arXiv:1711.02683v1 [astro-ph.HE] 7 Nov 2017 ueetof surement E/] neteemtlpo niomns uha galac- ( as stars such halo tic environments, metal-poor extreme in [Eu/H]) rcs lmnsi h nvrea s ugse by suggested ﬁst as universe the in elements process h rgnof origin The INTRODUCTION 1 MNRAS vn n nbe obektedgnrc neett ob- to inherent degeneracy the break to enables and event ( 2014 Kirby & Roederer Schramm & Lattimer 1957 Cameron eyi hmcleouinmdlig( modelling evolution chemical in tery e iiso their on limits per 9Arl2018 April 29 F,RtclmI,hsbe on ohv ag excess large a have to found been has of II, Reticulum UFD, ( galaxies (UFD) yield and rate the conﬁdence more of of with compute source to us dominant ables the are mergers NS merger binary (NS) that star neutron 2017 binary an a as of identiﬁcation ( the GW170817 event, wave tational a Beniamini Paz galaxies dwarf in material r-process of Retainment

c 4 3 2 1 2016b eateto hsc n srnm,TeJhsHpisUniv Hopkins Johns The Astronomy, and Universit´e Pie Physics 7095 of UMR (A Department Paris Sciences de of d’Astrophysique Institute W Institut Statistics University, and Washington Physics George Astronomy, The Physics, of Department r r 00TeAuthors The 0000 poeseeet,wiealohrUD aesrn up- strong have UFDs other all while elements, -process poesevents. -process nte aryrcn eeomn a entemea- the been has development recent fairly Another ; ine l 2017 al. et Pian ,ti ssrnl ugsieo nihetb single a by enrichment of suggestive strongly is this ), r 000 poesst ( site -process , r 1 odrr2017 Roederer poeseeetlaudne frexample (for abundances elemental -process – ; r ?? poeseeet saln-tnigmys- long-standing a is elements -process heeane l 2017 al. et Thielemann ie l 2016a al. et Ji 00)Pern 9Arl21 oplduigMRSL MNRAS using Compiled 2018 April 29 Preprint (0000) r poesaudne ( abundances -process 1 ( ed togceec oteidea the to credence strong lends ) 1974 .A a hw in shown was As ). , 2 bote l 2017c al. et Abbott rn Dvorkin Irina , ); ,ad oal,utafitdwarf faint ultra notably, and, ), ihe tal. et Eichler ; uprigtepsiiiyta Fsaetemi bidn lcs fth of blocks’ meta ’building words: galactic main Key in the [Eu/Fe] are of UFDs ﬂuctuations population. that halo the possibility and the values supporting mean the both ttesm ie eetosrain n signiﬁcant ﬁnd observations recent time, same the At h ytei of synthesis The ABSTRACT loetmt h itiuino bnacspeitdb hs mo these by predicted abundances merg of ∼ star distribution neutron the estimate a also accompanying macronova detected recently ftoeeeet ihnterhss eetmt h eanetfr retainment the large estimate We ques is hosts. the it their raises within This elements galaxies. those of (UFD) dwarf ultra-faint small tremely othsls ag rcino t a ro oteeet eestima We event. the to prior gas its of fraction large a lost has host efc eanetaddﬀrn oeso F vlto.Teresu into The taking evolution. ( UFDs, UFD in estimates of abundances previous models by with diﬀerent implied and as retainment rate perfect and event per mass odrre l 2016 al. et Roederer bote l 2017b al. et Abbott 0 . 7o Fssol have should UFDs of 07 ubdee l 1957 al. et Burbidge .Tercn gravi- recent The ). eimn tal. et Beniamini ∼ ie l 2016b al. et Ji ( 1989 ; 0 . ru tal. et Drout ,uls the unless 9, 3 aais wr;sas eto;sas abundances; stars: neutron; stars: dwarf; galaxies: o Silk Joe , n en- and ) r poeseeet skont nov xrml nrei explosion energetic extremely involve to known is elements -process .One ). and ) PSIS) r tMreCrePrs0;CR 8bsb rg,704Paris 75014 Arago, bd bis 98 CNRS 06; Curie-Paris Marie et rre r - ; ; sigo,D 05,USA 20052, DC ashington, eimn ta.2016b al. et Beniamini riy atmr D11 USA MD21218 Baltimore ersity, r poeseeti eyeegtc( energetic very is event -process 3 , fsotgmarybrt(R)rtsadms ejections mass and rates simulations. with observations (GRB) merger consistent from burst NS from are ray constraints gamma event with short Both as per of event. well mass per as and produced GW170817, rate mass implied of amount the the and events evtoso ik a tr,btentert of rate the between stars, Way Milky of servations hscudsrnl ﬀc h mle asof mass implied the aﬀect strongly could this ileetddrn hi egr ihvs mut fenerg of amounts vast ( with mergers their during ejected rial 2016 2016 oeduto h soito faN egra h rgnof origin the as merger NS a of the association the on doubt some eevdb obenurnsa ytm ( systems star initial neutron double and by parameters received orbital of distributions realistic stellar old evolu- galaxys’ of the composed of are Gyr ﬁrst UFDs tion, the that within fact (formed the material as well as o saeterhs aais oeo the of do some stars galaxies, neutron less host binary within their if merge Even escape as formation. not well after Gyr as a UFDs than in even conﬁned remain to eilta a ob rdcdi igeeeti re to order in event single a in abundances. produced observed the be match to has that terial r 4 & poesercmn.Terslsaecnitn with consistent are results The enrichment. -process ∼ 10 r h o saevlct fUD ( UFDs of velocity escape low The ; by shown was as However, ). poesmtra nRtclmI ( II Reticulum in material -process 0)o obenurnsa ytm hudb beto able be should systems star neutron double of 60%) rw ta.2014 al. et Brown 50 arse l 2017 al. et Tauris r)cudsilecp.I hsfato ssigniﬁcant, is fraction this If escape. still could erg) n ihtecntansfo the from constraints the with and ) ; ml htasgicn rcin(up fraction signiﬁcant a that imply ) es ta.2015 al. et Weisz r poesercmn vni ex- in even enrichment -process & eimn tal. et Beniamini 10 r(W787.We (GW170817). er cinadﬁdthat ﬁnd and action 52 rmne&Linden & Bramante akre l 2015 al. et Walker ino retainment of tion es eﬁdthat ﬁnd We dels. eimn Piran & Beniamini aeiiilycast initially have ) r)ad/o the or / and erg) t r consistent are lts A ethe te T r E poesmate- -process tl l v3.0 ﬁle style X r orstars, poor l con im- account poesma- -process galactic e r r -process ( -process 2016a France , kicks s. ), ), y 2 P. Beniamini, I. Dvorkin & J. Silk

