The Influence of Neutrinos on r-Process Nucleosynthesis in the Ejecta of Black Hole-Neutron Star Mergers

2.8 MB·

by  Luke F. Roberts

MNRAS000,000–000(0000) Preprint1February2016 CompiledusingMNRASLATEXstylefilev3.0
The Influence of Neutrinos on r-Process Nucleosynthesis in
the Ejecta of Black Hole–Neutron Star Mergers
Luke F. Roberts1 (cid:63), Jonas Lippuner1, Matthew D. Duez2, Joshua A. Faber3,
†
Francois Foucart4 , James C. Lombardi Jr.5, Sandra Ning1, Christian D. Ott1,
†
and Marcelo Ponce6,7
1 TAPIR, Walter Burke Institute for Theoretical Physics, MC 350-17, California Institute of Technology, Pasadena, California 91125, USA
6 2 Department of Physics & Astronomy, Washington State University, Pullman, Washington 99164, USA
1 3 Center for Computational Relativity and Gravitation and School of Mathematical Sciences, Rochester Institute of Technology, Rochester,
0 New York 14623, USA
2 4 Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, California 94720, USA
5 Department of Physics, Allegheny College, Meadville, Pennsylvania 16335, USA
n 6 Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
a 7 SciNet HPC Consortium, University of Toronto, Toronto, Ontario M5T 1W5, Canada
J
† NASA Einstein Fellow

8
2

]
E 1February2016
H
.
h ABSTRACT
p During the merger of a black hole and a neutron star, baryonic mass can become
- unboundfromthesystem.Becausetheejectedmaterialisextremelyneutron-rich,the
o
r-processrapidlysynthesizesheavynuclidesasthematerialexpandsandcools.Inthis
r
t work, we map general relativistic models of black hole–neutron star (BHNS) mergers
s
intoaNewtoniansmoothedparticlehydrodynamics(SPH)codeandfollowtheevolu-
a
[ tion of the thermodynamics and morphology of the ejecta until the outflows become
homologous. We investigate how the subsequent evolution depends on our mapping
1
procedure and find that the results are robust. Using thermodynamic histories from
v
the SPH particles, we then calculate the expected nucleosynthesis in these outflows
2
while varying the level of neutrino irradiation coming from the postmerger accretion
4
disk. We find that the ejected material robustly produces r-process nucleosynthesis
9
7 even for unrealistically high neutrino luminosities, due to the rapid velocities of the
0 outflow. Nonetheless, we find that neutrinos can have an impact on the detailed pat-
. tern of the r-process nucleosynthesis. Electron neutrinos are captured by neutrons to
1
produce protons while neutron capture is occurring. The produced protons rapidly
0
form low mass seed nuclei for the r-process. These low mass seeds are eventually in-
6
1 corporated into the first r-process peak at A 78, producing mainly Ge and Se. We
∼
: consider the mechanism of this process in detail and discuss if it can impact galactic
v
chemical evolution of the first peak r-process nuclei.
i
X
Key words: nuclearreactions,nucleosynthesis,abundances–neutrinos–stars:neu-
r tron – stars: black holes – hydrodynamics
a
1 INTRODUCTION may provide a significant fraction of the r-process material
found in our galaxy (Lattimer & Schramm 1976; Bauswein
Blackhole–neutronstar(BHNS)binarymergersarealikely
et al. 2014b). Within the next few years, it is likely that
candidate for Advanced LIGO and Advanced VIRGO de-
Advanced LIGO will detect gravitational waves from these
tections of gravitational waves (Aasi et al. 2015; Acernese
systems and constrain the BHNS merger rate. If electro-
et al. 2015), they may be responsible for short gamma ray
magnetic counterparts are detected, the merger-sGRB con-
bursts (sGRBs) (e.g. Lee & Ramirez-Ruiz 2007), and they
nection may be confirmed and production of the r-process
nuclei may be observed in situ (Metzger & Berger 2012).
(cid:63) email:[email protected] Theoriginofther-processnucleihasbeenalongstand-
(cid:13)c 0000TheAuthors
2 L. F. Roberts et al.
ing question in nuclear astrophysics (Burbidge et al. 1957). parameters, especially the black hole (BH) spin and mass
Core-collapse supernovae are appealing as a possible site (Foucartetal.2013;Hotokezakaetal.2013;Bausweinetal.
because of galactic chemical evolution considerations (e.g. 2014a; Kyutoku et al. 2015). More mass is ejected as the
Qian 2000; Argast et al. 2004), but there is significant dif- BH spin increases in the direction of the orbital angular
ficulty finding the requisite conditions for r-process nucle- momentum (Foucart et al. 2014). Increasing the spin de-
osynthesisinthisenvironment(e.g.Robertsetal.2010;Fis- creases the radius of the innermost stable orbit and de-
cher et al. 2010; Hu¨depohl et al. 2010). Conversely, it is creases gravitational binding at the radius at which the NS
relatively easy to find conditions neutron-rich enough for is tidally disrupted. Increasing the BH mass reduces the
r-process nucleosynthesis in the material ejected from bi- amountofmaterialremainingoutsideoftheBHaftermerger
nary neutron star (NS) and BHNS mergers (Freiburghaus (for fixed NS properties), since the tidal radius scales as
et al. 1999). Due to the long delay time from binary forma- (M /M )1/3R while the innermost stable orbit of the
BH NS NS
tiontomergerandthelargeamountofmaterialejectedper BH scales as M for fixed BH spin. The fraction of the
BH
mergerevent,itischallengingtogetsimplemodelsofgalac- mass outside the horizon which is unbound, however, also
ticchemicalevolution,whichinvokecompactobjectmergers increaseswiththeBHmass,makingtherelationbetweenBH
forr-processproductiontoagreewiththeobserveddistribu- mass and unbound mass nontrivial (Kyutoku et al. 2015).
tionofr-processelementsinlowmetallicityhalostars(Qian Becausethemassandspindistributionsofstellarmass
2000;Argastetal.2004).Nevertheless,recentworkstaking BHsandtheexpectednumberofBHNSsysteminourgalaxy
into account more complex models of galaxy formation get are not well known (e.g. The LIGO Scientific Collabora-
reasonable agreement with the observed distribution of r- tion 2010), it is difficult to estimate the contribution of
process elements (Matteucci et al. 2014; Shen et al. 2015; these events to the r-process material found in the galaxy
van de Voort et al. 2015; Ishimaru et al. 2015) and it is (Bauswein et al. 2014a). Nonetheless, it is timely to inves-
possible to get r-process enrichment at very low metallicity tigate the detailed composition of the ejecta because the
when different channels of binary formation are considered merger rate is likely to soon be constrained by Advanced
(Ramirez-Ruiz et al. 2015). Therefore, it is plausible that LIGO (The LIGO Scientific Collaboration 2015). Addition-
compact object mergers could be the source of the galactic ally,therearesomehintsthattheinfraredexcessassociated
r-process nuclei. withGRB130603B(Tanviretal.2013;Bergeretal.2013)is
Recently,ithasbeenrecognizedthatweakinteractions consistentwiththateventbeingpoweredbytheradioactive
can significantly affect the final composition of binary NS decayofr-processproductsintheejectaofaBHNSmerger
outflows (Wanajo et al. 2014; Goriely et al. 2015; Sekiguchi (Hotokezakaetal.2013).Asimilarexcesshasrecentlybeen
et al. 2015; Foucart et al. 2015a; Palenzuela et al. 2015; observed in the afterglow of GRB060614 (Yang et al. 2015;
Radice et al. 2016). Likewise, the final state and remnant Jin et al. 2015).
