Origin of the p-process radionuclides 92Nb and 146Sm in the early Solar System and inferences on the birth of the Sun

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by  Maria Lugaro

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92
Origin of the p-process radionuclides Nb and
146
Sm in the early Solar System and inferences on
the birth of the Sun
MariaLugaro∗†,MarcoPignatari∗ ‡, UlrichOtt§¶,KaiZuberk, ClaudiaTravaglio∗∗‡,Gyo¨rgyGyu¨rky††, andZsoltFu¨lo¨p
††
∗KonkolyObservatory,ResearchCentreforAstronomyandEarthSciences,HungarianAcademyofSciences,H-1121Budapest,Hungary,†MonashCentreforAstrophysics,
MonashUniversity,VIC3800,Australia,‡Nugridcollaboration,§FacultyofNaturalScience,UniversityofWestHungary,H-9700Szombathely,Hungary,¶Max-PlanckInstitute
forChemistry,D-55128Mainz,Germany,kInstitutfu¨rKern-undTeilchenphysik,TechnischeUniversit¨atDresden,D-01069Dresden,Germany,∗∗OsservatoriodiTorino,I-10025,
PinoTorinese,Italy,and††AtomkiInstituteforNuclearResearch,HungarianAcademyofSciences,H-4001,Debrecen,Hungary
SubmittedtoProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica
6
1 The abundances of 92Nb and 146Sm in the early Solar System are known in the ESS: 92Nb and 146Sm. These nuclei are pro-
0 determined from meteoritic analysis and their stellar production is ton rich, relative to the stable nuclei of Nb and Sm, which
2 attributedtothepprocess. Weinvestigateiftheiroriginfromther- meansthattheycannotbeproducedbyneutroncaptureslike
monuclear supernovae deriving from the explosion of white dwarfs thevastmajority ofthenucleiheavierthanFe. Instead,their
n with mass above the Chandrasekhar limit is in agreement with the
nucleosyntheticoriginhasbeentraditionallyascribedtosome
a abundance of 53Mn, another radionuclide present in the earlySolar
flavor of the so-called p process [4, 5], for example, the dis-
J Systemand produced in the same events. A consistent solutionfor
92Nb and 53Mn cannot be found within the current uncertainties integration of heavier nuclei (γ process). Unfortunately, the
2 and requires that the 92Nb/92Mo ratio in the earlySolarSystem is possible astrophysical sites of origin of p-processnuclei in the
2 atleast50%lowerthanthecurrentnominalvalue,whichisoutside Universeare not well constrained.
its present errorbars. A different solutionis to invoke another pro- Core-collapse supernova explosions (CCSNe [6]) deriving
] duction site for 92Nb, which we find in the α-rich freezeout during from the final collapse of massive stars have been considered
R
core-collapsesupernovaefrommassivestars. Whicheverscenariowe as a possible site for the γ process, specifically, occurring in
S consider, we find that a relatively long time interval of at least ∼ theO-Ne-richzonesof theCCSN ejecta [7]. However,models
. 10Myrmusthaveelapsedfromwhenthestar-formingregionwhere never managed to reproduce the complete p-process pattern
h theSunwasbornwasisolatedfromtheinterstellarmediumandthe
observed in the bulk of the Solar System material [8, 9, 10].
