Cosmic Neutron Star Merger Rate and Gravitational Waves constrained by the R Process Nucleosynthesis

1.3 MB·English

by  E. Vangioni

Mon.Not.R.Astron.Soc.000,1–??(2015) Printed5October2015 (MNLATEXstylefilev2.2)
Cosmic Neutron Star Merger Rate and Gravitational Waves
constrained by the R Process Nucleosynthesis
Elisabeth Vangioni1⋆, Ste´phane Goriely2, Fre´de´ric Daigne1, Patrick Franc¸ois3,
5
1 and Krzysztof Belczynski4
0
1SorbonneUniversite´s,UPMCUnivParis6etCNRS,UMR7095,Institutd’AstrophysiquedeParis,98bisbdArago,75014Paris,France
2
2Institutd’Astronomieetd’Astrophysique,CP226,Universite´LibredeBruxelles,1050Brussels,Belgium

t 3GEPI,Paris-MeudonObservatory,61Avenuedel’Observatoire,F-75014Paris,France
c
4AstronomicalObservatory,UniversityofWarsaw,Al.Ujazdowskie4,00-478Warsaw,Poland
O

2
5October2015

]
E
H ABSTRACT
. Thecosmicevolutionoftheneutronstarmerger(NSM)ratecanbededucedfromtheobserved
h
cosmic star formation rate. This allows to estimate the rate expected in the horizon of the
p
gravitationalwave detectors advancedVirgo and ad LIGO and to compare those rates with
-
o independentpredictions.Inthiscontext,therapidneutron-captureprocess,orr-process,can
r beusedasaconstraintassumingNSMisthemainastrophysicalsiteforthisnucleosynthetic
t
s process. We compute the early cosmic evolution of a typical r-process element, Europium.
a EuyieldsfromNSMaretakenfromrecentnucleosynthesiscalculations.Thesameapproach
[
allowstocomputethecosmicrateofCoreCollapseSuperNovae(CCSN)andtheassociated

2 evolutionofEu.
v We find that the bulk of Eu observationsat [Fe/H] > −2.5 can be rather well fitted by
5 eitherCCSNorNSMscenarios.However,atlowermetallicity,theearlyEucosmicevolution
1 favorsNSMasthemainastrophysicalsiteforther-process.Acomparisonbetweenourcal-
1 culationsandspectroscopicobservationsatverylow metallicitiesallows usto constrainthe
1 coalescencetimescaleintheNSMscenarioto∼0.1–0.2Gyr.Thesevaluesareinagreement
0
withthecoalescencetimescalesofsomeobservedbinarypulsars.Finally,thecosmicevolu-
.
1 tionofEuisusedtoputconstraintsoni)theNSMrate,ii)themergerrateinthehorizonof
0 thegravitationalwavedetectorsadvancedVirgo/adLIGO,aswellasiii)theexpectedrateof
5 electromagneticcounterpartstomergers(”kilonovae”)inlargenear-infraredsurveys.
1
: Key words: Cosmology: dark ages, first stars, Physical Data and Processes: gravitational
v
waves,nucleosynthesis,Stars:supernovae,neutronstars.
i
X
r
a
1 INTRODUCTION propertiesofthepromptemissioninshortandlongGRBs(see.g.
Guiriecetal. 2010)suggestthatthesamedissipationprocessisat
Recently, a special attention has been paid to neutron star (NS)–
workinthesetwoclassesofbursts(Bosˇnjak&Daigne 2014)and
NS or NS–black hole (BH) mergers (hereafter NSM), con-
thatthemaindifferencesarethelifetimeofthecentralengine,lead-
sidered today as the most promising sources of gravitational
inginthecaseofbinarycompactobjectstoshorterevents,andthe
waves for ground-based detectors such as advanced Virgo/ad
densityof thecircumburst medium, leading toweaker afterglows
Ligo (Phinney 1991; Narayanetal. 1991; Virgocollaboration
(Nakar 2007). In addition, hydrodynamic simulations have con-
2009; Abadieetal. 2010; LIGOScientificcollaboration 2011;
firmedthatanon-negligibleamountofmatter,typicallyabout10−3
Aasietal. 2014a,b,c; Belczynskietal. 2014) but also because
to 10−2 M , can be ejected quasi-isotropically (Jankaetal. 1999;
several evidences (seeBerger 2014, for a recent review) suggest ⊙
Rosswogetal. 1999, 2004; Oechslinetal. 2007; Gorielyetal.
inadditionthattheseeventsaretheprogenitorsofshortgamma-ray
2011; Bausweinetal. 2013; Gorielyetal. 2013; Justetal. 2015;
bursts(GRB)(Paczynski 1986;Eichleretal. 1989;Narayanetal.
Wanajoetal.2014)andthatthematterejectedinsuchNSMevents
1992;Mochkovitchetal. 1993).Recentsimulationsshowthat,af-
isessentiallymadeofr-processnuclei,sheddinganewlightona
ter the merger, the relic BH-torus system can produce an ultra-
oldmystery.
relativistic ejection along its rotation axis (Rezzollaetal. 2011),
The r-process, or the rapid neutron-capture process, of stel-
potentially leading to a short GRB. The similarities between the
larnucleosynthesisisinvokedtoexplaintheproductionofthesta-
ble(andsomelong-lived radioactive) neutron-richnuclides heav-
⋆ e-mail:[email protected] ierthaniron thatareobserved instarsof variousmetallicities,as
(cid:13)c 2015RAS
2 E. Vangioni,S. Goriely,F. Daigne,P.Franc¸ois,K. Belczynski
wellasinthesolarsystem(forareview,seeArnouldetal.2007). Kistleretal. 2013; Trentietal. 2013). Computing the NSM rate
The r-process remains the most complex nucleosynthetic process requirestodetermine poorly known parameters, namely thefrac-
tomodelfromtheastrophysicsaswellasnuclear-physicspointsof tion of NS ina binary system with another NS or a BH, and the
view.Thesite(s)ofther-processis(are)notidentifiedyet,allthe characteristiccoalescencetimescaleofsuchasystem.Toconstrain
proposedscenariosfacingseriousproblems.Complex—andoften these parameters, we model the associated evolution of a typical
exotic—siteshave been considered inthe hope of identifying as- r-processelement,Europium,byassumingNSMasthemainastro-
trophysicalconditionsinwhichtheproductionofneutronsislarge physicalsiteofther-processandadopting themostrecent nucle-
enoughtogiverisetoasuccessfulr-process. osyntheticcalculations(Gorielyetal.2011;Bausweinetal.2013;
Progress in the modelling of type-II supernovae and long Justetal.2015),andwecompare totheavailableobservations in
GRBshasraisedalotofexcitementabouttheso-calledneutrino- old stars of the Galactic halo and in external galaxies. Once the
driven wind environment. However, until now a successful r- mergerratehasbeendetermined,itispossibletoestimatetheex-
process cannot be obtained ab initio without tuning the relevant pectedeventrateforthenewgenerationofgravitationalwavede-
parameters(neutronexcess,entropy,expansiontimescale)inaway tectors (advanced Virgo and LIGO), as well as the expected de-
that is not supported by the most sophisticated existing models tectionrateofkilonovaeinpresentandfutureoptical/near-infrared
(Wanajoetal.2011;Janka2012). large surveys. The same approach can be followed to determine,
Early in the development of the theory of nucleosynthesis, without any new parameter, the CCSN rate, hence the predicted
an alternative to the r-process in high-temperature supernova en- evolutionofEuropiuminthealternativescenariowherer-process
vironmentswasproposed (Tsuruta&Cameron1965).Itrelieson elementsareproducedmainlyinsuchstellarexplosions.