product of binary NS mergers has been shown to depend In this work, we investigate the long term hydrody-
onseveralpropertiesofthesystem,e.g.importantrolesare namics of the BHNS ejecta and the nucleosynthesis that
playedbythemicrophysicalnuclearequationofstate(EOS), occurs therein. For the first time, we focus on how neutri-
electromagnetic fields and neutrino effects (Neilsen et al. nos might affect the detailed nucleosynthesis patterns that
2014;Palenzuelaetal.2015).IncontrasttobinaryNSmerg- are produced. Even for unrealistically large neutrino lumi-
ers,thematerialejectedduringBHNSmergersisunlikelyto nosities, we find that the distribution of the pre-neutron
undergo significant numbers of weak interactions. Electron captureelectronfractionisnotsignificantlyalteredandthe
and positron captures are supressed relative to the rates in second and third r-process peaks are robustly produced in
theshockheatedejectaofbinaryNSmergersduetothelow almostallofthematerial.Thisisincontrasttothedynami-
entropypresentinthetidalejecta.Thehighoutflowspeeds calejectaofbinaryNSmergers,whereweakprocessingmay
andlowneutrinoluminositiesencounteredintheseevents— preventanr-processfromoccurringinasignificantamount
comparedtobinaryNSmergers—alsomakeitunlikelythat ofthematerial(Wanajoetal.2014;Gorielyetal.2015).Of
neutrino interactions will drastically change the number of course, the BHNS result is expected because the outflows
neutrons present at the onset of r-process nucleosynthesis happen relatively early before the remnant disk can start
(Foucartetal.2014;Foucartetal.2015b).Therefore,BHNS toemitneutrinos,thereisnohypermassiveNScontributing
mergershavebeenlongthoughttobelikelysitesforproduc- to the neutrino flux, and the tidal ejecta possesses a very
tionofheavyr-processnucleosynthesis(Lattimeretal.1977; high velocity. More interestingly, we find that electron neu-
Lattimer&Schramm1976),althoughcalculationswhichdo trinocapturesbyneutronscanprovideseednucleiforalow
not include the effect of neutrinos show that only the sec- mass r-process that produces material in the first r-process
ondandthirdr-processpeaksareproduced(Bausweinetal. peakatA∼78.Nonetheless,inourmodels,theratioofthe
2014a). first peak to the second peak is sub-solar with and without
UnderstandinghowBHNSmergerscontributetogalac- the inclusion of neutrino captures. When comparing to the
ticchemicalevolutionrequiresknowledgeofthemergerrate, yields of low metallicity halo stars with sub-solar Ge abun-
predictions for the amount of mass ejected per merger, the dances (Roederer et al. 2014), we find that this first peak
kinetic energy of the ejecta, and predictions of nuclei syn- production can bring our models closer to agreement with
thesized in these outflows. Although there are no observed the observed abundances of Ge, As, and Se, although the
BHNSbinaries,theoreticalpredictionssuggestthattherate abundances are still somewhat low.
of BHNS binary mergers could be up to a tenth of the rate This paper is organized as follows: in Section 2, we
of double neutron star binary mergers (Abadie et al. 2010; present the BHNS systems we have simulated, explain how
Bauswein et al. 2014a). The amount of mass ejected dur- the ejected material is mapped into our smoothed particle
ing BHNS mergers can depend sensitively on the binary hydrodynamics (SPH) code, and describe our nuclear re-
MNRAS000,000–000(0000)
Neutrinos and BHNS r-Process Nucleosynthesis 3
action network. Then, in Section 3.1, we discuss the effect For this study, we use the ejecta from three systems.
of weak interactions on the electron fraction distribution in The first, called “M12-7-S9”, with parameters M =
NS
the ejecta. In Section 3.2, we present the integrated nucle- 1.2M , M = 7M , χ = 0.9, produces a very large
(cid:12) BH (cid:12) BH
osynthesis from our models and discuss neutrino induced ejecta mass of 0.16M . The second, “M14-7-S8”, with
(cid:12)
production of the first r-process peak. In Section 3.4, we M = 1.4M , M = 7M , χ = 0.8, has ejecta mass
NS (cid:12) BH (cid:12) BH
discuss uncertainties in the results from our nucleosynthe- 0.06M ,oneofourlowerejectamasscases.Thethirdcase,
(cid:12)
sis calculations and their possible implications for galactic “M14-5-S9”,hasparametersM =1.4M ,M =5.6M ,
NS (cid:12) BH (cid:12)
chemical evolution and for abundance observations in low χ =0.9 and ejects a mass of 0.084M .
BH (cid:12)
metallicity halo stars.
2.2 SPH evolution of ejecta
After ∼5ms, the ejecta has detached from the merger rem-
2 METHODS nantandismovingforthemostpartballistically.However,
the outflow is not yet homologous. Also, it is possible that
2.1 Relativistic Merger Simulations and Binary
pressure forces will subsequently become important again
Systems
because of recombination heating or collision of streams of
The BHNS merger simulations used in this work have been matter (although this turns out not to be the case). There-
described in detail in our previous papers (Deaton et al. fore, we continue the hydrodynamic evolution of the out-
2013;Foucartetal.2014).Herewereviewthemajorfeatures flowusinganSPHcode,StarSmasher (Gaburovetal.2010;
anderrorestimatesofthemergersimulations,referringread- Ponce et al. 2012). The SPH code is Newtonian, but since
erstoFoucartetal.(2014)fordetails.Thefullyrelativistic theflowisonlymildlyrelativistic(v/c≈0.2),andfromthe
Einstein-hydrodynamics system is evolved with the Spec- beginning somewhat far from the black hole (> 10M ),
BH
tral Einstein Code (SpEC) (SXS Collaboration 2000). Neu- this is probably adequate for our purposes. (See check on
trinocoolingandleptonnumberevolutionareincorporated this below.)
through a neutrino leakage scheme (Deaton et al. 2013). The StarSmasher code is the successor to the earlier
To model the NS, we employ the Lattimer-Swesty StarCrash code (Lombardi et al. 2006). It represents flu-
EOS (Lattimer & Swesty 1991) with an incompressibility ids in the standard SPH way, using a finite number of fluid
K = 220MeV and a symmetry energy S = 29.3MeV elements or “particles.” In its current implementation, the
0 ν
(hereafterLS220),usingthetableavailableathttp://www. particles may have different masses (Gaburov et al. 2010),
stellarcollapse.org and described in O’Connor & Ott which simplifies the construction of initial data from finite
(2010). This EOS yields a neutron star radius that lies volumerepresentations.StarSmasher usesvariablesmooth-
withintheallowedrangeofradii,asdeterminedbyHebeler ing lengths to maximize resolution, using a formalism de-
et al. (2013) from nuclear theory constraints and the exis- rived consistently from a particle-based Lagrangian to en-
tenceofneutronstarsofmass∼2M (Demorestetal.2010; sure proper energy and entropy evolution (Lombardi et al.
(cid:12)
Antoniadis et al. 2013). For LS220, a 1.2 (1.4)M neutron 2006; Springel & Hernquist 2002; Monaghan 2002).
