aa r X i v : . [ a s t r o - ph . C O ] S e p Primordial Nucleosynthesis
Alain C oc Centre de Sciences Nucl´eaires et de Sciences de la Mati`ere (CSNSM), CNRS / IN2P3,Univ. Paris-Sud, Universit´e Paris–Saclay, F–91405 Orsay Campus, FranceE-mail: [email protected] (Received August 10, 2016)Primordial or big bang nucleosynthesis (BBN) is now a parameter free theory whose predictions arein good overall agreement with observations. However, the Li calculated abundance is significantlyhigher than the one deduced from spectroscopic observations. Most solutions to this lithium problem involve a source of extra neutrons that inevitably leads to an increase of the deuterium abundance.This seems now to be excluded by recent deuterium observations that have drastically reduced theuncertainty on D / H and also calls for improved precision on thermonuclear reaction rates.
KEYWORDS:
Big bang nucleosynthesis, Lithium, Deuterium, Thermonuclear reaction rates
1. Introduction
Primordial nucleosynthesis is one of the three historical strong evidences for the hot big bangmodel. Its last free parameter, the baryon–to–photon ratio of the Universe, is now deduced fromobservations of the anisotropies of the cosmic microwave background radiation (CMB), with a pre-cision better than one percent [1]. There is a good agreement between the primordial abundances of He and D, deduced from observations, and from primordial nucleosynthesis calculations. However,the Li calculated abundance is significantly higher than the one deduced from spectroscopic observa-tions. Solutions to this problem that have been considered include stellar surface depletion of lithium,nuclear destruction during BBN or solutions beyond the standard model (see [2] for a review). Ex-periments have now excluded a conventional nuclear physics solution (see e.g. [3] and referencestherein), even though a few uncertain reaction rates could marginally a ff ect Li / H predictions. Thislithium problem has recently worsened. Most non–conventional solutions lead to an increase of deu-terium production. However, recent deuterium observations have drastically reduced the uncertaintyon primordial D / H abundance [4], excluding such increase. With a precision of 1.6% on the observedD / H value [4], comparison with BBN predictions requires that the uncertainties on thermonuclearreaction rates governing deuterium destruction be reduced to a similar level.
2. Recent results
In our latest work [5], we adopted for the baryon–to–photon ratio, the constraints obtainedwith the largest set of CMB data (TT,TE,EE + lowP), without any external data, giving Ω b · h = ± N ν = τ n = ± et al. [14] have re–evaluated the Be(n, α ) He cross section, based on He( α ,n) Be, He( α ,p) Li and Li(p, α ) He experimental data, using charge symmetry and / or detailedbalance principles. An improved evaluation of the He( α, γ ) Be reaction rate has been published [8],using a Monte–Carlo based R–matrix analysis. The e ff ect of these re–evaluations can be seen betweencolumns 2 and 3 in Table I, while columns 4 shows the e ff ect of the re–evaluated reaction rates [5] or deuterium destruction (see § Table I.
