NNeutrinos in Cosmology and Astrophysics
A.B. Balantekin, G.M. Fuller Physics Department, University of Wisconsin, Madison WI 53706 USA Department of Physics, University of California, San Diego, La Jolla CA 92093 USANovember 10, 2018
Abstract
We briefly review the recent developments in neutrino physics and astrophysics which haveimport for frontline research in nuclear physics. These developments, we argue, tie nuclear physicsto exciting developments in observational cosmology and astrophysics in new ways. Moreover,the behavior of neutrinos in dense matter is itself a fundamental problem in many-body quantummechanics, in some ways akin to well-known issues in nuclear matter and nuclei, and in someways radically different, especially because of nonlinearity and quantum de-coherence. The self-interacting neutrino gas is the only many body system driven by the weak interactions.
Experiments have now revealed many of the fundamental properties of neutrinos, including their mass-squared differences and three (mixing angles θ , θ , θ ) of the four parameters characterizing theunitary transformation between the neutrino vacuum energy (mass) states and the weak interaction(flavor) eigenstates (a recent review is given in [1]). We now lack only the fourth parameter, the CP-violating phase, and the absolute neutrino rest masses and the way these are arranged, i.e., whethernature has chosen the normal or inverted mass hierarchy.Moreover, the fact of nonzero neutrino rest masses immediately begs the question of whether thereexist right-handed, so-called sterile neutrinos. There are many models for sterile neutrino states whichare not really sterile by virtue of vacuum mixing with ordinary, active neutrinos. The mass scales ofthese sterile species are not well predicted in these models, and can range from masses comparable tothe unification scale, all the way down to the sub-eV regime. There are even intriguing experimentalhints for the existence of sterile neutrinos with masses in the eV range.All of these neutrino properties, measured and unmeasured, may figure prominently in key astro-physical environments, for example in core collapse supernovae and in the early universe and Big BangNucleosynthesis (BBN). This connects fundamental neutrino physics to the breathtaking advances inastrophysical numerical modeling and to the near-fantastic increase in the volume and scope of ob-servational data obtained from both from ground- and space-based observatories. The reasons for theneutrino-astrophysics tie-in are twofold: neutrinos can carry and transport the bulk of the entropy andenergy in these environments, along the way influencing composition; and the weak interaction, includ-ing neutrino interactions, is unique in being able to change isospin, i.e., inter-converting neutrons and1 a r X i v : . [ nu c l - t h ] M a r rotons. The latter issue is fundamentally dependent on the flavor states of the neutrinos, and thesecan change.The charge to neutrino physicists and astrophysicists is then clear: we must be able to calculatehow neutrinos change their flavors as they move from dense nuclear matter-like environments (eitherin the Early Universe or in supernova proto-neutron star cores) to relatively low density environments(like the supernova envelope or the post-weak decoupling epoch in the early universe). Historically thisneutrino flavor evolution problem in astrophysics has been approached with a “separation of scales.”At relatively low densities a Schr¨odinger-like equation governs the coherent limit, where forwardscattering of neutrinos on electrons, quarks/nucleons, and other neutrinos dominates over inelasticand direction-changing processes, and in-medium oscillation lengths are short compared to neutrinomean free paths. At high densities, a Boltzmann treatment of neutrino energy, number, and heattransport is used. In that limit neutrino inelastic and direction-changing scattering is dominant andflavor oscillations are ignored because oscillation lengths are long compared to mean free paths. Theway the problem has been approached in supernova environments, the Boltzmann equation is used inthe neutron star and in the region immediately above it, and the Schr¨odinger/coherent approach isemployed further out in the envelope where the density is lower. We now know that this separation ofscales fails in some cases, an outstanding example of which is the “neutrino halo” effect [2].To follow neutrino flavor evolution in the general case, i.e. in a medium of any density, requires aset of full neutrino quantum kinetic equations (QKE’s). Obviously, these equations should reduce to:(1) the Boltzmann transport equation in the high density limit where scattering-induced de-coherencedominates and flavor conversion can be neglected; and (b) a Schr¨odinger-like equation in the low densitylimit. However, all manner of plausible-looking QKE’s have the same asymptotic limits, and this hasnecessitated