(cid:12)
star has a radius R of 12.8 (12.7)km and a compactness Stable shock evolution is achieved using artificial vis-
NS
C =GM /(R c2) of 0.139 (0.163). cosity with a Balsara switch (Balsara 1995) to suppress ar-
NS NS
During the SpEC simulations, the dynamical ejecta is tificial viscosity in shear layers; fortunately, accurate shock
tracked for only about 5ms before it exits the computa- evolution is not important for our application. Self-gravity
tional grid. However, during this time, the specific energy forces are neglected, so the gravitational force is simply a
(u ) of fluid elements becomes nearly constant, so it is of- functionofpositiongivenbytheblackholepotentialandit
t
ten possible to confidently identify unbound material. Con- is implemented in the Newtonian and Paczyn´ski-Wiita ap-
vergenceofourSpECsimulationswasobservedtobefaster proximations (Ponce et al. 2012; Paczynski & Wiita 1980).
thansecond-order.Assumingsecondorderconvergencegives Inordertoavoidsmalltimestepsduetorapidmotion,par-
aconservativerelativeerrorofupto60%inthemassandki- ticles are removed if they come too close to the BH. These
neticenergyofejectedmaterial.Evenifthetrueerrorwere particles would eventually fall into the BH anyway, so this
thislarge,whichisunlikely,itwouldnotaffecttheresultsof procedure does not affect the ejecta properties.
thepresentinvestigation.Aswewillsee,variationsofejecta As initial data to the SPH simulation, hydrodynamic
properties between different binary systems, which are of datafromasnapshotoftheSpECmergersimulation(taken
similarmagnitude,havenegligibleeffectonthefinalnuclear aftertidaldisruptionbutbeforethetidaltailhitstheouter
abundances. boundary) are output on a uniform Cartesian mesh. StarS-
In the simulations of Deaton et al. (2013) and Foucart masher reads these data, reflects them to add the lower
etal.(2014),weconsideredBHNSbinarysystemswithmul- hemisphere not evolved by SpEC, interpolates to an hexag-
tiple masses and spins. The BH mass M was taken to be onalclose-packedlattice,andassignsaparticleofappropri-
BH
5.6M ,7M ,or10M ,coveringmostoftheestimatedmass ate density to each nonvacuum lattice point. The evolution
(cid:12) (cid:12) (cid:12)
distribution for stellar mass black holes (O¨zel et al. 2010; isthencontinuedinStarSmasher usingtheLS220EOSwith
Farr et al. 2011). The neutron star gravitational mass M no neutrino effects. The electron fraction Y of each parti-
NS e
was taken to be 1.2M or 1.4M , which is typical for NSs cle is constant during the SPH evolution, and no neutrino
(cid:12) (cid:12)
(Kiziltan et al. 2013). For these masses, ejecta is produced cooling or absorption is considered. If a particle falls below
only for at least moderately high BH spins, meaning that the LS220 density or temperature table range, the entropy
for most cases the Kerr spin parameter must be χ >0.7 S ishenceforthsettobeconstant,andaS ∝ρT3,P ∝ρ4/3
BH
(Foucart 2012). extrapolation of the EOS is used. This only happens when
MNRAS000,000–000(0000)
4 L. F. Roberts et al.
pressure is negligible, and the entropy evolution in StarS- 10 1
−
masher is not used in our post-processing nucleosynthesis t=0
calculations (see below). t= 1.6ms
−
Although relativistic effects are not expected to be 10−2 t=500ms,P1,Res1
important, the translation from relativistic to Newtonian t=500ms,P1,Res2
physicsmustaccountfortwosubtleties.First,thelate-time M](cid:12) t=500ms,P2,Res1
behaviorofanejectafluidelementismostsensitivetoitsen- [ 10−3 t=500ms,P2,Res2
ergy,especiallywhetheritisboundorunbound,soitisim- Mbin t=500ms,P1,from−1.6ms
portant that this be appropriately translated. We therefore
rescale the velocity vector so that the specific kinetic plus 10−4
potential energy of each particle in the Newtonian frame-
work is equal to its relativistic specific energy −u −1 in
t
theSpECsimulation.Second,thereisnoaprioriguarantee 10−5
0.0 0.1 0.2 0.3 0.4
thatthecoordinatesysteminwhichthenumericalrelativity
E [M c2]
simulation evolves will be close to any known coordinates.
(cid:12)
Fortunately, SpEC’s “damped harmonic” coordinates lead
the spacetime to settle nearly in harmonic coordinates, so
Figure 1. The distribution of specific kinetic plus potential en-
we transform in StarSmasher to Schwarzschild coordinates
ergyintheunboundpost-mergermatter,shownforsystemM12-
(ignoring the BH’s spin, whose effects will not be impor-
7-S9 at a time shortly after the disruption of the NS (t = 0)
tantfarfromthehole),withasimpleradialtransformation
and500mslater,longafterthedistributionhassettled.Foreach
r → r +M . In the region of interest, the numerically
BH energy bin, we integrate the density of all particles with energy
evolved spacetime is nearly Minkowski, and the deviation insidethatbin,givingaNewtonianmassforeachenergybin.We
from Minkowski is mostly Schwarzschild and so can be ad- show2resolutions,“Res1”and“Res2”,correspondingtoaround
equately modeled by a Paczyn´ski-Wiita potential. Lastly, 79,000 and 175,000 particles, respectively. We evolve using two
onemustdistinguishbetweentherestframebaryondensity methods: “P1” turns off pressure forces and imposes adiabatic
used in the EOS and the mass integrand density used to internalenergyevolutionwithinaradiusofabout100MBH.“P2”
assignthemassoftheSPHparticle,whichistherestframe includespressureforceseverywherebutremovesboundparticles
after10ms.AnotherSPHrunbegun1.6msearlierinthemerger
baryon density times a Lorentz factor and a metric deter-
has nearly stationary energy distribution if evolved with P1. A
minantfactor.BecauseSPHparticlemassisaconstant,the
simulation using P2 with a Paczyn´ski-Wiita potential gives re-
mass integrand density only needs to be calculated and in-
sults almost identical to P2 with the standard Newtonian point
tegrated over at the initial time.
potential.
A straightforward evolution of the fluid equations pro-
duces a generally realistic evolution but with some clearly
unphysicalartifacts.Namely,matterontheupperandlower ter for the most part orbits the black hole in an accretion
surfacesoftheejectedtidaltailblowawayfromtheequator, disk or is “eaten” when it comes within the prescribed dis-
somethingunexpectedgiventheoverallweaknessofpressure tance from the central point mass. Both because of the ex-
forces and not indicated in the SpEC evolution. This verti- clusion of full relativity and the lack of a transport process
calexpansionhasnoinfluenceontheenergydistributionor todriveaccretion,thediskevolutioncannotberegardedas
nucleosynthesis results, but it does affect the shape of the believable. We find that, for P2 evolutions, if we allow the
outflow. Convergence tests show that it is not a transient disk to evolve for long periods of time, some fraction of the
causedbyaninsufficientnumberofparticles,soitislikelyan mass becomes weakly unbound. This is not perhaps incor-
artifactofthetransitiontoNewtonianphysics.Itcanbere- rect given the physics included, but it cannot be regarded
movedbyreducingpressureforcesneartheblackhole.Inour as physical, so we remove this contamination by eliminat-
simulationslabeled“P1”,weturnoffpressureforceswithin ing bound particles after 10ms of SPH evolution. For P1
10M of the black hole, while within 100M , pressure is evolutions, this removal is not necessary.
