On the R-Process Enrichment of Dwarf Spheroidal Galaxies

0.43 MB·

by  Joseph Bramante

DRAFTVERSIONNOVEMBER4,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
ONTHER-PROCESSENRICHMENTOFDWARFSPHEROIDALGALAXIES
JOSEPHBRAMANTE1,TIMLINDEN2
1DepartmentofPhysics,225NieuwlandScienceHall,
UniversityofNotreDame,NotreDame,IN46556,USAand
2CenterforCosmologyandAstroParticlePhysics(CCAPP)andDepartmentofPhysics
TheOhioStateUniversity,ColumbusOH,43210,USA
DraftversionNovember4,2016
ABSTRACT
6 RecentobservationsofReticulumIIhaveuncoveredanoverabundanceofr-processelements,comparedto
1 similar ultra-faint dwarf spheroidal galaxies (UFDs). Because the metallicity and star formation history of
0
ReticulumIIappearconsistentwithallknownUFDs, thehighr-processabundanceofReticulumIIsuggests
2
enrichmentthroughasingle,rareevent,suchasadoubleneutronstar(NS)merger. However,wenotethatthis

v scenario is extremely unlikely, as binary stellar evolution models require significant supernova natal kicks to
o produceNS-NSorNS-blackholemergers,andthesekickswouldefficientlyremovecompactbinarysystems
N from the weak gravitational potentials of UFDs. We examine alternative mechanisms for the production of
r-processelementsinUFDs,includinganovelmechanismwhereinNSsinregionsofhighdarkmatterdensity

2 implode after accumulating a black-hole-forming mass of dark matter. We find that r-process proto-material
ejectionbytidalforces,whenasingleneutronstarimplodesintoablackhole,canoccurataratematchingthe
] r-processabundanceofbothReticulumIIandtheMilkyWay. Remarkably,darkmattermodelswhichcollapse
E
asingleneutronstarinobservedUFDsalsosolvethemissingpulsarproblemintheMilkyWayGalacticcenter.
H
Weproposetestsspecifictodarkmatterr-processproductionwhichmayuncover,orruleout,thismodel.
.
h
p
The Dark Energy Survey has discovered a new dwarf neutrons. Within recent decades, core collapse supernovae
-
o spheroidal galaxy, named Reticulum II, which lies at a dis- havebeenconsideredasasourceofr-processmaterials(Dun-
r tance of only ∼30 kpc from Earth (Bechtol et al. 2015; Ko- can et al. 1986; Meyer et al. 1992). However, r-process el-
t
s posov et al. 2015). The proximity of Reticulum II bene- ements in Milky Way (MW) stars show characteristic peak
a fits indirect searches for dark matter (DM) annihilation. In abundancesatatomicmassesA=80,130,195(Burbidgeetal.
[ fact, an analysis of data from the Fermi Large Area Tele- 1957),andtheentropyprovidedbycore-collapsesupernovae

scope found a tentative (2.4 – 3.2σ local significance) ex- appearstoolowtoreproducethethirdpeak(Qian&Woosley
2
cessinGeVγ-raysemanatingfromthepositionoftheRetic- 1996; Thompson et al. 2001; Fischer et al. 2010). Al-
v
ulum II dwarf (Drlica-Wagner et al. 2015; Geringer-Sameth ternatively, decompressing neutron fluid ejected from, e.g.,
4
8 etal.2015;Hooper&Linden2015). Spectroscopicmeasure- the merger of a neutron star (NS) with another NS or a
7 ments of Reticulum II stars identify Reticulum II as an ul- black hole (BH), reproduces the A=195 peak (Lattimer &
6 trafaint dwarf spheroidal galaxy (UFD), with total stellar lu- Schramm 1976; Lattimer et al. 1977; Eichler et al. 1989;
0 minosity of only 2360±200 L(cid:12) and a mass to light ratio of Davies et al. 1994; Freiburghaus et al. 1999), and could
. 470±210 (Simon et al. 2015), making it an excellent target be the source of most r-process elements (Symbalisty &
1
for DM indirect detection studies (Simon et al. 2015; Bon- Schramm1982;Arnouldetal.2007;Surmanetal.2008;Shen
0
nivardetal.2015). et al. 2015; Matteucci et al. 2014; van de Voort et al. 2015;
6
RecentmeasurementsofstellarspectraindicatethatReticu- Cescutti et al. 2015). More recent proposals for r-process
1
lumIIisuniqueamongknownUFDs.Themajorityofstarsin production include the accretion induced collapse of white
:
v ReticulumIIareoverabundantinelementsheavierthanZinc, dwarfs (Woosley & Baron 1992) and rapidly rotating mag-
i a signature of rapid neutron capture (aka r-process) enrich- netars(Metzgeretal.2008).
X
ment(Jietal.2015a;Roedereretal.2016a). Thisisintrigu- Anothermethodtodistinguishbetweenr-processmodelsis
r ing, because nine similar UFDs, namely Segue 1, Hercules, to utilize the stochasticity of r-process enrichment in small,
a
LeoIV,SegueII,CanesVenaticiII,BootesI,BootesII,Ursa isolated, metal poor systems (e.g. UFDs). For example, lest
MajorII,andComaBerenices,showonlytracer-processen- they overproduce r-process elements, frequent iron core col-
richment (Ji et al. 2015b), which may be consistent with r- lapse supernovae must each produce a small r-process abun-
process materials accreted through interactions of these sys- dance((cid:46)10−7M ),andalsointhiscaser-processabundance
(cid:12)
tems with the Galactic disk. Moreover, the s-process metal- shouldscalewithstellarmetallicity. Ontheotherhand,dou-
licityofReticulumII,[Fe/H]=-2.65+0.07 (Simonetal.2015) ble NS mergers are expected to be rare and so they can pro-
−0.07
is consistent with, and even lower than, other UFDs (Kirby duce copious r-process materials ((cid:38) 10−4 M ). Thus, the
(cid:12)
et al. 2008; Koch & Rich 2014; Frebel et al. 2014; Ji et al. observationofsignificantr-processenrichmentinReticulum
2015b). Two of the nine stars observed by Ji et al. (2015a) II (alongside its typical metallicity for an ultrafaint dwarf
shownor-processenrichment,apossibleindicationofmulti- spheroidal galaxy), and the lack of r-process enrichment in
plestarformationepochs. anyotherUFD,pointstowardsarareevent,likeadoubleNS
The excess of neutron-rich elements in Reticulum II has merger,forther-processenrichmentofReticulumII(Jietal.
implications for the production of heavy r-process elements, 2015a). However,aswewillshow,NSmergersinUFDsap-
which occurs at astrophysical sites harboring copious free peartooraretoaccountfortheenrichmentofReticulumII.
