Proceedings ISAPP School \Neutrino Physics and Astrophysics," 26 July{5 August 2011, Villa Monastero, Varenna, Lake Como, Italy Neutrinos and the Stars Georg G. Raffelt Max-Planck-Institute f¨urPhysik (Werner-Heisenberg-Institut) F¨ohringerRing 6, 80805 M¨unchen, Germany Summary. | The role of neutrinos in stars is introduced for students with little prior astrophysical exposure. We begin with neutrinos as an energy-loss channel in ordinary stars and conversely, how stars provide information on neutrinos and possible other low-mass particles. Next we turn to the Sun as a measurable source of neutrinos and other particles. Finally we discuss supernova (SN) neutrinos, the SN 1987A measurements, and the quest for a high-statistics neutrino measurement from the next nearby SN. We also touch on the subject of neutrino oscillations in the high-density SN context. 1. { Introduction Neutrinos were first proposed in 1930 by Wolfgang Pauli to explain, among other problems, the missing energy in nuclear beta decay. Towards the end of that decade, the role of nuclear reactions as an energy source for stars was recognized and the hydro- arXiv:1201.1637v2 [astro-ph.SR] 19 May 2012 gen fusion chains were discovered by Bethe [1] and von Weizs¨acker [2]. It is intriguing, however, that these authors did not mention neutrinos|for example, Bethe writes the fundamental pp reaction in the form H + H D + +. It was Gamow and Schoen- ! berg in 1940 who first stressed that stars must be powerful neutrino sources because beta processes play a key role in the hydrogen fusion reactions and because of the feeble c Societ`aItaliana di Fisica 1 2 Georg G. Raffelt neutrino interactions that allow them to escape unscathed [3]. Moreover, the idea that supernova explosions had something to do with stellar collapse and neutron-star forma- tion had been proposed by Baade and Zwicky in 1934 [5], and Gamow and Schoenberg (1941) developed a first neutrino theory of stellar collapse [4]. Solar neutrinos were first measured by Ray Davis with his Homestake radiochemical detector that produced data over a quarter century 1970{1994 [6] and since that time solar neutrino measurements have become routine in many experiments. The neutrino burst from stellar collapse was observed only once when the star Sanduleak 69 202 in the Large Magellanic Cloud, − about 160,000 light years away, exploded on February 23, 1987 (Supernova 1987A). The Sun and SN 1987A remain the only measured astrophysical neutrino sources. Stars for sure are prime examples for neutrinos being of practical relevance in nature. The smallness of neutrino masses compared with stellar temperatures ensures their role as radiation. The weak interaction strength ensures that neutrinos freely escape once produced, except for the case of stellar core collapse where even neutrinos are trapped, but still emerge from regions where nothing else can directly carry away information except gravitational waves. The properties of stars themselves can sometimes provide key information about neutrinos or the properties of other low-mass particles that may be emitted in analogous ways. The Sun is used as a source of experimental neutrino or particle measurements. The SN 1987A neutrino burst has provided a large range of particle-physics limits. Measuring a high-statistics neutrino light curve from the next nearby supernova will provide a bonanza of astrophysical and particle-physics informa- tion. The quest for such an observation and measuring the diffuse neutrino flux from all past supernovae are key targets for low-energy neutrino astronomy. The purpose of these lectures is to introduce an audience of young neutrino re- searchers, with not much prior exposure to astrophysical concepts, to the role of neutrinos in stars and conversely, how stars can be used to gain information about neutrinos and other low-mass particles that can be emitted in similar ways. We will describe the role of neutrinos in ordinary stars and concomitant constraints on neutrino and particle prop- erties (Section 2). Next we turn to the Sun as a measurable neutrino and particle source (Section 3). The third topic are collapsing stars and the key role of supernova neutrinos in low-energy neutrino astronomy (Section 4). 2. { Neutrinos from ordinary stars . 