supernova neutrinos of dif-ferent flavors have similar luminosities but different spec-tra?” Astropart. Phys. , 377–384 (1995), arXiv:astro-ph/9503068.[51] G¨unter Sigl and Georg G. Raffelt, “General kinetic de-scription of relativistic mixed neutrinos,” Nucl.Phys. B406 , 423–451 (1993).[52] Sovan Chakraborty, Rasmus Sloth Hansen, Ignacio Iza-guirre, and Georg G. Raffelt, “Self-induced neutrino fla-vor conversion without flavor mixing,” JCAP , 042(2016), arXiv:1602.00698 [hep-ph].[53] Sagar Airen, Francesco Capozzi, Sovan Chakraborty, Ba-sudeb Dasgupta, Georg G. Raffelt, and Tobias Stirner,“Normal-mode Analysis for Collective Neutrino Oscilla-tions,” JCAP , 019 (2018), arXiv:1809.09137 [hep-ph]. [54] Shashank Shalgar and Irene Tamborra, “Dispelling amyth on dense neutrino media: fast pairwise conversionsdepend on energy,” (2020), arXiv:2007.07926 [astro-ph.HE].[55] Ian Padilla-Gay, Shashank Shalgar, and Irene Tamborra,“Multi-Dimensional Solution of Fast Neutrino Conver-sions in Binary Neutron Star Merger Remnants,” (2020),arXiv:2009.01843 [astro-ph.HE].[56] Shashank Shalgar, Ian Padilla-Gay, and Irene Tamborra,“Neutrino propagation hinders fast pairwise flavor con-versions,” JCAP , 048 (2020), arXiv:1911.09110 [astro-ph.HE].[57] Francesco Capozzi, Basudeb Dasgupta, Alessandro Mi-rizzi, Manibrata Sen, and G¨unter Sigl, “Collisional trig-gering of fast flavor conversions of supernova neutrinos,”Phys. Rev. Lett. , 091101 (2019), arXiv:1808.06618[hep-ph].[58] Meng-Ru Wu, Rodrigo Fern´andez, Gabriel Mart´ınez-Pinedo, and Brian D. Metzger, “Production of the entirerange of r-process nuclides by black hole accretion discoutflows from neutron star mergers,” Mon. Not. Roy.Astron. Soc. , 2323–2334 (2016), arXiv:1607.05290[astro-ph.HE].[59] Meng-Ru Wu, Jennifer Barnes, Gabriel Mart´ınez-Pinedo,and Brian D. Metzger, “Fingerprints of heavy elementnucleosynthesis in the late-time lightcurves of kilonovae,”Phys. Rev. Lett. , 062701 (2019), arXiv:1808.10459[astro-ph.HE].[60] Joel de Jesus Mendoza-Temis, Meng-Ru Wu, GabrielMart´ınez-Pinedo, Karlheinz Langanke, AndreasBauswein, and H.-Thomas Janka, “Nuclear robustnessof the r process in neutron-star mergers,” Phys. Rev. C92 , 055805 (2015), arXiv:1409.6135 [astro-ph.HE].[61] John J. Cowan, B. Pfeiffer, K.L. Kratz, Friedrich K.Thielemann, Christopher Sneden, Scott Burles, DavidTytler, and Timothy C. Beers, “R-process abundancesand chronometers in metal-poor stars,” Astrophys. J. , 194 (1999), arXiv:astro-ph/9808272.[62] Brian D. Metzger and Rodrigo Fern´andez, “Red orblue? A potential kilonova imprint of the delay untilblack hole formation following a neutron star merger,”Mon. Not. Roy. Astron. Soc. , 3444–3453 (2014),arXiv:1402.4803 [astro-ph.HE].[63] Luke Bovard, Dirk Martin, Federico Guercilena, Almu-dena Arcones, Luciano Rezzolla, and Oleg Korobkin,“ r -process nucleosynthesis from matter ejected in binaryneutron star mergers,” Phys. Rev. D , 124005 (2017),arXiv:1709.09630 [gr-qc].[64] Zewei Xiong, Andre Sieverding, Manibrata Sen, andYong-Zhong Qian, “Potential Impact of Fast Fla-vor Oscillations on Neutrino-driven Winds and TheirNucleosynthesis,” Astrophys. J. , 144 (2020),arXiv:2006.11414 [astro-ph.HE].