the fact that at high densities (typically ρ > 1010 g/cm3) mat- Thepaperisorganizedasfollows:inSect.2,weselectthree
tertends tobecomposed of nuclei lyingontheneutron-rich side possiblescenariosfortheSFR,whicharerepresentativeofthecur-
of the valley of nuclear stability as a result of free-electron cap- rentuncertaintiesathighredshift,andwedescribehowtheCCSN
tures. The astrophysical plausibility of this scenario in account- andNSMratescanbededucedfromtheSFR,bothscenariosstill
ing for the production of the r-nuclides has long been ques- depending on given unknown parameters. In Sect.3, we describe
tioned. It remained largely unexplored until the study of the de- thechemicalevolutionmodelthatweusetodeducefromthecos-
compression of cold neutronised matter resulting from tidal ef- micSFRtheexpectedevolutionoftheabundancesofvariouschem-
fects of a BH on a NS companion (Lattimer&Schramm 1974; icalelementsinstar-formingstructures.Weshowthatthethreesce-
Lattimeretal.1977;Meyer1989).Manyinvestigationswithgrow- nariosconsideredinthepaperforthecosmicSFRarecompatible
ing sophistication have now confirmed NSM ejecta as viable withalargesetofobservations,hencevalidatingthepresentmodel.
sites for strong r-processing (Arnouldetal. 2007; Gorielyetal. In§4.2,weshowhowthemodelcanbeextendedtoheavyelements
2011; Bausweinetal. 2013; Gorielyetal. 2013; Justetal. 2015; producedbyther-process.InSect.4,wepresentthepredictedcos-
Freiburghausetal.1999;Gorielyetal.2005;Metzgeretal.2010; micevolutionofEu,assumingeithertheCCSNortheNSMasthe
Robertsetal. 2011; Korobkinetal. 2012; Wanajoetal. 2014). In mainastrophysicalsiteofther-process.Wemakeadetailedcom-
particular, recent nucleosynthesis calculations (Justetal. 2015) parisonwithobservationsatlowmetallicitieswhichcorrespondto
show that the combined contributions of both the dynamical theearlyevolutionintheUniverseandappeartobethemostdis-
(prompt) ejecta expelled during the binary NS-NS or NS-BH criminativebetweenbothsites.IntheNSMcase,thisallowsusin
merger and the neutrino and viscously driven outflows generated additiontoconstrainthepropertiesofthebinarysystem,inpartic-
duringthepost-mergerremnantevolutionoftherelicBH-torussys- ularcoalescencetimescale.Theresultinglowerandupperlimitson
temsleadtotheproductionofr-processelementsfromA&90upto themergerrateareusedinSect.5tomakepredictionsfortheex-
thoriumanduraniumwithanabundancedistributionthatreproduce pectedeventrateinthehorizonofadvancedVirgo/LIGO,aswell
extremelywellthesolardistribution,aswellastheelementaldistri- asforthekilonovarateinfuturesurveys.Finally,wedrawourcon-
butionspectroscopically determined invery-low-metallicitystars. clusionsinSect.6.
The ejected mass of r-process material, combined with the pre-
dictedastrophysicaleventrate(around10−5yr−1intheMilkyWay
(Dominiketal. 2012) can account for the majority of r-material
inourGalaxy(Gorielyetal.2011;Bausweinetal.2013;Justetal. 2 PREDICTINGTHENSMRATE
2015).
2.1 Thecosmicstarformationrate(SFR)
In NSM, nearly all of the ejecta are converted to r-process
nuclei, whose radioactive decay heating leads to potentially ob- ThecosmicSFRisakeyingredienttomodeltherateofstellarex-
servable electromagnetic radiation in the optical and infrared plosiveevents,suchasCCSNandNSM.Theredshiftevolutionof
bands(Li&Paczyn´ski 1998;Metzgeretal.2010)with100–1000 theSFRdensityisnowratherwellconstrainedbymanyobserva-
times fainter peak brightnesses than those of typical supernovae tions.Recent datafromtheHubbleUltraDeepFieldhavesignif-
anddurationsofonlydays(Gorielyetal.2011;Robertsetal.2011; icantly extended the range of redshift for its determination, from
Bausweinetal.2013).These“macronovae”or“kilonovae”arein- redshiftz=4upto10(Bouwensetal.2007;Bouwensetal 2008,
tensely searched for (with a recent, possible first success in as- 2011,2014;Oeschetal.2012,2013,2014).Evenmorerecentob-
sociation with the short GRB 130603B, see Bergeretal. 2013; servationsofhighzgalaxiesandGRBstendtofavoralargeamount
Tanviretal.2013).Theirunambiguousdiscoverywouldconstitute ofstillunseenSFRatz>9(Kistleretal.2013;Wang2013).This
thefirstdetectionofr-materialinsitu. laststudysuggeststhatSFRdensitymayonlydeclineoutatz=11
In the present paper, our primary goal is to predict the cos- andthatGRBsmaybeusefulinexploringtheunseenfaintdwarf
mic evolution of the NSM that can be deduced from the ob- galaxiesathighredshift.Behroozietal.(2013)re-analyzedtheav-
served history of the star formation rate (SFR), including the re- erage star formation historiesfrom z = 0 to8 and obtained con-
cent constraints obtained at high redshift (Behroozietal. 2013; sistentresultswithobservedgalaxystellarmassfunctions,specific
Behroozi&Silk 2015; Oeschetal. 2014; Bouwensetal 2014; starformationratesandSFR.Moreover,high-redshiftgalaxyevo-
(cid:13)c 2015RAS,MNRAS000,1–??
CosmicNSM RateandGW constrainedbytheR Process 3
Foreachmode,theIMFslopeissettotheSalpetervalue,i.e. x =
Time (Gyr)
13.67 5 1 0.5 0.1024 1.35.
Star formation is assumed to start at the initial time of t =
0
100 Myr corresponding to a redshift of z = 30. We adopt the
following cosmological parameters, Ω = 0.27,Ω = 0.73 and
m Λ
H = 71 km/s/Mpc (h = 0.71) and a primordial power spectrum
0
withapower-law index n = 1. The aget of theUniverse isthen
relatedtotheredshiftby
dt 9.78h−1Gyr
= . (2)
dz (1+z) Ω +Ω (1+z)3 0.5
Λ m
As seen(cid:2)in Fig. 1, the SF(cid:3)R2 mode is an intermediate case,
whereas SFR1 and SFR3 are respectively close to the lower and
higher values of the current measurements at high redshift. We
checkedthateachofthesethreescenariosiscompatiblewithalarge
setofindependentobservationalconstraintsdiscussedinSect.3.2,
especially the Thomson optical depth tothe cosmological micro-
wavebackground(CMB)andthecosmicevolutionof[Fe/H].This
ledtotheinclusionoftheadditionalPopIIIcomponentathighred-
shiftintheSFR1case,thestandardmodealonebeingtooweakin
thiscasetofulfillthereionizationconstraint(seeSect.3.2.1).