These results have motivated us to take a more detailed merger (Rosswog et al. 1999). It is ejected on a dynamical look at how inhomogeneous r-process enrichment may occur time-scale (which is of the order of milliseconds). This com- in ultra faint dwarfs as a consequence of ejecta from rare ponent exists for NS-BH only if the BH has relatively low events (such as, but not restricted to, binary NS mergers), mass and / or is spinning rapidly (otherwise the NS could be that take place in dwarf galaxies with low escape velocities. completely swallowed by the BH). For a NS-NS merger, this There is a general consensus, both theoretical (Griﬀen et al. component depends critically on the immediate product of 2016) and observational (Frebel et al. 2010), that UFDs are the merger (BH or hyper-massive NS). The masses of the dy- −3 −2 remnants of a large population of dwarfs that long ago dis- namical ejecta typically span the range 10 −10 M⊙ with solved to form the galactic halo stellar population. There- velocities of order the escape velocity, 0.2−0.3c (correspond- 49 51 fore, understanding the typical enrichment of r-process and ing to kinetic energies of Ekin ∼ 4 × 10 − 2 × 10 erg). For iron in those galaxies, could be crucial also to our under- BH-NS mergers the masses increase to 0.1M⊙ (and the ve- standing of metal poor halo stars. locities are similar). The high velocity component of the dy- Here we explore simple models for enrichment of r- namically ejected material is squeezed into polar directions process elements from a very small number of r-process and produces the so-called ’blue macronova’ (Oechslin et al. events in gas-rich dwarf galaxy precursors of today’s ultra 2007; Hotokezaka et al. 2013; Sekiguchi et al. 2015). This faint galaxies. We focus mainly on binary NS mergers, but material is mainly composed of elements with A < 140, the results are easily applicable to any other potential r- so that the opacity remains suﬃciently low and the lumi- process sources that have been suggested in the literature, nosity peaks early enough (Kasen et al. 2017). Some of the such as long GRBs (Metzger et al. 2008; Vlasov et al. 2014) tidally ejected material will be ejected closer to the equato- or peculiar supernovae (SNe) (Suzuki & Nagataki 2005; rial plane. This material may be more lanthanide-rich and Fryer et al. 2006; Winteler et al. 2012; Nishimura et al. contribute partially to the ’red macronova’. 2015; M¨osta et al. 2015). Furthermore, these calculations • Disk wind ejecta During the merger an accretion disc also apply to retainment of iron from core collapse SNe. In is formed. At early times after its formation, the disk is hot what follows, we model the retainment of r-process ejecta and emits many neutrinos. These neutrinos deposit their en- and calculate the retainment fraction. We include diﬀerent ergy at larger radii and drive an outﬂow of material from the mass loss models (such as SN-driven mass loss and active disk (Perego et al. 2014; Just et al. 2015). This component galactic nucleus, AGN, driven outﬂows) as well as iron en- is expected to be small if the merger immediately produces richment due to SNe. For a Reticulum II - like galaxy, we a BH, but can become very signiﬁcant if the central NS sur- show that unless a signiﬁcant (∼ 90%) amount of gas has vives for longer than ∼ 50msec. The mass ejected in this −2 −1 been removed from the galaxy prior to the r-process event wind is of order 10 − 10 M⊙. It is ejected at veloci- and/or unless the r-process explosion was extremely ener- ties of 0.05 − 0.1c (thus corresponding to kinetic energies of 52 49 51 getic (∼ 10 erg), the retainment fraction of r-process mate- Ekin ∼ 5 × 10 − 3 × 10 erg) and is trailing behind the rials is large (with typical values around ∼ 0.9). Furthermore dynamical ejecta. This material is rather isotropic and is we evaluate the probability of ﬁnding single r-process en- expected to be the main contributor to the ’red macronova’. richment events in dwarf galaxies, and the typical expected The overall kinetic energy of the merger ejecta is there- iron and r-process abundances in such galaxies. These are 50 51 consistent with observations of galactic metal-poor stars. fore expected to be between Ekin = 10 − 5 × 10 erg. The paper is organized as follows. We begin in §2 with We note also that these expected theoretical components a brief description of the properties of r-process ejecta from described here, match well with the recent observations compact mergers as constrained by theory and observations. of GW170817 (Covino et al. 2017). In particular the tem- We then discuss the spreading of r-process matter in its perature and luminosity evolution of the macronova asso- environment in §3 with speciﬁc implications to Ret II and ciated with GW170817 suggest an expansion velocity of GW170817. In §4 we describe our method for calculating the 0.1c − 0.3c (Kasliwal et al. 2017). Combining this with the estimated ejecta mass of ∼ 0.05M⊙ we ﬁnd a kinetic energy retainment of an ejecta of an explosion with given energy 50 51 within its host galaxy. In §5 we explore diﬀerent models for of Ekin ∼ 5 × 10 − 4 × 10 erg for the r-process ejecta the gas loss in UFDs and its implications on the observed in GW170817. Future observations will enable us to nar- abundances of r-process elements. We then use these models row down the full distribution of energetics and r-process to estimate the amount of r-process mass created by one abundances associated with the diﬀerent ejecta components event as well as the rate of these events in §6. We address (Rosswog et al. 2017; Cˆot´eet al. 2017). the overall expected distributions of enrichment patterns in UFDs in §7. Finally, we discuss some implications of this work and conclude our results in §8. 3 SPREAD OF R-PROCESS EJECTA The r-process ejecta expands into its environment, un- 2 R-PROCESS EJECTA FROM COMPACT dergoing a similar evolution to that of a supernova rem- MERGERS nant. Initially the ejecta is expanding freely (at its ini- tial velocity). This stage lasts until the ejecta has collected r-process ejecta is thought to take place in two diﬀerent an interstellar matter (ISM) mass which is of the order sites: NS-NS and NS-black hole (BH) mergers (see Metzger of its initial mass. For a spherical ejecta this occurs at (2017) for a recent review). 18 1/3 −1/3 r = 1.5 × 10 Mej,−2n0 cm, where Mej is the ejecta −2 • Dynamical ejecta This is material that becomes un- mass (in units of 10 M⊙) and n0 is the particle den- bound from the merging binary due to tidal forces during the sity (in cm−3). At this stage, the material starts decelerat-