p birth of the Sun. This is in agreement with results obtained from
For instance, CCSN models cannot reproduce the relatively
- radionuclides heavier than iron produced by neutron captures and
o lendsfurthersupporttotheideathattheSunwasborninamassive largeabundancesof92,94Moand96,98Ru. Takingintoaccount
r star-formingregiontogetherwithmanythousandsofstellarsiblings. nuclear uncertainties has not solved the problem [11, 12], ex-
t cept for a possible increase of the 12C+12C fusion reaction
s
a short-livedradionuclides | SolarSystemformation | supernovae rate [13, 14]. Another process in CCSNe that can produce
[ the light p-process nuclei up to Pd-Ag, including 92Nb, is the

Radionuclides with half lives of the order of 1 to 100 mil- combination of α,proton,neutroncaptures,andtheirreverse
1
reactions in α-rich freezeout conditions [15]. Neutrino winds
lion years (Myr) were present in the early Solar System
v
from the forming neutron star are also a possible site for the
(ESS) and represent a clue to investigate the circumstances
6
production ofthelight p-processnuclei[16,17,18],although,
of the birth of the Sun [1]. The abundances of some of these
8
nuclei in theESS, as inferred from analysis of meteorites and
9
reported relative to the abundance of a stable nucleus, are
5
given with error bars as low as a few percent. However, our
0
ability to exploit radionuclides as chronometer for the events
. Significance
1 thatledtothebirthoftheSunisunderminedbythefactthat
0 ourunderstandingof theirproduction bynuclear reactions in
Radioactivenucleiwithhalflivesoftheorderofmillionofyears
6 starsisstillrelatively poor. Thisisbecauseitrelies onstellar were present in the Solar System at its birth and can be used
1 models that include highly uncertain physics related to, e.g., as clocks to measure the events that predated the birth of the
: mixing, the mechanisms of supernova explosions, and nuclear Sun. Twoofthesenucleiareheavyandrichinprotonsandcan
v beproducedonlybyparticularchainsofnuclearreactionsduring
reaction rates. Here we focus on the origin of radionuclides
i somesupernova explosions. We have used their abundances to
X heavier than Fe. Among them, 92Nb, 129I, 146Sm, and 182Hf derive that at least 10millionyears passedbetween the last of
haveabundancesintheESSknownwitherrorbarslowerthan theseexplosionsandthebirthoftheSun. Thismeansthatthe
r
a 20%. Lugaro et al. [2] recently proposed a decoupled origin regionwere the Sunwas bornmust have livedat least as long,
for129Iand182Hf: Theformerwasproducedbyrapidneutron which ispossible onlyifitwas verymassive.
captures (r process) in a supernova or neutron star merger
Reserved for Publication Footnotes
roughly 100 Myr before the formation of the Sun, and the
latter by slow neutron captures (s process) in an asymptotic
giant branch star roughly 10–30 Myr before the formation of
theSun. Fromthesetimescalesitwasconcludedthatthestar
forming region where the Sun was born may have lived for a
fewtensofmillionyears,whichispossibleonlyifsucharegion
was very massive and gave birth to many hundreds of stellar
siblings [3].
Here, we turn to the investigation of the origin the other
two radionuclides heavier than Fe whose abundances are well
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one of its possible components (the so-called νp-process [19]) sults close to those of the detailed GCE models for the four
cannot produce 92Nb because it is shielded by 92Mo [5, 20]. ratios considered here using as p /p the average of
radio stable
Thesame occurs in thecase oftherp-process in X-raybursts the values given in Table 1 of TR141, T = 9200 Myr from
[21]. Neutrino-inducedreactionsinCCSNe(theν-process)can TR14, δ = 8 Myr, and K= 2 (Table 1). This means that
also produce some 92Nb [22], but no otherp-process nuclei. roughly (1/K)(T/δ)≃ 600 SNIa p-process events contributed
Thermonuclear supernovae (SNeIa) deriving from the ex- totheSolarSystemabundancesofthestableisotopes consid-
plosion of a white dwarf that accreted material from a main eredhere. Fortheunstableisotopes,itdependsontheirmean
sequence companion to above the Chandrasekhar limit have life: because 97Tc and 98Tc have relatively short mean lives,
been proposed as a site of the γ process [23, 24, 25]. In these thesecondtermofthesuminEq. 1representingthememory
models, heavyseed nucleiareassumed tobeproduced bythe of all theeventspriorthelast event countsfor 26% of theto-
s process during the accretion phase and, given a certain ini- tal, hence, most of their ESS abundances come from the last
tials-processdistribution,itispossibletoreproducethehigh event. On the other hand, for 92Nb and 146Sm, due to their
abundancesof92,94Moand96,98RuintheSolarSystem. How- longhalflives,thesecond termofthesumisthemost impor-
ever, there are still many uncertainties related to the origin tant. For example, in the case of 92Nb it accounts for 85%
and the features of the neutron-capture processes activated of the total amount of 92Nb. In these cases the ratios from
during the white dwarf accretion leading to SNIa. Recently, Eq. 1 are very close to the corresponding ISM steady-state
Travaglio et al. [26] (hereafter TR14) analyzed in detail the ratio, i.e., the production ratio multiplied byKτ/T.