2 Bramante&Linden
- 10Myr 50Myr 100Myr 500Myr 1Gyr 10Gyr atametallicity[Fe/H]=-2.30findingtheresultstobeidenti-
10km/s <0.0001 <0.0001 <0.0001 0.0011 0.0016 0.0023 caltowithinthelevelofPoissonnoise1. Inwhatfollowswe
20km/s <0.0001 0.0004 0.0008 0.0085 0.0125 0.0183 quotethestatisticalresultsforsimulationsathighermetallic-
50km/s <0.0001 0.0064 0.0136 0.0569 0.0801 0.1345 ity,asthelargernumberoftestsystemsdecreasedthePoisson
100km/s 0.0002 0.0151 0.0378 0.1519 0.2202 0.4497 noisefortheserareevents. Weremainagnosticastothebest
modelsofbinarystellarevolutionandmarginalizeourresults
Table1
overall16modelspresentedin Dominiketal.(2012). Con-
servatively(realistically)assumingthattheNS-NSorNS-BH
The Number of Expected NS-NS and NS-BH mergers within the popula-
tionofUFDsconsideredinJietal.(2015a),forvariousvaluesoftheUFD mergermustoccurwithin1Gyr(100Myr)fromsystemfor-
escapevelocity,andthemaximumageoftheNS-NSorNS-BHmergernec- mationtoproducer-processmaterialsbeforetheformationof
essarytoproducer-processenrichmentintheReticulumIIdwarf. Wenote the remaining UFD stellar population, we find that 2.1 (1.5)
thattheconstraintsinSection1arguestronglyforamaximumkickvelocity
NS-NS and NS-BH mergers would be expected among the
∼10kms−1 andanage∼100Myr,whichresultsintheproductionofvir-
tuallynoNS-NSorNS-BHmergers. Theremainderofthecolumnsshown UFDpopulation,inlinewithexpectations.
inthistabledonotillustratereasonableparameterspacechoices,butmerely However, the progenitor compact objects in a NS-NS and
illustratetherobustnessofourresulttocorybanticvariations. NS-BHmergermustundergosignificantnatalkickstomove
the system into a tightly bound, eccentric orbit (Willems
& Kalogera 2004). At the time of reionization, the pro-
In this article we examine the viability of many r-process genitors of observed UFDs are expected to have masses
production models in light of the r-process abundances now ∼107 M (Salvadori & Ferrara 2009; Webster et al. 2015;
(cid:12)
observedinbothUFDsandtheMW.Wealsoproposeanew Bland-Hawthorn et al. 2015), and escape velocities given
r-processproductionsite: theneutron-richfluidejectedfrom by(Bovill&Ricotti2011):
DM-induced implosions of NSs. We find that DM-induced
NS implosions could account for both the r-process abun- (cid:18) M (cid:19)1/3(cid:20)1+z(cid:21)1/2km
danceobservedinReticulumIIandtheMW.InSection1we v = 10.9 (1)
esc 107M 9.5 s
study the rate of NS mergers in UFDs and find this scenario (cid:12)
for r-process production to be disfavored at >3σ. Section 2 ExaminingthemodelsofDominiketal.(2012)andremov-
examinesalternativeproposalsforr-processproduction.DM- ing binaries that received a center of mass kick (during ei-
imploded NSs are introduced as an r-process production site thercompactobjectformationevent)largerthan10km/s(20
inSection3,andDMr-processenrichmentofUFDsandthe km/s), we find that the total UFD population would be ex-
MW is compared to other proposals in Section 4. Section 5 pectedtoproduce<0.0001(0.0008)mergerswithin100Myr
notesthatacomparisonbetweenther-processenrichmentof after binary formation, and 0.0016 (0.0125) mergers within
UFDs and that of globular clusters can provide a diagnostic 1Gyrafterbinaryformation. InTable1wesummarizethese
test specific to DM dominated r-process production. In Sec- results,includingseveraladditionalmodelsforboththemaxi-
tion6, weconcludewithadditionalapplicationsofr-process mummergerageandescapevelocityfortheUFDpopulation.
observationstostudiesofDM,primordialblackholes,andby We note that Reticulum II may have a unique star formation
extensiontheprimordialpowerspectrum. history, DMhaloformationhistory, orescapevelocity, com-
paredtootherUFDs. IncaseReticulumIIhasspecialprop-
1. NEUTRONSTARMERGERSINUFDS erties compared to other UFDs, we recalculated the number
Duetothelow-starformationrateinUFDs,itisreasonable of expected NS mergers, based on the 2.6×103 M of star
(cid:12)
to ask whether any NS-NS or BH-NS mergers are expected formationobservedinReticulumII.Withthissmallerstellar
in the population of observed UFDs. Observations indicate population,wefindthatr-processeventsinReticulumIIfrom
thatthetotalstarformationhistoryofall10UFDsstudiedby aNSmergerbecomeslesslikely.
Jietal.(2015a)amountstoonly1.0×105 M (Bechtoletal.
(cid:12) 2. ALTERNATIVEASTROPHYSICALMODELS
2015; McConnachie 2012). While mass loss and tidal dis-
ruption may distort these measurements, we note that these In the prior section we have considered the merger of bi-
observationslieonthemass-metallicityrelationship,indicat- naries, occurring through the joint stellar evolution of two,
ing that the mass lost from these systems has not drastically initiallyboundstars. However,alternativescenariosarepos-
affected their stellar populations since the onset of their first sible. Forexample, inglobularclusters, themajorityofstel-
supernovae(Kirbyetal.2008). Inordertocalculatethetotal lar encounters are believed to occur through n-body dynam-
number of NS-NS and NS-BH binary progenitors in UFDs, ics,duetothehighstellardensityinglobularclustercenters.
weemployaKroupa (Kroupa&Weidner2003)initialmass However,UFDs,areexpectedtobeunderdense(comparedto
functionwithaminimumstellarmassof0.08M andahigh- globularclusters)bynearlysixordersofmagnitude, making
(cid:12)
mass index of α = 2.7, and conservatively assume a binary stellar encounters negligible. A more important considera-
fractionofunity,withaflatsecondarymassdistribution(Kob- tion,iswhetherNS-NSandNS-BHmergersinUFDscouldbe
ulnickyetal.2006). UsingthesevalueswefindthattheUFD enhancedduetoKozaioscillationsintriplesystems(Thomp-
population could form ∼800 initial binary systems with an son 2011; Sharpee & Thompson 2013). Notably, the eccen-
initialprimarymassexceeding5M . tricities induced in the binary orbit through the Kozai mech-
(cid:12)
To calculate the number of NS-NS mergers produced by anism can vastly decrease the merger time between widely
this ensemble of systems, we utilize the results of Dominik separated binary companions. If we remove our cuts on the
et al. (2012) , noting that the modeled results are produced
at a higher metallicity of [Fe/H] = -1.0, and that this choice 1 We acknowledge the Synthetic Universe Project
(www.syntheticuniverse.org) for making the intermediate data products
is conservative given that NS-NS mergers are similarly effi-
of Dominik et al. (2012) publicly available for usage in these calcula-
cient at both metallicities (Dominik et al. 2013). We have tions, as well as Michal Dominik and Chris Belczynski for providing the
confirmed this result using a simulation of 2.0×106 binaries low-metallicitydatasetfromDominiketal.(2013).
3
binarymergertimeintheprevioussection(assumingthatthe lived,andmanyformafterthe500Myrsimulationtimenec-
Kozai Mechanism produces a binary merger within the re- essary to produce r-process enrichment in our model. Addi-
quired100Myrtimeframeregardlessoftheinitialbinarycon- tionally, observations of globular clusters indicate that low-
figuration)thenwewouldproduce1.7(2.0)NS-NSandNS- mass X-Ray binary formation is stronger in higher metallic-
BH binaries with maximum kick velocities of 10 km/s (20 ity systems than at low-metallicities (Kim et al. 2013). Al-
km/s). However,thefractionoftriplesinUFDsisunlikelyto together, it seems r-process enrichment of Reticulum II via
beunity,anditmayalsobedifficulttokeepthesewidelysep- directcollapseofaNSisdisfavored.
arated, low-mass, triple systems bound due to the mass loss A final possibility is that a NS merger occurred in Retic-
andnatalkicksofeachsupernova. Afullinvestigationofthis ulum II, but that the NS binary was sourced by another star
effectiswarranted,butliesbeyondthescopeofthispaper. forming region, such as the ancient stars of the MW bulge.