Primordial abundances compared to observations.a b c d Observations Cyburt et al. [10] Y p ± ± ± / H ( × − ) 2.635 2.635 2.452 2.45 ± ± ± He / H ( × − ) 1.047 1.047 1.070 1.07 ± ± ± Li / H ( × − ) 5.040 5.131 5.651 5.61 ± + . − . [13] 4.68 ± Baseline (a), update of Be(n, α ) He [14] and He( α, γ ) Be [8] rates (b), together with D(d,n) He,D(d,p) H and D(p, γ ) He new rates [5] (c), Monte Carlo (1 σ ) (d) from Coc et al. [5].It is apparent in Table I that the lithium prediction is higher than observations by a factor ≈ ff erences with our work. They virtually disappear when the new rates discussed aboveare adopted in both calculations (Tsung-Han Yeh, priv. comm. ), except for He, due, apparently, todi ff erent corrections to the weak rates. Li and D nucleosynthesis
For the CMB deduced baryon–to–photon ratio, Li is produced indirectly by He( α, γ ) Be, where Be will much later decay to Li, while Be is destroyed by Be(n,p) Li(p, α ) He. The solutions to thelithium problem generally rely on an increased late time neutron abundance to boost Be destructionthrough the Be(n,p) Li(p, α ) He channel. Figure 1 summarizes the results on Li and D predictionsby di ff erent models than include late time neutron injection aiming at reducing the Be + Li pro-duction, but at the expense of D overproduction. These models involve mirror neutrons, dark matterdecay or annihilation [15] or coupled variation of constants (a ff ecting the H(n, γ ) H rate) [16] asextra neutron sources. These extra neutrons, inevitably, also boost the D and H production throughthe H(n, γ ) H and He(n,p) H channels, respectively [17]. The dashed curve [5] represent an approx-imation [Eq. 7.4 in [5]] of the interplay between Li / H and D / H when neutrons are injected towardsthe end of BBN ( T < He(n,p) H reaction isneglected but it shows up in the lower limit ( ≈ . × − in Fig. 1) reached in Li / H: Li is pro-duced by the He(n,p) H( α, γ ) Li reaction at low temperature when the Li(p, α ) He is reaction isless e ffi cient. The figure shows that many models [17, 18] are able to bring the lithium abundancewithin the observational limits but at the expense of an increased D / H abundance ( ≈ × − ), nowexcluded by observations. In addition, it was noted by Kusakabe et al. [17] that the ratio of H + n to Be + n cross sections increases with energy, rendering less e ffi cient the injection of non–thermalizedneutrons (from heavy relic decays e.g. [18]) for destroying Be without overproducing deuterium.Leaving aside this unsolved lithium mystery, the precision of 1.6% (or better [19]) on the ob-served D / H value [4], requires that the uncertainties on the D(p, γ ) He, D(d,n) He and D(d,p) H ratesthat govern deuterium BBN destruction be reduced to a similar level. Indeed, a +
1% variation of theserates induces a respectively -0.32, -0.46 and -0.54% variation of D / H [5]. Achieving such a precisionon nuclear cross sections is a very di ffi cult task: data from di ff erent experiments need to be combinedkeeping in mind the importance of systematic uncertainties, in particular concerning the absolutenormalization. Two main philosophies are found in evaluations of reaction rates: i ) follow closelyexperimental S –factor experimental data or ii ) use theoretical input for the shape of the S –factor. We -10 -4 -5 -5 D/H L i/ H Fig. 1.
Lithium–deuterium anti–correlation in BBN induced by di ff erent models involving neutron injection(dots: update of Fig. 9 in Ref. [15], green circles: Fig. 7 in Ref. [15] and blue triangles, Fig. 12 in Ref. [16]).The horizontal and vertical dotted lines rerepresents the observational Li / H [13] and D / H [4] constraints whilethe dashed line is a qualitative explanation of the anti–correlation. chose the second option, with Marcucci et al. [20] [D(p, γ ) He] and Arai et al. [21] [D(d,n) He andD(d,p) H] as theoretical S –factors, keeping the normalization ( α ) as a free parameter that has to bedetermined by comparison with experimental data. The procedure we followed [5] for the D(p, γ ) Hereaction was i ) to select experimental datasets [22–25] for which systematic uncertainties were pro-vided, ii ) determine for each data set, by χ minimization, the normalization factor to be applied tothe theoretical S –factor of Marcucci et al. [20], iii ) add quadratically the systematic uncertaintiesand iv ) perform a weighted average of the normalization factor. We obtained α = . ± . et al. S –factor, and calculate thethermonuclear D(p, γ ) He reaction rate and associated uncertainty. This result is quite robust giventhe data and the theoretical S –factor, as verified using bayesian techniques instead [26]. Comparisonbetween experimental data, fits and theories is displayed in Fig. 2 (normalized to the Marcucci et al. (2005) theoretical S –factor). It shows that previous fits [27–29] were driven down by the scarce dataat BBN energies. This is not the case anymore when the theoretical energy dependence of Marcucci et al. (2005) is assumed. However, an improved calculation of the S –factor by Marcucci et al. (2016)[30] lies significantly above the previous calculation: if one applies the same renormalisation methodone finds α = . ± . He and D(p, γ ) He except that he theoretical S –factor is taken from Arai et al. [21]. All three reaction rates are higher than previousevaluations at BBN temperatures leading to a decrease in the D / H prediction, as shown in Table I. Inaddition, if we now use the theoretical S –factor from Marcucci et al. (2016), we obtain an additionalreduction of ∆ (D / H) = -0.072 × − that vanished if we rescale it ( α = H(p, γ ) He -3 -2 -1 E CM (MeV) R e l a t i v e t o M a rc u cc i + Bys08Cas02Sch97Ma97Descouvemont+ 2004Cyburt+ 2004Coc+ 2015Adelberger+ 2010Marcucci+ 2016
Fig. 2.