Figure1.CosmicSFRasafunctionofredshift.ThreeSFRmodesconsid- 2.2 TheNSMrate
eredinthepaper,SFR1(solidline),SFR2(dottedline)andSFR3(dashed
2.2.1 TheCCSNrateandtheNSbirthrate
line). Observations are taken from Behroozietal. (2013) (red points),
Bouwensetal (2014); Oeschetal. (2014) (and references therein) (blue Once the evolution of cosmic star formation rate is known, the
points)andKistleretal.(2013)(blackpoints).
CCSNrate can bedirectly deduced if the mass-range of the pro-
genitorsisknown.WeusethepredictionsfromWoosley&Weaver
(1995)andassumethattheremnantofstarswithmass8<M/M <
lutionhasalsobeenpredictedbyBehroozi&Silk(2015)who,in- ⊙
30isaNS,andthatmoremassivestarsproduceaBH.Thisleadsto
cludingrecentconstraints(Behroozietal.2013;Oeschetal.2013;
thefollowingNSbirthrateattimet(relatedtoredshiftzbyEq.2):
Kistleretal.2013;Trentietal.2013),probedtheunobservedz>8
galaxypopulations.TheresultingobservationallyconstrainedSFR R˙ (t)= dmΦ(m)Ψ(t )Ξ (m,Z(t )) , (3)
is illustrated in Fig. 1 as a function of the redshift. The corre- NS Z ∗ NS ∗
sponding evolution of the cosmic SFR density as a function of
whereΦ(m)istheinitialmassfunction(IMF)integratedoverthe
redshift can be parametrized by the following form proposed by
wholestellarmassrange,Ψ(t)theSFR,t theformationtimeofthe
∗
Springel&Hernquist(2003),
progenitor,suchthatt +τ(m,Z(t ))=t,Z(t )themetallicityatthe
∗ ∗ ∗
ψ(z)=ν aexp[b(z−zm)] , (1) epochofformationoftheprogenitor,τ(m,Z(t∗))thelifetimeofa
a−b+bexp[a(z−zm)] starformedwithmassmandmetallicityZ(t∗),andΞNS(m,Z(t∗))is
1ifthestellarremnantisaNS,0otherwise.Thelifetimesofstars
whereν(inM /yr/Mpc3)andz correspondtotheastrationrateand
⊙ m come from (Maeder&Meynet 1989) and the stellar metallicity-
theredshiftattheSFRmaximum,respectively,whilebandb−a
dependent remnants are taken from (Woosley&Weaver 1995).
fixtheSFRslopeatlowandhighredshifts,respectively.
The BH birth rate is given by a similar equation, using now
Duetothefundamental importanceoftheSFRinpredicting Ξ (m,Z(t )) = 1 if the remnant is a BH, 0 otherwise, and the
BH ∗
the stellar explosive event rates, and more generally the cosmic
CCSNrateisthesumofthesetworates.Thecorresponding evo-
chemical evolution, we consider in the present paper three SFR lutionofthesethreeratesdeducedonthebasisofSFR1andSFR2
modes(seeFig.1),whichcoincideatlowredshift,wheretheyre-
isplotted in Fig. 2. On the observational point of view, the local
produce theavailabledata, anddiffer athighredshift, takinginto
CCSN rate is well determined, thanks to large surveys dedicated
accountthecurrentuncertainties: tothesearchofsupernovae(Mattilaetal.2012).Ascanbeseenin
• SFR1includesastandardmodeofpopulation(Pop)II/Istars Fig.2,theagreementwiththepredictiondeducedfromthecosmic
SFRisgood.
formationbetween0.1and100M ,andadditionallyaPopIIIstel-
⊙
larmodeathighredshiftbetween36and100M .Thecorrespond-
⊙
ingparametersforeachmodeinEq.(1)are,respectively,ν=0.18
2.2.2 TheNSmergerrate
and0.0025,z =2.0and12.0,a=2.37and4.0,andb=1.80and
m
3.36. In contrast to the to the CCSN rate, the astrophysical esti-
• SFR2includesauniquemodeofstarformationbetween0.1 mate of compact-binary coalescence rates depends on a num-
M and100M ,withthefollowingparameters:ν=0.15,z =1.7, ber of assumptions and unknown model parameters and are still
⊙ ⊙ m
a=2.8,b=2.45; rather uncertain (Abadieetal. 2010). Among the various esti-
• SFR3alsoincludesauniquemodeofstarformationbetween mates,theratepredictions for NS-NSbinary systemsisthemost
0.1M and100M ,withthefollowingparameters:ν=0.36,z = reliable one since they are based on extrapolations from ob-
⊙ ⊙ m
2.6,a=1.92,b=1.5. served binary pulsars in our Galaxy. These estimates lead to
(cid:13)c 2015RAS,MNRAS000,1–??
4 E. Vangioni,S. Goriely,F. Daigne,P.Franc¸ois,K. Belczynski
Dominiketal.(2013)calculatedthecosmologicalmergerratesof
NS-NS,NS-BH,BH-BHsystemsasafunctionofredshiftassum-
ing different SFR histories. While in most cases NS-NS systems
dominatethemerger ratesinthelocal Universe, BH-BHmergers
arefoundtodominateathighredshift.
SFR
0.1 Inthepresent study,themergerrateisdeterminedassuming
thattheformationrateofNS-NS/BHbinarysystemsisafractionα
oftheNSbirthrateR˙ andthatthesebinarysystemsmergeafter
Core Collapse SNII NS
0.01 adelay∆t ,thevalueofwhichisdiscussedbelow.Thisleadsto
NS formation NSM
thefollowingmergerrateattimet:
R˙ (t)=αR˙ (t−∆t ) . (4)
NSM NS NSM
Inourmodel,bothαand∆t andtakenasfreeparameters.The
NSM
predictedevolutionofthemergerrateisplottedinFig.2forSFR1
BH formation
andSFR2,assuming α = 0.002and ∆t = 0.2Gyr.Theinde-
mergers NSM
pendent estimate of the local rate taken from the compilation by
Abadieetal.(2010)isindicatedforcomparison.
2.2.3 Thecoalescencetimescale
Thecoalescence timescale∆t isdefined asthedelaybetween
NSM
theformation of thebinary system of twoNS or aNSand aBH
SFR
0.1 (notethatitdoesnotincludethelifetimeofthetwostarprogeni-
torsofthecompactobjects).Itisakeyingredient asitleadstoa
differentcosmicevolutionofNSMcomparedtoCCSN,forwhich
Core Collapse SNII
0.01 thereisnoadditionaldelayaftertheformationofaNS/BH.
NS formation
The angular momentum lossdue tothe emission of gravita-
tionalwavesgovernsthecoalescencetimescale.Itsvaluestrongly
dependsonthepropertiesofthebinarysystem,andinparticularon
theinitialseparationa(ororbitalperiodT)since∆t ∝a4(resp.
NSM
∆t ∝ T8/3) (Peters&Mathews 1963, see also Kalogeraetal.