2 1. Some basics of stellar evolution. { An ordinary star like our Sun is a self- gravitating ball of hot gas. It can liberate gravitational energy by contraction, but of course its main energy source is nuclear binding energy. During the initial phase of hydrogen burning, the effective reaction is 4 (1) 4p + 2e− He + 2ν + 26:7 MeV : ! e In detail, the reactions can proceed through the pp chains (Table I) or the CNO cycle (Table II). The latter contributes only a few percent in the Sun, but dominates in slightly Neutrinos and the stars 3 Table I. { Hydrogen burning by pp chains. Termination Reaction Branching Neutrino Name (Sun) Energy [MeV] + p + p ! d + e + νe 99.6% < 0:423 pp p + e− + p ! d + νe 0.44% 1.445 pep d + p ! 3He + γ PP I 3He + 3He ! 4He + 2p 85% 3He + 4He ! 7Be 15% 7 7 Be + e− ! Li + νe 90% 0.863 Beryllium 7 7 Be + e− ! Li∗ + νe 10% 0.385 Beryllium PP II 7Li + p ! 4He + 4He 7Be + p ! 8B + γ 0.02% 8 8 + B + p ! Be∗ + e + νe < 15 Boron 8 4 4 PP III Be∗ ! He + He 3 4 + 7 hep He + p ! He + e + νe 3 × 10− < 18:8 hep more massive stars due to its steep temperature dependence. Neutrinos carry away a few percent of the energy, in detail depending on the reaction channels. Based on the solar 1 33 1 photon luminosity of ( ) L = 3:839 10 erg s− one can easily estimate the solar × 10 2 1 neutrino flux at Earth to be about 6:6 10 cm− s− . × In the simplest case we model a star as a spherically symmetric static structure, excluding phenomena such as rotation, convection, magnetic fields, dynamical evolution such as supernova explosion, and so forth. Stellar structure is then governed by three conditions. The first is hydrostatic equilibrium, i.e. at each radius r the pressure P must balance the gravitational weight of the material above, or in differential form dP G M ρ (2) = N r ; dr − r2 R r 2 where GN is Newton's constant, ρ the local mass density, and Mr = 0 dr0 ρ(r0) 4πr0 the integrated stellar mass up to radius r. Energy conservation implies that the energy flux Lr flowing through a spherical sur- face at radius r can only change if there are local sources or sinks of energy, dL (3) r = 4πr2 ρ : dr 1 1 The local rate of energy generation , measured in erg g− s− , is the sum of nuclear and gravitational energy release, reduced by neutrino losses, = + : nuc grav − ν (1) Following astrophysical convention, we will use cgs units, often mixed with natural units, where ¯h = c = kB = 1. 4 Georg G. Raffelt Table II. { Hydrogen burning by the CNO cycle. Reaction Neutrino Energy [MeV] 12C + p ! 13N + γ 13 13 + N ! C + e + νe < 1:199 13C + p ! 14N + γ 14N + p ! 15O + γ 15 15 + O ! N + e + νe < 1:732 15N + p ! 12C + 4He Finally the flow of energy is driven by a temperature gradient. If most of the energy is carried by electromagnetic radiation|certainly true at the stellar surface|we may 4 express the thermal energy density by that of the radiation field in the form ργ = aT 15 3 4 where the radiation-density constant is a = 7:57 10− erg cm− K− or in natural × units a = π2=15. The flow of energy is then 4πr2 d(aT 4) (4) L = ; r 3κρ dr 2 1 where κ (units cm g− ) is the opacity. The photon contribution (radiative opacity) is 1 1 κ ρ = λ − : In other words, (κ ρ)− is a spectral average (\Rosseland mean") γ h γ iRosseland γ of the photon mean free path λγ . Radiative transfer corresponds to photons carrying energy in a diffusive way with typical step size λγ . Energy is also carried by electrons 1 1 1 (\conduction"), the total opacity being κ− = κγ− + κc− . In virtually all stars there are regions that are convectively unstable and energy trans- port is dominated by convection, a phenomenon that breaks spherical symmetry. In practice, convection is treated with approximation schemes. In our Sun, the outer layers beyond about 0:7 R (solar radius) are convective. The stellar structure equations must be solved with suitable boundary condition at the center and stellar surface. From nuclear, neutrino and atomic physics calculations one needs the energy-generation rate and the opacity κ, both depending on density, tem- perature and chemical composition. In addition one needs the equation of state, relating the thermodynamic quantities P , ρ and T , again depending on chemical composition. For detailed discussions we refer to the textbook literature [7, 8]. However, simple reasoning can reveal deep insights without solving the full problem. For a self-gravitating system, the virial theorem is one of those fundamental propositions that explain many puzzling features. One way of deriving it in our context is to begin with the equation of hydrostatic equilibrium in eq. (2) and integrate both sides over the R R 3 R R 3 2 entire star, dr 4πr P 0 = dr 4πr G M ρ/r where P 0 = dP=dr. The rhs is the 0 − 0 N r gravitational binding energy Egrav of the star. After partial integration of the lhs with R R 2 the boundary condition P = 0 at the surface, one finds 3 0 dr 4πr P = Egrav.