Ratio of experimental [22–25], fitted [5, 27–29] and new theoretical [30] S –factors to the theoret-ical one [20]; the horizontal lines correspond to the theoretical S –factor scaled by α ± ∆ α [5]. (Systematicuncertainties in the range 4.5–9% are not shown.)
4. Summary and conclusions
As conclusions, we list below our comments regarding frequently asked questions concerningbig bang nucleosynthesis. • There is no nuclear solution to the lithium problem.
Extensive sensitivity studies [7] have notidentified reactions, beyond those already known, that could have a strong impact on lithiumnucleosynthesis. Unknown resonances that could su ffi ciently increase the cross sections of reac-tions that destroy Be were not found experimentally (see e.g. [3] and references therein) and inany case would have too low strengths [31] because of the Coulomb barrier. • However, without solving the lithium problem , uncertainties a ff ecting a few reaction rates, like He( α, γ ) Be, may still a ff ect the lithium production. The role of the Be(n, α ) He reaction ispresently assumed to be negligible with respect to Be(n,p) Li. However, depending on theresults of ongoing experiments (these proceedings), it could reduce the lithium production by afew percents. The up to now overlooked Be(n,p γ ) Li channel could also have a similar e ff ect[32]. • The e ff ect of electron screening or modification of decay lifetime is negligible. For reactions ofinterest to BBN, screening a ff ects the laboratory cross sections at too low energies [e.g. .
20 keV or D(d,p) H or He(d,p) He] to a ff ect measurement at BBN energies [ ≈
100 keV], on the onehand. On the other hand, the e ff ect screening during BBN is completely negligible [33, 34]. It iswell known that the lifetime of Be that decays by electron capture is modified in a plasma [35].However, because of the Boltzmann suppression factor, at T < ≈ • Many exotic solutions to the lithium problem have been investigated (e.g. [36]), but most relyon extra neutron sources that overproduce deuterium to levels now excluded by observations [4, 19]. Few solutions beyond the Standard Model that do not su ff er from this drawback are left,e.g. [37]. • Stellar physics solutions requires a uniform reduction of surface lithium over a wide range ofe ff ective temperature and metallicity. With some fine–tuning, this could be achieved by the com-bined e ff ects of atomic di ff usion and turbulence in the outer layers of these stars [38], or bylithium destruction, followed by a self–regulated re-enrichment of lithium by late time accretion[39]. • There is no Li problem anymore. A few years ago, observations [40] of Li in a few metal poorstars had suggested the presence of a plateau, at typically Li / H ≈ − , orders of magnitudehigher than the BBN predictions of Li / H ≈ . × − [41]. The uncertainties on the D( α, γ ) Licross section have been experimentally constraint by a LUNA measurement [42] and by theory[43] confirming the BBN value. However, later, the observational Li plateau has been ques-tioned due to line asymmetries which were neglected in previous abundance analyses. Hence,there is no remaining evidence for a plateau at very low metallicity [44] that can be used toderive a primordial Li abundance. • With the high precision on D / H observations, the D(p, γ ) He, D(d,n) He and D(d,p) H rates needto be known at the percent level! This demands accurate measurement at BBN energies wheredata are scarce (see Fig. 2), to be compared with theories. The theoretical work of Arai et al. [21] was focused on low energies and does not correctly reproduce the D(d,n) He and D(d,p) Hexperimental data above ≈
600 keV. It is highly desirable that these calculations be extended upto ≈ Acknowledgments
I am indebted to my collaborators on these topics: Pierre Descouvemont, St´ephane Goriely,Fa¨ırouz Hammache, Christian Iliadis, Keith Olive, Patrick Petitjean, Maxim Pospelov, Jean-PhilippeUzan, and especially to Elisabeth Vangioni.
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