MNRAS 000, 1–?? (0000) r-process retainment 3

ing, following the self-similar Sedov-Taylor expansion. Here Amin is the minimum atomic number of the synthesized r- r(t) ∝ ( E )1/5t2/5 (where E is the kinetic energy of the process elements, see discussion at the end of §6 for more mpn0 ejecta and mp the proton mass). This stage lasts up un- details). These masses correspond to an abundance of 2.6 . til tTR, when the decrease in temperature due to radiative [Eu/H] . 3.4 for Amin = 90 (or 2.2 . [Eu/H] . 2.5 for cooling overcomes the temperature decrease due to adia- Amin = 69). These values may be decreased signiﬁcantly if batic expansion (Ostriker & McKee 1988). After an inter- turbulent mixing occurs, whereas additional r-process events mediate stage between tTR and ∼ 2tTR (Haid et al. 2016), in the region could increase this abundance. the blast wave enters the pressure driven phase (Cox 1972), in which the radius evolves as r ∝ t2/7. It is typically dur- ing this stage that the blast wave reaches its maximum ra- 4 CALCULATION OF RETAINMENT dius, obtained when the shock velocity becomes compara- FRACTION ble to the velocity dispersion of the environment, σv. For a homogeneous medium, the transition time depends some- We outline here our method for calculating the average frac- what on the ionization of the medium and is approximately tion of mass that is retained when an r-process event of en- −0.53 4 ergy E takes place in a given UFD galaxy, characterized by tTR ≈ 4n0 × 10 yrs (Haid et al. 2016). We can now es- timate the maximum radius (denoted as rfade) as its half light radius r1/2 and velocity dispersion σv. The cal- culation does not assume a speciﬁc model for the r-process −0.4 σv 0.28 −0.365 mechanism, and relies only on the total energy of the explo- rfade = 70 E n parsec (1) 4km s−1 51 0 sion. Since core-collapse SNe (ccSNe) have similar energies to neutron star mergers’ ejecta, similar retainment values where E ≡ E/1051erg. Speciﬁcally, for a velocity of σ = 51 v are expected for either mechanism. Furthermore, these re- 4km s−1 (comparable to the velocity dispersion in Ret II 51 tainment values would be applicable to any other material and other ultra-faint dwarves), an energy of 10 erg and for that is synthesized in SNe, such as iron. n = 1cm−3, this leads to a ﬁnal radius of ≈ 70pc which is 0 The method presented here is generic, but for the sake slightly more than twice the half-light radius of Ret II. This of concreteness we consider the same sample of UFD galaxies suggests that some of the r-process material created in any studied by Beniamini et al. (2016b). It includes ﬁve UFDs: given explosion may be ejected outside of its host galaxy. Reticulum II, Segue I, Segue II, Coma Berenices and Ursa Recently, Macias & Ramirez-Ruiz (2016) have used a Major II. All of these are composed of old stellar material similar approach to ﬁnd the minimum amount of mass into (Simon & Geha 2007) and have signiﬁcantly fewer stars then which r-process material can be injected. This in turn pro- naively expected from their halo masses, indicating signiﬁ- vided them with a maximum abundance that can be asso- cant mass loss during their evolution. Walker et al. (2009) ciated with a given r-process mass that is created in the show that a good approximation for the distribution of the explosion, and led them to conclude that r-process events −3.5 halo mass in dwarf galaxies is need to synthesize a minimum of 10 M⊙ of r-process ma- 2 3 terial per event, in order to be able to explain the observed 5r1/2σ (r/r1/2) M (r)= v . (3) abundances of extremely metal-poor Galactic halo stars. h G 1+(r/r )2 Finally, it is interesting to apply these estimates to 1/2 the recent detection of r-process elements in the macronova accompanying GW170817. Observations of the accompa- As a ﬁducial model we assume here that the initial gas den- nying gamma-ray burst (GRB) afterglow suggest that the sity follows the same distribution as the dark matter and environment surrounding the merger has a density n ≈ that the total initial gas mass is Mg,0 = Mh(r

MNRAS 000, 1–?? (0000) 4 P. Beniamini, I. Dvorkin & J. Silk the complexities that would require a full hydrodynamical (ii) Removal of mass by SNe. Each SN is assumed to re- calculation we assume here that the density the explosion move a constant fraction of the gas mass. has to push through is spatially constant and equal to the (iii) A constant rate of mass outﬂow from the galaxy. density at the explosion center. We then calculate the volu- A comparison of these models is shown in Fig. 2. In the metric fraction of the “explosion sphere” that overlaps with following we describe these models in more detail. r90 which gives us a retainment fraction, ξ. This process is repeated 104 times, to fully sample the distribution of explo- sion locations. We then calculate the mean value of ξ, which 5.1 Top hat evolution gives us the average retainment fraction for an explosion of energy E, occurring in a galaxy with r1/2,σv and with a The simplest model for mass loss is to assume that the gas fraction Mg/Mg,0 of the initial gas remaining in the galaxy: mass remains constant at its initial level, and suddenly de- creases over a brief time-scale towards the end of star for- M ξ ≡ ξ(σ ,r , E, g ) (4) mation. This model is less physically motivated than those v 1/2 M g,0 discussed in §5.2, §5.3. Its main purpose is to serve as a basis Fig. 1 depicts the retainment value, ξ, for diﬀerent ex- for comparison with previous works and with the other mod- plosion energies and diﬀerent vales of Mg/Mg,0. For an ex- els of mass loss explored in this paper. The typical r-process 51 plosion with E = 10 erg and Mg /Mg,0 =1(Mg/Mg,0 = to hydrogen abundance predicted by this model (assuming 0.1), the retainment value for Ret II is expected to be a single event occurs in a given galaxy and that full mixing 50 ξ ≈ 0.9 (ξ ≈ 0.7). For E = 10 erg the retainment frac- occurs) is nr/H = mr/Mg,0 where nr/H is the relative den- tion increases to ξ ≈ 0.93 if Mg/Mg,0 = 1 (or ξ ≈ 0.86 if sity of some r-process element (e.g. Europium) as compared Mg/Mg,0 = 0.1). Alternatively, for more energetic r-process to hydrogen, and mr is the amount of that element’s mass 52 events with E = 10 erg, ξ ≈ 0.77 for Mg/Mg,0 = 1 (or that is synthesised in one r-process event. ξ ≈ 0.16 if Mg/Mg,0 = 0.1). As a comparison we consider also the retainment fraction for GW170817. As suggested by the discussion in §3, the value for this considerably larger 5.2 Mass loss by SNe galaxy is now close to unity: ξ & 0.95. The energy of a typical ccSNe 1 is ∼ 1051erg. This is com- It is useful to deﬁne an additional parameter, parable or larger than the binding energy of UFDs which is

