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AST301 the Lives of the Stars

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AST301 the Lives of the Stars AST301 The Lives of the Stars A Tale of Two Forces: Pressure vs Gravity I. The Sun as a Star What we know about the Sun •Angular Diameter: q = 32 arcmin (from observations) •Solar Constant: f = 1.4 x 106 erg/sec/cm2 (from observations) •Distance: d = 1.5 x 108 km (1 AU). (from Kepler's Third Law and the trigonometric parallax of Venus) •Luminosity: L = 4 x 1033 erg/s. (from the inverse-square law: L = 4p d2 f) •Radius: R = 7 x 105 km. (from geometry: R = p d) •Mass: M = 2 x 1033 gm. (from Newton's version of Kepler's Third Law, M = (4p2/G) d3/P2) •Temperature: T = 5800 K. (from the black body law: L = 4pR2 σ T4) •Composition: about 74% Hydrogen, 24% Helium, and 2% everything else (by mass). (from spectroscopy) What Makes the Sun Shine? Inside the Sun Far Side Gary Larson Possible Sources of Sunlight • Chemical combustion – A Sun made of C+O: 4000 years • Gravitational Contraction – Convert gravitational potential energy – T = U/L = GM82R8/L8 ~ 107 years • Accretion – Limitless, but M8 increases 3% / 106 years • Nuclear Fusion – Good for ~1010 years How Fusion Works E=mc2 • 4 H ⇒ He4 + energy • The mass of 4 H atoms exceeds the mass of a He atom by 0.7%. • Every second, the Sun converts 6x108 tons of H into 5.96x108 tons of He. • The Sun loses 4x106 tons of mass every second. • At this rate, the Sun can maintain its present luminosity for about 1011 years. • 1010 or 1011 years ??? Nuclear Fusion Proton-Proton (PP I) reaction Releases 26.7 MeV 10 < Tcore < 14 MK How Fusion Works Source: Wikipedia Beyond PP I PP II: dominates for 14 < Tcore < 23 MK • 3He + 4He ⇒ 7Be + g 7 - 7 • Be + e ⇒ Li + ne + g • 7Li +p+ ⇒ 24He + g • 16% of L8 PP III: dominates for Tcore > 23 MK • 3He + 4He ⇒ 7Be + g • 7Be + p+ ⇒ 8B + g 8 8 + • B ⇒ Be + e + ne • 8Be ⇒ 24He • 0.02% of L8 Nuclear Timescale • 1010 years • Sun has brightened by 30% in 4.5 Gyr • Photons take 105 – 106 yrs to diffuse out – Gamma-rays thermalize to optical photons How do we know? • The p-p reaction also produces neutrinos. • Neutrinos – do not interact strongly with matter, – pass right through the Sun, and – arrive at Earth in 8 minutes. • Solar neutrinos: first detected by Ray Davis of BNL in the 1960s • Observations agree with “standard solar model” predictions Cosmic Gall, by John Updike Neutrinos, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold-shoulder steel and sounding brass, Insult the stallion in his stall, And, scorning barriers of class, Infiltrate you and me! Like tall And painless guillotines, they fall Down through our heads into the grass. At night, they enter at Nepal And pierce the lover and his lass From underneath the bed - you call It wonderful; I call it crass. Practical Solar Evolution Driven by pressure balance: 4H -> 4He Source: Wikipedia Why is the Sun Brightening? P=nkBT • Core pressure P is set by the mass of the Sun • The number density n decreases when 4p+èa • nT is ~constant, so core temperature T goes up. • Nuclear reaction rate µ Tb, where – b ~4 (PP) – b ~16 (CNO cycle) • Luminosity L µ the nuclear reaction rate. Solar Threats Short term • Magnetic activity (week 9/10) • Flaring and Coronal Mass Ejections Long term (week 11) • Increase in solar luminosity “…My God, it’s full of stars!” There are 400 Billion Stars in the Galaxy How does the Sun rank? • Masses: 0.076 – 120 M¤ -4 6 • Luminosities: 10 – 10 L¤ • Temperatures: 1800 K – 250,000 K (T¤~5800K) The Hertzsprung- Russell Diagram • X-axis: color, temp, spectral type • Y axis: absolute magnitude, luminosity Reveals giants, dwarfs, and the main sequence (distances from parallax) Spectral Types • O: Hottest stars; temps from ~20,000K to > 100,000K. Weak helium absorption. Example: z Oph • B: Temperatures from 10,000 to 20,000K. Noticeably blue. Examples: Rigel, in Orion, and Spica, in Virgo. • A: Temperatures from 8000-10,000K. They appear white. Strong absorption lines of hydrogen. Examples: Vega, Altair, Sirius. • F: slightly hotter than the Sun. Absorption lines of metals appear. Example: Procyon • G: temperatures between 5000 and 6000K. Appear yellow. Examples: Sun, a Centauri, Capella. • K: Temperatures 3000 - 5000K. Appear orange. Examples: Arcturus, Aldebaran • M: the coolest stars; 2000 - 3000K. Molecules can survive (H2O, CO, VO, TiO). Noticeably red. Examples: Betelgeuse, Antares. • L, T, and Y objects are brown dwarfs, not stars Luminosity Classes • I: supergiants • II: bright giants • III: giants • IV: subgiants • V: dwarfs - the main sequence • VI: subdwarfs • WD: white dwarfs A luminosity, or pressure sequence. Observable in the spectra. The Sun is G2V H-R Diagram Understanding the H-R Diagram Most stars are on the main sequence. – Stars spend most of their life on the main sequence – Most stars are faint and red Sun has V=4.8, B-V=0.62 Understanding the H-R Diagram • Most stars are on the main sequence. – Stars spend most of their life on the main sequence – Most stars are faint and red • Giants and supergiants are visible from great distances because they are very luminous. – Giants and supergiants are rare. Sun has V=4.8, B-V=0.62 All Together Now… Mass Functions Charbrier 03 Parameterizations II. The Formation of Stars Stars form in molecular clouds (part of the interstellar medium) Molecular clouds Cold: temperatures 10 - 100 K Big: sizes up to tens of light years In pressure equilibrium (Pg = nkT) Stable against collapse… Cloud Collapse • Thermally-supported non-rotating cloud • Inside-out collapse – R = cst – Macc = ṁ t 2 2 – GmaccmH/R = mHv (by VT); v=cs 2 – G(ṁ t)/cst = cs 3 -6 -1 -1 3 – ṁ = cs /G = 2x10 M¤ yr (cs/0.2 km s ) Virial Theorem: <U> = <2K> cs: sound speed mH: mass of Hydrogen atom (proton) How Bright is a Protostar? • L = E/T -½ – Let T = tff ~ (Gr) 3 -3 14 6 – For r = 10 mH cm , tff ~ 10 sec = 3x10 yrs – Let M = 1 M¤ 2 48 – E = 1/2 Egrav ~GM /R ~ 2x10 erg 48 6 • L ~ 2x10 erg/3x10 yrs ~ 5L¤ • T =GM2/RL = the Kelvin-Helmholtz timescale From dust to stars • Small perturbations disturb equilibrium • Gravitational collapse ensues • Angular momentum is conserved • Star + disk forms Evidence for Disks A star is born! • Quasi-equilibrium collapse • Core temperature increases • At 106K, deuterium fusion (1H + 2D è 3He) halts collapse (stellar birthline) • Protostars are cool and luminous Star Formation Timescales As a star collapses, it converts gravitational potential energy Eg into heat, which is radiated away. 2 2 2 Eg = GM /R (E = GM /Rinitial - GM /Rfinal) The timescale to radiate this away is tKH = Eg/L (Kelvin-Helmholtz timescale) L is the luminosity. For the Sun, this is 30 million years Collapse to the Main Sequence • When 2D is exhausted, collapse resumes. • Collapse stops when the core temperature reaches about 107 K, and the PP reaction can start up. • Equilibrium is maintained until core 1H is exhausted. • Gas pressure balances gravitational collapse. This is the main sequence Structure of Stars Equilibrium supported by steady H-burning • Hydrostatic equilibrium: 2 2 – g(r) = GM(r)/r ; FG=GM(r)/r rdr – dP =-GM(r)r/r2 dr • Continuity of mass: dM(r) = 4pr2rdr • dT/dr depends on energy transport – Radiative – convective • dL = 4pr2e(r)dr Stellar Timescales It takes the Sun about 30 million years to collapse from the birthline to the main sequence (the Kelvin-Helmholtz timescale) The nuclear timescale of ~1010 years sets the main sequence lifetime of the Sun H-R Diagram On MS, L µ Tb b ~ 3 on upper MS Stellar Lifetimes • Stars generate luminosity through fusion of H into He • The lifetime of a star is proportional to the amount of fuel it has (mass) divided by the rate at which it expends the fuel (luminosity) • The lifetime τ ~ M/L ~ M-2 (because L ~ M3) • τ ranges from 4x106 years for O stars to ~1012 years for M stars Stellar Threats None • stars are too far away for direct affects – Nearest star: 4.4 light years – Typical separation: ~1 pc or 3 ly • stars do not collide 7 – <separation>/R* ~ 5 x 10 III. Main Sequence Evolution • Location on the MS is set by mass • Luminosity L is set by core temperature Tc • Nuclear fusion acts as thermostat 2 4 • Tphotosphere is set by L~ R Tph 2 • Core pressure balance: nkTc ~ GM/R • Result of fusion: 4H èHe; n decreases • T increases to compensate • Nuclear reaction rate increases ➝ L increases • Tph increases • Stars evolve up and to left in MS (but not much) • Solar luminosity has increased by 30% in 4.6 Gyr The Faint Young Sun Paradox 4.6 Gya, the Sun was fainter than today. • The Earth would have been even colder – (see discussion of Earth’s equilibrium temperature) • If frozen, it would never have melted – (Water has a very high heat capacity) But there has been liquid water for 4 Gyr IV. End of the Main Sequence In a star like the Sun: • After 1010 years, the core is mostly He • He does not fuse at 107 K • Core shrinks • Shell outside core heats up and fuses H • Large area èlarge luminosity • Star becomes a red giant V.
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