A second possibility includes r-process enrichment from Assuming a total star formation of 1010 M within the first
(cid:12)
only a small subset of supernova events, such as those that Gyr after bulge formation (Wyse 2009), we calculate an ex-
produce a rapidly spinning, high-magnetic field, magne- pectedpopulationof∼4×105 doubleNSmergers,themajor-
tar(Metzgeretal.2008;Nishimuraetal.2015;Tsujimoto& ityof whichhappen farfromthe MWbulge duetothe natal
Nishimura 2015). While none have been observed, they are kicks given to the NS population. Using the kick velocities,
expectedtobeshortlived,andsomayhaveescapeddetection andbinarymergertimescalculatedinDominiketal.(2012),
thus far. Since the rate of rapidly rotating magnetars can be wefindonlyaprobabilityofonly0.008%thatabinarymerger
adjustedfreely,itisdifficulttoutilizestochasticityarguments could occur within 100 pc of Reticulum II, assuming an av-
todeterminewhetherthismechanismcouldproduceasingle erageseparationbetweentheMWcenterandReticulumIIof
r-processeventthroughoutthepopulationofUFDs. 20kpcduringthatepoch. However,thisnumbermaydramat-
Some authors have argued for r-process enrichment con- ically increase if the Reticulum II dwarf resided close to the
nected to the accretion induced collapse of a white dwarf MWbulgeduringearlyperiodsofintensestarformation.
into a NS (Woosley & Baron 1992). While this method is
connected to binary dynamics, its rate, dynamical equation 3. THER-PROCESSFROMDARKMATTER
of state, and r-process yield are unknown (Fryer et al. 1999;
The r-process abundance in Reticulum II and the MW,
Thompson et al. 2001; Piro & Thompson 2014). However,
couldresultfromdarkmatterinstigatingloneNSimplosions
similar to core collapse supernovae, individual accretion in-
thatejectneutron-richfluid. Extensiveradiosearchesbythe
duced collapse events imply r-process abundance scales lin-
GreenBanksTelescopeandAreciboarrayoftheinnerparsecs
early with star formation rate, and thus metallicity, while
oftheMilkyWaygalaxy,havenotrevealedtheexpectedpop-
ReticulumIIandotherobservedUFDsaremetalpoor.
ulationofgalacticcenter(GC)pulsars(Macquartetal.2010;
Itshouldalsobeconsideredwhetherr-processenrichment
Wharton et al. 2012; Dexter & O’Leary 2014; Chennaman-
of Reticulum II might result from direct, accretion-induced
galam & Lorimer 2014). In Bramante & Linden (2014), we
collapse of a NS, an event that should be significantly rarer
foundthatDMcouldimplodeNSsintheGCandthusaccount
thantheAICofwhitedwarfs.AICofaneutronstarwouldre-
forthemissingpulsars.Darkmatter,moredenseinthecentral
sultaftereitherahigh-massorlow-massX-Raybinaryphase
parsecoftheMilkyWay,canaccumulateatthecenterofNSs
with mass transfer rates near the Eddington limit, which is
and form a star-consuming BH within t ∼105−108 years,
∼10−8 M yr−1 for a NS. Assuming a maximum NS mass c
(cid:12) dependingonthemass,localDMdensity(ρ ),andnucleon
of2M andaninitialNSmassof1.4M ,thiscorresponds DM
(cid:12) (cid:12) scatteringcross-section(σ )oftheDMparticle.
to persistent Eddington limited accretion over the course of nX
OutsidethecenteroftheMilkyWay,measurementsofthe
60 Myr. While some NS systems (e.g. the recently discov-
characteristic age of pulsars, corroborated by the ages of bi-
eredM82X-2(Bachettietal.2014)),mayproduceX-Raylu-
nary partner white dwarfs, indicate that disk pulsars reach
minositiesthatsignificantlyexceedtheEddingtonlimit,these
agesofatleast∼Gyr(Bramante&Elahi2015). Thisputsan
systems are thought to be transient, with the majority of ob-
upperboundonσ foranumberofDMmodels(Goldman&
served NS X-Ray binaries having maximum luminosities no nX
Nussinov 1989; Starkman et al. 1990; Bertone & Fairbairn
morethanafactoroftwoabovetheEddingtonLimit(Grimm
2008; Kouvaris 2008; de Lavallaz & Fairbairn 2010; Kou-
etal.2003). Inthecaseofhigh-massX-Raybinaries,model
varis&Tinyakov2011a;McDermottetal.2012;Kouvaris&
runs performed at low metallicity (Z = 0.02Z ) predict only
(cid:12) Tinyakov 2011b; Kouvaris 2012; Bramante et al. 2013; Bell
0.03 NS X-Ray binaries which produce consistent emission
etal.2013;Bertonietal.2013;Bramanteetal.2014;Güver
approaching the Eddington Luminosity for a starburst of
et al. 2014; Zheng et al. 2015; Ángeles Pérez-García & Silk
the size expected in all observed UFDs – 105 M (Linden
(cid:12) 2015;Britoetal.2015;Kurita&Nakano2016).
et al. 2010). Systems with significantly brighter emission,
Although NSs in the Milky Way disk may be as old as
suchasM82-X2havestablemasstransferperiodslimitedto
1010 yrs, NSs can still quickly implode in the Galactic cen-
∼105 yr(Fragosetal.2015). Inthecaseoflow-massX-Ray
ter. TheDMcapturerateinNSsscaleslinearlywithρ and
DM
binaries,RocheLobeoverflowsystemsmaypersistonmuch
σ . Therefore,becauseDMdensityatthecenteroftheMW
nX
longer timescales. Constraining ourselves to systems which
isupto104timesdenserthaninthedisk,pulsarsinthecentral
transfer 0.6 M within 500 Myr, we consider any persistent
(cid:12) parsecscancollapseafter(cid:46)106 yrs,andarepotentiallysen-
system with an X-Ray luminosity above 0.1L , or approx-
edd sitiveto104 timeslargerσ (deLavallaz&Fairbairn2010;
imately 1×1037 erg s−1. Studies by (Fragos et al. 2008) in- nX
Bramante & Linden 2014). During NS collapse, the recon-
dicate that approximately 1.7×10−4 persistent LMXBs, with
figurationoftheNS’smagnetosphereradiates∼1042ergina
luminosities exceeding 1037 erg s−1, would be produced in a
millisecond;henceDM-inducedNSimplosionscouldalsobe
105 M system. While this model assumes higher metallic-
(cid:12) thesourceoffastradiobursts(FRB)(Fuller&Ott2015).
ityandcontinuousstarformation,thisisconservativeforour
For concreteness, in the following calculation of the r-
calculation, aslow-massX-Raybinariesareextremelylong-
processyieldfrom aDMinducedNS implosion, weassume
4 Bramante&Linden
a non-annihilating, negligibly self-interacting DM candidate 10Gyrforρ ∼104 GeVcm−3,see(Bramanteetal.2013).
DM
with a mass m = 10 PeV, that can either be bosonic or As the BH grows, the Roche limit expands, passing through
X
fermionic, and with a DM-nucleon scattering cross-section theentireNSbythetimeM ∼0.02M .