production of 92Nb and 146Sm in SNeIa using multidimen- Although we can recover the values of the ratios produced
sional models and concluded that such an origin is plausible by the full GCE models using Eq. 1, we need to keep in
for both radionuclides in the ESS. Here, we consider these mind some distinctions. The ratios derived by TR14 using
results and combine them with new predictions of the pro- thefullGCEmodelrepresentvaluesatanabsolutetime9200
duction of p-process nuclei in α-rich freezeout conditions in MyrfromthebirthoftheGalaxy,whentheISMreachessolar
CCSNetoinvestigatetheoriginof92Nband146Smandtouse metallicity. From these values, we can evaluate an isolation
it to further constrain the circumstances of the birth of the timescale (T ): the interval between the time when the
isolation
Sun. material that ended up in the Solar System became isolated
from the ISMand thetimeof theformation of theSolar Sys-
tem. T is derivedsuch that theratio between theESS
isolation
Abundance ratios and related timescales ratioandtheISMratioforagivenradioactiveandstablepair
In simple analytic terms the abundance ratio of a short-lived issimplygivenbye−Tisolation/τ. Inreality,however,somemix-
(T1/2 <100 Myr)radioactivetoastableisotopeinthemate- ing could have occurred. An ISM mixing timescale (Tmixing)
rial that ended up in the Solar System, just after a given nu- between different phases of theISMshould be of theorder of
cleosynthetic event and assuming that both nuclides are only 10-100Myr. Theeffectofsuchprocesswasanalyticallyinves-
produced by this type of event, can be derived using the for- tigated by [31], from which [5] derived that theratio between
mula [2, 27]: the ESS ratio and the ISM ratio for a given radioactive and
stable pairis given by1+1.5x+0.4x2, wherex= Tmixing/τ.
N p δ e−δ/τ Inthispicture,therequirementisthatthecomposition ofthe
radio =K× radio × × 1+ , [1]
N p T (cid:18) 1−e−δ/τ(cid:19) star-forming region where the Sun was born must have been
stable stable
affected by mixing with the ISM, hence, Tmixing represents a
where pradio/pstable is the production ratio of each single lower limit for Tisolation.
event, τ is the mean life (=T /ln 2) of the radionuclide, Values derived using Eq. 1, instead, represent ratios in the
1/2
T the timescale of the evolution of the Galaxy up to the for- matterthatbuiltuptheSolarSystemjustafterthelast,final
mation of the Sun (∼ 1010 yr), and δ the recurrence time addition from a nucleosynthetic event. From them, we can
betweeneachevent. Thevalueofδisessentiallyafreeparam- evaluate a last-event timescale (Tlast): the interval between
eterthatmayvarybetween10and100Myr[28]. Thenumber the time of the last event and the time of the formation of
Kisalsoafreeparameterthataccountsfortheeffectofinfall the Solar System. Tlast represents an upper limit of Tisolation
of low-metallicity gas, which dilutes the abundances, and the and is derived such that the ratio between the ESS ratio and
fact that a fraction of the abundances produced, particularly theISMratioforagivenradioactiveandstablepairissimply
for stable isotopes, is locked inside stars [29]. The value of given by e−Tlast/τ (as for T ). The more δ/τ is lower
isolation
K changes dependingon whether theisotopes involved are of than unity, the closer the ratio derived from Eq. 1 is to the
primary or secondary origin, i.e., whether they are produced ISM ratio, and the closer T to T . The main draw-
last isolation
from the H and He abundances in the star or depend on the back of this approach is that the K and theδ values in Eq. 1
initial presence of CNO elements, respectively. These effects are uncertain. The advantages are that there are not further
are complex to evaluate analytically, but the general result is complicationswithregardstomixingintheISMandthatthis
that K > 1 [30]. Lugaro et al. [2] did not consider the num- description is relatively free from uncertainties related to the
ber K in their evaluation of ratios from Eq. 1, which means setting of the time of the birth of the Sun. In the model of
that effectively they used K=1 and their reported timescales TR14,thisisdefinedasthetimewhentheGalacticmetallicity
represent conservativelower limits. reachesthesolarvalue. However,stellaragesandmetallicities
TR14 did not use Eq. 1, but included the yields of in theGalaxy are not strictly correlated [32]. Chemodynami-
92Nb, 97Tc, 98Tc, and 146Sm (and their reference isotopes cal GCE models also including the effect of stellar migration
92Mo, 98Ru, and 144Sm) from their SNIa models into full, [33, 34] are required to obtain the observed spread, but have
self-consistent Galacticchemicalevolution(GCE)simulations not been applied to the evolution of radioactive nuclei yet.
