Chapter 7 Particle physics in the stars

Transcription

1 Chapter 7 Particle physics in the stars Stellar evolution 1. Early stage - protostar. Hydrogen burning. Helium burning 4. Production of heavy elements 5. Electron degenerary pressure and stellar stability Relics of stars 6. White dwarfs 7. Supernovae neutrinos from SN1987A 8. Neutron stars and pulsars 9. Black holes Primordial development of the universe: matter and radiation decoupled when kt 0.eV z 1000 t y 1. Introduction astro-particle physics 1

2 1. Introduction - From z 1000 onwards universe is matter dominated, is almost totally dark Consists of clouds of neutral atoms & molecules, predominantly hydrogen Stars condense out of gas clouds as soon as z 0 0 Light is produced Since then star formation is continuous astro-particle physics 1. Gravitational collapse - 1 Cloud of gas mean density ρ - time required to collapse under gravity= free fall time tff π = 1 cloud to protostar typically 6000y Gρ Condensation of gas = transformation of gravitational potential energy U in kinetic (heat) energy K of gas particles K energy transferred to dissociation of molecules, ionization of atoms radiation of photons hydrostatic equilibrium as long as pressure of heated gas inward gravitational pressure astro-particle physics 4

3 1. Gravitational collapse - Cloud will condense when E grav >> E kin Condensation when r > Jeans radius kt r > rcrit = πρgm kt ρ > ρcrit = 4π M mg Or when mass larger than Jeans mass 1 Examples: H and molecular clouds astro-particle physics 5 5kT M > MJ Gm 4πρ m=mass particle 1 1. Early stages - 1 Stars can condense out of gas clouds, interstellar matter (ISM) As soon as r > Jeans radius and M > Jeans mass Several competing processes gravitational potential energy loss transformed in kinetic energy + radiation energy (photons) gas heats up, star shines light equilibrium when E grav = E kin (virial theorem) Star radiates energy (photons) from enveloppe contracts further & heats up Sun would stop shining after 10 7 y - age of solar system = 4.5 Gyr Sun needs other source of energy M thermonuclear reactions start 10 M tnucl = 10 yr Typical lifetime of nuclear fusion reactions L L astro-particle physics 6

4 Exothermic reactions = source of energy in star First pp cycle Then CNO cycle Then fusion to heavy elements, up to 56 Fe Creation of heavier elements than 56 Fe is endothermic Low mass stars : only pp cycle and H burning to He Massive stars (>15M) : production of heavy elements 1. Early stages - 56 Fe astro-particle physics 7 1. Early stages - First stage of pp fusion is weak interaction (short range process) + Coulomb barrier between protons In core of Sun thermal energy of protons kt 1keV quantum mechanical tunneling barrier penetration probability rises with E E G = Gamow energy p+ p d + e + ν + 0.MeV 1 e V = = 0.6MeV r = 1. fm 0 0 4π r astro-particle physics 8 e E P( E) exp G = E 1 490keV = exp 10 kev

5 1. Early stages - 4 Probability for fusion enhanced because of Maxwellian distribution of kinetic energy : rises at low E Two effects compensate so that fusion can happen But: when protons collide they will rather interact strongly - prob for weak interaction 1/10 0 Mean life for p+p d/he+x order of Gyrs But: when core of star gets very dense due to gravitational contraction: H burning starts astro-particle physics 9. Hydrogen burning pp cycle - 1 Production of energy in Sun in several steps leading to p He + e + ν e + 6.7MeV 85% of 4 He produced via p+ p d + e + ν p+ e + p d + ν p d He + + γ He + He He + p 4 + e Light stars, M < 1.5 M : burning stops here Heavy stars M > 1.5 M : burning of He and production of C,N,O Very massive stars M > 15 M : heavier elements astro-particle physics 10 e 5

6 . Hydrogen burning pp cycle - When star commences H burning: lights up (γ) Starts life as main sequence star in Hertzsprung-Russell diagram log(luminosity L) vs log(surface temperature Ts) Or magnitude vs colour Red giant: massive stars with H burning near surface - envelope expands and Ts decreases Light stars become white dwarfs as long as M < M ch M15 globular cluster high Ts Low Ts astro-particle physics 11 V = Magnitude with V filter White dwarfs. Hersprung Russell diagram astro-particle physics 1 6