Ψ ≡ ξMg,0/Mg . (5) approximately 2 4 This parameter describes the ratio between the amount of M1/2 50 σv r1/2 U = −1.2G ≈−3.4 × 10 −1 (6) mass implied by abundance observations in UFDs in two r1/2 3km s 30pc cases. The ﬁrst, taking into account gas loss before the r- process event as well as retainment considerations, and the It is therefore reasonable to assume that a single SN can second, where both these considerations are absent (e.g., signiﬁcantly disturb the gas in these galaxies and cause a certain fraction of that gas to become unbound. We adopt a as in Beniamini et al. (2016b)). Mg < Mg,0 will increase the observed abundance for a given synthesized mass, while simple model, whereby a constant fraction f of the galaxy’s ξ < 1 means that only some of this r-process material really gas remains after each ccSN. We assume that the iron pro- remains in the galaxy (thus working in the opposite direc- duction of ccSNe is similar to that measured by SNe obser- tion, towards reducing the abundance). Interestingly, in all vations in the local universe, i.e. 2/3 of SNe are type II and the cases considered above Ψ > 1. Thus, the implied amount produce 0.02M⊙ (Drout et al. 2011; Kushnir 2015) and 1/3 of r-process mass produced per event is reduced by Ψ as are type Ib,Ic and produce 0.2M⊙ (Li et al. 2011). We fur- −3 −2 ther assume that, as implied by observations of double NS compared with 6 × 10 M⊙ . m˜ r−process . 4 × 10 M⊙ obtained from UFD observations under the assumption of (DNS) systems in the galaxy, 60 − 70% of stellar collapses to neutron stars are ultra-stripped SNe that involve virtu- complete retainment and with Mg = Mg,0 (Beniamini et al. 2016b). In order to keep the same amount of total r-process ally no iron production (Beniamini & Piran 2016). Over- abundance (which is constrained by observations of classical all, the mean amount of iron per ccSNe is approximately dwarfs and the Milky Way), the rate of the events would mF e = 0.03M⊙. have to be increased by the same amount. We return to the The value of f for each UFD galaxy can be estimated estimates of the synthesized mass and the rate in §6 after from the total V-band stellar luminosity of UFD galaxies, exploring diﬀerent models for mass loss in UFDs. LV . As described in §4 we assume that the gas mass required to create the stars in UFDs is roughly ten times larger than the resulting stellar mass observed in those galaxies (notice that the ﬁnal value of f depends only logarithmically on this 5 MODELLING THE GAS LOSS IN DWARF number). This implies that GALAXIES Mf M∗ LV N As shown above, the probability of retainment depends on = 10 = f SN (7) Mg,0 LV Mg,0 the amount of gas that resides in the host dwarf galaxy at the time of explosion. We explore here three diﬀerent models where M∗/LV = 3 in solar units (see §4) and NSN can be for the mass loss in UFDs:

(i) “Top hat” evolution - The gas mass remains constant, 1 since star formation took place only in the ﬁrst ∼ Gyr after the then is completely removed on a short time-scale ∼Gyr after birth of these galaxies, type Ia SNe are unlikely to signiﬁcantly formation. contribute to the gas loss or iron production in these galaxies

MNRAS 000, 1–?? (0000) r-process retainment 5

51 51 Eexp = 10 [erg],Mg/Mg,0 = 1 Eexp = 10 [erg],Mg/Mg,0 = 0.1 101 101 0.9 0.9

0.8 0.8

0.7 0.7

] 0.6 ] 0.6

1 RetII 1 RetII − − 0.5 0.5 [km s [km s

v 0.4 v 0.4 σ σ

0.3 0.3

0.2 0.2

100 0.1 100 0.1

100 101 102 100 101 102 r1/2[parsec] r1/2[parsec] 52 52 Eexp = 10 [erg],Mg/Mg,0 = 1 Eexp = 10 [erg],Mg/Mg,0 = 0.1 101 101 0.9 0.9

0.8 0.8

0.7 0.7

0.6 ] 0.6 ] 1 RetII 1 − − 0.5 0.5 RetII [km s [km s v 0.4 v 0.4 σ σ

0.3 0.3

0.2 0.2

100 0.1 100 0.1

100 101 102 100 101 102 r1/2[parsec] r1/2[parsec] 50 50 Eexp = 10 [erg],Mg/Mg,0 = 1 Eexp = 10 [erg],Mg/Mg,0 = 0.1 101 101 0.9 0.9

0.8 0.8

0.7 0.7 ] 0.6 ] 0.6 1 RetII 1 RetII − − 0.5 0.5 [km s [km s v v 0.4 σ

0.4 σ

0.3 0.3

0.2 0.2 100 100 0.1 0.1

100 101 102 100 101 102 r1/2[parsec] r1/2[parsec]