to evaluate the abundance ratios 92Nb/92Mo, 97Tc/98Ru,
98Tc/98Ru, and 146Sm/144Sm in the interstellar medium
(ISM) at the time of the birth of the Sun, assuming that the 1WeaverageonlythevaluesgivenformetallicitiesintherangeZ=0.01–0.02,sinceweare
production of p nuclei only occurs in SNIa. These detailed focusingoneventsthatoccurredcloseintimetotheformationoftheSun.Variationsinthisrange
models reproduce the abundances of the stable reference iso- ofZarewithin25%.WhenconsideringalsoZdownto0.003theyarewithinafactorof2.The
onlyexceptionis98Tc/98Ru,whichvariesby50%intherangeZ=0.01–0.02andbyafactor
topes considered here [25]. With Eq. 1 we can recover re-
of6whenalsoconsideringZ=0.003.
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We expect these models to produce a range of abundances of 92Nb/92Mo, in other words, SNIa nucleosynthesis results in
theradioactive nuclei at any given metallicity, but we cannot too high production of 53Mn relative to 92Nb, and to their
predictbased on firstprinciples ifthesevariations will besig- ESS abundances.
nificant. Finally, it should be noted that, while T and A three times lower 53Mn/55Mn ratio in SNIawould result
isolation
Tmixing are required to be thesame for all the different types fromatenfoldincreaseofthe32S(β+)32Pdecay[43],inwhich
ofnucleosyntheticeventsthatcontributedtotheSolarSystem case T would decrease to ≃ 9 Myr. This possibility
isolation
matter, T is in principle different for each typeof event. needstobefurtherinvestigated. Ontheotherhand,apossibly
last
longer half life for 53Mn (seediscussion in [44]) would further
increase thedifference. Toreconcile theESS92Nbabundance
with an isolation time of 15 Myr, the half life of 92Nb should
The SNIa source be almost a factor of three higher, which seems unrealistic.
WeevaluateTisolation andTmixing assumingthatthep-process The current half life is the weighted average of two experi-
radionuclides were produced by SNeIa and comparing the mentsthatproducedsimilarresultsinspiteofbeingbasedon
abundance ratios obtained by TR14 to those observed in the differentnormalizations: thefirst[45]isnormalizedtothehalf
ESS(Table1). TR14carefullyanalysedthenuclearuncertain- life of 94Nb, which is not well known, and the second [46] to
tiesthataffecttheproductionof92Nband146SminSNeIa. In an assumed value of the 93Nb(n,2n)92Nb cross section. An-
theproductionof92Nb,(γ,n)reactionsplaythedominantrole other option is that the 92Nb/92Mo ratio in the ESS is lower
with some contribution from proton induced reactions. The than 2.2 ×10−5, i.e., 21% lower than the current lower limit.
nuclear uncertainties are related to the choice of the γ-ray It is harder to reconcile the different Tmixing: when using the
strength function and, to a lesser extent, the proton-nucleus lowest (K=1) ISM 53Mn/55Mn ratio and the upper limit for
optical potential. Since the rates of some of the most im- the ESS ratio, we obtain a lower limit for Tmixing of 24 Myr.
