Evolved Massive Stars

Wolf-Rayet Stars

• Classification• WNL - weak H, strong

He, NIII,IV• WN2-9 - He, N III,IV,V

earliest types have highest excitation

• WC4-9 - He, C II,III,IV, O III,IV,V

• WO1-4 - C III,IV O IV,V,VI

• WN most common, WO least

Wolf-Rayet Stars

• log L/L > 5.5

• log Teff > 4.7 (but ill defined - photosphere is at different radii and Teff for different )

• ~ 10-6 - 10-4 M yr-1

• vwind ~ 1-4x103 km s-1

• ~ 1/2 of kinetic energy in ISM within 3 kpc of sun is from WR winds

• Wind energy comparable to SN

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˙ M

Wolf-Rayet Stars

• Have lost H envelope - M > 40 M or binary with envelope ejection

• WNL WNWCWO is an evolutionary sequence and a mass sequence

• Mass loss first exposes CNO burning products - mostly He,N• Next partial 3 burning - He, C, some O• finally CO rich material• Lowest mass stars end as WN, only most massive become WO• Surrounded by ionized, low density wind-blown bubble• Metallicity dependence for occurrence of WRs

– in Galaxy observed min mass for WR ~ 35 M

– in SMC min mass ~ 70 M

– WOs found only in metal-rich systems

Wolf-Rayet Stars

• High luminosities result in supereddington luminosities in opacity bumps produced by Fe peak elements at ~70,000K and 250,000K

• Without H envelope these temperatures occur near surface• Radiative acceleration out to sonic point of wind • Wind driven by continuum opacity instead of line opacity• Photosphere lies in optically thick wind

Advanced Burning Stages

• No observations - these stages are so short that they are completed faster than the thermal adjustment time of the star - the stellar surface doesn’t know what’s happening in the interior

• Hydrodynamics may render the previous statement untrue

• For stars >~ 8 M C ignition occurs before thermal pulse-like double shell burning– limits s-process to producing elements with A < 90

• C burning and later (T > 5e8 K) dominated are neutrino cooled - energy carried by , not photons

• Near minimum mass C ignition is degenerate and often off-center since cooling starting in core - maximum T occurs outside core

Advanced Burning Stages

• C burning and later (T > 5e8 K) dominated are neutrino cooled - energy carried by , not photons

• When does cooling take over?– at low T, energy loss rate ≈1.1x107T9

8 erg g-1 s-1 for T9 < 6 & < 3x105 g cm-3

= L/M ~ 3.1x104S/R erg g-1 s-1 after H burning

– set = – rates equal for S /R = 1 at T9 = 0.62; S /R = 0.1 at T9 = 0.46

cooling

• photons must diffuse, so rate of energy loss 2T ’s must traverse star, interacting with and depositing

energy in material ~ R2N/c ~ 1/3M2/3

’s are ~ free streaming; even in stellar material interaction cross sections are small– cooling is local - ’s don’t interact with star to depositi energy

before escaping– since ’s don’t interact, they provide no pressure support

• Homework: What does this imply about late burning stages?

cooling• several paths for neutrino creation

plasmon decay - plasma excitation decays into pair photoneutrino process - pair replaces in -e- interaction neutrino-nuclear bremsstrahlung - ’s of breaking radiation replaced by pairs • At low T photoneutrino dominates, cooling/g independent

of • At higher T e-e+ annihilation dominates, suppressed w/

increasing • At high , low T e- degeneracy inhibits pair formation &

plasmon rate dominates• Overall rate increases w/ T

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e− + e+ →ν + ν 10−20 of e− + e+ → 2γ( )

cooling

cooling

cooling

• The URCA process - generating changes in neutron excess and thereby heating & cooling through mass movements of material undergoing weak interactions

• rate of emission of energy by escaping neutrinos/mole

• If A = 0 entropy decreases & there is cooling• A = 0 if there is no composition change

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dE

dt+

dP

dt= −εemiss

dE

dt+ P

dV

dt= T

dS

dt+ NAμ i

dYi

dti

∑A

1 2 4 3 4

TdS

dt= −εemiss − NAμ i

dYi

dti

∑A

1 2 4 3 4

cooling

• If composition is changing

• for e- capture and decay w/ energy release Q

• if affinity is positive, e- capture (ec) is driven to completion & dYZ/dt is negative - generates entropy

• if affinity is negative, decay is driven to completion & dYZ/dt is positive - also generates entropy

€

dYZ

dt=

dYe

dt= −

dYZ −1

dt= −

dYν

dt

μ i = ui + mic2 chemical potential

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NAμ i

dYi

dti

∑ = uZ − uZ −1 + ue − Q( )affinity

1 2 4 4 4 3 4 4 4 dYZ

dt

cooling

• If conversion is slow, process is reversible and no heat generated

• If fast, degeneracy energy transferred into ’s inefficient & heat generated

• depending on rate of cooling, heating or cooling can occur

• For fluid with mass motions (convection)

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TdS

dt= −εemiss − NA ui

∂Yi

∂ti

∑ − T(v ⋅∇S) − NA ui(v ⋅∇Yi)i

∑advection of entropy & material

1 2 4 4 4 4 3 4 4 4 4

cooling

• affinity will change with T, as fluid moves, as will S• More complications from nuclear excited states• De-excitation releases ’s which heat material• In convection or waves ’s may be deposited in

different place from capture or decay - net energy transport

where the Urca pair are nuclei c & d and c & d are the rates of energy emission as antineutrinos from decay of c and as neutrinos from e- capture on d, respectively

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TdS

dt= −εemiss − NA ui

∂Yi

∂ti

∑ − T(v ⋅∇S) − NA ui(v ⋅∇Yi)i

∑advection of entropy & material

1 2 4 4 4 4 3 4 4 4 4

€

net = −dYZ

dt(uZ − uZ −1 + ue − Q) Yc +d mec

2 −εc −εd