7 . Helium burning CNO cycle Stars with M M no other elements than He are created Sun = 86% H + 14% He % heavy el. Stars with M>M : core temperature high (10 8 K - kev) He burning starts High T and pressure increased higher luninosity - outer envelope expands, surface T decreases Moves to red giant branch in HR diagram He burning in core He+ He Be H moved to outer shells Be + He C * Production of C and O 1 1 C* C + γ Needed for life He + C O + γ astro-particle physics 1 4. Heavy element production - 1 Massive stars - M > 15 M - evolve further through production of heavy elements Heavier elements are in core where T is highest C burning starts when 8 T ( core) 5 10 K kev 9 ρ ( core) 10 kg m Production of heavy elements C+ C Ne+ He Na Mg S,Ar,Ca,.. Up to 56 Fe p n astro-particle physics 14 7

8 5. Stellar stability Different pressures in stellar core: radiation pressure, gas pressure, gravitational pressure At high density: also electron degeneracy pressure Outward electron pressure and inward gravitational pressure in competition: leads to stability of star or collapse astro-particle physics Electron degeneracy pressure 1 Consider gas of electrons at absolute T- electrons fall into quantum states of lowest E : degenerate gas Pauli exclusion principle: each quantum state must be occupied by only 1 electron At T=0 all energy levels up to E F (Fermi energy) filled density of electrons which fill up these states? Nb of electron states in volume V Fermi momentum n = electron number density p F 4π pdp 4π p F N = gv e = gv e n h h p 0 F = h 8π n = N / V astro-particle physics

9 5. Electron degeneracy pressure cases: electrons non-relativistic or relativistic Non-relativistic: p F << m e c and E=p /m e E 5 NR h P NR = = n V 8π 5m e ENR p dp = ge4π p V P NR rises me h faster with n Relativistic case: p F >> m e c and E pc than P R 1 1 E 4 R hc P R = = n V 8π 4 ER dp = ge4π p ( pc) V h astro-particle physics Electron degeneracy pressure Comparison to gravitational pressure 1 4 P Egrav G 4π m A Pgrav = = M 5 Z GM Egrav = 5 R Z ρ n = A mp Only pressure by non-relativistic electrons can counter gravitational pressure: P~n 5/ vs n 4/ Equality of pressures condition for stellar stability n astro-particle physics 18 9

10 5. Electron degeneracy pressure 4 Condition for stability: non-relativistic electrons 1 1 h pf < mec n > 8π mc e Density for which P grav = P NR 5 4mG e M AmP 4π ρ = ρ ρ 6 h < Z equil nucleon equil Mass of star must be below Chandrasekhar limit (Z/A=1/ for most elements) Z M CH = 4.91 M 1.4M A astro-particle physics White dwarfs - 1 Stars with M M : T in core too low for C burning fusion stops when no He left He burning is pushed to spherical shell around core surface temperature increases Stellar envelope expands and escapes : planetary nebula around star Mass of star decreases luminosity decreases If at end M<M ch : no collapse cools down and becomes white dwarf stays as such If M<M ch : star collapses astro-particle physics 0 10

11 6. White dwarfs - Typical masses : 0.5M -M Average density = 10 6 mean solar density Surface T of order of solar T emit white light Typical radius: 1% of solar radius Luminosity 10 - of solar luminosity shine for Gyr, even with no nuclear energy source astro-particle physics 1 7. Type II supernovae For stars with 10 M < M : follow whole cycle of stellar fusion Finally: very hot Fe core surrounded by shell with Si burning While Si burns in shell around Fe core, core T and M increase neutron degeneracy P keeps stability Finally M > M ch, star becomes unstable and collapses Result : explosion = core-collapse or type II supernova Heavy elements are sent in space Rate: about 1/century in Milky Way Example: Crab Nebula, SN1987A astro-particle physics 11

12 7. Crab Nebula 6500 Ly From Earth SN explosion seen in China in 1054 Radio waves Visible light Neutrinos? ultraviolet X-rays: pulsar astro-particle physics 7. Supernovae evolution - 1 Last step in fusion process of massive star is production of 56 Ni, decaying in 56 Fe Fusion to heavier elements would cost energy no increase in temperature core of 56 Ni + 56 Fe grows, gets denser huge gravitational pressure electron degenerary pressure Further compaction several e - in same energy state forbidden When M > M ch : electron degenerary P insufficient to support gravitational P stars weighs too much! Outer matter collapses to centre of star astro-particle physics 4 1