portant reactions are constrained experimentally, the nuclear To reconcile the 92Nb/92Mo ratio to this timescale an ESS
uncertainties on the 92Nb production are moderate, resulting 92Nb/92Mo=1.6×10−5 is required, 43% lower than the cur-
in possible variations in the ISM ratio of less than a factor rent lower limit. A different solution is to look into another
of two. The 146Sm/144Sm ratio, on the other hand, is de- production site for 92Nb.
termined by (γ,n)/(γ,α) branchings, mainly on 148Gd. The
uncertaintyrangereportedbyTR14isbasedonthreechoices
ofthe148Gd(γ,α)144Smrate. Withrespecttotwopreviouses- The CCSN source
timates[35,36],thenewrateof[37]resultsina146Sm/144Sm Asmentionedabove,theγ-processinCCSNmodelsdonotef-
ratio higher by a factor of two in SNIa, but lower by at least ficientlyproducep-processisotopesintheMo-Ruregion, but,
afactoroftwoinCCSNe[37]. Realistically, the146Sm/144Sm other CCSN nucleosynthesis components may contribute to
ratio may have an even higher nuclear uncertainty, possibly these isotopes. Pignatari et al. 2013 [47] computed CCSN
uptooneorderofmagnitude,owingtothelackofexperimen- models with initial mass of 15 M that carry in the ejecta
⊙
tal data at therelevant low energies for the148Gd(γ,α)144Sm an α-rich freezeout component. There, production of the p-
rate itself and for the low energy α-nucleus optical poten- process nuclei up to 92Mo occurs due to a combination of
tial required for the extrapolation [38]. For 92Nb/92Mo, if α, proton, and neutron captures and their inverse reactions
we compare the maximum value allowed within nuclear un- during the CCSN explosion in the deepest part of the ejecta,
certainties of 3.12 ×10−5 to the lower limit of the ESS value, where 4He is the most abundant isotope. The stellar evolu-
we derive a maximum T of 5.4 Myr and a maximum tion before theCCSN explosion was calculated with the code
isolation
Tmixing of 3.7 Myr. It is also possible to recover a solution GENEC[48]andtheexplosion simulations werebasedonthe
for 146Sm/144Sm consistent with these values, given the large prescriptionsforshockvelocityandfallbackby[49]. Thestan-
uncertainties. Currently, the value of the half life of 146Sm is dard initial shock velocity used beyondfallback is 2×109 cm
debated between the two values of 68 and 103 Myr [39, 40]. s−1 for all themasses, and we also experimented by reducing
Here,wehaveusedthelowervalue,ifweusedthehighervalue it down to 200 times lower. Results are presented for CCSN
we would obtain longer timescales than those reported in Ta- modelscomputedwithtwosetupsfortheconvection-enhanced
ble 1. neutrino-driven explosion: fast-convection (the rapid setup)
We extend the study of TR14 to investigate if the origin and delayed-convection (the delay setup) explosions [49]. In
of 92Nb and 146Sm is compatible with that of the radionu- this framework, nuclear uncertainties are insignificant com-
clide 53Mn. This nucleus provides us a strong constraint pared to model uncertainties. A post-processing code was
because near Chandrasekhar-mass SNeIa are also the ma- used to calculate the nucleosynthesis before and during the
jor producers of Mn in the Solar System [41] and, together explosion [50]. The results are summarized and compared to
with the stable 55Mn, they produce 53Mn, whose solar abun- theSNIamodels in Figure 1.