Figure 1. Fraction of r-process mass retained in galaxies with σv,r1/2 for an r-process explosion energy Eexp and assuming that a fraction Mg/Mg,0 of the gas remains in the galaxy at the time of the r-process event. Black crosses denote observations of UFDs with no r-process material detected and Ret II is marked in purple. MNRAS 000, 1–?? (0000) 6 P. Beniamini, I. Dvorkin & J. Silk

×10-7 1.5 30 top hat top hat SN driven outflows SN driven outflows constant outflow 25 constant outflow

] 1 20 1 − ) t yr (

)[ 15 t SN ( n SN ˙ n 0.5 10

5

0 0 0 2 4 6 8 10 0 2 4 6 8 10 t[yrs] ×108 t[yrs] ×108

Figure 2. SN rate (left) and accumulated number of SNe for a Ret II-like galaxy and for the diﬀerent outﬂow models discussed in this work.

related to the V-band luminosity of dwarf galaxies using NSN Rrp/SN ≪ 1. We therefore expect that at most one r- the initial mass function (IMF) of UFDs (Geha et al. 2013) process event takes place in such galaxies and that it typi- and is approximately NSN ≈ 0.026LV . Using Eq. 7 we can cally occurred after ∼ NSN /2 SNe have exploded. now estimate f from the observed parameters. Under the This allows us to calculate the relative increase of r- assumption that gas loss is done predominantly through SNe process abundance as compared with the case of no mass and that f is constant throughout the galaxy’s evolution, we loss and perfect retainment ﬁnd that for Ret II f ≈ 0.92 and for the entire sample of NSN /2 −NSN /2 UFDs considered here hfi = 0.9. Thus, observations imply Ψ ≈ ξ(σv,r1/2,E,f )f . (10) that about 10% of the gas is expelled by each SN occurring For Ret II, the result is ξ ≈ 0.84 and Ψ ≈ 2.5. in these galaxies. We turn now to estimate the average expected abun- We can now calculate the relative iron to hydrogen den- dance of r-process elements. We denote the supernovae rate sity ratio, nFe/H using (number of SNe per unit time) byn ˙ SN (t) (and equivalently nSN (t) is the number of SNe that exploded up to a time t). NSN MF e mF e 1−i i For simplicity, we assume here thatn ˙ SN (t) is proportional nFe/H = = f ξ(σv,r1/2,E,f ) (8) Mg Mg,0 Xi=1 to the star formation rate, which is constant per unit mass up to a time T∗, after which it drops to zero. This implies nSN (t) where ξ is the average retainment fraction (see Eq. 4). n˙ SN (t) ∝ Mg (t) and using Mg = Mg,0f we obtain a The further back in this process a SN occurred, the more diﬀerential equation for nSN (t) times the iron that was synthesized in that SN was par- nSN (t) tially expelled from the galaxy. At the same time, the more n˙ SN (t)= A(f)f (11) mass has been removed from the galaxy, the harder it is where A(f) is a normalization constant that can be deter- to retain Fe from future SNe. Since the former eﬀect is mined by the total number of SNe that occurred in the UFD stronger than the latter (see §4), the last SN contributes (which in turn can be gauged by its total stellar luminosity). the most towards the observed abundance. For a given ob- Assuming f < 1, this equation has the solution (see also Fig. served value of n , the required NSN increases with f Fe/H 2) and NSN 6 NSN (f =1) = Mg,0nFe/H /(mF eξ). Stated dif- − ferently, for a given NSN , nFe/H decreases with f. 1 − f nSN (t) = A(f)t log(f) (12) We turn now to estimate the abundance of r-process −N (t) elements. Given that r-process events are much rarer than which at T∗ gives 1 − f SN = A(f)T∗ log(f), where −4 ccSNe, with the relative rate being 2.5 × 10 . Rrp/SN . NSN = nSN (T∗) is the total number of SNe. Denoting by −3 1.4 × 10 (Beniamini et al. 2016b), we can estimate the r0 the SNe rate implied by the total amount of stars formed probability of k r-process events taking place before 1 6 when f = 1 (i.e. r0 = NSN (f = 1)/T∗ ≈ 0.026LV /T∗) and n 6 NSN SNe exploded, using Poisson statistics, imposing that the same amount of stars are formed for f < 1 ( n˙ SN (t)dt = r0T∗) we ﬁnd A(f): (nR )k −nRrp/SN rp/SN R Pr(k, n)= e . (9) 1 − f −r0T∗ k! A(f)= . (13) T∗ log(f) Since for any of the known UFDs, the observed iron abun- dances imply NSN . 100, we have that generally nRrp/SN < Assuming that a single r-process event takes place in a

MNRAS 000, 1–?? (0000) r-process retainment 7

UFD (and that on average it happens after NSN /2 SNe) we To calculate pi we apply a Monte Carlo method. For obtain each galaxy we estimate the SNe rate from LV (see §5) and

mr mEu −r0T∗/2 extract the r-process event rate using the relative r-process nr/H = N /2 ξ = ξf , (14) Mg,0f SN Mg,0 to SNe rate, Rrp/SN . We use Poisson statistics to calcu- late the probabilities of obtaining a given number of events Notice that ξ increases with f while at the same time from those rates and the times at which they occur. Fi- f −r0T∗/2 decreases. Since the latter is the dominating factor, nally, integrating over the star formation rate between each the relative r-process abundance is a decreasing function of two events, allows us to estimate the number of stars with f. given Fe, Eu abundances and consequently we obtain their mean values. We repeat this process 105 times for each set of 5.3 Constant mass loss rate model parameters and measure the fraction of realizations which result within the observed values of [Fe/H],[Eu/H]. We consider here the possibility of a constant outﬂow of gas This provides us with a value for Pi. out of the galaxy The results of the likelihood analysis are shown in Fig.