13 7. Supernovae evolution - Radpidly shrinking core T increases fast production of high energy γ Photo-disintegration of Fe at high T reaction of mainly L R 56 4 γ + Fe 1 He+ 4n Endothermic: reaction absorbs 145 MeV per disintegrated Fe energy decreases & gravitational collapse speeds up core heats up 4 γ + He p+ n Neutronization & production of ν e + p n+ ν e Nb of e- decrease electron degenerary P decreases Collapse halted by strong n+n interactions & nucleon degenerary P density in core = O(atomic nuclei) astro-particle physics 5 7. Supernovae evolution - Core gigantic nucleus of neutrons after collapse will form a neutron star 1 For core of M=1.5 M R = r 0A 15km ( r0 = 1. fm) M 57 A = m P mp 17 ρ N = 10 kg m 4π r When collapse halted: infalling matter bounces back outgoing pressure wave visible explosion heavy elements sent in space What remains is neutron star: eg Crab Nebula astro-particle physics 6 1

14 7. Neutrinos in SN explosions - 1 Neutrinos are produced during the neutronization phase electrons are converted to neutrinos e p n+ ν e e + Fe Mn+ ν e Total gravitational energy released in 1.5 M star collapse = E in neutron star 5 A 59 Egrav = GmP = MeV 5 r0 For nucleons <100 MeV/nucleon> Core density so high that energy is locked in core : thermal equilibrium between p,n,e-,e+,ν,γ γ e + + e ν + ν i = e, µ, τ i i astro-particle physics 7 7. Neutrinos in SN explosions - Neutrinos interact through CC and NC with n,p,e Mean free path between CC interactions for E=0MeV λ = m m E in MeV σn ρ E A R t 1s Time to diffuse through core of radius R λc Neutrinos are only particles able to escape others bound by nuclear interaction Neutrinos carry 99% of E grav : 100MeV/nucleon divided over 6 neutrino flavours : <15MeV> per ν Expect flux leaving core: neutrinos in s astro-particle physics 8 14

15 7. SN1987A neutrinos - 1 Explosion in 1987 Large Magellic Cloud (LMC) 60 kpc = Ly from Earth Visible with naked eye Also few 10 neutrinos observed just before optical burst Neutrinos detected in large water Cherenkov detectors: Kamioka (Jp) and IMB (USA) Light = 1% of energy released pre Post astro-particle physics MeV neutrinos as predicted Burst of about 10s simultaneous in both detectors Flux at Earth earth φ ν 7. SN1987A neutrinos - 10 cm 10 Δ t = From arrival time difference for neutrinos with energies E 1 (10MeV) and E (0MeV) Lm Δ t = ΔtEarth Δ tsn = < 10s 4 ν c 1 1 c E1 E m ( ν ) < 0 ev astro-particle physics 0 15

16 8. Neutron stars After SN explosion a neutron star is left behind: mainly n, also p,e,heavy nuclei Neutron can decay with mean lifetime 887s Decay is prevented when decay p and e fill all allowed quantum states (Pauli exclusion principle!) Equilibrium between reactions n p+ e + ν + 0.8MeV e astro-particle physics 1 Pulsars = rotating neutron stars Discovered in 1968 by Hewish et al. Emit radiation at regular and short intervals: periods of ms 8.5s Radiation = radio, X-rays Eg pulsar in Crab Nebula binary systems: pulsar + companion star pulsar accretes matter near magnetic poles (aurora) production of X-rays 8. Pulsars - 1 θ astro-particle physics 16

17 8. Pulsars - Rotation period: outward centrifugal force in equilibrium with inward gravitational force (test mass m) GMm R & 15, 1.5 π τ = > 1ms ω mω R< R = km M = M Pulsar radiation due to rotating magnetic dipole 4 Electromagnetic power radiated P µω sin θ Magnetic field at surface 10 8 T Decelleration due to energy loss in radiation Eg Crab dω 9 1 =.4 10 & ω = 190 s dt astro-particle physics 9. Black holes - 1 Stability in neutron star controlled by neutron degeneracy pressure Analoguous to stability of white dwarf - n star collapses when neutrons gas becomes relativistic M > Mmax 5M Collapse into black hole When physical radius is below Schwarzschild radius : no light paths to outside world GM Rschw = c Example M = 5M R = 15km schw astro-particle physics 4 17

18 9. Black holes - Experimental evidence for BH : binary systems of visible star + BH Matter falls into BH X-ray production Massive BH at centres of galaxies Milky Way: BH of M 4x10 6 M - evidence from motion of stars near centre Active Galactic Nuclei: M 10 8 M - production of jets of high energy gamma rays - origin of very high energy cosmic rays? 1% of galaxies are active astro-particle physics 5 18