BH (cid:12)
σ (cid:38)10−45cm2. ThereareadditionalDMmodels,e.g. shift- To approximate the time for a natal black hole to grow to
nX
symmetricbosons(Bramante&Linden2014)andHiggspor- MBH ∼0.02 M(cid:12), at which point it squeezes and consumes
tal fermions (Bramante & Elahi 2015), which would induce thebulkoftheNS,weemploytheBondiaccretionrateasin
GCpulsarcollapseforDMmassesm =keV−PeV. Wecon- (Markovic1995;Kouvaris&Tinyakov2014). TheBondiac-
X
siderPeVmassDMbecauseitspredictedcross-sectioncom- cretionrateofneutronfluidontotheblackholeisdMBH/dt=
plements imminent direct detection searches and it may be 4πλ G2M2 ρ /v3, where, in what follows, we take typical
s BH n s
responsible for type Ia supernovae ignition (Bramante 2015; valuesfortheneutronfluid’ssoundspeedv ∼0.3c,density
s
Graham et al. 2015). We assume NSs with radius RNS ∼ ρn ∼1015g/cm3, and accretion constant, λ=0.25, (Shapiro
10 km, mass MNS ∼1.5 M(cid:12), temperature TNS ∼104 K, and &Teukolsky1983). BecausetheBHgrowthrateaccelerates
central density ρ ∼ 1015gcm−3. With these parameters, withaddedmass,thetimefortheBHtoconsumetheremain-
NS
anyσnX inexcessof10−45 cm2 saturatesthegeometriccross- deroftheNSissetbyitsinitialmass. FormX=10PeVmass
sectionforDMcaptureinaNS.Therefore,∼PeVmassDM- DM, a BH forms once ∼10−14 M DM has collected at the
(cid:12)
induced NS collapse models are robust against variations in center of the NS, (Colpi et al. 1986; Bramante 2015). This
σ . Fordetails,see(Bramante2015). BHgrowsuntiltheRochelimitencompassestheNSafter
nX
Hereafterwedemonstratethatduringthegrowthofasmall
v3 (cid:18)10−14M (cid:19)
BejHectiendsidaesaaNreSsu,l∼to1f0t−i5d−al1s0q−u1eMez(cid:12)innge.uTtroonp-rreiccihseflluyiddectoeurmldinbee timp∼ 4πλsG2sMBHρn (cid:39)50 MBH (cid:12) yrs. (4)
themassejected,itwouldbenecessarytoperformadetailed
This also implies that in a span of ∼ 1 ms, the remaining
hydrodynamicsimulationoftidalforcesduringthe(likelytur-
1.4M ofneutronfluidcrossestheRochelimit.
bulent) process of a NS’s rapid inward accumulation onto a (cid:12)
Finally, we note that because the bulk of the NS is ac-
growing black hole. We leave hydrodynamic simulations to
cumulated within ∼ 1 ms, this disfavors the canonical r-
futurework. Intheremainderofthissection,we(1)findthe
processproductionmechanismproposedforcorecollapsesu-
maximum mass of r-process elements ejected, (2) show that
pernovae (Woosley et al. 1994), wherein an outpouring of
thephysicalconditionspromptingneutronfluidejectionina
neutrinos heat nuclear material expelled from the surface of
NS-BH merger are also present when a NS implodes into a
aproto-neutronstar(Duncanetal.1986). Inthestandardsce-
blackhole,and(3)findthatsubstantialmassejectionbyneu-
nario,whichassumessteady-stateneutrino-drivenmassejec-
trinoemissionmustoccuroutsideasteady-stateregime.
tionfromacollapse-heatedNS,theneutrinosandneutronstar
Tosetanupperlimitonthemassthatescapesfromanim-
crustmustbeinthermalequilibrium,whichisestablishedaf-
plodingNS,wespecifythebindingenergyoftheimplosion,
ter ∼1 s, too long compared to a ∼1ms timescale for the
E ≈ 3GM2 (R−1 −R−1)/5 = 3×1057(M /1.5M ) GeV,
i NS Sch. NS NS (cid:12) DM-inducedNSimplosion.
where R is the star’s Schwarzschild radius. We compare
Sch.
thisbindingenergytotheenergyrequiredtoaccelerateanu- 4. DARKR-PROCESSPRODUCTIONINUFDSANDTHEMW
cleontoescapevelocity(v ∼0.7c)atthesurfaceoftheNS,
ej ThissectionexaminestheDMr-processenrichmentofthe
E =γ(v )m ,wherem isthenucleonmass. Themaximum
a ej n n Milky Way and UFDs. Results in the previous section indi-
massofejectedmaterialis
catethateachDM-inducedNSimplosionresultsin1.5M of
(cid:12)
(cid:18) (cid:19)(cid:18) (cid:19) NSmaterialcrossingtheRochelimitofablackhole. Recent
E M 1.4
Mej≤mnEi (cid:46)0.2 1.5MNS γ(v ) M(cid:12). (2) simulations of NS-BH mergers find that ∼10−4−10−1 M(cid:12)
a (cid:12) ej of ejecta is expelled at ∼0.1−0.3 c as NSs cross the Roche
R-process production accompanies a NS-BH (or NS-NS) limit of 3−10 M(cid:12) mass black holes, with lower mass and
mergerwhenejectedneutron-richfluidsdecompress,provid- higher spin BHs tending to yield higher mass ejecta, (see
ing enough free neutrons to synthesize heavy elements (Lat- e.g. Shibata & Taniguchi 2011; Foucart et al. 2013; Deaton
timer et al. 1977; Tanaka et al. 2014; Bauswein et al. 2014). et al. 2013; Bauswein et al. 2014; Kyutoku et al. 2015).
ThemechanismforneutronfluidexpulsionfromaNSasitap- Hereafter, we show that MW and UFD r-process enrich-
proachesablackhole,firstdescribedin(Wheeler1971)asthe ment from DM-induced implosions, favors an ejecta mass
"tubeoftoothpaste"effect,wasdevelopedinFishbone(1973); M ∼10−5−10−3M .
ej (cid:12)
Mashhoon(1975);Lattimer&Schramm(1976). Asneutron Studiesoftheproductionandhydrodynamicredistribution
fluidcrossestheRochelimitofablackhole(orothercompact ofr-processelementsintheMilkyWay(Argastetal.2004),
body), the tidal squeeze from the black hole will eventually have recently been significantly improved to account for the
exceedtheself-gravityoftheneutronfluid. Theresultingse- time-evolved migration of r-process elemental abundances,
verecompressionpropelsstreamsofneutronfluidawayfrom including the affects of galactic subsystem mergers, mixing
theblackhole. in the interstellar medium, and (outflows from) star forma-
Hereweverifythatduringdark-matter-inducedNSimplo- tionduringthedynamicalevolutionoftheMilkyWay(vande
sions,theentireNScrossestheRochelimitasitflowsintothe Voort et al. 2015; Shen et al. 2015; Wehmeyer et al. 2015).
