PHYS Further Stellar Evolution Prof. Maurizio Salaris

PHYS 383 - Further Stellar Evolution Prof. Maurizio Salaris PROF. 1

Standard Big Bang model and the problem of galaxy formation Stellar evolution can put independent constraints on the cosmological model and galaxy formation mechanisms 2

Time evolution of chemical abundances 5

Nuclear reactions and time-evolution of chemical element abundances R is the number of reactions per unit time and unit mass 6

Massive stars Intermediate-mass stars Low-mass stars 25

H-burning shell dominates Core He-burning dominates 33

Pressure-temperature domain covered by WDs 45

Theoretical M-R relationship obtained from evolutionary models 46

i) Log(L/L o ) > 1.5 Neutrino cooling Different thermal structures due to initial conditions tend to converge to a unique one. ii) 1.5<log(L/L o )< 3 Fluid cooling ( 1<Γ < 180) iii) Log(L/L o )< 3 Crystallization (Γ>180) -Latent heat release iv) Debye cooling (c V drops as T 3 ) 48

Effect of changing envelope thickness/chemical composition on WD cooling times The opacity of the envelope regulates the rate of energy release from the surface. Lower opacity means faster energy release, hence shorter cooling times. 49

Carbon burning always operates in two steps characterized by the onset of an off-centre (due to a moderate electron degeneracy and neutrino energy losses, the maximum temperature Is attained off-centre) convective instability, the flash, followed by the development of a convective flame which propagates all the way to the center. The large released of energy during the carbon flash induces a substantial expansion of the central regions and the quenching of the instability. After structural readjustments and return to core contraction, a second convective zone develops and grows in the regions previously occupied by the flash. The associated nuclear luminosity is considerably reduced compared to the one generated during the flash allowing a steady state to be reached where almost all the energy deposited at the base of the flame is instantaneously carried away by neutrinos. The deflagration then propagates to the center with typical velocities of the order of 10-3 -10-2 cm s -1. When it reaches the centre, convection disappears and carbon proceeds on the outskirt of the newly formed neon-oxygen core. At the same time, the second dredge-up takes place. For some masses, convection develops on top of the He-burning shell and merges with surface convection, bringing to the Surface also products of He-burning (mainly C). This phenomenon is called dredge-out. Green maximum H- burning Blue maximum Heburning Red maximum C- burning After the 2 nd dredge-up thermal pulses starts (with associated 3 rd dredge-up and The so-called super-agb (SAGB) phase starts 50

If after the carbon burning phase the degenerate core mass grows to the Chandrasekhar mass electron-capture reactions are activated at the centre and induce core collapse, leading to the formation of a neutron star. Whether or not the SAGB core mass reaches this critical value depends on the interplay between mass loss and core growth. If during the post-c burning evolution the mass loss rate is high enough, the envelope is lost before the core mass reaches the Chandrasekhar mass and the remnant is a ONe white dwarf (WD). On the contrary, if the mass loss rate is not large enough, the endpoint of SAGB evolution is probably The explosion as electron-capture supernova and the formation of a neutron star remnant. Thermal pulses during the SAGB phase Initial-final mass relation EC SN Protons locked into 24 Mg and 20 Ne nuclei capture free electrons (and transform into neutrons). Electron capture decreases the electron pressure, hence the total pressure in an electron-degenerate environment. The ONe core collapses, the density increases, electron capture is even more favoured. When the central density reaches ~ 2.5 10 10 g/cm 3 oxygen burning ignites in a degenerate environment. The burning front (deflagration) propagates outwards, causing the transformation of the matter into elements of the iron-peak. The collapse goes on, producing a neutron star in the core. Presumably (extensive calculations have not been performed yet) the envelope is expelled in the same way as for Type II supernovae (without the need of neutrino energy input). These explosions (if they happen) are associated to Type II supernovae with lower luminosity than the average (smaller mass of Ni produced) and low energy explosions 51

Typical chemical composition of the core (mass fractions) 16 O~ 0.50-0.70 20 Ne~0.15-0.35 23 Na~0.05-0.05 22 Ne~0.001-0.01 Advanced burning stages Neutrino losses play a dominant role in the evolution of a massive star beyond core He burning At high temperature (T>10 9 K ~0.08 MeV) neutrino emission from pair production start to become very efficient H burning shell γ ν γ ν γ + γ e + e ν + ν e He exhausted core (CO Core) e H exhausted core (He Core) γ ν ν γ He burning shell ν γ ν γ γ ν γ ν Core Burning 52

Advanced burning stages Evolutionary times of the advanced burning stages reduce dramatically 53

Pre-SuperNova Stage H H burning shell He CO NeO O SiS Fe He burning shell C burning shell Ne burning shell O burning shell T~4.0 10 9 K Si burning shell 55