Mg,0 − Mf 3 for the three diﬀerent mass loss models considered in this Mg(t)= Mg,0 − t (15) T∗ work. The 2σ limits on the best ﬁt parameters are: −4 −2 As in §5 we assume thatn ˙ SN (t) ∝ Mg (t). This implies that (i) Top hat model - 2 × 10 M⊙ . Rrp/SN . 1.5 × 10 , −6 −5 1 2 5×10 . mEu . 4×10 M⊙. This model is similar to the N (M T∗t − (M − M )t ) SN g,0 2 g,0 f one considered by Beniamini et al. (2016b), with the main nSN (t)= 1 2 (16) 2 T∗ (Mg,0 + Mf ) change being due to adding the possibility of ξ < 1 (i.e. not see also Fig. 2. Assuming once more that an r-process event all Fe or Eu are retained in the galaxy). The results reported takes place on average after NSN /2 SNe have occurred, the here are consistent with the values found in that work. −4 mean time of the event and the gas mass in the galaxy at (ii) SN driven outﬂows - 2 × 10 M⊙ . Rrp/SN . 1.5 × −2 −6 −5 that time are 10 , 10 . mEu . 2×10 M⊙. The main diﬀerence from the previous case, is a value of mEu lower by ∼ 2. This is T∗ 1 2 2 htrpi = Mg,0 − (Mg,0 − M ) (17) due to the typical value of Ψ = ξMg,0/Mg ≈ 2.5 at the time Mg,0−Mf 2 f q of the r-process event (see §5.2). −4 1 2 2 (iii) Constant outﬂow - 2 × 10 M⊙ . R . 1.5 × Mg (htrpi)= 2 (Mg,0 − Mf ) (18) rp/SN −2 −6 −5 q 10 , 2 × 10 . mEu . 3 × 10 M⊙. This model results in For Ret II, this leads to Mg /Mg,0 = 0.7 and Ψ = values that are somewhat closer to the top hat model. Once ξMg,0/Mg ≈ 1.3. Finally, the relative r-process to hydro- more, this can be related to the value of Ψ ≈ 1.3 at the time gen abundance is of the event, which is closer now to unity. mr nr/H = ξ (19) All three models provide similar results and are sta- 1 2 2 2 (Mg,0 − Mf ) tistically consistent with the available data. We also com- q pare the preferred values of the rate and Eu mass per which is slightly larger than for the top hat case. event with the limits from the recently observed binary NS merger, GW170817 (Drout et al. 2017; Pian et al. 2017). Notice that the luminosity and time-scale of the observed 6 R-PROCESS EVENT RATES AND MASS macronova constrain the total amount of r-process mate- PER EVENT rials created in the merger, and the opacity of the ejecta, We apply here a likelihood analysis in order to estimate that may become dominated by lanthanide elements with the best ﬁt parameters for the r-process event rate and the A > 140. As opposed to the abundance measurements r-process mass created per event. We use Eu as a repre- in UFDs, these observations do not directly constrain the sentative r-process element, as it is known to be predomi- Eu mass. Thus in order to convert the former to an Eu nantly synthesized via the r-process and there are reliable mass, we need to assume the minimum atomic number of measurements and/or upper limits for its abundance. We the r-process elements that are synthesized in the merger. consider the same sample of UFDs with observational con- The main uncertainty is whether or not the so called ﬁrst peak r-process elements are created. We therefore assume straints of σv, r1/2, [Fe/H], [Eu/H] and LV considered by Beniamini et al. (2016b) (see description of the sample in either Amin = 69 or Amin = 90 to calculate mEu. We §4). This sample includes Ret II in which r-process elements turn now to estimating the rate relative to SNe. The ob- served neutron star merger rate as implied by GW170817 is were detected and four other UFDs for which there are up- +3200 −3 −1 rNSM,obs = 1540−1220 Gpc yr . We use the local observed per limits on [Eu/H]. We deﬁne a likelihood function to be +1.4 4 −3 −1 maximized core-collapse SNe rate of rccSNe,obs = 7.1−1.310 Gpc yr (Drout et al. 2011; Li et al. 2011). For consistency with our

L(Rrp/SN ,mEu, f)=ΠiPi(nEu/H , nFe/H |Rrp/SN ,mEu) assumptions in §5, this rate needs to be converted to the in- trinsic collapse rate, assuming f = 0.6−0.7 of stellar col- (20) weak lapses are ultra-stripped SNe (Beniamini & Piran 2016) and where the product runs over the UFD galaxies in our sample, thus unobservable. This is also in accord with the ’missing and Pi is the probability of obtaining the observed Fe and SNe problem’ (Horiuchi et al. 2011). Finally, only a certain Eu abundances in the i−th galaxy for given values of the fraction fMerg of the general population of merging double model parameters: Rrp/SN ,mEu. neutron stars are expected to both remain conﬁned in UFD