BH BH
reduced by a factor varying linearly with distance between Our standard evolutions use roughly 75,000 particles.
zero (at 10M ) and one (at 100M ). Within this range, ThemassprofileoftheejectaM12-7-S9isshowninFigure2.
BH BH
the specific entropy is held constant, because otherwise the Figure 3 shows snapshots of the SPH particles and fluid
pressure reduction would keep the fluid from adiabatically density after ≈0.5 s of starting the SPH evolution.
cooling. Simulations labeled “P2” have full pressure forces
everywhere.
2.3 Nuclear reaction network and weak
Wecheckthatourevolvedresultsareinsensitivetothe
interactions
timeatwhichwetransitionfromSpEC/relativistictoStarS-
masher/Newtonian physics by starting from two different To calculate the composition of a Lagrangian fluid element
snapshots1.6msapartandfindingnegligiblevariationinthe in the ejecta, we require the evolution of its density as a
evolved energy histograms, which are shown inFigure 1. In function of time as well as its initial composition and en-
fact, even the initial energy histograms are not very differ- tropy. To allow evolution at very late times, we extrapolate
ent,soafterthefirst≈2mstheinfluenceofpressureonthe the density histories of the particles taken from the SPH
kinematicsoftheejectaisnegligible.Thecodes’mainfunc- simulation assuming homology, ρ ∝ t−3. In addition to the
tion is to provide the density evolution as particles follow density, we extract the entropy and electron fraction along
their ballistic trajectories. these trajectories. The extracted electron fraction is con-
Ourinterestisonlyinunboundmatter.Theboundmat- stant due to the neglect of weak reactions during the SPH
MNRAS000,000–000(0000)
Neutrinos and BHNS r-Process Nucleosynthesis 5
clear statistical equilibrium (NSE) composition—with the
P1,radial
modified Helmholtz EOS described in Lippuner & Roberts
0.15 P1,vertical
(2015)—wefindtemperaturedifferenceslessthanafewper-
P2,radial
centbetweenthetwoEOSintheregionwheretheyoverlap.
](cid:12) P2,vertical Once the density evolution of the Lagrangian particles
M
[ 0.10 has been extracted and extrapolated, we evolve the com-
nterior RReess12 pcoodsietiSoknyoNfetth(eLpipaprtuincleers&usiRnogbtehretsn2u0c1le5a)r. Trehaectniounclneaertwnoertk-
Mi
0.05 work employed includes 7843 different isotopes extending
fromneutronto337Cn.Weemployboththeforwardreaction
112
rates and the nuclear data tabulated in REACLIB (Cyburt
et al. 2010). Inverse reaction rates are calculated assuming
0.00
102 103 104 105 detailed balance. In addition to the REACLIB reactions,
neutron induced fission rates from Panov et al. (2010) and
r or z [km]
cyl
spontaneousfissionratescalculatedfromtheapproximation
ofFrankel&Metropolis(1947)usingthespontaneousfission
barriers of Mamdouh et al. (2001) are included. Symmetric
Figure2.Themass(computedbydensityintegral)interiortoa
givencylindricalradiusr orverticalheight|z|forbinaryejecta fission fragments are assumed.
cyl
M12-7-S9. Profiles are computed at a time 500 ms after merger, The entropy generated via nuclear transmutations is
by which point the ejecta profile has settled and will thereafter self-consistently included in the evolution, similarly to
spread nearly homologously. The vertical interior mass appears Freiburghaus et al. (1999). At 3 ms after merger—the
to asymptote to a nonzero value on the left, indicating that a time at which the SpEC simulations are mapped to StarS-
significantnumberofparticlesremainneartheequator.Weshow masher—the particles are typically at temperatures over
results for two resolutions with two ways of handling pressure
10GK.Atthesetemperatures,NSEholds,butweakinterac-
forces.Simulationswithpressureforcescompletelyturnedoffgive
tionsaregenerallyfarfromequilibrium.Tofollowchangesin
profilesnearlythesameasP1profiles.
the electron fraction at high temperature, SkyNet includes
an NSE evolution mode where strong interactions are as-
sumed to be in equilibrium and only weak interactions are
55××110044 5×104 tracked. This mode is used until the temperature drops be-
10
low 7 GK, at which point the full nuclear reaction network
] is evolved. Because inverse strong reactions are calculated
m
y [km]y [k 00 y [km] 0 8 veviaolduettioanilemdobdaelsanisces,mthooetthr.ansitionbetweenthetwoSkyNet
To track the potential importance of neutrino irradi-
--55××110044 -5×104
ation of the ejecta, electron neutrino capture, electron an-
6
tineutrino capture, electron capture, and positron capture
5×5×110044 -5×104 x [km0] 55××110044 -5×104 x [km0] 5×104 sity 3]10 bnyeuftrreienonuccalpetounrsearraeteinscaluredegdiviennbboyth evolution modes. The
nm
z [km]z [km] 00 z [km] 0 log-de[g/c8 λν = G(cid:90)2F2(∞π12+¯h73cg6A2)
6 × d(cid:15)epe(cid:15)e((cid:15)e−Q)2f¯ν((cid:15)e−Q)(1−fe((cid:15)e)), (1)
-5×-51×10044 -5×104 Q˜
-5-5××110044 xx [[kmk00]m] 55××110404 --55××110044 xx [k[mk00]m] 55××110044 where fe is the electron distribution function, GF is the
Fermi coupling constant, g is the weak axial vector cou-
A
pling constant, (cid:15) is the electron energy, p is the electron
e e
Figure3.Outflow’sprofileatarepresentativesnapshotfromthe momentum, Q is the energy transfer from the nucleons to
SPH evolution of M12-7-S9. Upper/bottom-left panels: xy/xz- thefinalstateelectron,andf¯ν istheangle-averagedneutrino
projection of SPH-particles; upper/bottom-right panels: density distribution function. The Q-value is defined in the direc-
(inlog-scale[gcm−3])viewsinthexy/xz-planesrespectively. tionofelectronorpositroncaptureandQ˜ =max(Q,m c2).
e
The electron and positron capture rates, λ and λ , are
e+ e−
calculated from similar expressions with the distribution
evolution. The LS220 EOS is only valid for baryon densi- functions interchanged. This expression assumes there is
tiesandtemperaturesaboveρ=108g cm−3 andT ≈1GK, no momentum transfer to the nucleons and neglects weak
whichdoesnotincludetheentireregioninthetemperature magnetism corrections. Although these corrections are po-
density plane in which neutron capture occurs. Since cor- tentially significant in the case of neutrino driven winds
rectionstotheEOSduetonuclearinteractionbecomeneg- (Horowitz2002),theyareunlikelytosignificantlyaffectthe
ligible below ρ∼1012g cm−3, we switch from LS220 to a evolution of the electron fraction in BHNS merger ejecta.