dance is well determined in the ESS (Table 1). We calculate In comparison to the SNIa models, the CCSN models pro-
the ISM 53Mn/55Mn ratio from Eq. 1 using the same val- duce less 53,55Mn, 56Fe, and 144,146Sm, and almost no 98Ru
ues for δ, K, and T derived above and the production ratio and97,98Tc. Ontheotherhand,no60FeisproducedinSNeIa,
53Mn/55Mn=0.108predictedbythesameSNIamodelusedto andthecosmicoriginofthisisotopehastobeascribedtoother
derivethep-processabundances. Thisisderivedfromthe53Cr typesofsupernovae,includingCCSNe. Significantproduction
abundance given by [24], but, we note that different models of 92Nb and 92Mo occurs in CCSN models of 15 M , with
⊙
produce very similar 53Mn/55Mn ratios [42]. Wecalculate an production factors for 92Mo comparable to those of the SNIa
ISM53Mn/55Mnratioof2.41×10−4,which,afteranisolation models, and92Nb/92Moratios uptofivetimeshigher. CCSN
time of 5.4 Myr, results in a ratio of 5.82 ×10−5, one order modelswithinitialmasslargerthan15M donotejectmate-
⊙
ofmagnitudehigherthantheESSvalue. Anisolation timeof rial exposedtotheα-richfreezeout duetothemoreextended
at least 19 Myr is instead required to match the 53Mn/55Mn fallback. Theα-richfreezeoutefficiencyalsostronglydepends
constraint. IfwemaketheconservativeassumptionthatK=1, on the shock velocity. When its standard value is reduced,
insteadof2,tocalculatetheISM53Mn/55MnratiofromEq. 1 even only by a factor of two, the amounts of 92Mo and 92Nb
we obtain T ≃ 15 Myr. This value is strongly incom- ejected becomenegligible. This isbecausefor lowershock ve-
isolation
patiblewith theupperlimit of5.4 Myrrequiredtomatchthe locities the bulk of α-rich freezeout nucleosynthesis is shifted
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toward lighter elements closer to the Fe group. Only some Another possibility is that the 92Nb was instead predomi-
γ-processcomponentisproducedinthesecases,whichispoor nantlyproducedbyCCSNethatexperiencedtheα-richfreeze-
in92Mo. Insummary,theα-richfreezeout conditionssuitable out, corresponding in our models to low initial stellar masses
to produce 92Mo and 92Nb are more likely hosted in CCSNe experiencingacore-collapsewithhighshockvelocities. Inthe
with initial mass of 15 M or lower and shock velocities at extreme scenario where all the 92Nb and 92Mo in the ESS
⊙
least as large as those provided by [49]. came from such events we have derived lower limits for the
Weexplored thepossibility that the92Nb in theESS came timingofthelastofthem. Thesearealsostillconsistentwith
from the α freezeout production experienced by these 15 M a relatively long T of at least 7 Myr, since T ∼
⊙ isolation isolation
CCSN models. Since the premise of Eq. 1 is that both the T whenδ<<τ,whichisverifiedfor92Nbwhenδ=10Myr.
last
stableandunstableisotopespresentintheESSwereproduced Clearly, 92Nb could have been produced by both SNIa and
onlybythistypeofevent,undersuchassumption,wecanap- CCSN events. Full GCE models are required, including both
plyEq. 1onlytocalculatethe92Nb/92Moratiostoderivethe SNIa, the α-rich freezeout component of CCSN considered
time of the last such α freezeout event, since the other iso- here, and the possible production in the neutrino winds. Be-
topes are not produced in any significant abundances2. The causetheα-richfreezeoutCCSNeeventsofinitialmass15M
⊙
calculationsarehamperedbytheerrorbarsontheESSratios produce higher amounts of 92Nb than SNIa, we expect that
and the large uncertainties related to the choice of the free adding them tothebalance will increase theISM92Nb/92Mo
parameters enteringinEq. 1. However,toinferfurtherinfor- ratioatthetimeoftheformationoftheSolarSystem,leading
mation on the birth of the Sun we are particularly interested to longer T , and an easier match with the 53Mn/55Mn
isolation
in determining the lower limit of T because this provides constraint. In conclusion, a higher-precision determination of
last
ustheshortest possibletimescale, within alltheuncertainties theESS92Nb/92Moratioisurgentlyrequired. Thiswillallow
above, for the life of the star forming region where the Sun ustodetermineifSNIaarethemajorsourceoflightp-process
was born. Using K=1 in Eq. 1 and the upper limit of the nuclei in the Galaxy or if CCSNe also play a role; and which
ESS 92Nb/92Mo ratio we inferred a lower limit for T of 10 fraction of the53Mn in theESS originated from SNIa.
