Astronomy 218 Life of the Sun Life on the Outside During its life on the main sequence, any fluctuations in a star are quickly restored. The star is in hydrostatic equilibrium, any changes are gradual or cyclical. Prominences, sunspots & convection come and go. For the Sun, 3.94 × 1026 W is carried off by radiation, 3.84 × 1026 W by photons from the photosphere and 9 × 1024 W by neutrinos from the core. 8 −1 −14 −1 The solar wind carries off ~ 10 kg s ~ 10 M☉ yr A Matter of Mass The stellar luminosity comes at a cost, as hydrogen is converted into helium. For the Sun, 3.94 × 1026 W requires 640 billion kg of hydrogen be converted to helium every second. For massive stars, the rate can be millions of times larger. Eventually, the exhaustion of hydrogen in the core, after billions of years for Sun-like stars or mere millions for massive stars, will cause the star to evolve. While mass is important in determining the main sequence lifetime, it is evolution beyond this point where the mass of the star is of greatest import. Low-mass stars go quietly, massive stars go out with a bang! Evolution of the Core Even for a star, the conversion of billions of kg of hydrogen to helium μ = 0.6 leaves a mark, gradually changing the composition of the star’s core. This secular change in composition 0.1 R☉ changes the interior conditions. μ = 0.8 The mean molecular mass changes from its initial value, μ μ = 1.3 = 0.6, to μ = 1.3, over 10 billion years as hydrogen in the core becomes exhausted. Hydrostatic Response This change in the mean molecular mass causes significant change in the star’s core because a decline in μ leads to a change in pressure. Maintaining the pressure, as hydrostatic equilibrium requires, in the face of a doubling in μ requires the core to contract so that the product ρT also doubles. But doubling ρT increases the rate of nuclear energy 4 2 generation, since ε(ρ,T,X)PP ∝ ρT X . While this is partially overcome by the decline in the hydrogen mass fraction, X, the total effect is a boost in ε. This boosts the star’s luminosity. Zero-Age For the Sun, its luminosity has grown from an initial value of ~0.7 L☉. By the time the Sun exhausts its central hydrogen, its luminosity will approach 2.2 L☉. An increase in the luminosity of the star causes changes in the star’s atmosphere, increasing its size. This causes the star to move, in the H-R diagram, not just up but to the right. Since we define the main sequence to mark the location of core hydrogen burning, this changing μ introduces a spread. The borders are called the zero-age main sequence (ZAMS) and the terminal-age main sequence. Hydrogen Exhaustion The exhaustion of fuel in the core presents a problem, as luminosity must be maintained. With no hydrogen burning in the core, the remaining source is gravitational contraction. Eventually, the contraction exposes matter above the core to hydrogen burning conditions and a burning shell is ignited. This thin shell is much more luminous than the main sequence core had been. The Red Giant Branch The initial contraction of the core will cause the envelope of the star to swell (R ~ 1.6 R☉), forming the subgiant branch. Ignition of the hydrogen burning shell boosts the luminosity, further expanding the envelope, climbing the red giant branch over 105 years. As a red giant, the Sun will engulf Venus, with a radius of 170 R☉ (= 0.8 AU) and a luminosity of 2300 L☉. Triple Alpha Helium burning occurs via the triple alpha process, combining 3 α-particles (4He nuclei) into 12C. Helium burning requires temperatures of 100 MK to overcome the larger Coulomb repulsion of 2 protons per reactant. −12 4 τ ~8 10 s After 2 He 4He Be 4He form 8Be, a 4 third He must 4 4He Proton He react within Neuton ~10−12 s before γ-ray photon 8 8 4He Be Be decays 12 into 2 4He. C

2 30 4 4 ε(ρ,T)3α ∝ ρ T . He He Helium Flash! Because the core has been compressed by a factor of one thousand, reaching a central density ~ 108 kg m-3, helium burning begins with a flash. The electrons in the compressed gas no longer form an ideal gas. The electrons are degenerate, with the Pauli Exclusion principle preventing two electrons from occupying the same quantum state, maintaining higher particle velocities. This results in a degeneracy pressure that is almost independent of temperature. When helium begins fusing 108 K, the pressure does not change, even as the temperature rises further, accelerating helium burning. Only when the temperature exceeds 3.5 × 108 K is degeneracy lifted and thermal pressure dominant. Horizontal Branch With degeneracy lifted, the enormous energy output of the helium flash declines and the star settles into a new equilibrium on the Horizontal Branch.