multi-species non-degenerate ideal gas EOS consistent with The α-effect locks free protons in heavy nuclei and thereby
the nuclei included in our network along with the electron prevents significant competition from electron antineutrino
EOSofTimmes&Arnett(1999)forournetworkevolutions. capture (Fuller & Meyer 1995). We assume that the neu-
Whenkeepingtheentropyfixedandassuminganinitialnu- trino distribution has a Fermi-Dirac shape in energy space
MNRAS000,000–000(0000)
6 L. F. Roberts et al.
andneutrinosofallenergiesareemittedfromasinglespher- 0.08
ical surface, which results in the distribution function
Full NSL
fν((cid:15),µ,r)= eθx(pµ((cid:15)−/Tµν0)(r+))1, (2) 0.07 Lνe,52 =0νe
L =0.2
where µ is the cosine of the angle of neutrino propagation 0.06 νe,52
relative to the radial direction, µ0 =(cid:112)1−(rν/r)2, Tν de- Lνe,52 =1
fines the neutrino spectral temperature, θ is the Heaviside 0.05 Lνe,52 =5
step function, (cid:15) is the neutrino energy, and rν is the radius ]⊙ Lνe,52=25
ofneutrinoemission.Insideofrν,µ0isassumedtosmoothly M
approachnegativeoneoveratenthofr .Thevalueofr can [0.04
ν ν s
befixedbychoosinganeutrinoluminosity,Lν,andspectral as
M
temperature. This model is crude, considering the disk like 0.03
geometryoftheneutrinoemittingregion,butitissufficient
for this study given that we are parameterizing the proper-
0.02
tiesoftheneutrinofieldanyway.Inthefollowingsections,we
considermodelswithfixedelectronneutrinoluminositiesof
Lνe ={0,0.2,1,5,25}×1052erg s−1. The electron antineu- 0.01
trino luminosity is always fixed to be L = 1.5L , but
ν¯e νe
our results are insensitive to this choice due to the α-effect.
0
These values are in the range found in the simulations of 0.05 0.10 0.15 0.20 0.25
Foucartetal.(2015a)andthedifferencebetweenthevalues
Y
e
accountsforre-leptonizationofthedisk.Sinceonlycharged
currentinteractionsareincludedinthenuclearnetwork,the
propertiesoftheheavyflavoredneutrinofieldsdonotaffect
Figure 4. Mass weighted histogram of the electron fraction in
our results. We employ constant luminosities to reduce the
theejectafrommodelM12-7-S9assumingfixedelectronneutrino
numberofparametersaffectingournucleosynthesiscalcula- luminositiesof{0,0.2,1,5,25}×1052 ergs−1.Forcomparison,we
tions. alsoshowtheelectronfractionhistogramina1.2M(cid:12)LSneutron
Whereavailable,beta-decayandelectroncapturerates star(cyanline).
from Fuller et al. (1982) and Langanke & Mart´ınez-Pinedo
(2000) are used. For nuclei for which these rates are not
atuvareilaabrelea,ptphreoxeffimecattseloyfienlcelcutdroendbbyloacsksiunmgianngdthpaotsitthroenenctaipre- 110001 λλνe λλe+ Ye 0.5
beta-decaystrengthisprovidedbyagroundstatetoground ν¯e e− 0.4
state transition as described in Arcones et al. (2010). The 10−1
mvaacturuixmeilsemeqeunatlitsocthhoesRenEAsuCcLhIBthbatettah-deebcaetyar-adteec.aTyhriastperoin- 1s]− 10−2 0.3 Ye
cedureassumesamaximalQ-valueandthereforeprovidesa λ[ 10−3 0.2
lowerlimitontheimportanceofmediumdependenteffects. 10 4
−
We perform nucleosynthesis postprocessing for all of 0.1
10 5
the ejected SPH trajectories. The network integration be- −
gins at three milliseconds after merger. The initial condi- 10−6 10 2 10 1 1000.0
tions are specified by the density and electron fraction at − −
Time [s]
whichthistemperatureisreachedandbyNSE.Thenuclear
abundancesarethenevolvedintimealongwiththeentropy
of the fluid element, which is self-consistently evolved due Figure 5. Evolution of the electron fraction and weak rates as
to nuclear transmutation. The nuclear evolution is followed afunctionoftimeforacharacteristicfluidelement.Theelectron
until 1013 s after the merger, which allows for the decay of neutrino luminosity is assumed to be 1053ergs−1. Because of
all but a handful of long lived unstable isotopes. therelativelylowentropyoftheBHNSejectaandbecauseofthe
low initial density of our calculations, neutrino interaction rates
dominatetheelectronandpositroncaptureratesbutneitherhave
alargeimpactontheelectronfractionoftheoutflow.Theincrease
3 RESULTS AND DISCUSSION
in Ye seen after around 100 ms is due to beta-decay during the
3.1 The Electron Fraction of the Ejecta r-process.
The electron fraction of the material ejected during the
BHNS merger is the most important parameter in deter- of the NS from which the material was ejected (Just et al.
mining the nucleosynthesis that occurs within the outflow 2015). If there are not a substantial number of weak inter-
(e.g., Lippuner & Roberts 2015). Given the short dynam- actions during and after the merger, the electron fraction
ical timescales and the lack of a hypermassive central NS will be low enough that an r-process involving a significant
after the merger, it has often been assumed that the elec- number of fission cycles will occur: the outer layers of a NS
tron fraction of the dynamical ejecta from BHNS mergers have Y <0.1 and the critical value for producing r-process
e
issetsolelybytheinitialbeta-equilibriumelectronfraction materialatlowentropyisY ≈0.25(e.g.Kasenetal.2015;
e
MNRAS000,000–000(0000)
Neutrinos and BHNS r-Process Nucleosynthesis 7
Lippuner & Roberts 2015). Neutrinos can impact the elec- large radius to find the final electron fraction
tron fraction of the ejecta of binary NS mergers (Wanajo
et al. 2014; Goriely et al. 2015; Foucart et al. 2015a; Palen-
zuelaetal.2015;Radiceetal.2016).InbinaryNSmergers, (cid:20) (cid:18) (cid:19)(cid:21)
r
a large fraction of the prompt ejecta comes from the shock Ye,f ≈Ye,eq 1−exp −vτ (r0)Y
ν 0 e,eq
heated material in the interaction region of the two NSs
(cid:18) (cid:19)
r
(Palenzuelaetal.2015).Theincreasedtemperaturesandthe +Y exp − 0 , (5)
e,i vτ (r )Y
large neutrino fluences near this material increases Y sig- ν 0 e,eq
e
nificantly and can sometimes drastically alter the character
ofnucleosynthesisintheoutflow.IntheBHNScase,thereis
no interaction region during the tidal disruption of the NS, where r = t v. Using the outflow velocity and neutrino
0 ν,on
and matter ejection when the tidal stream self-intersects is luminosities calculated in the M12-7-S9 model of Foucart
very subdominant (Foucart et al. 2015b). The case M14-5- et al. (2014) (v ≈ 0.25c, L ≈ 1053erg s−1, and t ≈
νe ν,on
S9 has the most massive ejection from the tidal stream col- 3ms) we find that the post neutrino interaction electron
lision(Deatonetal.2013)oftheseBHNS,butevenforthis fraction is Y ≈ 0.07 if the Y is close to a half. Given
e,f e,eq
casetheimprintofthissecondaryejectasourceontheover- that the r-process is robustly produced below Y ≈ 0.25,
e
all outflow composition is small. Therefore, the ejected ma- this suggests that neutrino interactions are much less likely
terialhasaloweraverageentropyandelectronfractionthan to play a significant role in determining the composition of
neutron star–neutron star (NSNS) merger ejecta and there the ejecta in BHNS mergers relative to binary NS mergers,
is no significant neutrino emission until a disk has formed although this estimate is sensitive to t and the velocity
ν,on
around the BH. Here, we consider the extent to which neu- of the outflow.