Vlasenko, Fuller, and Cirigliano [3] to derive them from fundamental considerations inquantum field theory. This produces QKE’s broadly similar to those found in Raffelt & Sigl [4] andStrack & Burrows [5]. Traditionally the neutrino flavor evolution problem in astrophysics has beenapproached with a “separation of scales.”Solving the QKE’s is a numerical nightmare, essentially differing from traditional neutrino transportcalculations through (sometimes very) high frequency quantum phases. Hence the appeal of a separationof scales approach is clear. But as we shall see below, even that approach, flawed as it is, is fraughtwith unresolved many-body physics problems. Neutrinos influence almost every aspect of the physics of the early universe. This fact, combined withseveral recent, or expected future, developments in observational cosmology and neutrino experimentpromise to “box-in” any new physics in the neutrino sector. There are five key developments.1) Observations of the cosmic microwave background (CMB) radiation have given us a precisemeasurement of the baryon content of the universe: this corresponds to a baryon-to-photon ratio η ≈ . × − . Future observations will get this number to better than 1% precision. This quantityis a key parameter in Big Bang Nucleosynthesis (BBN). Moreover, global minimization of the CMB andother cosmological data gives us the cosmological parameters, the age and the curvature parameter.2) The advent of large, ten-meter class telescopes like Keck, has revealed the primordial deuteriumabundance, again to fairly good precision [6]. This is significant, because the chief determinant of the H yield in BBN is the baryon density, which we know very well from 1). Any discrepancy betweenthe observed primordial deuterium and that predicted by BBN calculations using the CMB-determinedbaryon density could have its origin in neutrino sector physics. Though the dependence of the BBNdeuterium yield in BBN is much weaker than that of He, we may be able to infer the deuteriumprimordial abundance with more confidence and fewer systematic issues.2) Observations of the Silk damping tail (higher wave number end) of the CMB power spectrum cangive a measure of the primordial He abundance. This determination is completely independent of thevalue obtained via the linear regression/compact blue galaxy approach. A high-precision determinationof primordial helium abundance combined with 1) and 2), is highly restrictive of new physics in theneutrino sector.4) CMB observations can give a measure of the ratio of energy density in relativistic particles tothat carried by particles with nonrelativistic kinematics at the epoch of photon decoupling. This epochcorresponds to photon temperature T CMB ≈ . ρ rad at this epoch is expressed in terms of a parameter N eff , ρ rad = (cid:34) (cid:18) (cid:19) / N eff (cid:35) π T . (1)With this definition, standard model physics and cosmology predicts N eff ≈ .
046 [7]. The excess over 3,corresponding to three flavors of neutrinos with black body, Fermi-Dirac-shaped energy spectra, arisesfrom e ± -pair annihilation into out of equilibrium neutrino pairs near and during the BBN epoch. Itis important to note that N eff parameterizes all relativistic energy density at the photon decouplingepoch, not just that contributed specifically by the known active neutrinos. Any measurement of N eff significantly different from 3 . N eff are consistent with the standard model, but have largeuncertainties. In the near future the Planck satellite collaboration will report an analysis of their datawhich should give N eff to 10% [8].5) Finally, the CMB plus observations of smaller-scale large scale structure, e.g., the Lyman alphaforest, promise a good limit on what is usually termed the sum of the light neutrino masses, (cid:80) m ν .The best constraints in this regard will probably come from experiments that utilize weak gravitationallensing of the CMB, and these may well get down to the (cid:80) m ν < . (cid:80) m ν are tantamount to a probe of the relic neutrino energy spectrum and density,once the rest masses are known.Sterile neutrinos are a case in point when it comes to the constraining or revealing power of theobservations/considerations in 1)-5). The experimental and observational constraints on sterile neutri-nos are discussed in Refs. [10] and [11]. For example, if there were a sterile neutrino with a rest mass ∼ ν e and ¯ ν e energy spectra at the BBN epoch could be atricky issue, however, necessitating a QKE solution. Core-collapse supernovae, like some epochs in the early universe, are neutrino-dominated dynamicalsystems. In these supernovae essentially all the gravitational energy released during collapse escapesin the form of intense neutrino fluxes emerging from the newly-born neutron star. During the firstten seconds or so of the existence of the neutron star, these neutrino fluxes drive a wind from its3able 1: Many-body systems in physics.