black hole formed at its center. Initially, the Roche limit for Particularly,ithasbeenshownthat,aslongasr-processpro-
theneutronfluidsurroundinganewlyformedBHis ductioneventsoccuratsiteswhereneutronstarshaveformed
within the inner kpc of the Milky Way, models will match
(cid:18) M (cid:19)1/3(cid:18)1014gcm−3(cid:19)1/3 the observed r-process abundance and scatter in [Fe/H] ver-
R (cid:39)20 BH m, (3)
Roche 10−10M ρ sus [Eu/Fe] to presently available precision. The work of
(cid:12) NS
(vandeVoortetal.2015)demonstratedthatr-processchemi-
where∼10−10M isthemaximumDMmassaNScollectsin cal evolution is consistent with observations so long as two
(cid:12)
5
1013 star merger scenario. This conclusion is supported by simu-
lations, showing that after r-process elements are produced,
they are mixed through the outer ∼30 kpc of the MW on (cid:46)
3 yrs)1012 DM rm-partoccheesss MamWount GyArstipmreevscioaulessly(veaxnpldaeinVeodo,rttheetoabl.se2r0v1e5d;aSbhuenndeatncael.a2n0d15sc).at-
-m ter of r-process elements observed in the MW require ∼
c1011 104 M ofr-processproductionover∼1010 yrs,withasub-
V (cid:12)
Consistent with missing pulsars, stantial fraction produced within ∼107 yrs of the initial star
e
G type Ia SN ignition, and FRBs formation epoch. The second requirement is fulfilled natu-
(c 1010 rallybyGCNSimplosions, whichoftenoccurwithin∼107
× t yrsintheinnerkiloparsec,forDMparametersthatsolvethe
M missing pulsar problem (the parameter space shown within
D 109 Excluded by 5 Gyr old pulsars near earth the green band in Figure 1). In Figure 1 we show DM-NS-
ρ
implosion parameters for which a per-NS-implosion ejecta
mass M would provide 104 M of r-process elements over
108 ej (cid:12)
10-5 10-4 0.001 0.01 0.1 the lifetime of the MW, also fulfilling the requirement that
the first implosions occur within 107 yrs. The thick lines in
M (M )
ej ⊙ Figure 1 show parameter space, where the fraction of NSs
Figure1. They-axisistheintegratedtimeandlocalDMdensityrequired formed in the inner kpc, that collapse within 1010 yrs pro-
toimplodeaNS,i.e.,aNSsurroundedbyDMdensityρDM implodesafter vide for the MW’s total r-process abundance. These thick
timetc.Thex-axisindicatestheaverager-processmassejectedinaNSim- lines have been made by using the aforementioned Sofue
plosion. Thegreenbandindicatesparameterspacefavoredforthemissing
stellar distribution profile, along with an NFW dark matter
pulsarproblem,GCimplosionsasFRBcandidates,andDMignitionoftype
Iasupernovae. Thegreyregionisexludedbyoldpulsarsfoundnearearth. halo profile, ρNFW(r)=ρ /((r/r )(1+r/r )2), where we take
DM 0 s s
ThethickblacklineshowsparameterspacewhereNSimplosionsintheMW ρ =0.24 GeVcm−3 and r =20 kpc. To find the number of
GCprovide104M(cid:12)ofr-processelements,consistentwithobservations,for ne0utron stars contained wisthin radius r, we use the Kroupa
theNFWDMprofiledetailedinthetext. Thethickredandbluelinesshow
afactorofthreevariationintotalMilkyWayr-processmassproductionfor &Weidner(2003)initialmassfunctionasinSection1anda
anNFWDMprofile.Thedottedlinesshowthesameparameterspace,where minimum zero-age main sequence mass of 8 M , normaliz-
(cid:12)
104M(cid:12)ofr-processelementsareproduced,butassumeaBurkertdarkmat- ingwiththeassumptionthat∼0.5%of(cid:38)8M(cid:12) starsformed
terdensityprofile,withaconstantdarkmatterdensity,ρDM=50GeV/cm3, in the central 10 kpc will evolve to form NSs. Assuming a
inside the central kiloparsec of the Milky Way. These lines truncate at
constant 200 km/s MW DM velocity dispersion, we calcu-
iρmDpMltocd∼ef5or×a1m0a1x1imGeuVmyMrsW,aDboMvedwenhsiictyhonfeuρtDroMn=st5a0rsGienVth/ecmM3W. willnot late the number of neutron stars formed close enough to the
galactic center, that they will implode within the lifetime of
theMilkyWay.
criteria were met by an underlying neutron star-sourced r-
To demonstrate that these results are robust against varia-
processproductionmodel: (1)thetimeforr-processproduc-
tionsintheassumedDMhalodensityprofile,wealsoemploy
tion to occur after neutron star formation should fall within
tmin ∼3×106−3×108 yrs, (2) the amount of r-process el- a Burkert dark matter halo profile (Burkert 1996), ρBDuMrk(r)=
ements produced should be ∼104 solar masses, implying a ρB0/((1+r/rs,B)(1+r2/rs2,B)),wherewetakeρB0 =50GeV/cm3
ratebetween10−5and10−6r-processeventspersolarmassof and rs,B =1 kpc. The Burkert profile is flat or “cored" at its
starsintheMilkyWay.Buildingontheseresults,weconsider center, and with the aforesaid parameters, DM will have a
thescenarioofneutronstarimplosion-inducedr-processpro- constant 50 GeV/cm3 density inside the central kpc of the
ductionintheMWtobeviable,solongasitmatchestheper Milky Way. Figure 1 shows that in preferred NS-implosion
stellarmassrate(10−5−10−6M −1),totalr-processabundance parameterspace,thisdoesnotsubstantiallychangetheresult.
(cid:12)
(∼104M total r-process materials in the MW), and mini- In Figure 2 we display the expected rate of NS implo-
(cid:12) sions in UFDs analyzed in (Ji et al. 2015a). The star forma-
mum time for r-process enrichment to begin (t <108 yrs)
min tion histories of UFDs are an area of active research; in ac-
foundin(vandeVoortetal.2015).
cordwiththeresultsof(Brownetal.2014;Bland-Hawthorn
Inordertoobtainthenumberofneutronstarswhichformed
et al. 2015), we show the number of r-process events after
closeenoughtothecenterofthegalaxythattheycouldhave
500 Myr, assuming half the UFD stars formed in a burst at
already imploded (compared to longer-lived NSs outside the
z∼5. We take a Plummer stellar density in UFDs, ρ (r)=
galacticcenter),wemodelthestellardensityoftheinner∼30 p
kpc of the MW using velocity-curve-fitted density parame- (3MUFD/4πb3)(1+r2/b2)−5/2, where b∼42 pc. We assume
ters provided in (Sofue 2013), namely ρ∗(r)=(cid:80)3i=1ρie−r/ai, tthheesdaomubel0e.e5x%poNnSenftoiarmlNatSioknicfkramctoiodnelasinin(FtahuecMheWr-,Gaingdueursein&g
where (ρ =4×104, ρ =2×102, ρ =0.1 M pc−3) and
1 2 3 (cid:12) Kaspi 2006), we find that 2% of NSs formed inside a UFD
(a =0.0038, a =0.12, a =3 kpc). One small difference
1 2 3 will experience a natal kick <5 km/s, and so remain bound
between the neutron star implosion scenario and the neutron
insidethecentralparsecs. Notethatasingleeventwhichpro-
starmergerscenario,isthat,forparametersthatmatchtheto- duces ∼10−3−10−4 M r-process materials within 500 Myr
tal observed r-process abundance, NS-implosions will occur (cid:12)
in the ten surveyed ultra-faint dwarf spheroidals (along with
mostlywithinthecentralkpc,wheretheDMdensityis(cid:38)100
ReticulumII)isconsistentwiththeobservedr-processabun-
greaterandneutronstarimplosionscanoccur. However,neu-
danceinthesesystems(Jietal.2016;Roedereretal.2016b).