trinointeractionscanalterthedistributionofYe justbefore Tomakethismoreconcrete,werunnucleosynthesiscal-
r-process nucleosynthesis begins in the ejecta. culationsfortheM12-7-S9modelincludingneutrinointerac-
We estimate the effect of neutrino captures on the tionsinducedbyaconstantneutrinoluminosity,modeledas
BHNS outflows by considering the maximum disk neutrino describedabove.Similarresultsarefoundfortheothertwo
luminosities found by Foucart et al. (2014). The neutrino modelsdiscussedinSection2.1.InFigure5,theweakinter-
luminosity coming from the disk in both electron neutrinos actionratesandtheelectronfractionareshownforasingle
andantineutrinosisaround1053erg s−1.Althoughthesim- particle. Because our Lagrangian trajectories start at 3 ms
ulationsofFoucartetal.(2014)usedagrayleakageapprox- after the merger, the initial density in the ejected material
imation, we can get some estimate of the average neutrino is below about 1010g cm−3 and lepton captures are domi-
energies from the temperature of the emission region which nated by neutrino captures for neutrino luminosities above
wasaround5MeV,whichsuggestsaverageneutrinoenergies about1052erg s−1.Theneutrinointeractionratesfalloffas
around (cid:15)ν ≈ 3.15T ∼ 15MeV (e.g., Foucart et al. 2015b). apowerlawintime,sincethisparticularparticleismoving
We can then estimate the neutrino processing timescale as away from the merger site at constant velocity in a nearly
radialdirection.Otherparticlescandeviatefrompowerlaw
(cid:16) r (cid:17)2
τ (r)≈67.8ms L−1 T−1 , (3) behavior at early times, but not strongly. As was expected
ν 250km νe,53 νe,5 fromourestimatesabove,theneutrinointeractiontimescale
islongcomparedtotheoutflowtimescaleandverylittleevo-
where r is the radius of the fluid element, L is the
electron neutrino luminosity in units of 1053erνge,5s3−1, and lutionoftheelectronfractionoccursduringthefirst10ms.
The evolution of Y after about 20 ms is driven by beta-
T is the electron neutrino spectral temperature in units e
νe,5 decays occurring during the r-process.
of 5 MeV. Electron antineutrinos are unlikely to contribute
significantly to the neutrino interaction timescale. This is To look at the effect of weak interactions globally, the
because in the low entropy outflows of BHNS mergers al- distribution of Ye in the material ejected in model M12-
most all protons are locked in heavy nuclei and thus have 7-S9 is shown in Figure 4 for a range of assumed neu-
very low neutrino capture cross-sections. trinoluminosities.TheGRHDsimulationsdescribedinSec-
The change in Y due to neutrino interactions can be tion 2.1 include electron and positron captures, but do not
e
estimated by assuming that the tidal ejecta has a constant include neutrino captures. The SPH simulations which fol-
velocityv,theneutrinoluminosityisconstant,electronand low the long term evolution of the ejecta include no weak
positron capture are unimportant, protons are locked into interactions. Therefore, we include weak interactions in our
heavynuclei,andthereisafinitetimeaftermergeratwhich post-processing nucleosynthesis calculations to assess their
neutrinos start being emitted from the disk. With these as- impact on Ye. As we expect, the ejected material is very
sumptions,theevolutionofY asafunctionofradiusisgiven neutron-rich,butbecomesslightlylessneutronrichwithin-
e
by creasing electron neutrino luminosity. The distribution of
the electron fraction in the whole NS is also shown to em-
dY θ(r−vt ) phasize that the ejecta in the absence of neutrinos has a
e = ν,on (Y −Y ), (4)
dr vτν(r)Ye,eq e,eq e significantly lower Ye than the average Ye of a cold 1.2M(cid:12)
NS calculated using the LS220 EOS. The beta-equilibrium
where Y = (cid:104)Z(cid:105) /(cid:104)A(cid:105) , and t is the time af- value of Y increases with density, so that the outer lay-
e,eq nuclei nuclei ν,on e
ter merger at which the neutrino luminosities reach their ers of the NS—which comprise most of the ejecta—have a
saturation value. lowerelectronfraction.Theaverageelectronfractioninthe
Assumingaconstantaverageprotonandneutronnum- ejecta is 0.053, 0.053, 0.054, 0.062, and 0.127, for neutrino
bers of the heavy nuclei, this can easily be integrated to luminosities of {0,0.2,1,5,25}×1052 erg s−1.
MNRAS000,000–000(0000)
8 L. F. Roberts et al.
10 3 massnumber78dependsontheneutrinoluminosity,incon-
−
trasttothesecondandthirdpeakswhichareindependentof
theneutrinoluminosity.Nonetheless,inallcasesitisunder-
10 4
− produced relative to the solar abundance when normalizing
e to the second and third peaks. This first peak production
c
n
a10 5 is driven by low mass r-process seed production after ma-
d −
n terial falls out of NSE. This material is composed of heavy
u
b nuclei and free neutrons when strong equilibrium ceases to
A10 6
− hold. Since the material is still relatively close to the accre-
Lνe,52=0 Lνe,52=5 tiontorusafewmillisecondsafteritisejected,asignificant
10−7 Lνe,52=0.2 Lνe,52=25 number of electron neutrinos can be captured by the free
Lνe,52=1 Solar neutrons. The produced protons then rapidly capture neu-
50 100 150 200 250 trons and form deuterium, which can then capture another
Mass Number deuteron to form an alpha particle. These alpha particles
canthenundergoaneutron-catalyzedtriple-alphareaction,
similartowhatoccursinneutron-richneutrinodrivenwinds
Figure 6. Comparison of the integrated nuclear abundances (Hoffman et al. 1997), to produce low mass seed nuclei for
in model M12-7-S9 assuming different fixed neutrino irradiation the r-process. This non-equilibrium neutrino induced seed
from the nascent accretion disk. We also include the classical productioncreatesadistinctsetofseednucleithatcanun-
scaledsolarabundancer-processdistributionfromArlandinietal. dergoneutroncapture,sincetheseedsproducedbytheNSE
(1999)forcomparison.Forallruns,weassumeLν¯e =1.5Lνe. distribution tend to be between mass 78 and 100. A large
numberofthelowmassseedsdonotgetprocessedpastthe
N =50, Z =28 point in the r-process path before neutron
3.2 Nucleosynthesis and Neutrino Induced
exhaustion occurs because of the long beta-decay half lives
Production of the First r-Process Peak
in that region of the chart of the nuclides. Therefore, these
We now consider the detailed nucleosynthesis in the ejecta neutrinoproducedseednucleiareresponsibleforproducing
of model M12-7-S9, both with and without neutrinos. We the first peak r-process nucleosynthesis seen in our simula-
focusontheeffectneutrinoscanhaveontheisotopicabun- tions. This effect of neutrino irradiation of the outflow is
dances of the ejecta. In Figure 6, the integrated nucleosyn- distinctfromtheonediscussedbyWanajoetal.(2014)and
thesis from model M12-7-S9 is shown. Since the neutrino Goriely et al. (2015), where the neutrino luminosities are
emission from the accretion torus formed after the BHNS high enough to push the electron fraction over ∼0.25 and
merger is uncertain, we calculate the final nucleosynthetic stop production of the second and third peaks.