last
MyrwhenusingthedelaysetupCCSNmodel(Table2). How-
ever, we stress that K=1 representsa very conservative lower
ACKNOWLEDGMENTS. ML is a Momentum (“Lendu¨let-2014” Programme)
limitbecausetheproductionfactor92Mo/92Mo⊙ oftheCCSN project leader of the Hungarian Academy of Sciences. MP acknowledges support
delaymodeliscomparabletothatoftheSNIamodel(140ver- toNuGridfromNSFgrantsPHY09-22648(JointInstituteforNuclearAstrophysics,
sus 172). This means that we would need a similar number JINA), NSF grant PHY-1430152 (JINA Center for the Evolution of the Elements)
of events (which scales as 1/Kδ) to reproduce the 92Mo solar andEUMIRGCT-2006-046520. MPacknowledgesthesupportfromthe“Lendu¨let-
2014”ProgrammeoftheHungarianAcademyofSciences(Hungary)andfromSNF
abundance - although the exact value would depend on the (Switzerland).
metallicity dependenceof 92Mo/92Mo in the CCSN models,
⊙
which we did not explore. The lower limit of T from the
last
rapidsetupCCSNmodelisinsteadanegativevalue. However,
the production factor 92Mo/92Mo of the rapid model is five References
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Fig. 1. ResultsfortheradioactiveandstablenucleiofinterestfromtheCCSNmodelsascomparedtothosefromSNIa(TR14).TheCCSNmodelswiththedelaysetup
haveinitialmasses15,20,25,32and60M⊙andmetallicity0.02. TheCCSNmodelswiththerapidsetupareforastarofinitialmass15M⊙anddifferentreductionfactors
fortheshockvelocity. Therateby[36]wasusedforthe148Gd(γ,α)144Smreaction. Asmentionedinthetext,usingthenewrateby[37]wouldresultin146Sm/144Sm
ratioshigherinSNIaandlowerinCCSNe.
Table 1. Decay rates, ESS ratios, SNIa production and ISM ratios, and timescales for the isotopes of interest
53Mn 60Fe 92Nb 97Tc 98Tc 146Sm
T1/2(Myr) 3.7 2.6 35 4.2 4.2 68
τ(Myr) 5.3 3.8 50 6.1 6.1 98
referenceisotope 55Mn 56Fe 92Mo 98Ru 98Ru 144Sm
ESSratio (6.28±0.66)×10−6 (5.39±3.27)×10−9 (3.4±0.6)×10−5 < 4×10−5 < 6×10−5 (9.4±0.5)×10−3
reference [52]∗ [53] [54, 55] [55, 56] [55,57] [26, 58]
productionratio† 0.108 < 10−9 1.58×10−3 2.39× 10−2 4.22×10−4 0.347
ISMfromGCE‡ 1.72+1.40×10−5 4.08×10−5 6.47×10−7 7.0+9.7×10−3
−0.06
ISMfromEq. 1§ 2.41×10−4 < 10−12 1.86×10−5 5.68×10−5 1.00×10−6 7.70×10−3
T ¶ 19 –20 - ≤5.4 > 0.12 - ≤62
isolation
Tmixing 40 –45 - ≤3.7 > 0.08 - ≤50
∗Themostrecentvalueof6.8×10−6givenby[59]isincludedinthegivenerrorbars.
†AverageoftheratiosfromTable1ofTR14frommetallicitiesfrom0.01to0.02,exceptfor53Mn/55Mnfrom[24]and60Fe/56Fefrom[42].
‡FromTables2,3,and4ofTR14
§UsingK=2,δ=8Myr,andT=9200Myr.
¶ReportedrangesreflecttheerrorbarsontheESSandISMratios.
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Table 2. 92Nb/92Mo from the CCSN models of 15 M , ISM ratios, and inferred lower limits for T
⊙ last
delaysetup rapidsetup
productionratios 8.20×10−3 5.30×10−3
δ =10Myr δ =50 Myr δ =100 Myr δ =10 Myr δ =50Myr δ =100 Myr
ISMratio∗ 4.92×10−5 7.06×10−5 1.03×10−4 3.18×10−5 4.56×10−5 6.66×10−5
lowerlimit of T † 10 29 48 - 7 25
last
∗FromEq. 1usingT=9200MyrandK=1toobtainaconservativelowerlimit.
†UsingtheESSupperlimitof4.0×10−5.
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