tronstarmergersarealsoexpectedtooccurmostlywithinthe
We then find the radius within which NSs implode within
centralfewkpc,sowedonotexpectthesubsequentchemical
500 Myr in the UFD. The UFD DM density is assumed
andhydrodynamicalevolutionofr-processenrichmentinthe
to follow an NFW profile as defined above, with ρ =
NSimplosionscenariotodiffersubstantiallyfromtheneutron 0
6 Bramante&Linden
observationsdiscovermoreUFDswithr-processenrichment,
r 100 10-41 andmoreextensivesurveysofglobularclustersfindnosuch
-Process Events in 500 My0.000.001.11110 DCMC-SiNnNdeuSc emd erNgSe ris,m vplesocs=i1oN0nSs0 , mkvmeesr/cgs= e(1r,u0 nvrkeemsca/=lis1st0i ck)m/s 100000....3000-36910.31Probability of one event errspfhK--rineapponoWvrrrrmczineooceaeocchitevtheehmhxaosseaeasssevnsmcnetiohaiontlivta,slntalehaUatellrtlohodiFakwwiopbsDinsrcunogesswknvdt.rsdhaoieunvaaeurcantiflttafidliNc6aoce.tatSnfiieluoeoCtrmrenrnbOnatrtashaeNtnleleyreraCrwgyrtvoLreieeevsfUsrlmudseylNSpsaoIoietOSpnrfevxeoNmUeptmrhultFbaeneoaiDnrlnRrgiaksaDeter.erir-tMoylAsipycnrsidusotstodo,lecurlilefiioptmlgisawrnosiordnn,IdIsipaanuyflrdnoglcsowydrted,etauttshmwhhrucafeees--t,
R
tion in quickly rotating magnetars could potentially explain
10-4 10-4
104 105 106 107 theobservedsignal,whiletheremainingmodelsforr-process
Total Stellar Mass of UFDs (M ) productionappearintensionwiththedata.
⊙
We have found that DM-induced NS implosions could be
Figure2. The number of r-process events expected after 500 Myr in the the source of r-process enrichment in UFDs and the MW.
ensembleofUFDsanalyzedinJietal.(2015a),assuminghalfofthetotal This establishes a connection between the high DM density
starsforminaburstatthebirthoftheUFDs.Thegreenlineandbandmatch
inUFDsandther-processenrichmentobservedinReticulum
theDM-NS-implosionlineandbandshowninFigure1.Theextremelyhigh
densityofr-processelementsinReticulumIIcomparedtootherUFDsfavors II. In addition, the DM-induced r-process scenario predicts
O(1)r-processeventsintegratedoverthispopulation. thatejectafromDM-inducedNScollapsewillpoweranFRB
kilonova afterglow, akin to the signal expected from NS-NS
10−2 GeV/cm3 and scale factor rs =1.5 kpc, in accord with mergerkilonovae(Li&Paczynski1998;Metzgeretal.2010;
a107 M(cid:12) DMhaloatredshiftz∼5(Klypinetal.2011). For Gorielyetal.2011;Kasenetal.2013). Ourfindingsalsoim-
fixedDMdensity, DMcapturebyNSsinthe central50par- ply an r-process signature for primordial black hole capture
secs of UFDs will be ∼200 times greater than in the MW, onNSs(Abramowiczetal.2009;Capelaetal.2013;Pani&
becauseDMcaptureinNSsscalesinverselywithhaloveloc- Loeb2014;Defillonetal.2014;Grahametal.2015), andin
itydispersion,whichisabout1km/sinthecentral50parsecs turn, small scale primordial perturbations (Carr et al. 1994).
oftheUFDatz∼5. Figure2showsthatforUFDswiththe Of course, as with other proposed r-process sites (i.e. core
aforestated stellar and DM density profile, the DM-induced collapsesupernovae,swiftlyrotatingmagnetars,andneutron
NSimplosionmodelpredictsO(1)eventwithin500Myr, in star mergers), DM-induced NS implosions may also provide
linewithobservationofhighr-processabundanceinReticu- afractionofthetotalr-processelementsintheMilkyWay.
lumII,giventhestochasticityofr-processenrichmentinthe It is worth noting that Reticulum II is now unique among
UFD population. We also calculated the expected rate for a UFDsintwoindependentways:(1)itistheonlyUFDprovid-
BurkertDMprofile,withρ =10−2GeV/cm3andscalefac- ingapossibleγ-raysignal,and(2)itistheonlyUFDshow-
0,B
torr =50pc.Aswithther-processenrichmentoftheMilky ing signs of r-process enrichment. In the case that r-process
s,B
Way,thischangedtheresultbylessthanafactoroftwo. productioniscausedthroughtheDMinducedcollapseofsin-
gle NSs, these two observations are both consistent with en-
5. R-PROCESSENRICHMENTOFUFDSVS.GLOBULARCLUSTERS hanced DM density in the central region of the Reticulum II
Onepotentialdiagnosticthatcandifferentiatebaryonicand dwarf. Further observations will be necessary to rule out, or
DM mechanisms of r-process production is r-process en- confirm,thecontributionofDMtoboththeγ-raysignaland
richment in globular cluster populations compared to that in ther-processenrichmentofReticulumII.Theresultsofthese
UFDs. Bothenvironmentsexhibitsimplestarformationhis- studieshavethepotentialtoprovidenewinsightsintothena-
tories, dominated by a single massive star formation event, tureofDM.
and contain stars with extremely low and uniform metallici-
Acknowledgements:
ties. Thesystemsdifferintwoimportantaspects: (1)theDM
We thank John Beacom, Keith Bechtol, Chris Belczyn-
densityinthecenterofUFDsisextremelyhigh,(2)thestellar
ski, Michal Dominik, Alex Drlica-Wagner, Jennifer John-
densityofglobularclustersisordersofmagnitudehigherthan
son,VickyKalogera,PaulLasky,AdamMartin,GrantMath-
UFDs,significantlyenhancingthebinary(andternary)stellar
ews, Annika Peter, Kris Sigurdson, Rebecca Surman, Todd
processeswhichliebehindthemajorityofproposedbaryonic
Thompson, and MacKenzie Warren for helpful discussions,
r-processmechanisms.
andtheABHMWorkshopfortheirhospitalitywhilethiswork
Intriguingly, Roederer (2011) studied 11 globular clus-
was completed. JB thanks the Aspen Center for Physics,
ters and found no stars with an r-process enrichment
which is supported by National Science Foundation grant
[Eu/Fe]>1.2,aresultthatagreeswithearlierstudiesofNGC
PHY-1066293. TLissupportedbytheNationalAeronautics
6397,NGC6752and47Tuc,whichfoundaverage[Eu/Fe]ra-
andSpaceAdministrationthroughEinsteinPostdoctoralFel-
tiosbelow0.47(Jamesetal.2004). Ontheotherhand,sixof
lowshipAwardNo. PF3-140110.
theninestarsobservedinReticulumIIcontain[Eu/Fe]ratios
exceeding 1.68 (Ji et al. 2015a; Roederer et al. 2016a). The
preference for significant r-process enrichment in Reticulum REFERENCES
II (compared to any globular cluster) is difficult to explain
Abramowicz,M.A.,Becker,J.K.,Biermann,P.L.,Garzilli,A.,Johansson,
in terms of any binary (or ternary) stellar mechanism, since
F.,&Qian,L.2009,Astrophys.J.,705,659
the rate of such encounters is expected to be orders of mag-
Argast,D.,Samland,M.,Thielemann,F.K.,&Qian,Y.Z.2004,Astron.