yields of M12-7-S9 assuming electron neutrino luminosities
of {0,0.2,1,5,25}×1052erg s−1. In all cases, the electron
3.3 Details of the First Peak Production
antineutrino luminosity is fixed at 1.5L to very approx-
νe Mechanism
imately account for re-leptonization of the neutrino emit-
tingdisk(Foucartetal.2015a).Becauseoftheα-effect,the We now consider the details of the process by which abun-
results are insensitive to the chosen electron antineutrino dances in the first peak are indirectly produced by electron
luminosity. The electron neutrino and antineutrino average neutrino captures by neutrons. The total number fraction
energies are fixed at 12MeV and 15MeV, respectively. The of heavy nuclei produced by neutrino induced seed produc-
resultsfortheothertwosimulatedbinarysystemsaresimi- tion can be estimated by using the results from Section 3.1
lar and they are discussed briefly below. as follows. Low mass seed production proceeds via the neu-
In general, we confirm previous work that has shown troncatalyzedtriplealphaprocess,soittakessixprotonsto
BHNSmergersdynamicallyejectalargeamountofr-process make a seed nucleus. The rate of proton production is just
richmaterial(e.g.Robertsetal.2011;Justetal.2015).Both Y˙ ,sothetotalnumberoflowmassseednucleiproducedby
e
thesecondandthirdr-processpeaksarerobustlyproduced, neutrino interactions is
independent of the neutrino luminosity. Given the low elec- Y −Y
tron fractions found in the ejecta at the start of neutron Ys,ν ≈ e,f 6 e,i
capture,robustproductionofther-processisnotsurprising (cid:20) (cid:18) (cid:19)(cid:21)
Y −Y r
(Lippuner & Roberts 2015). In all of the models, reactive = e,eq e,i 1−exp − 0 . (6)
6 vτ (r )Y
flowproceedspastthethirdpeakbeforeneutronexhaustion ν 0 e,eq
occurs in the vast majority of the simulated fluid elements This estimate implies that around 2×10−3 seed nuclei per
and they undergo fission cycling. We find that fission cy- baryonareproducedbythisprocess,assumingtheneutrino
cles occur in the ejecta and the number of cycles is weakly luminosityis1053erg s−1.Thisnumberisingoodagreement
dependent on the neutrino luminosity (for the luminosities with the values extracted from our nucleosynthesis calcula-
considered here). Therefore, the abundance pattern above tions. Comparing this to the total final abundance of the
massnumber∼90islikelytoberobusttovariationsinthe firstpeakforasingleejectaparticleshowninFigure7,itis
totalneutrinoluminosityandthepropertiesofthemerging clear that only about 10% of this material gets trapped in
system. In all models, the third r-process peak is over pro- the first peak.
duced relative to the second peak. This is discussed further Seed nuclei indirectly produced by neutrinos are not
in Section 3.4. processedpasttheN =28closedshellrapidly.Ifsuchrapid
Wefindthattheabundanceofthefirstr-processpeakat processingwerethecase,thefinalamountofmassinthefirst
MNRAS000,000–000(0000)
Neutrinos and BHNS r-Process Nucleosynthesis 9
1.2 1.2
10−3 YY11sstt YYss,,νν 10−3 YY11sstt YYnn
10 4 YY11sstt,,fifinnaall YYnn 1.0 10 4 YYss,,νν 1.0
− −
0.8 0.8
s,ν10−5 s,ν10−5
Y Y
0.6 n 0.6 n
,1st10−6 Y ,1st10−6 Y
Y1100−−87 LLννee,,5522==01..00 LLννee,,5522==510.0.0 00..24 Y1100−−87 LLLLννννeeee,,,,55552222====0125....0050 LLννee,,5522==2400..00 00..24
10 9 Lνe,52=2.5 Lνe,52=20.0 0 10 9 Lνe,52=10.0 Lνe,52=60.0 0
− −
100 100
4 4
K] 3 K] 3
[G 2 10−1τ[s] [G 2 10−1τ[s]
T T
TT
1 ττ((66,,2255)) 1 TT ττ((2266,,2288))
ττ((2266,,2288)) ττ((66,,2255))
0 10 2 0 10 2
10 2 10 1 100 − 10 2 10 1 100 −
− − − −
Time [s] Time [s]
Figure7.Illustrationofhowthefirstr-processpeakisproduced Figure 8. The same as Figure 7, except for a different ther-
by electron neutrino captures on neutrons for a single SPH par- modynamic trajectory. This SPH particle had initial Ye = 0.05,
ticle. This SPH particle had initial Ye = 0.11, initial entropy initialentropys=4.33kB baryon−1,andanasymptoticvelocity
s=9.7kB baryon−1,andanasymptoticvelocityv/c=0.5.Top v/c = 0.29. Because of the lower velocity, lower initial entropy,
panel:Thesolidlinesshowtheabundanceofmaterialinthefirst andlowerYepresentinthisparticlerelativetotheparticleshown
r-process peak, Y1st, as a function of time (i.e. material with in Figure 7, neutrino interactions significantly alter the thermo-
72 ≤ A ≤ 79), the dashed lines show the integrated number dynamic state of the material and τ . This causes the first
(6,25)
ofprotonsproducedbyweakinteractionsaftertimetdividedby peakabundancetovarynon-monotonicallywiththeneutrinolu-
six,Ys,ν =(cid:82)t∞dtYn/6(λνe+λe+),andthedottedlinesshowthe minosity.
neutron abundance Yn. Ys,ν gives the number of low mass seed
nucleiproducedbyneutrinointeractions.Theneutrinoseednuclei
producedatearlytimesareburnedpastthefirstr-processpeak,
buttheseednucleiproducedafterthetimewhenYs,ν =Y1st,final
do not get burned passed the first peak before neutrons are ex-
hausted,andsotheywillendupinthefirstpeak.Bottompanel:
Thesolidlinesshowthetemperatureoftheparticleasafunction
oftime,thedashedlinesshowthetimescaletoprocessmaterialto
the first peak, τ , and the dotted lines show the destruction
(6,25)
timescaleofthefirstpeak,τ ,whicharedefinedinthetext.
(26,28)
In this particle, there is no significant variation with neutrino
luminosity of the temperature or the r-process path. Therefore,
the two timescales do not change with the amount of neutrino
irradiation.
peak would be set by the number of seed nuclei produced
Figure9.Ther-processpathfortheSPHparticleshowninFig-
after a time just before neutron exhaustion. To illustrate
ure 8 for different neutrino luminosities at 100 ms into the cal-
when the nuclei trapped in the first peak are produced, we
culation. The inset shows the mass summed abundances at the
show the total number of seed nuclei produced by neutrino same time. Notice how the path differs for different neutrino lu-
interactions after time t minosities.