Chemical Stratification at PreSN Stage 16 O, 24 Mg, 28 Si, 29 Si, 30 Si 28 Si, 32 S, 36 Ar, 40 Ca, 34 S, 38 Ar 14 N, 13 C, 17 O 12 C, 16 O 12 C, 16 O s-proc 56,57,58 Fe, 52,53,54 Cr, 55 Mn, 59 Co, 62 Ni 20 Ne, 23 Na, 24 Mg, 25 Mg, 27 Al, s-proc NSE Each zone keeps track of the various central or shell burnings Supernova classification 56

Supernova (Death of a star) Type Ia No hydrogen Thermonuclear explosion of a white dwarf star No bound remnant ~10 51 erg kinetic energy v ~ 5,000 30,000 km s -1 No neutrino burst E optical ~ 10 49 erg L peak ~ 10 43 erg s -1 for 2 weeks Radioactive peak and tail ( 56 Ni, 56 Co) 1/200 yr in our Galaxy Makes about 2/3 of the iron in the Galaxy There are also Type Ib and Ic supernovae that share many of the properties of Type II but have no hydrogen in their spectra Type II Hydrogen in spectrum M > 8 solar masses Iron core collapses to a neutron star or black hole ~10 51 erg kinetic energy v ~ 2,000 30,000 km s -1 Neutrino burst ~ 3 x 10 53 erg E optical ~ 10 49 erg L peak ~ 3 x 10 42 erg s -1 for about 3 months (varies from event to event) Radioactive tail ( 56 Co) 2/100 yr in our Galaxy Makes about 1/3 iron and all the oxygen plus many other elements A fundamental parameter that characterizes the end of massive stars is the mass of their helium core when they die. As the mass of the helium core increases, the density gradient around the core gets shallower. Consequently, such stars are harder to explode. Even in successful explosions, where a strong outward shock is born, mass may later fall back onto a neutron star remnant, turning it, within seconds to tens of hours, into a black hole (BH). One usually distinguishes black holes that are produced promptly or directly from those made by fallback. While the helium core mass governs the explosion mechanism, the hydrogen envelope is largely responsible for determining the spectrum (at peak) and light curve of common Type II supernovae. Stars having massive hydrogen envelopes when they die will be Type IIp;low-mass envelopes will give Types IIL and IIb. An exception are supernovae of Types Ib and Ic, whose light curves do depend sensitively on the helium core mass since all the hydrogen envelope has been removed. > < 57

A single 25 solar mass supernova ejects 3 solar masses of Oxygen For example 58

Contraction continues in spite of electron degeneracy because the Fe core mass is above the Chandrasekhar mass. 59

Consider a collapse of a core of M c =1.5M o from a white dwarf radius (R i ~ 0.01 R o ) to a final neutron star radius R f (~ 10 Km) << R i The collapse releases an amount of gravitational energy equal to: ΔE g -G M c2 [(1/R i ) (1/R f )] G M c2 / R f 10 53 erg The binding energy of the envelope for a 10M o star is of the order of 10 51 erg. The energy needed for supplying the observed expansion velocity of the ejecta ( 10000 Km s -1 ) is of the order of 10 52 erg Neutrinos can easily remove 10 53 erg of energy Explosion 60

Composition of the ejecta The Iron Peak elements are those mostly affected by the properties of the explosion, in particular the amount of Fallback. 61

Types of remnants Light Curves of Type II Supernovae 62

Masses of neutron stars in binary systems. 63

ρ < 10 7 g/cm 3 crystallized ions (A,Z) + non rel. degenerate electrons e - 10 7 < ρ < 4.3 10 11 g/cm 3 free e - (relativistic), p and n (degenerate) and nuclei (A,Z). Since E F > M A (A,Z-1)-M A (A,Z), one has e - +p n+ν and nuclei become more neutron rich 4.3 10 11 < ρ < 5 10 14 g/cm3 nuclear interactions make energetically favourable for some neutrons to drip out of their parent nuclei. Above 2.8 10 14 g/cm 3 nuclei dissolve. ρ > 5 10 14 g/cm 3 relativistic p, n and e -. At increasingly larger densities it is energetically favourable to convert e- into μ via weak interactions. At even higher densities nucleons can be converted into other baryons like hyperons mesons (pions or kaons, for example n p + π - ) and even into a uniform mixture of quarks. Uncertainties in the mass-radius relationship 64

A black hole is an astronomical object whose escape velocity is larger than the speed of light A black hole is an object smaller that its Schwarzschild radius R s =2.95 Km for the Sun R s =8.86 mm for the Earth 65