[65] Sajad Abbar, Huaiyu Duan, Kohsuke Sumiyoshi, To-moya Takiwaki, and Maria Cristina Volpe, “Fast Neu-trino Flavor Conversion Modes in MultidimensionalCore-collapse Supernova Models: the Role of the Asym- metric Neutrino Distributions,” Phys. Rev. D ,043016 (2020), arXiv:1911.01983 [astro-ph.HE].[66] Milad Delfan Azari, Shoichi Yamada, Taiki Morinaga,Hiroki Nagakura, Shun Furusawa, Akira Harada, Hiro-tada Okawa, Wakana Iwakami, and Kohsuke Sumiyoshi,“Fast collective neutrino oscillations inside the neutrinosphere in core-collapse supernovae,” Phys. Rev. D ,023018 (2020), arXiv:1910.06176 [astro-ph.HE].[67] Taiki Morinaga, Hiroki Nagakura, Chinami Kato, andShoichi Yamada, “Fast neutrino-flavor conversion in thepreshock region of core-collapse supernovae,” Phys. Rev.Res. , 012046 (2020), arXiv:1909.13131 [astro-ph.HE].[68] Hiroki Nagakura, Taiki Morinaga, Chinami Kato, andShoichi Yamada, “Fast-pairwise Collective Neutrino Os-cillations Associated with Asymmetric Neutrino Emis-sions in Core-collapse Supernovae,” Astrophys. J. ,139 (2019), arXiv:1910.04288 [astro-ph.HE].[69] Robert Glas, H.-Thomas Janka, Francesco Capozzi,Manibrata Sen, Basudeb Dasgupta, Alessandro Mirizzi,and G¨unter Sigl, “Fast Neutrino Flavor Instability inthe Neutron-star Convection Layer of Three-dimensionalSupernova Models,” Phys. Rev. D , 063001 (2020),arXiv:1912.00274 [astro-ph.HE].[70] Lucas Johns, Hiroki Nagakura, George M. Fuller, andAdam Burrows, “Neutrino oscillations in supernovae: an-gular moments and fast instabilities,” Phys. Rev. D ,043009 (2020), arXiv:1910.05682 [hep-ph].[71] Sajad Abbar, “Searching for Fast Neutrino Flavor Con-version Modes in Core-collapse Supernova Simulations,”JCAP , 027 (2020), arXiv:2003.00969 [astro-ph.HE].[72] Sajad Abbar, “Turbulence Fingerprint on Collec-tive Oscillations of Supernova Neutrinos,” (2020),arXiv:2007.13655 [astro-ph.HE].[73] Sajad Abbar and Maria Cristina Volpe, “On Fast Neu-trino Flavor Conversion Modes in the Nonlinear Regime,”Phys. Lett. B790 , 545–550 (2019), arXiv:1811.04215[astro-ph.HE].[74] Joshua D. Martin, Changhao Yi, and HuaiyuDuan, “Dynamic fast flavor oscillation waves in denseneutrino gases,” Phys. Lett.
B800 , 135088 (2020),arXiv:1909.05225 [hep-ph].[75] Soumya Bhattacharyya and Basudeb Dasgupta, “Late-time behavior of fast neutrino oscillations,” Phys. Rev.D , 063018 (2020), arXiv:2005.00459 [hep-ph].[76] Francesco Capozzi, Madhurima Chakraborty, SovanChakraborty, and Manibrata Sen, “Fast flavor con-versions in supernovae: the rise of mu-tau neutrinos,”(2020), arXiv:2005.14204 [hep-ph].[77] Else Pllumbi, Irene Tamborra, Shinya Wanajo, H.-Thomas Janka, and Lorenz H¨udepohl, “Impact of neu-trino flavor oscillations on the neutrino-driven wind nu-cleosynthesis of an electron-capture supernova,” Astro-phys. J. , 188 (2015), arXiv:1406.2596 [astro-ph.SR].[78] Charles J. Horowitz and Gang Li, “Charge conjuga-tion violating interactions in supernovae and nucleosyn-thesis,” Phys. Rev. Lett.82