1(cid:90) ∞
Y (t)= Y (λ +λ )dt (7)
s,ν 6 n νe e+
t are exhausted and t be the time after which neutrino
prod
in Figure 7, along with the time dependence of the first producedseednucleigettrappedinthefirstpeak.Seednu-
peak abundance, Y , and the neutron abundance Y . Y clei produced at times earlier than t = t −τ will
1st n s,ν prod ex 1st
isjustthenumberfractionofprotonsproducedbyweakin- be burned past the first peak, while seed nuclei produced
teractions after time t divided by six, since it requires six within a time τ of neutron exhaustion will end up in the
1st
protons to produce a seed nucleus that can capture neu- first peak. We can estimate τ by looking for solutions of
1st
trons. Material will be processed through the first peak on Y (t ) = Y . Inspecting Figure 7, we find t is
s,ν prod 1st,final prod
some timescale τ . Let t be the time at which neutrons 70 to 100 ms and t is 520 to 600 ms for L ranging
1st ex ex νe,52
MNRAS000,000–000(0000)
10 L. F. Roberts et al.
from 20 to 1. Thus we estimate that τ , the time it takes adifferentLagrangianparticlethatexhibitsnon-monotonic
1st
forseednucleitobeprocessedtotheN =28closedshellof behaviorofthefirstpeakabundancewiththeneutrinolumi-
thefirstpeak,isbetween450and500msforthisparticular nosity. The first peak abundance increases at low luminos-
fluid element. ity, decreases with luminosity around L = 1053erg s−1,
νe
We now attempt to explain what sets this timescale. and then increases with luminosity again. This particle has
Assumingthatbeta-decayoccursonamuchlongertimescale a lower asymptotic velocity than the particle shown in Fig-
than neutron capture and photodissociation, the timescale ure 7 and therefore experiences more neutrino irradiation.
to go from charge Z to charge Z is given by Additionally, it has lower initial entropy and Y , which
1 2 e
means neutrino interactions can have a larger effect on its
τ (t)= (cid:88)Z2 (cid:80)NY(Z,N) . (8) thermodynamic state.
(Z1,Z2) (cid:80) Y τ−1 ThelowerpanelofFigure8clearlyshowsthatneutrinos
Z=Z1 N (Z,N) β−,(Z,N) significantlyalterthethermodynamicstateoftheconsidered
Here, τ−1 is the beta-decay timescale of a nu- particle and that the low mass r-process path is shifted by
β−,(Z,N)
cleus with N neutrons and Z protons. When (n,γ) reac- theinclusionofneutrinointeractions.Ther-processpathsat
tions are in equilibrium with (γ,n) reactions—such that variousneutrinoluminosities100msintothecalculationare
µn+µ(Z,N) =µ(Z,N+1)—these timescales are only func- showninFigure9.Inparticular,τ(26,28) changesdrastically,
tions of the density, temperature, and neutron abundance, τ(6,25) alsoundergoeschanges,theneutronabundanceisde-
i.e.τ =τ (ρ,T,Y ).Thisisoftenthecaseatthe creased,andthetotalnumberofseedsincreasesatincreased
(Z1,Z2) (Z1,Z2) n
high temperatures encountered during r-process nucleosyn- initialYe andtemperature,correspondingtolargerneutrino
thesis in these outflows, but the equilibrium can start to luminosities in this fluid element. Additionally, increasing
breakdownatlowertemperatures.Thismakesitclearthat theentropyoftheoutflowreducestherateatwhichmaterial
changing the temperature and electron fraction of a par- can bypass the A = 8 stability gap. The large difference in
ticular fluid element can change the path of the r-process thefirstpeakprocessingtimescale,τ(26,28),seeninFigure8
and alter the time it takes material to be processed from is due to the r-process path shifting from being far beyond
one charge number to another. The quantities τ and theN =50,Z =28closedshellsatlowertemperatures(and
(6,25)
τ are shown in the bottom panel of Figure 7. Note lower neutrino luminosities) to proceeding through closed
(26,28)
that τ +τ is approximately the time it takes a shells at higher temperatures (and higher neutrino lumi-
(6,25) (26,28)
seed nucleus to get to the start of the first peak and then nosities). This significantly alters how first peak nuclei are
get processed through the first peak, which we called τ produced throughout the calculation and breaks the linear
1st
above. We see from the bottom panel of Figure 7 that dependence on the neutrino luminosity.
τ is constant throughout the period during which the Evenintheabsenceofneutrinos,thereissomeproduc-
(6,25)
r-process is occurring and its value is in good agreement tionoffirstpeaknuclei.Aswehavementioned,thismaterial
with our 450 to 500 ms estimate for τ . Because this isproducedbyfissionofheavynuclei.Sinceweareemploy-
1st
timescale is determined by beta decay, the final first peak ingsymmetricfissionfragmentdistributions,itislikelythat
abundance goes linearly with the neutrino luminosity. The more realistic fission fragment distributions will result in a
lifetimesofisotopesalongtheN =50closedshellare40ms, broader distribution of fission daughters and more material
110 ms, and 110 ms, for the reactions 76Fe(β−,n)75Co, beingleftbehindinthisregion.Nonetheless,itseemslikely
77Co(β−,n)76Ni, and 78Ni(β−)78Cu. These are consistent thattherewillbeatleastsomeproductionofthefirstpeak
with the τ ≈100 ms we find in Figure 7. We also evenintheveryneutron-richoutflowsofBHNSmergers,as
(26,28)
note that at around 600 ms into the calculation—which longasneutrinoluminositiesfromthepostmergerremnant
is after neutron exhaustion—there is a further increase in are above about 1052erg s−1 within a hundred milliseconds
the first peak abundance. This is driven by the reaction ofthemerger.Wealsoemphasizethatneutrinoinducedpro-
80Ni(β−,n)79Cu. Significant production of 80Ni occurs just duction of the first peak does not produce enough material
before neutron freeze-out and it has a half-life of 175 ms. in our models to agree with the solar r-process abundances
This suggests that the neutrino flux between times when they are normalized to the second peak. Instead, the
t = t −τ −τ and t = t −τ will deter- abundance is around an order of magnitude too low.
1 ex (6,25) (26,28) 2 ex (6,25)
mine the amount of neutrino induced first peak production
thatoccurs.Seednucleiproducedbeforetimet willgetbe-
1 3.4 Isotopic and Elemental Abundances, Galactic
yondthefirstpeakbeforeneutronsareexhausted,whileseed
Chemical Evolution, and Low Metallicity
nuclei produced after time t will not reach the first peak
2 Halo Stars
beforeneutronexhaustionoccurs.Therefore,theimportant
quantity for understanding neutrino induced production of In Figure 10, the integrated abundances from the models
the first peak will be the neutrino luminosity centered at a M12-7-S9, M14-7-S8, and M14-5-S9 are shown for a fixed
timearound70msaftermerger,withinawindowofaround neutrino luminosity of 1053erg s−1 (and L = 1.5L ).
ν¯e νe
100 ms. Clearly,thereislittlediscernibledifferencebetweenthepre-
Wehaveshownthattheproductionoffirstpeaknuclei dictednucleosynthesisfromthesemodels.Theelectronfrac-
goes linearly with the electron neutrino luminosity for the tioninalmostalloftheejectainallthreemodelsisbelowthe
specificLagrangianparticleshowninFigure7,butFigure6 threshold for fission cycling to occur (Lippuner & Roberts
shows that production of the first peak appears to saturate 2015) and the entropy of the ejecta is quite low. These are
atluminositiesabove∼5×1052erg s−1.Belowthisluminos- conditions that result in a second and third peak nuclear
ity, the dependence of first peak production on luminosity abundance pattern that is quite insensitive to the detailed
is approximately linear as expected. In Figure 8, we show properties of the ejecta (Lippuner & Roberts 2015, e.g.).
MNRAS000,000–000(0000)