nitudehigherintheglobularclusterpopulation. Ifupcoming Astrophys.,416,997
7
Arnould,M.,Goriely,S.,&Takahashi,K.2007,Phys.Rept.,450,97 Graham,P.W.,Rajendran,S.,&Varela,J.2015,Phys.Rev.,D92,063007
Bachetti,M.,Harrison,F.A.,Walton,D.J.,Grefenstette,B.W., Grimm,H.-J.,Gilfanov,M.,&Sunyaev,R.2003,MNRAS,339,793
Chakrabarty,D.,Fürst,F.,Barret,D.,Beloborodov,A.,Boggs,S.E., Güver,T.,Erkoca,A.E.,HallReno,M.,&Sarcevic,I.2014,JCAP,1405,
Christensen,F.E.,Craig,W.W.,Fabian,A.C.,Hailey,C.J., 013
Hornschemeier,A.,Kaspi,V.,Kulkarni,S.R.,Maccarone,T.,Miller, Hooper,D.,&Linden,T.2015,JCAP,1509,016
J.M.,Rana,V.,Stern,D.,Tendulkar,S.P.,Tomsick,J.,Webb,N.A.,& James,G.,François,P.,Bonifacio,P.,Carretta,E.,Gratton,R.G.,&Spite,F.
Zhang,W.W.2014,Nature,514,202 2004,A&A,427,825
Bauswein,A.,ArdevolPulpillo,R.,Janka,H.T.,&Goriely,S.2014, Ji,A.P.,Frebel,A.,Chiti,A.,&Simon,J.D.2015a,ArXive-prints
Astrophys.J.,795,L9 —.2016,Nature,531,610
Bechtol,K.,etal.2015,Astrophys.J.,807,50 Ji,A.P.,Frebel,A.,Simon,J.D.,&Geha,M.2015b,ArXive-prints
Bell,N.F.,Melatos,A.,&Petraki,K.2013,Phys.Rev.,D87,123507 Kasen,D.,Badnell,N.R.,&Barnes,J.2013,Astrophys.J.,774,25
Bertone,G.,&Fairbairn,M.2008,Phys.Rev.,D77,043515 Kim,D.-W.,Fabbiano,G.,Ivanova,N.,Fragos,T.,Jordán,A.,Sivakoff,
Bertoni,B.,Nelson,A.E.,&Reddy,S.2013,Phys.Rev.,D88,123505 G.R.,&Voss,R.2013,ApJ,764,98
Bland-Hawthorn,J.,Sutherland,R.,&Webster,D.2015,Astrophys.J.,807, Kirby,E.N.,Simon,J.D.,Geha,M.,Guhathakurta,P.,&Frebel,A.2008,
154 Astrophys.J.,685,L43
Bonnivard,V.,Combet,C.,Maurin,D.,Geringer-Sameth,A.,Koushiappas, Klypin,A.,Trujillo-Gomez,S.,&Primack,J.2011,Astrophys.J.,740,102
S.M.,Walker,M.G.,Mateo,M.,Olszewski,E.W.,&BaileyIII,J.I. Kobulnicky,H.A.,Fryer,C.L.,&Kiminki,D.C.2006,ArXiv
2015,Astrophys.J.,808,L36 Astrophysicse-prints
Bovill,M.S.,&Ricotti,M.2011,Astrophys.J.,741,17 Koch,A.,&Rich,R.M.2014,ApJ,794,89
Bramante,J.2015,Phys.Rev.Lett.,115,141301 Koposov,S.E.,Belokurov,V.,Torrealba,G.,&Evans,N.W.2015,
Bramante,J.,&Elahi,F.2015,Phys.Rev.,D91,115001 Astrophys.J.,805,130
Bramante,J.,Fukushima,K.,&Kumar,J.2013,Phys.Rev.,D87,055012 Kouvaris,C.2008,Phys.Rev.,D77,023006
Bramante,J.,Fukushima,K.,Kumar,J.,&Stopnitzky,E.2014,Phys.Rev., —.2012,Phys.Rev.Lett.,108,191301
D89,015010 Kouvaris,C.,&Tinyakov,P.2011a,Phys.Rev.,D83,083512
Bramante,J.,&Linden,T.2014,Phys.Rev.Lett.,113,191301 —.2011b,Phys.Rev.Lett.,107,091301
Brito,R.,Cardoso,V.,&Okawa,H.2015,Phys.Rev.Lett.,115,111301 —.2014,Phys.Rev.,D90,043512
Brown,T.M.,Tumlinson,J.,Geha,M.,Simon,J.D.,Vargas,L.C., Kroupa,P.,&Weidner,C.2003,Astrophys.J.,598,1076
VandenBerg,D.A.,Kirby,E.N.,Kalirai,J.S.,Avila,R.J.,Gennaro,M., Kurita,Y.,&Nakano,H.2016,Phys.Rev.,D93,023508
Ferguson,H.C.,Muñoz,R.R.,Guhathakurta,P.,&Renzini,A.2014, Kyutoku,K.,Ioka,K.,Okawa,H.,Shibata,M.,&Taniguchi,K.2015,Phys.
ApJ,796,91 Rev.,D92,044028
Burbidge,E.M.,Burbidge,G.R.,Fowler,W.A.,&Hoyle,F.1957,Reviews Lattimer,J.M.,Mackie,F.,Ravenhall,D.G.,&Schramm,D.N.1977,ApJ,
ofModernPhysics,29,547 213,225
Burkert,A.1996,IAUSymp.,171,175,[Astrophys.J.447,L25(1995)] Lattimer,J.M.,&Schramm,D.N.1976,ApJ,210,549
Capela,F.,Pshirkov,M.,&Tinyakov,P.2013,Phys.Rev.,D87,123524 Li,L.-X.,&Paczynski,B.1998,Astrophys.J.,507,L59
Carr,B.J.,Gilbert,J.H.,&Lidsey,J.E.1994,Phys.Rev.,D50,4853 Linden,T.,Kalogera,V.,Sepinsky,J.F.,Prestwich,A.,Zezas,A.,&
Cescutti,G.,Romano,D.,Matteucci,F.,Chiappini,C.,&Hirschi,R.2015, Gallagher,J.2010,Astrophys.J.,725,1984
A&A,577,A139 Macquart,J.-P.,Kanekar,N.,Frail,D.,&Ransom,S.2010,Astrophys.J.,
Chennamangalam,J.,&Lorimer,D.R.2014,Mon.Not.Roy.Astron.Soc., 715,939
440,86 Markovic,D.1995,Mon.Not.Roy.Astron.Soc.,277,25
Colpi,M.,Shapiro,S.L.,&Wasserman,I.1986,Phys.Rev.Lett.,57,2485 Mashhoon,B.1975,ApJ,197,705
Davies,M.B.,Benz,W.,Piran,T.,&Thielemann,F.K.1994,ApJ,431,742 Matteucci,F.,Romano,D.,Arcones,A.,Korobkin,O.,&Rosswog,S.2014,
deLavallaz,A.,&Fairbairn,M.2010,Phys.Rev.,D81,123521 MNRAS,438,2177
Deaton,M.B.,Duez,M.D.,Foucart,F.,O’Connor,E.,Ott,C.D.,Kidder, McConnachie,A.W.2012,Astron.J.,144,4
L.E.,Muhlberger,C.D.,Scheel,M.A.,&Szilagyi,B.2013,Astrophys. McDermott,S.D.,Yu,H.-B.,&Zurek,K.M.2012,Phys.Rev.,D85,