System Primary interaction Number of particles
Nuclei Strong at most ∼
250 particlesCondensed matter Electromagnetic at most N A particlesNeutrinos in SN Weak ∼ particlessurface in which various nuclear species may be synthesized. In a core-collapse supernova environmentneutrino-neutrino interactions are not negligible, as the gravitational binding energy of the progenitormassive star is converted into ∼ neutrinos during the cooling process of the proto-neutron star.The total energy carried by those neutrinos is 10 ergs, as compared to the total optical and kineticenergy of these events which is 10 ergs. The interactions between those copious neutrinos lead to novelcollective and emergent effects, such as conserved quantities and interesting features in the neutrinoenergy spectra. Collective neutrino oscillations play a crucial role both for neutrinos and antineutrinos.There is a growing literature on the collective neutrino oscillations, a good starting point is a recentreview [13]. Collective neutrino oscillations produce an interesting effect, called spectral swappings orsplits, on the final neutrino energy spectra: at a particular energy these spectra are almost completelydivided into parts of different flavors [14, 15].It is interesting to note that core-collapse supernovae are the only many-body systems driven bythe weak interactions (see Table 1). This table nicely illustrates that astrophysical extremes allow usto test physics that cannot be tested elsewhere: Neutrino-neutrino interactions, which represent a partof the Standard Model, are not accessible with any other experimental tools.A complete theoretical treatment of all the many-body effects due to neutrino-neutrino interactionswould be very complicated and usually several simplifying assumptions are made. The coherent scatter-ing of the neutrinos off one another is considered dominant. Even with this restriction solving the fullmany-body problem is exceedingly difficult. Instead a mean-field approximation which represents thesaddle-point solution of the path integral for the full many-body system [16] is typically used. In ad-dition, the Hamiltonian describing the system depends on the angles between all the pairs of neutrinomomenta. Earlier calculations employed an average of these angles (”single-angle” approximation),however increasingly sophisticated multi-angle calculations are now available. A recent calculationwith three flavors finds that multi-angle formulation reduces the adiabaticity of flavor evolution in thenormal neutrino mass hierarchy, resulting in lower swap energies [17]. It seems that the single-angleapproximation seems to be sufficient in some cases, but is inadequate in other situations.The saddle-point approximation effectively reduces the full neutrino Hamiltonian with one- andtwo-body terms to an one-body Hamiltonian. This is reminiscent of the random-phase approximationin many-body theory where quadratic products of the operators are ”linearized” by replacing one ofthem with a ”mean-field” value. Corrections to the saddle-point approximation are expected to besmall, but they have not yet been calculated. In the single-angle limit, using a formal analogy betweenthe many-neutrino Hamiltonian and the Hamiltonian describing BCS superconductivity, one can writedown the conserved quantities of the system [18]. It turns out that the invariants of the full Hamiltonianare also invariants of the one-body Hamiltonian when they are properly linearized.This provides furtherconfidence in the aptness of the linearization procedure itself.Another assumption which was recently relaxed is the assumption of forward scattering. Neutrinosthat scatter in non-forward directions could create a ”neutrino halo” that would interact with theother outgoing neutrinos. The fraction of outflowing neutrinos interacting with this neutrino halo issignificant [2]. The halo could be a significant effect in every supernova environment except very latetime neutrino driven wind. It was argued that the multiangle effects could suppress self-induced flavorconversion during the accretion phase [19]. However, the halo changes the nature of the flavor evolution,4urning it into a boundary value problem instead of an initial value one. A full numerical treatment ofthe halo, taking into account this effect, has been only performed for O-Ne-Mg core-collapse supernovae[20].Core-collapse supernovae are likely sites for several nucleosynthesis scenarios. One of these is nucle-osynthesis via neutrino-induced nucleon emission (the ν -process) [21]. For example, the conversion of Ne into F in the outer shells via neutrino capture would account for the entire observed abundanceof F. In the absence of collective oscillations, one expects a hierarchy E ν e < E ¯ ν e < E ν µ ,ν τ , ¯ ν µ , ¯ ν τ in theenergy spectra of the neutrino fluxes that pass through those outer shells. While the MSW resonancegoverned by δm is at solar densities, the resonance governed by δm is at matter densities that existin those outer shells of a supernova. It was recently pointed out that MSW effect for the invertedhierarchy, by