BH formation NSM
2001;Hughes 2009).Thisdependenceleadstoanexpectedbroad
mergers
rangeofvaluesfor∆t ,withhoweverlargeuncertaintiesrelated
NSM
tothedistribution of possible initial orbital parameters inNS/NS
andNS/BHbinaries(seeHughes 2009,forarecent review). For
a binary system of two 1.4 M NS, the coalescence timescale is
⊙
∆t = 64 Myr for a = 10−2 AU (resp. T = 5.2 h). Only
NSM
seven NS/NS binary systems are known with measured masses
Figure2.NSandBHbirthratesaswellastheCCSNandmergerratesas (Lorimer 2005,2008).Thecurrentorbitalparametersandthemea-
afunctionoftheredshiftforSFR1(upperpanel)andSFR2(lowerpanel). sured masses allow us to estimate the remaining time before the
Green andred points represent thelocal CCSN rate (Mattilaetal. 2012) merger. As at least one of the two NS is observed as a pulsar,
andthetotallocalmergerrate(Abadieetal.2010),respectively.TheSFR
the measurement of the pulsar period and its time derivative can
evolutionisalsoplottedforcomparison.
provide an estimate of the current age of the binary system. The
sum of these two timescales gives an estimate of ∆t . Using
NSM
the values listed in Lorimer (2008), coalescence timescales be-
a coalescence rate of about 100 Myr−1 per Galaxy, although tween100and400Myrarefoundinfourcases,andvalueslarger
this rate could plausibly range from 0.1 Myr−1 to 1000 Myr−1 than1Gyrinthethreeothercases.ThedoublepulsarPSRJ037-
(Kimetal. 2003; Kalogeraetal. 2004; Mennekens&Vanbeveren 3039corresponds tothelowestvalue, ∆t ≃ 180Myr. Thefa-
NSM
2014). Due to the lack of observational data, predictions of the mousbinarypulsarPSRB1913+16,whichhasbeenstudiedinde-
frequency of NS-BH mergers remains even more uncertain and tailsforyearsasatestofgeneralrelativity(Hulse&Taylor 1975;
relyexclusivelyontheoreticalstudies(Tutukov&Yungelson1993; Weiberg,NiceandTaylor 2010)ischaracterisedbyacoalescence
Voss&Tauris 2003; O’Shaughnessyetal. 2008; Dominiketal. timescale∆t ≃420Myr.
NSM
2012; Dominiketal. 2013; Mennekens&Vanbeveren 2014; The distribution of the coalescence timescale can be esti-
Postnov&Yungelson 2014). These population synthesis models matedusingapopulationsynthesiscodeforbinarysystems,which
estimategalacticmergerratesbetween2×10−9and10−5peryear. canbecalibratedwithobserved systems.Theresultisplottedfor
The range reflects the challenge in comprehensively modelling two different metallicities in Fig. 3. It has been obtained using
theformationandevolutionofstellarbinariesandtheirremnants. theStarTrackcodedescribedinBelczynskietal.(2002,2008a),
Bausweinetal. (2014) determined anindependent upper limit on wherestandardstellarevolutionmodelsareimplementedwiththe
themergerrateofNS-BHbinariesbycomparing thepredictedr- mostupdatedphysicsregardingtherelevantprocessesfortheevo-
processnucleosynthesisyieldsofsuchsystemswiththeobserved lution of binary systems. Fig. 3 has been produced using the re-
galactic amount of r-process material. A strict upper limit of the sultsofarecentlyupdatedversionofthecode(Mink&Belczyn-
averageNS-BHmergerrateofabout 6×10−5 peryearwasfound. ski in preparation), including new prescriptions for stellar wind
(cid:13)c 2015RAS,MNRAS000,1–??
CosmicNSM RateandGW constrainedbytheR Process 5
3 COSMICCHEMICALEVOLUTION
3.1 Modeldescription
Inadditionoftheratesofexplosiveevents(CCSN,NSM)discussed
intheprevioussections,thepredictedchemicalevolutioncanalso
be deduced from the cosmic evolution of the SFR. We use the
model developed by Daigneetal. (2006); Rollindeetal. (2009);
Vangionietal. (2014), which is based on a hierarchical model
forstructureformation(Press&Schechter1974;Sheth&Tormen
1999;Jenkinsetal. 2001;Wyithe&Loeb 2003).Weassumethat
theminimummassofdarkmatterhaloesforstar-formingstructures
is107 M .
⊙
Finally, for a given evolution of the cosmic SFR density, as
discussed in§2.1,themodel followstheevolution of baryons in
the Universe in terms of two main reservoirs. The first is associ-
atedwithcollapsedstructuresandisdividedintwosub-reservoirs:
theISMgas(massM (t))andthestarsandtheirremnants(mass
ISM
M (t)).Thesecondreservoir,theintergalacticmedium(IGM,mass
∗
M (t)), corresponds to the medium in between the collapsed
IGM
structures.Theevolutionofthebaryonicmassofthesereservoirs
isgovernedbyasetofdifferentialequations:
dM dM
IGM =− struct =−a (t)+o(t), (5)
dt dt b
Figure 3. Distribution of the coalescence timescale ∆tNSM for NS/NS
binarysystems.Thecoalescencetimescale∆tNSMisdefinedasthedelay dM∗ =Ψ(t)−e(t)and dMISM = dMstruct − dM∗ . (6)
betweentheformationofthetwoNSandthefinalmerger.Theplotshows dt dt dt dt
thefractionofmergerswithacoalescence timescale aboveagivenvalue
Inaddition,wehaveM (t)+M (t)= M (t),correspondingto
inMyr,fortwodifferentmetallicities. Thisdistributionhasbeenobtained ISM ∗ struct
from an updated version of the population synthesis model described in thetotalbaryonicmassofthestructures,andMIGM(t)+Mstruct(t)=
Belczynskietal.(2002).Itcoversabroadrangeofvalueswithadistribution constant(totalbaryonicmassoftheUniverse).
fallingapproximatelylikep(∆tNSM)∝∆tN−1SM. As can be seen, these equations are controlled by four rates
whichrepresentfourfundamentalprocesses:theformationofstars
through the transfer of baryons from the ISM, Ψ(t), which is di-
rectly fixed by the assumption SFR1, 2 or 3 discussed in § 2.1;
theformationofstructuresthroughtheaccretionofbaryonsfrom
theIGM,a (t);theejection of enriched gasbystars,e(t) and the
b
outflowofbaryonsfromthestructuresintotheIGM,o(t).
masslossrates(Vinketal. 2011;Vink&Grafener 2012),forsu- Inthemodel,wetrackthechemicalcompositionoftheISM
pernovamodels(Fryeretal. 2012),forthecommonenvelopphase andtheIGMasafunctionoftimeorredshift.Thedifferentialequa-
(Dominiketal. 2012),addingelectroncapturesupernovaeforNS tionsgoverningtheevolutionofthemassfraction XISM (XIGM)of
i i
formation (Belczynskietal. 2008a), and taking into account re- elementiintheISM(IGM)aregivenbyequations(6)and(7)in
cent observational constraints on massive stars in binary systems section2inDaigneetal. (2004).