Black Hole entropy i) If you throw a hot gas with entropy into a black hole, once it crosses the event horizon, the entropy would disappear. The random properties of the gas would no longer be seen once the black hole had absorbed the gas. The second law can only be salvaged if the black hole entropy increases in a way that compensates for the entropy carried by the gas. ii) It is possible to demonstrate that the area of en event horizon can never decrease These two facts point to the direction of identifying the area of the event horizon as being proportional to the black hole entropy. From thermodynamics, using the relationship T ds = dq (where dq is essentially the energy absorbed by the black hole when particles cross the event horizon and ds the associated variation of entropy) one derives that black holes have a temperature! A simplified derivation of the formula for the black hole entropy follows When a black hole absorbs a mass ΔM, its mass increases to M+ΔM and its area A increases too. For a Schwarzschild black hole, its area A Schw is given by A Schw =16 π G 2 M 2 / c 4 A variation of entropy of the black hole will be related to the heat (energy) absorbed through the following relationship ΔS = ΔQ/T BH = ΔMc 2 /T BH Where T BH is the black hole temperature. The particles trapped in the black hole will behave as standing waves, waves that "fit" inside the black hole with a node at the event horizon, with a wavelength λ=hc/2πkt BH proportional to the Schwarzschild radius r Schw. Therefore ξhc/(2πkt BH) = 2GM/c 2 where ξ is a constant of proportionality. The black hole temperature is therefore given by T BH = ξhc 3 /(4πGKM) λ=h/(2πp) E=cp (if much larger than the energy associated to the rest mass) KT~cp λ~hc/(2πkt) 66

From ΔS = ΔMc 2 /T BH, and noticing that differentiating A Schw =16 π G 2 M 2 / c 4 one obtains ΔMc 2 =(ΔA Schw c 6 )/(32 π G 2 M) Including the correct value for the constant ξ=1/(4π) provides: π Bekenstein & Hawking formula for black hole entropy Notice how both the gravitational constant and Planck constant enter this formula Black hole entropy seems to be huge. This is somewhat expected given that from a complex star one ends up with a black hole completely defined by very few parameters (M, J, Q, direction of axis of rotation, position of the mass centre, its 3-velocity). In comparison, for a star like the Sun S 10 58 K B On the other hand black hole entropy is puzzling. For example, it says that the number of states of a black hole is proportional to the area of the horizon, not the volume in the interior. 67

If a black hole has a temperature, than it must radiate (Hawking radiation). The associated luminosity is given by (for a blackbody): Does a black hole really disappear completely? What happens when its mass is reduced to the value of the Planck mass M pl =(hc/2πg) ½. At this mass scales we expect that quantum gravitational effects should be relevant What is the source of the black hole luminosity? This is a very speculative subject and the derivation is very simplified Consider a particle of mass m in a box of size L. The uncertainty principle tells us that the uncertainty in the momentum of the particle is Δp h/(2 π L) and an uncertainty in the energy equal to ΔE hc/(2 π L) (given that E~cp for E mc 2 ) When the uncertainty of E exceeds 2mc 2, one can create a pair particle-antiparticle out of the vacuum. This condition is satisfied within a distance λ=h/(2πmc) The so-called Compton wavelength associated to the particle m. The Compton wavelength is always smaller than the de Broglie wavelength associated to the particle. As long as the pair is confined within a distance λ they annihilate - almost instantaneously - within a time t h/(δe 2 π) 68

What is the source of the black hole luminosity? Let s now consider a pair of virtual particles in the gravitational field of a black hole. The pair becomes real when the work done by the gravitational forces to separate the two components by a distance λ (their Compton wavelength) is equal to 2mc 2 (i.e. equal to the energy necessary to create them). The tidal gravitational force across a distance λ is of order (GmM)/r 3 λ, where M is the black hole mass and r the distance from the singularity. Therefore, to create a pair of particles of mass m the black hole gravitational field has to do a work (GmM)/r 3 λ 2 ~ 2mc 2 The maximum field strength is at the Schwarzschild radius r~(gm)/c 2. This means that particles are created preferably when λ R s. If one particle falls in the black hole and one escapes the event horizon, the black hole loses a net energy mc 2 Hawking radiation decreases the black hole energy, hence its mass, therefore the black hole temperature increases 69

Endpoints of binary interactions Examples of mass transfer/common envelope Energy gain from accretion onto a 1M o black hole, neutron star, and white dwarf, compared with energy gain by nuclear burning of hydrogen Energy release Compact object Accretion Nuclear burning Black hole (0.1 0.42) mc 2 Neutron star 0.15 mc 2 0.007 mc 2 White dwarf 0.00025 mc 2 0.007 mc 2 71

Single-degenerate scenario The shaded area marks a region where a 0.2M o accumulated He could ignite and destroy the entire WD MS RGB RGB/HB WD WD WD A possible evolution to a Chandrasekhar-mass thermonuclear supernova MS MS MS MS MS/RGB MS/RGB When about 10-4 to 10-5 M o of H have accumulated, H ignites through the CNO cycle. The burning happens in a degenerate environment, T increases and reaches 10 8 T so that some He is transformed into C. Eventually, the radiation pressure gets strong enough to expel into space probably all the accreted material plus some of the preexisting layers. The cycle then is repeated as long as the accretion is efficient. 72

Double-degenerate scenario 73

Type Ia supernovae as standard candles 74