J.,776,47 023519
Defillon,G.,Granet,E.,Tinyakov,P.,&Tytgat,M.H.G.2014,Phys.Rev., Metzger,B.D.,Martinez-Pinedo,G.,Darbha,S.,Quataert,E.,Arcones,A.,
D90,103522 Kasen,D.,Thomas,R.,Nugent,P.,Panov,I.V.,&Zinner,N.T.2010,
Dexter,J.,&O’Leary,R.M.2014,Astrophys.J.,783,L7 Mon.Not.Roy.Astron.Soc.,406,2650
Dominik,M.,Belczynski,K.,Fryer,C.,Holz,D.,Berti,E.,Bulik,T., Metzger,B.D.,Thompson,T.A.,&Quataert,E.2008,ApJ,676,1130
Mandel,I.,&O’Shaughnessy,R.2012,Astrophys.J.,759,52 Meyer,B.S.,Mathews,G.J.,Howard,W.M.,Woosley,S.E.,&Hoffman,
Dominik,M.,Belczynski,K.,Fryer,C.,Holz,D.E.,Berti,E.,Bulik,T., R.D.1992,ApJ,399,656
Mandel,I.,&O’Shaughnessy,R.2013,Astrophys.J.,779,72 Nishimura,N.,Takiwaki,T.,&Thielemann,F.K.2015,Astrophys.J.,810,
Drlica-Wagner,A.,etal.2015,Astrophys.J.,809,L4 109
Duncan,R.C.,Shapiro,S.L.,&Wasserman,I.1986,ApJ,309,141 Pani,P.,&Loeb,A.2014,JCAP,1406,026
Eichler,D.,Livio,M.,Piran,T.,&Schramm,D.N.1989,Nature,340,126 Piro,A.L.,&Thompson,T.A.2014,Astrophys.J.,794,28
Faucher-Giguere,C.-A.,&Kaspi,V.M.2006,Astrophys.J.,643,332 Qian,Y.Z.,&Woosley,S.E.1996,Astrophys.J.,471,331
Fischer,T.,Whitehouse,S.C.,Mezzacappa,A.,Thielemann,F.K.,& Roederer,I.U.2011,Astrophys.J.,732,L17
Liebendorfer,M.2010,Astron.Astrophys.,517,A80 Roederer,I.U.,Mateo,M.,Bailey,III,J.I.,Song,Y.,Bell,E.F.,Crane,
Fishbone,L.G.1973,ApJ,185,43 J.D.,Loebman,S.,Nidever,D.L.,Olszewski,E.W.,Shectman,S.A.,
Foucart,F.,Deaton,M.B.,Duez,M.D.,Kidder,L.E.,MacDonald,I.,Ott, Thompson,I.B.,Valluri,M.,&Walker,M.G.2016a,ArXive-prints
C.D.,Pfeiffer,H.P.,Scheel,M.A.,Szilagyi,B.,&Teukolsky,S.A. —.2016b,AJ,151,82
2013,Phys.Rev.,D87,084006 Salvadori,S.,&Ferrara,A.2009,Mon.Not.Roy.Astron.Soc.,395,6
Fragos,T.,Kalogera,V.,Belczynski,K.,Fabbiano,G.,Kim,D.-W., Shapiro,S.L.,&Teukolsky,S.A.1983,Blackholes,whitedwarfs,and
Brassington,N.J.,Angelini,L.,Davies,R.L.,Gallagher,J.S.,King, neutronstars:Thephysicsofcompactobjects
A.R.,Pellegrini,S.,Trinchieri,G.,Zepf,S.E.,Kundu,A.,&Zezas,A. Sharpee,B.J.,&Thompson,T.A.2013,Astrophys.J.,766,64
2008,ApJ,683,346 Shen,S.,Cooke,R.J.,Ramirez-Ruiz,E.,Madau,P.,Mayer,L.,&Guedes,
Fragos,T.,Linden,T.,Kalogera,V.,&Sklias,P.2015,Astrophys.J.,802,L5 J.2015,ApJ,807,115
Frebel,A.,Simon,J.D.,&Kirby,E.N.2014,ApJ,786,74 Shibata,M.,&Taniguchi,K.2011,LivingRev.Rel.,14,6
Freiburghaus,C.,Rosswog,S.,&Thielemann,F.-K.1999,ApJ,525,L121 Simon,J.D.,etal.2015,Astrophys.J.,808,95
Fryer,C.L.,Benz,W.,Herant,M.,&Colgate,S.A.1999,Astrophys.J., Sofue,Y.2013,Publ.Astron.Soc.Jap.,65,118
516,892 Starkman,G.D.,Gould,A.,Esmailzadeh,R.,&Dimopoulos,S.1990,Phys.
Fuller,J.,&Ott,C.2015,Mon.Not.Roy.Astron.Soc.,450,L71 Rev.,D41,3594
Geringer-Sameth,A.,Walker,M.G.,Koushiappas,S.M.,Koposov,S.E., Surman,R.,McLaughlin,G.C.,Ruffert,M.,Janka,H.T.,&Hix,W.R.
Belokurov,V.,Torrealba,G.,&Evans,N.W.2015,Phys.Rev.Lett.,115, 2008,Astrophys.J.,679,L117
081101 Symbalisty,E.,&Schramm,D.N.1982,Astrophys.Lett.,22,143
Goldman,I.,&Nussinov,S.1989,Phys.Rev.,D40,3221 Tanaka,M.,Hotokezaka,K.,Kyutoku,K.,Wanajo,S.,Kiuchi,K.,
Goriely,S.,Bauswein,A.,&Janka,H.T.2011,Astrophys.J.,738,L32 Sekiguchi,Y.,&Shibata,M.2014,Astrophys.J.,780,31
8 Bramante&Linden
Thompson,T.A.2011,Astrophys.J.,741,82 Willems,B.,&Kalogera,V.2004,Astrophys.J.,603,L101
Thompson,T.A.,Burrows,A.,&Meyer,B.S.2001,Astrophys.J.,562,887 Woosley,S.E.,&Baron,E.1992,ApJ,391,228
Tsujimoto,T.,&Nishimura,N.2015,ApJ,811,L10 Woosley,S.E.,Wilson,J.R.,Mathews,G.J.,Hoffman,R.D.,&Meyer,
vandeVoort,F.,Quataert,E.,Hopkins,P.F.,Kereš,D.,&Faucher-Giguère, B.S.1994,Astrophys.J.,433,229
C.-A.2015,MNRAS,447,140 Wyse,R.F.G.2009,inIAUSymposium,Vol.258,IAUSymposium,ed.
Webster,D.,Bland-Hawthorn,J.,&Sutherland,R.2015,ApJ,799,L21 E.E.Mamajek,D.R.Soderblom,&R.F.G.Wyse,11–22
Wehmeyer,B.,Pignatari,M.,&Thielemann,F.K.2015,Mon.Not.Roy. Zheng,H.,Sun,K.-J.,&Chen,L.-W.2015,Astrophys.J.,800,141
Astron.Soc.,452,1970 ÁngelesPérez-García,M.,&Silk,J.2015,Phys.Lett.,B744,13
Wharton,R.S.,Chatterjee,S.,Cordes,J.M.,Deneva,J.S.,&Lazio,T.J.W.
2012,Astrophys.J.,753,108
Wheeler,J.1971,inStudyWeekonNucleiofGalaxies,ed.D.J.K.
O’Connell,539