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Home , Stellar core

AST301

The Lives of the A Tale of Two Forces:

Pressure vs I. The as a 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) •: 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% , 24% , and 2% everything else (by mass). (from spectroscopy)

What Makes the Sun Shine?

Inside the Sun

Far Side Gary Larson Possible Sources of

• Chemical combustion – A Sun made of C+O: 4000 years • Gravitational Contraction – Convert gravitational potential energy – T = U/L = GM82R8/L8 ~ 107 years • – Limitless, but M8 increases 3% / 106 years • – 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 How does the Sun rank?

• Masses: 0.076 – 120 M¤

-4 6 • : 10 – 10 L¤

• Temperatures: 1800 K – 250,000 K

(T¤~5800K) The Hertzsprung- Russell Diagram

• X-axis: color, temp, spectral type • Y axis: absolute , luminosity

Reveals giants, dwarfs, and the

(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: , 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: • 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: = <2K>

cs: sound speed

mH: mass of Hydrogen atom (proton) How Bright is a ?

• 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, fusion (1H + 2D è 3He) halts collapse (stellar birthline) • are cool and luminous 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

• : 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 – /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

V. Up the Giant Branch

• Timescale ~ 109 years • Core continues slow contraction, heats up • H-burning shell expands • Luminosity increases 8 • When Tc reaches 10 K, degenerate He core ignites • 3 4He è12C • Degeneracy lifts, core expands, He core + H shell • star: Timescale ~ 108 years Aside: Degeneracy

Pauli Exclusion Principle: no two electrons can have the same position and momentum (mv) •Normally, momentum is set by temperature •High pressure forces electrons towards the same position. •At high density, electrons attain momentum larger than expected from thermal temperature •This momentum provides pressure •Degenerate pressure is independent of temperature

Asymptotic Giant Branch

• Inert core continues slow contraction, heats up • H-burning shell expands • He-burning shell expands • Luminosity increases • C/O core never reaches ignition temperature • Shells are very luminous and unstable • Timescale ~106 years

VI. Endgame

• High luminosity ➝ large pressure • Large radius ➝ low surface gravity • Radiation pressure blows off outer layer of star – Sun loses about 40% of its mass • Bare stellar core is hot, compact, and inert Ring Nebula - M 57 Helix Nebula Hourglass Nebula MyCn 18 Catseye Nebula

Changes in the Sun

• In 109 years: temperature of Earth reaches 100C • In 1012 years Sun fills Earth’s orbit

What happens to Earth? Endpoints. I.

Stars like the Sun (up to 8 M¤) have enough gravitational pressure to get core temperatures high enough (about 108K) to fuse 4He to 12C and 16O.

The result is a CO The White Dwarf

The inert cooling core shrinks under gravity to form a white dwarf – Radius of the Earth – Mass of the Sun – Composition: carbon + oxygen

– Density ~ 106 gm/cm3

– Cool to about 4000K, then crystallize Do White Dwarfs Exist?

• Sirius A: mag -1.4 A0V • Sirius B: mag 8, ~B0 • Magnitude difference: 10 • Luminosity difference: 104 • L ~ R2T4 2 4 • (RA/RB) = (LA/LB)(TB/TA) • Temperatures ~ same

2 4 • \ (RA/RB) ~ 10 , or RA/RB ~ 100

• RA ~ 3 R¤, so RB ~ 3 REarth

(in actuality, TB>TA, and RB~REarth Intermediate Mass Stars

1.5 < M/M¤ < 8 • Higher mass Þ higher core temperature

• Higher Tc Þ different fusion path • CNO cycle: 4H Þ 4He using 12C as a catalyst • More efficient than PP Evolution similar to Sun Lower Mass Stars

• Tc never gets hot enough for He to fuse • End as white dwarfs with helium cores • But none exist yet! Brown Dwarfs

Mass < 0.076 M¤ (80 Jovian masses)

• Core becomes degenerate before TC reaches H ignition temperature • No stable H burning • Just cool off • Radius ~ Jovian radius High Mass Stars

• Spectral types O and B

• Masses up to ~ 120 M¤ 6 • Luminosities up to ~10 L¤

• Radii up to ~100 R¤ • What sets the upper mass limit? Radiation Pressure (L) exceeds gravity (M/R2) for massive stars Because L ~ M3, g ~ 1/M Core Temperatures

• Increased gravitational pressure ⇒

higher Tc 2 • Higher Tc ⇒ larger velocities (3kTc=mv ) • Larger v overcomes larger electric repulsion (~atomic number2) • Further nuclear reactions can occur Alpha capture Onion skin model Binding Energy Endpoints. II.