MNRAS 000, 1–?? (0000) 8 P. Beniamini, I. Dvorkin & J. Silk galaxies given their natal kicks, and merge before the end of 8 DISCUSSION AND SUMMARY star formation in their host galaxy. Beniamini et al. (2016a) estimate this fraction to be 0.06 . fmerge . 0.6. Putting it We have re-addressed the origin of r-process elements in all together we ﬁnd ultra faint dwarf galaxies. We have focussed on the implica- tions of diﬀerent gas loss models to the abundance evolution r R = f f NSM,obs ≈ 0.0028+0.0025 (21) patterns in those galaxies and in particular on how they rp/SN Merg weak r −0.019 ccSNe,obs aﬀect the fraction of r-process elements retained by those where we have used fmerge = 0.2 as the canonical value. galaxies. We ﬁnd that the retainment fraction in UFDs is ex- As can be seen in Fig. 3, our results for the UFD sam- pected to be large ∼ 0.9, unless either a large amount of the ple are marginally consistent with the values inferred from initial galaxy’s gas is removed prior to the r-process event GW170817 for Amin = 69 and result in somewhat lower and/or unless the r-process explosion is extremely energetic. masses per event than the values inferred for Amin = 90. We In particular, this method strongly constrains r-process ex- note however, that as shown by Beniamini et al. (2016b), plosions involving very large energies (& 1052erg) as these including classical dwarfs together with ultra faint dwarfs will require the synthesis of signiﬁcantly larger amounts of increases the estimates for the mass per event by a fac- r-process mass as compared with direct estimates from the tor of ∼ 6, while keeping the rate ﬁxed. Taking this eﬀect observed abundances that do not consider the eﬀects of re- into account will result in consistency with observations of tainment. For explosions involving a signiﬁcant amount of GW170817 assuming either Amin = 69 or Amin = 90. Fur- gas loss from the galaxy before the r-process event takes thermore, given that at the time of writing there is only one place, the situation is somewhat counter intuitive. Although UFD with observed r-process abundance and only one clear the retainment fraction is reduced in this case, the amount of determination of r-process heated macronova in association mass into which the r-process material is injected is reduced with a GW event, it remains undetermined whether or not even more. Overall, this means that a somewhat smaller in- there is any true discrepancy here. trinsic amount of r-process mass has to be created in those events, in order to explain the same observed abundances. For the dwarf galaxy gas loss we assume three diﬀer- ent models. First, a simple ’top hat’ model, where all of the 7 HOW RARE IS RET II? initial gas is removed suddenly towards the end of star for- Given that Ret II is the only UFD galaxy with measured mation. Second, episodic mass loss events driven by SNe, values of r-process materials, and that other UFDs, some and third, a constant gas outﬂow, that may, for instance, of which are more luminous than Ret II, only have upper be driven by an AGN (Silk 2017). All three models result limits on their r-process abundances, it is clear that Ret II in comparable r-process rates and an amount of r-process - like objects are rare. We set here to explore exactly how mass created per event that agrees to within a factor of rare should such galaxies be. ∼ 2. These results are consistent with previous estimates We perform a Monte Carlo simulation in which we use (Beniamini et al. 2016b) that did not consider retainment the observed σv,r1/2 of Ret II and use a Poisson distribu- (and that eﬀectively assumed a ’top hat’ model of mass loss) tion for the r-process event rate and a log-normal distribu- as well as with limits from the observed binary NS merger, tion for the r-process mass per event with the mean val- GW170817 (Drout et al. 2017). Given the small number of ues informed by the likelihood analysis in §6 (and with the UFDs observed so far for which r-process abundances or lim- width of the log-normal distribution equal half the mean). its are available, it is not yet possible to use the observed We then draw 105 realizations and calculate the cumula- data to select between the diﬀerent models. This may how- tive distribution functions of Fe and Eu. Fig. 4 depicts the ever be possible in the near future, as a large number of UFD results of these distributions compared with the observed galaxies are expected to be seen by upcoming missions. values of [Fe/H], [Eu/H] in Ret II. As expected from Eq. 8, Using our best ﬁt models for the rate and synthesized the top hat model typically produces lower iron abundances masses, we can constrain the rarity of r-process enriched than the other two models. The expected (2σ) ranges of UFDs and the typical r-process and iron abundances of [Fe/H] are −3.1 . [Fe/H] . −2.5 for the top hat model, such galaxies. All gas loss models considered here result −2.9 . [Fe/H] . −2.4 for the SN driven outﬂows model and in a fraction of ∼ 7.5% of UFD galaxies that have any r- −2.7 . [Fe/H] . −2.4 for the constant outﬂow model. For process enrichment. A fraction 0.1 − 0.27 of these are con- the top hat model, the fraction of realizations resulting in sistent with the speciﬁc observed [Eu/H] and [Fe/H] abun- a value of [Fe/H] consistent with the 1σ limits from obser- dances in Ret II. This implies that Ret II is a ∼ 1 − 2% vations is 0.93. This fraction reduces to 0.51 (0.27) for the event. Interestingly, the expected iron abundances −3.1 . SN driven outﬂows (constant outﬂow) model. In all three [Fe/H]. −2.4 are consistent with the observation of Galac- models, the probability of having an r-process event in Ret tic halo stars abundances −3.5 . [Fe/H]. −2 (Fields et al. II is ∼ 7.5%. Out of these, 37% − 41% of models result in 2002), as well as with the observation that these stars are values of [Eu/H] consistent with the 1σ observational limits found to have large star-to-star scatter in their lighter el- for Ret II. The expected (2σ) ranges of [Eu/H] in case there ement abundances. Speciﬁcally, Barklem et al. (2005) ﬁnd is at least one r-process event are −2.2 . [Eu/H] . −0.85 that ∼ 3% of metal-poor halo stars in their sample (8 out of for the top hat model, −1.83 . [Eu/H] . −0.79 for the SN 253) have [Eu/Fe]>1, similar to stars observed in in Retic- driven outﬂows model and −1.66 . [Eu/H] . −0.85 for the ulum II. Both the values of [Eu/Fe] and the frequency of constant outﬂow model. The overall probability of obtaining occurrence for such stars are naturally explained if those abundances of both Fe and Eu within the 1σ observational stars originate predominantly from UFDs. Indeed, the as- errors is between 8 × 10−3 and 2 × 10−2 in all three models. sociation of metal poor halo stars with UFDs has been

MNRAS 000, 1–?? (0000) r-process retainment 9

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GW170817 GW170817 rp/SN A =69 A =90 min min R -3 10-3

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Figure 3. Log-likelihood for r-process production as a function of the Eu mass per event mEu and the relative r-process to ccSN event rate, Rrp/SN , for UFD galaxies and the diﬀerent models of mass loss explored in this work. Also depicted are the inferred rate from GW170817. suggested by various previous studies (Frebel et al. 2010; luted by a factor 100/7 ≈ 14 for the 104 dwarfs in total, van de Voort et al. 2015; Ishimaru et al. 2015; Griﬀen et al. all now dissolved, that form the halo stars. So on average, 2016; Macias & Ramirez-Ruiz 2016). These results prompt the Eu to Fe density ratio is twice solar, or equivalently us to consider the role that UFDs play as the ’building < [Eu/Fe] >≈ 0.3 but with spatial variations of up to 100 blocks’ of larger galaxies, such as the Milky Way (MW) halo in the density ratio (or [Eu/Fe] ≈ 0.3 ± 2), depending on the stars. degree of dilution in the halo assembly process. Note that our model allows for mass loss to the intergalactic medium Finally, we conclude with some simple estimates. Sup- (IGM), although we assume that most of this is retained in pose the MW PopII is made of 104 dwarf precursors, taking 6 the halo as it forms. 10 M⊙ as the ﬁducial stellar mass of a building block. This gives us a prediction of spatial (mixing-dependent) varia- Of course this is not necessarily correct. A simple baryon tions in r-process as well as the mean value. The former budget argument tells us that half the baryons must be depends on a spatial diﬀusion model that we defer to a later lost to the IGM. This is based on simulations, which show discussion (see also Hotokezaka et al. (2015)). The latter can that the only model developed to day for accounting for be estimated as follows: Out of 104 UFD like precursors we the observed MW-type galaxy baryonic shortfall (Bregman predict ∼ 700 with r-process enrichment, each with an aver- 2007) involves AGN outﬂows in dwarf galaxy building blocks age enhancement of the Eu to Fe density ratio by ∼ 20 − 40 during the MW assembly phase. This AGN feedback by solar (depending on the mass loss model, see §7), but di- intermediate-mass black holes is justiﬁed by theoretical and