(Sanaetal. 2012).Additionally,theevolutionarymodelincludedin Thebaryonaccretionrate,a (t)iscomputedintheframework
b
thecodedoesnotallowfortheprogenitorstoundergoacommon- ofthehierarchical scenarioofstructureformationandthebaryon
envelope phase whileone of the massive binary stars isevolving outflowrate,o(t),fromthestructuresincludesaredshift-dependent
throughtheHertzsprunggap(seeBelczynskietal. 2007,formore efficiency,whichaccountsfortheincreasingescapevelocityofthe
details). This corresponds to a conservative assumption and ad- structuresasthegalaxyassemblyisinprogress.
ditional NS-NS mergers may form if this assumption is relaxed. Weusetheframeworkofthehierarchicalscenariowheresmall
Compared to the results of Belczynskietal. (2002), this updated structuresareformedfirst.Atredshiftz,thecomoving densityof
calculationpredictsafractionofundetectedgalacticmergingNS- darkmatterhalosinthemassrange[M,M+dM]is f (M,z)dM,
PS
NSsystemssignificantlysmaller,nowatthelevelof∼ 10%.As with
illustratedinFig.3,
∞
thedistributionofcoalescencetimescalespredictedbysucha dM Mf (M,z)=ρ , (7)
PS DM
Z
detailedcalculationshowsabroadrangeofvalues:atsolarmetal- 0
licity Z = Z (resp. at metallicity Z = 0.1Z ), it is found that where ρ is the comoving dark matter density. The distribution
⊙ ⊙ DM
29%(resp.28%)ofsystemshave∆t 6 100Myr,13%(resp. functionofhalos f (M,z)iscomputedusingthemethoddescribed
NSM PS
16%) have 100 < ∆t 6 300 Myr, 15% (resp. 14%) have inJenkinsetal. (2001).We adopt arms amplitude σ = 0.9 for
NSM 8
0.3 < ∆t 6 1Gyr,17%(resp.16%)have1 < ∆t 6 3Gyr, massdensityfluctuationsinasphereofradius8h−1 Mpc.Weas-
NSM NSM
and26%(resp.26%)have∆t >3Gyr.Theimpactofthemetal- sumethatthebaryondistributiontracesthedarkmatterdistribution
NSM
licityissmall.Itappearsclearlythatasignificantfractionofsys- withoutanybiassothatthedensityofbaryonsisjustproportional
temshasacoalescencetimescaleofafew100Myrorless.These tothedensityofdarkmatterbyafactorΩ /(Ω −Ω ).
b m b
systemsmay dominatetheearlyevolution of theNSmerger, and Thefractionofbaryonsatredshiftzwhichareinsuchstruc-
thereforetheevolutionofEuatredshiftdiscussedinSect.4. turesisgivenby
(cid:13)c 2015RAS,MNRAS000,1–??
6 E. Vangioni,S. Goriely,F. Daigne,P.Franc¸ois,K. Belczynski
∞
dM Mf (M,z)
fb,struct(z)= RMm∞in PS . (8)
dM Mf (M,z)
0 PS
R
Therefore,themassfluxa canbeestimatedby
b
3H2 dt −1 df
a (t) = Ω 0 b,struct . (9)
b b 8πG! dz! (cid:12) dz (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
In addition to the NS an(cid:12)d BH bi(cid:12)rth rates, the CCSN rate,
and the NS-NS and NS-BH merger rates discussed in § 2.2 (and
of special interest in the present study), several other quantities
arefollowedasafunctionoftheredshiftz,namelytheWDbirth 1
rate,thetypeIasupernova rate,theabundances ofvarious chem- 0.8
ical elements, including Fe and Eu, in the ISM and the IGM,
0.6
the ionizing flux from stars, the ionization state of the IGM and
theThomsonopticaldepthoftheCMB.Adetaileddescriptionof 0.4
thiscosmicevolutionmodelcanbefoundinDaigneetal. (2006);
0.2
Rollindeetal.(2009);Vangionietal.(2014).
0
0 5 10 15 20
3.2 Observationalconstraintsonthechemicalevolution
model
Wetestedthateachcosmicevolutionscenariodiscussedinthispa-
perfulfillstwoimportantobservationalconstraints,namelytheob-
served cosmic evolution of [Fe/H] (corresponds to the logarithm
of the abundance of iron normalized to the solar one) and the
measured Thomson optical depth of the CMB.Following thede-
tailedanalysispresentedinVangionietal.(2014)fordifferentpos-
sibleSFRusingthesamecosmicevolutionmodel,thisleadstothe
choiceofthethreeSFRspresentedin§2.1.TheSFR1andSFR2
casesaredirectlytakenfromtheirstudy.
SFR1corresponds toastandardSFRwithanadditional Pop
III star component at high redshift, mainly motivated by the fact
that the ionizing flux at high redshift produced by the standard
mode onlyisnot largeenough toreproduce theThomson optical
depthoftheCMB(see§3.2.1).
SFR2isaSFRenhancedathighz.Thethirdmodeconsidered
here,SFR3,ischosenastheupperlimitoftheSFRathighredshift
obtained fromtheconstraint oftheThomson optical depthof the
CMB(seeFig.4).AsshowninFig.1,SFR1fitstheobservational
Figure4.Reionisation.Evolutionasafunctionofredshiftoftheionizing
constraintsfromBehroozietal.(2013);Bouwensetal (2014)and
flux(toppanel),volumefillingfractionQion(middlepanel)andThomson
Oeschetal.(2014),whereasSFR2andSFR3takeintoaccountthe
opticaldepth(lowerpanel)forthethreeSFRmodes(conventions arethe
studiesof(Trentietal.2013)andKistleretal.(2013),respectively. sameasinFig.1).WMAP9results fortheoptical depthathighredshift
(Hinshawetal.2013)areindicatedbyaredstripinthelowerpanel.
3.2.1 Reionization
Concerningtheionizationhistory,theevolutionofthevolumefill-
ingfractionQ (z)ofionizedregionsatredshiftzisgivenby
ion
dQ (z) 1 dn (z) dt
whediorzne nb=isntbhe cidoonzmov−inαgBdnebnCs(itzy)Qin2ionb(za)ry(1on+s,z)n3io(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)nd(zz(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)),the com(o1v0-) fltwhuhexeerfevoorσltuThteioistnhtrohefeetSThFheoRvmohsliuosmtnoersicefiasl,tltiaennrgidnfgtrhaeccrtroieosssnulsQteinciogtnioTannh.doFmtihgseo.n4ioonsphitzoiicwnagsl
ing density of ionizing photons, α the recombination coeffi-
B depth,thevalueofwhichisfoundtoagreewellwiththemeasure-
cient,andC(z)theclumpingfactor.Thislastfactor istakenfrom
ment from CMB observations by WMAP9 (Hinshawetal. 2013)
Greif&Bromm(2006)andvariesfromavalueof2atz620toa
at high redshift. Asmentioned above, theSFR1scenario without
constantvalueof10forz<6.Theescapefraction, f ,issetto0.2
esc thePop III mode at high redshift would not fulfillthis constraint
foreachofourSFRmodes.Thenumberofionizingphotonsemit-
(Vangionietal. 2014) and SFR3is adjusted to reproduce the up-
tedbymassivestarsiscalculatedusingthetablesgivenin(Schaerer
per limit on the optical depth. Note that the last results from the
2002).Finally,theThomsonopticaldepthbetweenredshiftsz′=0
PlanckCollaboration (2014,2015)givearevisedThomsonoptical
andziscomputedfollowing(Greif&Bromm2006),i.e.
depthτ=0.079±0.017.ThisvalueislowerthantheWMAP9one
z dt (τ=0.089±0.014).Consequently,inthiscontext,thecontribution
τ=cσ n dz′Q (z′)(1+z′)3 (z′) , (11)
T bZ0 ion (cid:12)(cid:12)dz (cid:12)(cid:12) ofPopIIIstarsintheSFR1modelshouldbelowered.