converting the more energetic muon and tau antineutrinos into electron antineutrinos,boosts the ν -process nucleosynthesis yields of B and Li [22]. In the normal hierarchy this would nothappen: it is interesting to be able to relate the elemental abundances to the neutrino hierarchy. Onecaveat is that once the neutrinos reach the He shells, complete swappings between electron neutrinos (orantineutrinos) and other flavors due to the collective neutrino oscillations would not be distinguishablefrom the adiabatic MSW oscillations [23].The site of the r-process nucleosynthesis is an open question [24]. One needs a site which is the isospinmirror of the Early Universe, a hot gas expanding and condensing into nuclei as it cools. The high-temperature, high-entropy region outside the newly-formed neutron star in a core-collapse supernova wassuggested to be an r-process site [25]. The neutrino-driven wind, one candidate site where the r-processmay take place, yields about the observed amount of the r-process nuclei. Current hydrodynamicalsimulations of the neutrino-driven wind do not seem to reach the extreme conditions necessary for ther-process [26]. Since collective neutrino oscillations dominate the neutrino propagation much deeperthan the conventional matter-induced MSW effect, they would also impact r-process nucleosynthesisyields if the neutrino-driven winds are shown to be the appropriate sites [27, 28]. There are othersuggested sites for the r-process nucleosynthesis. They include He mantles of the metal-poor (i.e.,early) supernova progenitors [29] and neutron-star mergers [30].Electron fraction, or equivalently neutron-to-proton ratio (a controlling parameter for nucleosynthe-sis) is determined by the neutrino capture rates: ν e + n (cid:42)(cid:41) p + e − (2)and ¯ ν e + p (cid:42)(cid:41) n + e + , (3)Hence, aside from driving the wind, the most important impact of the neutrino fluxes for a potentialr-process is that neutrino interactions on free nucleons set the neutron richness of the outflow. Neutrino-nucleus interactions can also leave a noticeable imprint on the distribution of synthesized nuclei [31]. Asummary of neutrino processes relevant for flavor evolution in core-collapse supernovae is given in Fig.1. Progress in not only in calculating r-process nucleosynthesis but also in a number of research frontiersin nuclear astrophysics depends on understanding spin-isospin response in a broad range of nuclei fromstable isotopes to rare ions that can be studied in dedicated facilities. Currently many major acceleratorprojects around the world, at different stages of construction and operation, aim to explore the physicsof these exotic rare nuclei. Neutrinos indeed bridge the cutting-edge experimental efforts at the rareisotope facilities and laboratory probes of spin-isospin response of nuclei with nuclear astrophysics effortsaimed at learning about the origin of elements. 5igure 1: A summary of neutrino processes in core-collapse supernovae, highlighting the importance ofneutrino flavor evolution. It can be argued that neutrino rest mass and vacuum flavor mixing is physics beyond the StandardModel. Certainly the existence of sterile neutrino states falls into this category. Since neutrinos carry adominant fraction of the total energy and even entropy in the Early Universe, core collapse supernovaeand compact object merger environments, and since these venues can be the sites of key nucleosynthesisevents, their dynamics and local interactions may be important to understand. Furthermore, sincethe most important neutrino interactions for nucleosynthesis, the charged current isospin-changingreactions, are flavor dependent, this understanding will come only when neutrino flavor transformationin medium is understood.As a consequence, we believe that the nonlinear neutrino flavor transformation problem may lie atthe heart of many important problems in nuclear physics and astrophysics. These problems include theorigin of the lightest and heaviest nuclei in the nuclear astrophysics realm. On the pure nuclear physicsside, the many-body techniques required to solve the neutrino transport and flavor evolution problemsecho the techniques and insights developed to understand nuclear matter and nuclear structure.Given the expected golden future for observational cosmology, the real if chancy possibility of catch-ing a Galactic core collapse supernova neutrino burst in a new generation of terrestrial detectors, andthe anticipated future detection of compact object mergers with Advanced LIGO, we believe that adeeper understanding of neutrino flavor dynamics should be a goal for some of us in the nuclear theorycommunity.This work was supported in part by the U.S. National Science Foundation Grants No. PHY-1205024(U. Wisconsin) and PHY-0970064 (U. California, San Diego), in part by the University of WisconsinResearch Committee with funds granted by the Wisconsin Alumni Research Foundation, in part by theUniversity of California Office of the President, and in part by the LANL/DOE topical collaboration.
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