Fusion reactions up to 56Fe release energy • When the Fe core forms: 9 – Tc ~ 10 K

– M > 1.4 M¤ • Degeneracy pressure fails to support the star • The upper mass limit for a white dwarf (a star

supported by degenerate electrons) is 1.42 M¤. • Degeneracy pressure fails to support the star • This is the Chandrasekhar limit Supernovae • Cooling Fe core loses pressure support • Fe disintegrates, releasing neutrinos • Release of U plus n ⇒ outward shock – Shock blows the star apart • This is a type II • Core – collapses to ~15 km radius – supported by degenerate neutrons • This is a Supernovae In a supernova, the entire gravitational potential energy of the star is released in a few milliseconds

The outer envelope is ejected at high velocities (10,000 - 20,000 km/s).

1% of the energy comes out as light (1051 ergs); 99% comes out as neutrinos

A supernova can appear as bright as an entire galaxy.

The star is destroyed Historical Supernovae

• Crab. July 4, 1054. Seen in Asia and America * • Tycho’s supernova. 1572 • Kepler’s supernova. 1604 * • S Andromedae (in M31). 1885 • SN 1987A (in LMC). 1987 *

* remnant neutron star identified Supernovae

Chaco Canyon NM

Petroglyph thought to show Crab Supernova, 4 July 1054 SN 1987A The Debris of Stars • Supernovae create elements up to Fe via nuclear fusion • The high flux of neutrons builds up n-rich isotopes of all elements (the r-process) • n-rich isotopes decay by β- decay into stable isotopes • All known elements can be made this way Types of Supernovae

There are 2 main ways to get a stellar core more massive than 1.4 solar masses

•Massive stars (M>8M¤) make large cores – Massive star (core collapse) supernovae are Type II

•Adding mass to a 1.4M¤ white dwarf – White Dwarf supernovae are Type Ia

(there are other types) Beyond White Dwarfs: Neutron Stars

• The high mass core shrinks under gravity. • Temperature increases • Fe disintegrates into protons and neutrons • Protons and electrons combine to form neutrons + - 0 – p + e ⇒ n +ne • This cools the star • Without pressure support the core collapses • Gravitational potential energy is converted to heat, and the outer part of the star is ejected • The core may stabilize as a neutron star Neutron Star Internal Structure

Source: AAS/Astrobites

Neutron Stars

Concept introduced by:

•Baade & Zwicky (1934) ➡ Zwicky (1938) ê •Oppenheimer & Serber (1938) Do Neutron Stars Exist?

The first , PSR B1919+21, was discovered in 1967 by Jocelyn Bell Burnell.

The pulse period is 1.337 seconds.

The source? • Extraterrestrials (LGM-1)? • Something else? The Crab Pulsar

X-rays Optical P=0.033 seconds Evidence that PSRs are NS The Crab Nebula pulsar has a period of 0.033 seconds (shortest known pulsar period is ~1 msec)

Short periods can arise from: •Rotation: gravitational breakup occurs at 3 Pmin ~ √(r /GM). P=0.033 s ⇒ ρ~1011 g/cm3. •Vibration: n~√(Gρ) 30 Hz ⇒ ρ~5x1011 g/cm3. •Orbital motion: M~1M¤ and P=0.033 s è a=150 km, or ρ~5x1011 g/cm3.

Stars have ρ~1 g/cm3; WDs have ρ~ 106 g/cm3 Listening to Pulsars

• PSR B0329+54: A typical, normal pulsar. Period = 0.714519 sec, i.e. ~1.40 rotations/sec. • PSR B0833-45, The Vela Pulsar: center of the Vela SNR, ~10,000 years old. P = 89 msec; ~ 11/sec. • PSR B0531+21, The Crab Pulsar: The youngest known pulsar (957 yrs) ; the center of the Crab Nebula. P = 33 msec; 30/sec. • PSR J0437-4715: a millisecond pulsar, an old pulsar spun up by accretion of material from a binary companion star. P=5.7 msec; ~ 174/sec. • PSR B1937+21: second fastest known pulsar, P = 1.5578 msec, ~ 642/sec. The surface of this star is moving at about 1/7 c. Black Holes

If M > about 2.5-3 M¤, degenerate neutron pressure < PG, and gravity wins. Black Holes

• The escape velocity from a gravitational

potential is vesc=√(2GM/R) • This comes from Newton’s formulation of Kepler’s laws • What happens if M/R is so large that

vesc = c? (LaPlace asked this in about 1700) 2 • Schwarzchild Radius RSch=2GM/c Black Holes 2 • Rsch=2GM/c defines a surface, the Event Horizon

• If R < Rsch, you are inside the event horizon, and you cannot get out

• How big are black holes? – : ~3 km – Earth mass: ~1 cm 6 – Galactic center (2.5 x 10 M¤): 0.05 au 9 – M87 (10 M¤): 20 au Black Holes Don’t Suck But they have very strong tides! Black holes evaporate. Black holes have no hair. Consequences of High Gravity

• Events in strong gravitational fields involve high energies, velocities, and temperatures • Interactions generate high energy photons (X, g-rays) • Gamma Ray Bursts • Tidal forces can disrupt stars Threats from Stellar Remnants Nearby supernovae can affect Earth • Radioactive fallout • Cosmic rays • Gamma ray bursts (Week 13) The Winner

Gravity