(cid:12) (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
(cid:13)c 2015RAS,MNRAS000,1–??
CosmicNSM RateandGW constrainedbytheR Process 7
3.2.2 Cosmicchemicalevolution:iron
Our model includes the stellar lifetimes estimated by
Maeder&Meynet (1989) for intermediate mass stars with
0.9 < M/M < 8andbySchaerer(2002)formoremassivestars.
⊙
Lifetimesof low mass stars (M/M < 0.9), such as the old halo
⊙
stars where abundances of Eu are measured at low metallicity,
are long enough for the star to be still observed today, whatever
the redshift of formation. Stars formed at redshift z inherit their
initial chemical composition from the abundances in the ISM at
thesame redshift. Thus, theobserved abundances instarsreflect,
in a somewhat complex way, the yields of all massive stars that
have exploded earlier. The stellar yields adopted in our model
depend on the stellar mass and metallicity. By default, we use
the tables of yields from (Woosley&Weaver 1995) for massive
stars (8 < M/M < 40). An interpolation is made between the
⊙
different metallicities(Z = 0, 0.0001Z , 0.001Z , 0.1Z and Z )
⊙ ⊙ ⊙ ⊙
andmasses,andtabulatedvaluesareextrapolatedforstarsbeyond
40M , whichcorrespond toasmall fractionof the population of
⊙
massive stars (i.e. (40−x−100−x)/(8−x−100−x) ≃ 8% for the
SalpeterIMFofindexx=1.35).
Fig. 5 shows the [Fe/H] evolution as a function of time and
redshift for the three SFR modes. Data correspond to chemical
abundance determinations in about 250 damped Lyα (DLA) sys-
tems(Rafelskietal.2012, andreferencestherein)asafunctionof
theredshift.Intheirpaper,theypresent47DLAsystemsatz > 4
observedwiththeEchelletteSpectrographandImagerandtheHigh
ResolutionEchelleSpectrometerontheKecktelescopes(formore
detailsseeVangionietal.2014).WeuseEq.(2)toassociateatime
withtheobserved redshift for each observed DLA system. Asil-
lustrated inFig. 5, the cosmic evolution of the ironabundance is
reproducedbyeachofthethreescenarios,passingthroughtheup-
per limitof the points. However, note that these ironabundances
aremeasuredinthegasphasewhichshouldbeconsideredaslower
limits due to depletion into grains in the ISM. As seen in Fig. 5
(middle panel), the early iron evolution depends strongly on the
shapeoftheSFRathighz.Inparticular,itcanbeseenthatacos-
mic [Fe/H] = −4 enrichment is achieved at the very beginning,
∆t=t−t ≃0.015GyrforSFR2,0.05GyrforSFR3,and0.4Gyr
0
for SFR1. Thistimedelay in theearly Feenrichment can havea
drastic impact on the interpretation of the early cosmic chemical
evolutionwithrespecttoobservations,asdiscussedinSect.4.
3.2.3 Cosmicchemicalevolution:otherelements
AsdetailedinVangionietal.(2014),thepresentcosmicevolution-
arymodelhasbeenusedtopredictthe“standard”chemicalevolu-
tionoflightelements,suchasC,N,OorMgandtotestitspredic-
tivepowerwithrespecttoavailableobservations(Sudaetal.2008,
2011).ThesensitivitytodifferentSFRhasalsobeenexplored.
• Carbon, oxygen. It was found that the [C/H] evolution as a
function of the iron abundance is essentially independent of the
adoptedSFRmodelfor[Fe/H]> −2orz < 4.Athigherz(lower
metallicity), the SFR including a Pop III mode (like SFR1) was
shown to be in better agreement with the observation of ultra-
metal-poorcarbon-enhancedstars,whichpresentsasignificantdis-
persion.Similarconclusionsweredrawnfortheoxygenevolution,
wherethePopIIIcontributiontotheSFR1modelallowsforahigh
production of O at low metallicities with a local peak in [O/H]
at [Fe/H] ≈ −4.8. Interestingly, this model can also explain the Figure5.Ironevolution.[Fe/H]evolutionasafunctionoftimet(upper
panels)orredshiftz(lowerpanel)forthethreeSFRmodes(linesarethe
oxygenabundancesinultra-low-metallicitystars(seeinparticular
sameas defined in Fig. 1).Themiddle panel focusses onthe early time
Fig.9inVangionietal.2014).
evolution,withtheinsertemphasizingthethreedifferenttimedelaysaround
the[Fe/H]=-4ironenrichment.DatacorrespondtoDLAsobservationsas
(cid:13)c 2015RAS,MNRAS000,1–?? afunctionofredshift(Rafelskietal.2012).Eq.(2)isusedtoconvertzinto
8 E. Vangioni,S. Goriely,F. Daigne,P.Franc¸ois,K. Belczynski
• Magnesium. As in the oxygen case, the inclusion of a high-
massmodelinSFR1atlargeredshiftdirectlyimpactstheevolution
ofMginstarformingstructures.ThepredictedMgpatterninthe
SFR1 case is, however, not observed at low metallicity (see Fig.
10 in Vangionietal. 2014). However, new studies in high mass
starsshow that Mg evolution at low metallicityremains sensitive
tothepredictednucleosynthesis inmassivezero-metallicitystars.
SuchcalculationshavebeenrecentlyrevisitedbyHeger&Woosley
(2010) who showed that in their models no Mg is produced in
zero-metallicity stars more massive than 30 M . In this case, the
⊙
early production of Mg in the three SFR cases discussed here is
foundtoreproducewellthebulkofdata,asshowninFigure10bof
Vangionietal.(2014).
• Localstellarmetallicitydistributionfunction(MDF).
We show in Fig. 6 the MDF derived by Anetal. (2013) us-
ingtheSDSSphotometricCataloguetogether withour computed
MDF based on the SFR1 mode (the other modes giving very
similar results). As found by Anetal. (2013), the in-situ photo-
metric metallicity distribution has a shape that matches that of
the kinematically-selected local halo stars from NorrisandRyan
(1991). For this reason, we adopt their SDSS calibration catalog
MDFasareferencesinceitpresentstheadvantage of expressing
theMDFdirectlyasafunctionof[Fe/H].Theglobalshapeofour
computedMDFisshowninFig.6tobeingoodagreementwiththe Figure6.Localmetallicitydistributionfunction,i.e.normalizednumber
observation.Wepointoutheretheimpactofthechoiceoftheiron of stars as a function of the iron abundance [Fe/H]. The MDF is calcu-
yieldsandtherelateduncertainties.Wepresentfourcurvesreflect- latedwithSFR1modeandtheredcircles totheobservedMDFdeduced
ing uncertainties mainly related to the CCSN mass cut. The blue by(Anetal. 2013)using SDSS photometry. Wepresent fourcurves ob-
curvecorrespondstothestandardyieldsfromWoosley&Weaver tained with different Fe yields reflecting uncertainties mainly related to
theCCSNmasscut.Bluecurve:standardyieldsfrom(Woosley&Weaver
(1995) adopted in the rest of the paper, which are varying with
1995)withyieldsvaryingwithmetallicity,greencurve:sameafterdivid-
metallicity,thegreencurvetothesameyieldsdividedbyafactor
ingtheseyieldsbyafactor2,dot-dashblackcurve:sameusingonlyyields
2,thedot-dash blackcurvetoyieldscalculatedfromsolar metal-
calculatedfromsolarmetallicitystarsonly,redcurve:samewhenusingthe
licity stars only, and the red curve to Fe yields determined by
ironyieldsdeterminedby(Kobayashietal.2006).