MNRAS 000, 1–?? (0000) 10 P. Beniamini, I. Dvorkin & J. Silk

1 1 top hat top hat SN driven outflows 0.99 SN driven outflows constant outflow 0.8 constant outflow 0.98

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0.94 0.2 0.93

0 0.92 -4 -3.5 -3 -2.5 -2 -6 -5 -4 -3 -2 -1 0 [Fe/H] [Eu/H]

Figure 4. Cumulative distribution of [Fe/H] and [Eu/H] in an ensemble of galaxies with the same observed properties as Ret II and using the best ﬁt values for the Eu mass per event and r-process rate as given by the likelihood analysis in §6. Dashed black lines mark the mean measured abundance for Ret II and dashed gray lines depict 1σ limits on these values. observational evidence (Peirani et al. 2012). X-ray observa- Brown T. M., et al., 2014, ApJ, 796, 91 tions of massive spirals only detect a small fraction of the Burbidge E. M., Burbidge G. R., Fowler W. A., Hoyle F., 1957, missing baryons (Bogdan et al. 2017), and the baryons most Reviews of Modern Physics, 29, 547 likely are located within a few virial radii (Bregman 2016), Cameron A. G. W., 1957, PASP, 69, 201 arXiv:1710.05875 possibly in intergalactic gaseous ﬁlaments (de Graaﬀ et al. Cˆot´eB., et al., 2017, preprint, ( ) arXiv:1710.05849 2017). Covino S., et al., 2017, preprint, ( ) Another interesting aspect of retainment considerations Cox D. P., 1972, ApJ, 178, 159 Drout M. R., et al., 2011, ApJ, 741, 97 is pollution of the IGM by r-process elements. Since direct Drout M. R., et al., 2017, preprint, (arXiv:1710.05443) γ-ray emission from radioactive decay of r-process material Eichler D., Livio M., Piran T., Schramm D. N., 1989, Nature, is extremely weak, it is unfortunately not possible at the cur- 340, 126 rent stage to observationally constrain this material. Future Fields B. D., Truran J. W., Cowan J. J., 2002, ApJ, 575, 845 observations may be able to use such emission to test the Frebel A., Kirby E. N., Simon J. D., 2010, Nature, 464, 72 topic of retainment and probe the overall number of UFDs Fryer C. L., Herwig F., Hungerford A., Timmes F. X., 2006, ApJ, in the local group. 646, L131 Geha M., et al., 2013, ApJ, 771, 29 Griﬀen B. F., Dooley G. A., Ji A. P., O’Shea B. W., G´omez F. A., Frebel A., 2016, preprint, (arXiv:1611.00759) ACKNOWLEDGEMENTS Haid S., Walch S., Naab T., Seifried D., Mackey J., Gatto A., We thank Kenta Hotokezaka, Tsvi Piran and Ian Roederer 2016, MNRAS, 460, 2962 for helpful suggestions and comments on the manuscript. ID Hallinan G., et al., 2017, preprint, (arXiv:1710.05435) is supported by the EMERGENCE 2016 project, Sorbonne Hjorth J., et al., 2017, ApJ, 848, L31 Universit´es, convention no. SU-16-R-EMR-61 (MODOG). Horiuchi S., Beacom J. F., Kochanek C. S., Prieto J. L., Stanek K. Z., Thompson T. A., 2011, ApJ, 738, 154 Hotokezaka K., Kiuchi K., Kyutoku K., Okawa H., Sekiguchi Y.- i., Shibata M., Taniguchi K., 2013, Phys. Rev. D, 87, 024001 REFERENCES Hotokezaka K., Piran T., Paul M., 2015, Nature Physics, 11, 1042 arXiv:1710.05861 Abbott B. P., et al., 2017a, preprint, (arXiv:1710.05835) Im M., et al., 2017, preprint, ( ) Abbott B. P., et al., 2017b, Phys. Rev. Lett., 119, 161101 Ishimaru Y., Wanajo S., Prantzos N., 2015, ApJ, 804, L35 Abbott B. P., et al., 2017c, Astrophys. J., 848, L12 Ji A. P., Frebel A., Chiti A., Simon J. D., 2016a, Nature, 531, 610 Barklem P. S., et al., 2005, A&A, 439, 129 Ji A. P., Frebel A., Simon J. D., Chiti A., 2016b, ApJ, 830, 93 Beniamini P., Piran T., 2016, MNRAS, 456, 4089 Just O., Bauswein A., Pulpillo R. A., Goriely S., Janka H.-T., Beniamini P., Hotokezaka K., Piran T., 2016a, ApJ, 829, L13 2015, MNRAS, 448, 541 Beniamini P., Hotokezaka K., Piran T., 2016b, ApJ, 832, 149 Kasen D., Metzger B., Barnes J., Quataert E., Ramirez-Ruiz E., Bogdan A., Bourdin H., Forman W. R., Kraft R. P., Vo- 2017, preprint, (arXiv:1710.05463) gelsberger M., Hernquist L., Springel V., 2017, preprint, Kasliwal M. M., et al., 2017, preprint, (arXiv:1710.05436) (arXiv:1710.07286) Kushnir D., 2015, preprint, (arXiv:1502.03111) Bramante J., Linden T., 2016, ApJ, 826, 57 Lattimer J. M., Schramm D. N., 1974, ApJ, 192, L145 Bregman J. N., 2007, ARA&A, 45, 221 Li W., Chornock R., Leaman J., Filippenko A. V., Poznanski D., Bregman J., 2016, p. 15 Wang X., Ganeshalingam M., Mannucci F., 2011, MNRAS,

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