HB Stars have L ~100 L☉, but radius and temperature depend on mass (R☉,HB ~ 10 R☉, T☉,HB ~ 5000 K). Placement on the HB also can be affected by mass loss on the Red Giant branch. Helium burning lifetime for the Sun will be ~ 108 years. Helium Exhaustion A Horizontal branch star is powered by stable helium burning in the core topped by a hydrogen burning shell. As the helium in the core fuses to carbon and oxygen, the core contracts, becoming hotter, and burning helium faster. Higher luminosity and smaller nuclear energy release results in shorter helium burning lifetime. Once helium is exhausted, the core contracts, adding a helium burning shell to the existing hydrogen burning shell. asymptotic-giant branch The luminosity of the combined hydrogen and helium burning shells is the largest of the star’s life, driving the star’s envelope up the Asymptotic Giant Branch to its largest radius. As an AGB star, the Sun will have of 3000 L☉ or more and radius >200 R☉. It will engulf the Earth’s present orbit. Earth will be uninhabitable having become like Venus before the Sun is a subgiant. Envelope Instability The distended envelope of an AGB star is only weakly bound to the star’s carbon-oxygen core, making it subject Mira to tremendous mass loss. R~ 400 R☉ The outer layers are very cool and M ~ 1.2 M☉ convective. Radial expansion leads to significant recombination of hydrogen and helium, increasing the opacity which drives the envelope outward until decreasing density reduces the opacity. This produces pulsations and large luminosity variations (mV up to 10 magnitudes). In deeper layers, the extreme temperature dependence of the 3α reaction (T 30), coupled with the thinness of the shell results in unstable burning. The resulting bursts of nuclear energy send thermal pulses into the envelope. Losing the Envelope The combination of thermal pulses from the burning shells and envelope pulsations results in tremendous mass loss rates, −3 −1 as large as 10 M☉ yr

This is 109 times larger than the current solar wind.

The star now has essentially two separate parts: • A small, extremely dense and hot carbon-oxygen core, with a surface temperature > 10,000K. • An glowing envelope the size of our solar system. Planetary Nebula The glowing envelope is called a planetary nebula, because early astronomers viewing the fuzzy circular envelope mistook it for a planet. The nebular glow is due to fluorescence as UV photons from the core ionize atoms in the envelope, some of which were made in the AGB star. The characteristic circular shape is the result of increased brightness along tangential lines of sight. Spectacular view While many are spherical, there is a diversity of shapes.

Eskimo Nebula

Ring Nebula Cat’s Eye Nebula

M2-9 White Dwarf The planetary nebula continues to expand and dissipates, disappearing from view over ~25000 yr, carrying 40% of star’s mass (in the Sun’s case) back to the interstellar medium. With the nebula gone, the remaining core is roughly Earth sized, extremely dense and extremely hot. Degeneracy pressure keeps it from contracting and fusing carbon, thus its luminosity gradually fades over billions of years, unless there is external intervention. A Solar Timeline This timeline shows the entire evolution of a Sun-like star over time with each step ~108 years.

Even on this scale, the sub-giant and horizontal branch are brief. The helium flash, red giant branch, AGB and planetary nebula are too short lived to be seen. These stages are nonetheless important, as their brightness makes them visible across the Galaxy. Carbon, nitrogen and lead in us comes from these phases. A Sun’s Life The stages in the future of the Sun.

For other stars, the future may be similar or quite different, depending on their mass, their metallicity and their solitude. Each makes its own contribution to the ISM. Next Time Lives of other Stars.