Kobayashietal.(2006).
• Stellarmass.AsshownbyVangionietal.(2014),thecosmic
evolution of the stellar mass as a function of the redshift is also dynamicalexplosionandneutron-starcoolingmodels(Janka2012;
found to be in good agreement with cosmological observational Hu¨depohletal.2010;Fischeretal.2010).Inaddition,nucleosyn-
photometric data (see their Fig. 12b), in particular for the SFR1 thesispredictionsofthedetailedcompositionoftheejectedmatter
mode. remaindifficultduetotheremarkablesensitivityofr-processcal-
culationtothestillunknowninitialpropertiesoftheejecta.
Inconclusion, basedonthepreviousstudyofVangionietal.
In contrast, NS-NS or NS-BH mergers, which today are
(2014) withinthe same cosmological context and on thebasis of
clearly favored from a nucleosynthesis point of view, have been
thesameSFRcases, itcan beconcluded that thestandard chem-
claimedtoberuledoutasthedominantr-processsourcebyearly
ical evolution is rather well reproduced by the cosmic evolution
studies on the basis of inhomogeneous chemical evolution mod-
of the star formation considered in the present study, and conse-
els(Argastetal.2004),duetotheirlowratesofoccurrencewhich
quently that the present model is well suited to describe the av-
seem to be inconsistent with observations of low-metallicity r-
eraged chemical history. The evolution of Milky Way-like galax-
process-richstars.Inaddition,thesignificantamount ofr-process
iesappears to be not far fromthe averaged history. Asdiscussed
material ejected by a single NSM leads to a large scatter in r-
recentlyinFrebelandNorris (2015),thisopensthepossibilityof
process enrichment at later times that does not seem to be con-
”near-fieldcosmology”basedonstellararcheology,especiallyus-
firmedbyobservations.
ingthepopulationoftheoldeststarsinthehaloofourGalaxyand
Recent studies (Matteuccietal. 2014; Komiyaetal.
indwarfgalaxies.WewillusethisapproachinthenextSectionto
2014; Cescutti&Chiappini 2014; Mennekens&Vanbeveren
studythecosmicevolutionofr-processelements.
2014; Tsujimoto&Shigeyama 2014a,b; Shenetal. 2014;
vandeVoortetal. 2015; Ramirez-Ruizetal. 2015) have recon-
sidered the chemical evolution of r-process elements in different
4 COSMICEVOLUTIONOFR-PROCESSELEMENTS
evolutionary contexts, and reached rather different conclusions.
Asfarasthegalacticchemical evolutionisconcerned, CCSNre- Morespecifically,Matteuccietal.(2014)exploredtheEuproduc-
mainpromisingsites,especiallyinviewoftheirpotentialtosignif- tion in the Milky Way using a local chemical evolution model.
icantly contribute to the galactic enrichment (Argastetal. 2004). Theirobservationalconstraintsatlowmetallicitycomeessentially
However, they remain handicapped by large uncertainties associ- fromtheobservations ofEuinmetal-poor starsbyFranc¸oisetal.
atedmainlywiththestillincompletelyunderstoodmechanismthat (2007), without including the related error bars and upper limits.
is responsible for the supernova explosion and the persistent dif- The relevance of the NSM scenario on the production of Eu has
ficulties to obtain suitable r-process conditions in self-consistent beenstudiedbytestingtheeffectof (i)thecoalescence timescale
(cid:13)c 2015RAS,MNRAS000,1–??
CosmicNSM RateandGW constrainedbytheR Process 9
ofthebinarysystem(ii)theEuyieldexpectedtobeejectedfrom gether with the abundances found in dwarf spheroidal sys-
NSMand(iii)therangeoftheinitialmassoftheNSprogenitors. tems (Shertone,Coˆte´&Stetson 2001; Shertone,etal. 2003;
Similarly, the CCSN scenario has been explored by considering Geilseretal. 2005; CohenandHuang 2009; Letarteetal. 2010;
different possible Eu yields assuming a strong r-process taking Starkenburgetal. 2013; McWilliametal. 2013).It isinteresting
placeinCCSN.Inthisframework,NSMisfoundtobepotentially tonotethatthebulkofdatacomingfromexternaldwarfgalaxies
a major r-process source if the coalescence timescale is of the isembeddedingalacticones.Thesolarabundancesaretakenfrom
order of 1 Myr and the ejected Euyieldof theorder of 3×10−7 Lodders (2003).
M foramassrangeofprogenitorsofNSrangingbetween9and
⊙
ThedeterminationofEuabundancesuffersfromthefactthat
50 M . The scenario where both CCSN and NSM contribute to
⊙
onlyfewtransitionsarevisibleinthespectrumofmetalpoorstars.
the Eu synthesis is also compatible with observations provided
NSMproduce2×10−7M ofEupersystemandeachCCSNwith Thestrongest transitionsare rather weak and it becomes particu-
⊙
progenitorsintherangeof20–50M producearound10−8−10−9 larlydifficulttodetectandestimatetheabundanceofthiselement
⊙
at low metallicities. Typically, the strongest Eu line becomes al-
M ofEu.
⊙
mostundetectablebelow[Fe/H]≃−3.5.Thedetectionorthenon-
Inparallel,Komiyaetal.(2014)investigatedthechemicalen-
detectiondependsontheS/Nratioofthespectrum,onthepresence
richmentofr-processelementsusingahierarchicalgalaxyforma-
ornotofanoverabundanceofEuinagivenstarandfinallyonthe
tionmodel.TheCCSNscenario isfoundtoreproduce thescatter
temperatureandgravityofthestar.Thissituationclearlyshowsup
ofobservedrabundancesinlowmetallicitystarsifabout10%of
inthediagramswherethenumber oftruedetectionofEuatvery
CCSN inthe low-mass end (i.e. for progenitor mass of the order
lowmetallicityareonlyahandful.Moreover,duetothescarcityof
of10M )isthedominantr-processsourceandthestarformation
⊙
efficiencyamountstoabout0.1perGyr.ForNSMtobethemainr- verymetal poor starsinthehalo, thenew verymetalpoor candi-
datesarefaintandrequireasignificantfractionofobservingtime
processsite,acoalescencetimescaleofabout10Myrwithanevent
on10mclasstelescopes.Consequently, thenumber ofstarswith
rateabout 100timeslargerthancurrentlyobservedintheGalaxy
[Fe/H]≃ −3.5forwhichtheEuabundancehasbeenmeasuredis
needtobeconsidered.
small.Thesampleusedinthepresentpaperdoesnotrepresentan
We note that the coalescence timescale in the studies by
unbiasedsampleofstars,sothedistributionfunctionof[Eu/Fe]vs
Matteuccietal. (2014) and Komiyaetal. (2014) is constrained
to be surprisingly short compared to known systems in our [Fe/H]hasnosignificance.Inseveral stars,theupper limitofthe
Eu abundance has been computed. These upper limits are useful
Galaxy and theoretical predictions by stellar population models
as they complement the real measurement and show that, so far,
(seeSect.2.2.3).
