Stellar Evolution ASTR 2110 Sarazin. HR Diagram vs. Mass

Stellar Evolution ASTR 2110 Sarazin HR Diagram vs. Mass

Trip to Conference Away on conference in the Netherlands next week. Molly Finn, TA, will be our guest lecturer

Stellar Evolution ASTR 2110 Sarazin HR Diagram vs. Mass

Low Mass Star Take Sun, 1 star A. Main Sequence, H-burning in core (V) B-C. Core H Exhausted (IV) Energy leaves core Core contracts Energy can t escape star quickly Total energy ~ constant Envelope expands T eff drops M G H MS A B E C F D

Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C. Degenerate He Core (III) Core ~ 10-2 ~ R earth Core, L = 0, dt/dr = 0 T ~ const. in core T c high T (edge of core) high H around core Low Mass Star M R H burning in shell around core

Low Mass Star Take Sun, 1 M star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) H, high T è high L P c very high è push out envelope Giant star, R ~ AU Shell hot, photosphere cool è convective envelope G H MS A B E C F D

Red Giant Stars

Red Giant Stars

Red Giant Stars

Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash T c è >10 8 K He starts to burn in core Degenerate è very rapid Core expands rapidly Envelope contracts Low Mass Star M G H MS A B E C F He Flash D

Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash E. Horizontal Branch He Core, H Shell Burning Like MS, but He Burning in Core H Burning in Shell High L Short Lifetime Low Mass Star M G H MS A B E C F D

Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash E. Horizontal Branch He Core, H Shell Burning F. Asymptotic Giant Branch = Supergiant (I) Like giant, but Low Mass Star M H burning shell, He burning shell Inert carbon core G H MS A B E C F D

Take Sun, 1 Low Mass Star M star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash E. Horizontal Branch He Core, H Shell Burning F. Asymptotic Giant Branch = Supergiant (I) Never gets hot enough to burn C Star must die, but how?

Low Mass Star - Death G Asymptotic Giant Branch = Supergiant (I) Red supergiant Inert carbon/oxygen core E F D MS A B C H

M 8 M A) Main Sequence, H-burning in core (V) CNO burning of H Convective Core B) Red Supergiant (I) High Mass Star Core H exhausted, degenerate core, H shell burning Repeat for each fusion element up to Iron H è He è C è O è Fe

High Mass Star

High Mass Star

M 8 M A) Main Sequence, H-burning in core (V) CNO burning of H Convective Core B) Red Supergiant (I) High Mass Star Core H exhausted, degenerate core, H shell burning Repeat for each fusion element up to Iron H è He è C è O è Fe C) Ends as Red Supergiant, Inert Fe core, many burning shells

High Mass Star

M 8 M A) Main Sequence, H-burning in core (V) CNO burning of H Convective Core B) Red Supergiant (I) High Mass Star Core H exhausted, degenerate core, H shell burning Repeat for each fusion element up to Iron H è He è C è O è Fe C) Ends as Red Supergiant, Inert Fe core, many burning shells Fe è no fusion energy è Star must die

A) Main Sequence, H-burning in core (V) B) Red Supergiant (I) C) Ends as Red Supergiant, Inert Fe core, many burning shells Complication: High radiation pressure, very strong stellar winds Can lose a significant fraction of mass Wolf-Rayet (WR) stars: High Mass Star Entire envelope blown away Expose He or C or O cores (Still, Fe è no fusion energy è Star must die)

High Mass Star - Death A) Inert Fe core, many burning shells B) Either Red Supergiant or blue WR star

The End States of Stars ASTR 2110 Sarazin Neutron Star Interior

Stellar Corpses: End States of Stars Three possibilities 1. Nothing: Star blows up completely But, no fuel for explosion 2. Gravity è collapses to a point = black hole 3. Finite object remains ç consider first No nuclear fuel è L, T go to 0 Gravity never stops, need pressure to resist P gas proportional T è 0 P rad proportional T 4 è 0 P deg depends only on density

Degenerate Stars 4/3 " P c ρ % $ ' Upper limit since relativistic case # µ d & µ d = mass per degenerate particle dp dr = GMρ r 2 Hydrostatic equilibrium dp dr = P c R P R GMρ R 2

Degenerate Stars c R! # " ρ $ & % µ d 4/3 GMρ R 2 ρ ~ M R 3 c R! # " M R 3 µ d $ & % 4/3 cm 4/3 RR 4 µ GM 2 4/3 d R 5! M 2/3 c $ # & 1 " G % GMM R 2 R 3 µ d 4/3

Chandrasekhar Mass " M c % $ ' # G & 3/2 1 µ d 2 " M M Ch = 3.1 c % $ ' # G & do exactly 3/2 Chandrasekhar Mass 1 µ =1.4M 2 for µ = 2m d p d

Radius vs. Mass P deg 2 m " $ # ρ % ' & µ d 5/3 Non-relativistic case dp dr = GMρ r 2 Hydrostatic equilibrium P R 1 R 2 m " $ # ρ % ' & µ d 5/3 GMρ R 2 ρ ~ M R 3 R 2 Gm Mµ 5 d ( ) 1/3 M 1/3 Radius decreases with mass!

Radius vs. Mass

White Dwarfs Electrons Degenerate μ d = 1 m p Hydrogen μ d = 2 m p Helium, Carbon, etc. White dwarfs = cores of stars after H burning V min 3 / p 3 ρ µ d /V min = µ d p 3 / 3 p m e c WD unstable once electrons relativistic ρ µ d m e 3 c 3 / 3 = 3 10 7 gm/cm 3 100 tons/tsp M ρr 3 M Ch % ( R ' 3 * & Gc ) 1/2 1 µ d m e = 6 10 3 km R Earth

Radius vs. Mass

White Dwarfs White Dwarfs are supported by electron degeneracy pressure Chandrasekhar Mass " M M Ch = 3.1 c % $ ' # G & 3/2 1 µ d 2 =1.4M Amazing Result 1) Stellar mass from pure physics! Quantum mechanics and gravity Could have been predicted w/o knowing about stars 2) Typical stellar mass Some stars have finite corpses, some must collapse to point

White Dwarf Collapse M What if M > 1.4? Must collapse, but electrons can t be squeezed more? e + p + n +ν e Lots of neutrinos, escape n smaller than e è take up less space Spin = (1/2) è still become degenerate, but denser

Neutron Stars Degenerate Neutrons Nearly pure neutrons, packed together > nuclear density µ d = m n m p, also change m e m n m p ρ m p 4 c 3 / 3 10 16 gm/cm 3 10 11 tons/tsp R % ( ' 3 * & Gc ) 1/2 1 m p 2 =10 km M 3 M Mass limit more complex than WD due to nuclear force

Neutron Stars

Stellar Corpses: End States of Stars Three possibilities 1. Nothing: Star blows up completely But, no fuel for explosion 2. Gravity è collapses to a point = black hole 3. Finite object remains ç consider first If M (remnant) 3 completely M è gravity crushes

Black Holes Gravity crushes star to a point = singularity Surrounded by ``surface from which nothing can escape = event horizon

Early History Black Holes Late 1700 s, John Mitchell (geologist), Pierre Laplace (mathematician) Speed of light known, finite c Light = particles (?, not quite correct idea, Newton) Newtonian gravity Light cannot escape if v esc = 2GM/r > c Escape only if r > 2GM/c 2 = R S Schwarzschild Radius R S = 3 km (M/ M )