Cescutti&Chiappini (2014) computed inhomogeneous nostarbelow[Fe/H]≃ −3.5hasaveryhigh[Eu/Fe]ratio,i.e.of
theorderofwhatisfoundinstarsat[Fe/H]≃ −3.5.Althoughwe
chemical evolution models for the galactic halo, taking into ac-
cannotfullyruleouttheexistenceofsuchstarswith[Eu/Fe]>1.2
countthecontributionofelectron-captureandmagnetorotationally
driven supernovae (including fast-rotating progenitors), but not dex,thepresentsampleseemstoindicatethattheupper envelope
of the[Eu/Fe] stops to riseat [Fe/H] ≃ −3.0 Thishypothesis re-
NSM,toexplaintheEuscatterinmetal-poorstars.
ceives support fromtherecent study of Hansenetal.(2014) who
Mennekens&Vanbeveren (2014) also studied the temporal
analyzed4starswith[Fe/H]6 −4.00anddidnotreportanymea-
evolutionofthegalacticpopulationofdoubleNSbinaries,mixed
surement of the Eu abundance although the wavelength range of
systems with a NS and BH component, and double BH binaries.
thespectrausedinthisstudycoverstheEutransitionswavelength.
Theyconcludethat,exceptforthefirst100Myroftheevolutionary
phaseoftheGalaxy,doublecompactstarmergersmaybethema-
Theinspectionofobservedabundances(seeFig.7)showsthe
jorproductionsitesofr-processelements,anditisprobablethatthe
apparentexistenceoftwobranchesstartingbelow[Fe/H]≃ −2.5,
mixedNS-BHsystemsdominateoverdoubleNSbinarymergers.
thefirstonewithhighvaluesof[Eu/Fe]ashighas+2.0,thesec-
Finally,Shenetal.(2014)andvandeVoortetal.(2015)esti-
ondonewithdecreasingvaluesdownto[Eu/Fe]≃ −1.0at[Fe/H]
matedtheenrichmenthistoryofr-processelementsintheGalaxy,
≃−3.2.Asthesampleisbiased,itisdifficulttobefullyconfident
astracedbythe[Eu/Fe]ratio,usingahighresolutioncosmologi-
abouttherealityofthistwobranches.Theplotcouldalsowellbe
calzoom-insimulation.Unlikepreviousstudies,itwasfoundthat
interpreted as an increase of the dispersion as the metallicity de-
thenucleosyntheticproductsfromcompactbinarymergerscanbe
creases. Indeed, semi analytic models of merger tree which trace
incorporated intostarsofvery low metallicityandat earlytimes,
the chemical evolution of matter in different regions of the Uni-
even with a minimum time delay of 100 Myr and that compact
verse(fromover-tounder-denseregions)showclearlyadispersion
binary mergers could be the dominant source of r-process nucle-
growingasafunctionoftheredshift(Dvorkinetal.2015).
osynthesis.
InthepresentSection,webringourowncontributiontothis The origin of the stars with a high level of r-process ele-
difficultdebate. WefirstsummarizetheavailableEuobservations ments like Eu is still a matter of debate. A recent analysis by
andthenproposeadetailedcomparisonwithourpredictionsofthe Roedereretal.(2014b,c)hasshownandconfirmedthatthisover-
Euevolutionalongthecosmichistory,usingthethreepossiblecos- abundance isalsofound inmain-sequence turn-off starsrejecting
micSFRdensitydiscussedin§2.1. thehypothesisthatthestarwouldhaveproduceditselfsuchover-
abundances. They also did not find any compelling evidence to
suggestthatanoticeablehighfractionofhighlyr-processenriched
4.1 Eu:observations
starsaremembersofbinarysystems,assigningtheoriginofther-
We have gathered most of the recent observations on Eu abun- processenhancementtoacompanionstar.Theyalsoconfirmedthat
dance (Eu/H and [Eu/Fe] as a function of [Fe/H]) in metal thesepeculiar starsdonotpresent adifferentα-element chemical
poor stars(Franc¸oisetal.2007; Hondaetal.2004;Barklemetal. signaturefromthebulkoftheothermetalpoorstars.Therefore,the
2005; Simmereretal. 2004; Roederer 2011; Roedereretal. siteresponsiblefortheproductionofthisr-processenhancementis
2010, 2012, 2014a,b,c; Renetal. 2012; Worleyetal. 2013) to- notexpectedtoproduceanychemicalanomaliesforlightelements.
(cid:13)c 2015RAS,MNRAS000,1–??
10 E. Vangioni,S.Goriely,F.Daigne,P. Franc¸ois,K. Belczynski
Figure7.CosmicevolutionofEu:comparisonbetweenthetwopossibleastrophysicalsitesEu/Hand[Eu/Fe]vs[Fe/H].EvolutionofEu/Hand[Eu/Fe]
asafunctionof[Fe/H]eitherintheCCSN(bluelines)orintheNSM(blacklines)scenario.TheevolutioniscomputedforthethreeSFRmodesconsidered
inthepresentstudy,SFR1(solidlines),SFR2(dottedlines),SFR3(dashedlines).IntheCCSNscenario,theEuyieldis10−7M⊙persupernova.IntheNSM
scenario,theEuyieldis7×10−5M⊙permerger,thefractionofbinarycompactobjectsisα=0.002andthecoalescencetimescaleis∆tNSM=0.2Gyr.Data
pointscomefromdifferentreferences:blackpointsandupperlimitsatlowmetallicityfrom(Franc¸oisetal.2007),brownpointsathighermetallicityfrom
(Simmereretal. 2004),yellowfrom(Barklemetal.2005),magentafrom(Renetal.2012),redfrom(Roedereretal.2010,2014a,b),heavybluepointsfrom
(Roedereretal.2014c).Thebulkofblackpointsathighmetallicitycomefromdwarfspheroidalsystems(Shertone,Coˆte´&Stetson 2001;Shertone,etal.
2003;Geilseretal. 2005;CohenandHuang 2009;Letarteetal. 2010;Starkenburgetal. 2013;McWilliametal. 2013).
Figure8. SameasFig.7butwithouterrorbars.
4.2 Eu:yieldsfromCCSNandNSM ofr-processelementsintheCCSNscenarioessentiallydependson
the amount of r-process material ejected by the explosion, in the
Eachofthetwopossibler-processsites,CCSNandNSM,maypo-
NSMscenario,itisalsofunctionofthebinaryfractionofcompact
tentiallycontributetothegalacticr-processenrichment,butwewill
objectsαandthecoalescencetimescaleofthebinarysystem∆t .
NSM
assumeinthepresentworkthattheyaremutuallyexclusive,sothat
WedescribeheretheadoptedyieldsofEuexpected tobeejected
thether-processintheUniverseiseitheroriginatingfromCCSNor
fromCCSNorNSM.
NSMbutnotfromamixofbothsites.Whilethecosmicevolution
(cid:13)c 2015RAS,MNRAS000,1–??