Chapter 6: Stellar Evolution (part 2): Stellar end-productspeople.umass.edu/wqd/astro643/B_EVOL_2.pdf · 7K)7=2 Placing the above in Eq. 2 and then integrating it, we get ˝ cool

Chapter 6: Stellar Evolution (part 2): Stellarend-products

Final evolution stages of high-mass stars

Stellar end-productsWhite dwarfsNeutron stars and black holes

SupernovaeCore-collapsed SNePair-Instability Supernovae (PISNe)Type Ia SNe

Review

Outline

Final evolution stages of high-mass stars

Stellar end-productsWhite dwarfsNeutron stars and black holes

SupernovaeCore-collapsed SNePair-Instability Supernovae (PISNe)Type Ia SNe

Review

Final evolution stages of high-mass stars

I What do stars in the mass range of ∼ 8− 11M� eventuallyevolve to is still somewhat uncertain; they may just developdegenerate O-Ne cores.

I A star with mass above ∼ 11M� will ignite and burn fuelsheavier than carbon until an Fe core is formed which collapsesand causes a supernova explosion.

I For a star with mass & 15M�, mass loss by the stellar windbecomes important during all evolution phases, including theMS.

Kippenhahn Diagram

Mass-loss of high-mass starsFor stars with masses & 30M�,

I The mass loss time scale is shorterthan the MS timescale. The MSevolutionary paths of such starsconverge toward that of a 30M� star.

I Mass-loss from Wolf-Rayet stars leadsto CNO products (helium and nitrogen)exposed.

I The evolutionary track in the H-Rdiagram becomes nearly horizontal,since the luminosity is already close tothe Eddington limit.

I Electrons do not become degenerateuntil the core consists of iron.

When the degenerate core’s mass surpasses the Chandrasekhar limit(or close to it), the core contracts rapidly. No further source of nuclearenergy in the iron core, the temperature rises from the contraction,but not fast enough. It collapses on a time scale of seconds!

Mass-loss of high-mass starsFor stars with masses & 30M�,

I The mass loss time scale is shorterthan the MS timescale. The MSevolutionary paths of such starsconverge toward that of a 30M� star.

I Mass-loss from Wolf-Rayet stars leadsto CNO products (helium and nitrogen)exposed.

I The evolutionary track in the H-Rdiagram becomes nearly horizontal,since the luminosity is already close tothe Eddington limit.

I Electrons do not become degenerateuntil the core consists of iron.

When the degenerate core’s mass surpasses the Chandrasekhar limit(or close to it), the core contracts rapidly. No further source of nuclearenergy in the iron core, the temperature rises from the contraction,but not fast enough. It collapses on a time scale of seconds!

Mass loss of high-mass starsMass loss plays an essential role inregulating the evolution of very massivestars.

I WR stars are examples, following thecorrelation: log[Mv∞R1/2] ∝ log[L].

I How could M and vw be measured?I In general, mass-loss rates during all

evolution phases increase with stellarmass, resulting in timescales for massloss that are less that the nucleartimescale for M & 30M�. As a result,there is a convergence of the final(pre-supernova) masses to ∼ 5− 10M�.

I However, this effect is much diminishedfor metal-poor stars because themass-loss rates are generally lower atlow metallicity.

Kippenhahn diagram of the evolution ofa 60 M� star at Z = 0.02 with massloss. Cross-hatched areas indicatewhere nuclear burning occurs, andcurly symbols indicate convectiveregions. See text for details. Figurefrom Maeder & Meynet (1987).

Mass loss of high-mass starsMass loss plays an essential role inregulating the evolution of very massivestars.

I WR stars are examples, following thecorrelation: log[Mv∞R1/2] ∝ log[L].

I How could M and vw be measured?

I In general, mass-loss rates during allevolution phases increase with stellarmass, resulting in timescales for massloss that are less that the nucleartimescale for M & 30M�. As a result,there is a convergence of the final(pre-supernova) masses to ∼ 5− 10M�.

I However, this effect is much diminishedfor metal-poor stars because themass-loss rates are generally lower atlow metallicity.

Kippenhahn diagram of the evolution ofa 60 M� star at Z = 0.02 with massloss. Cross-hatched areas indicatewhere nuclear burning occurs, andcurly symbols indicate convectiveregions. See text for details. Figurefrom Maeder & Meynet (1987).

Mass loss of high-mass starsMass loss plays an essential role inregulating the evolution of very massivestars.

I WR stars are examples, following thecorrelation: log[Mv∞R1/2] ∝ log[L].

I How could M and vw be measured?I In general, mass-loss rates during all

evolution phases increase with stellarmass, resulting in timescales for massloss that are less that the nucleartimescale for M & 30M�. As a result,there is a convergence of the final(pre-supernova) masses to ∼ 5− 10M�.

I However, this effect is much diminishedfor metal-poor stars because themass-loss rates are generally lower atlow metallicity.

Kippenhahn diagram of the evolution ofa 60 M� star at Z = 0.02 with massloss. Cross-hatched areas indicatewhere nuclear burning occurs, andcurly symbols indicate convectiveregions. See text for details. Figurefrom Maeder & Meynet (1987).

Outline

Final evolution stages of high-mass stars

Stellar end-productsWhite dwarfsNeutron stars and black holes

SupernovaeCore-collapsed SNePair-Instability Supernovae (PISNe)Type Ia SNe

Review

Stellar end-products

It is primarily the mass of a star that decides the outcome at the endof the stellar evolution.

White dwarfsWDs are the stellar end-products of relativelylow-mass stars. Observations show two peaks inthe mass distribution of WDs:

I (Isolated) stars normally undergo the AGBphase, accounting for most of the WDsobserved with their mass peaking at0.67± 0.21 M� (Zorotovic et al. 2011).

I A helium white dwarf can theoretically bemade by mass transfer in a binary. But, manyHe white dwarfs apparently single, puzzlingly.

I But, mean white dwarf mass in CVs is high(∼ 0.83± 0.24 M�; Zorotovic et al. 2011),which cannot be explained by selectioneffects. We still don’t understand how CVsevolve. They may contribute to thesingle-degenerate progenitors of type Ia SNe.

The radii of WDs are not too different from theEarth’s (about 10−2R�). Thus, the average densityis near 106 g cm−3.

White dwarfsWDs are the stellar end-products of relativelylow-mass stars. Observations show two peaks inthe mass distribution of WDs:

I (Isolated) stars normally undergo the AGBphase, accounting for most of the WDsobserved with their mass peaking at0.67± 0.21 M� (Zorotovic et al. 2011).

I A helium white dwarf can theoretically bemade by mass transfer in a binary. But, manyHe white dwarfs apparently single, puzzlingly.

I But, mean white dwarf mass in CVs is high(∼ 0.83± 0.24 M�; Zorotovic et al. 2011),which cannot be explained by selectioneffects. We still don’t understand how CVsevolve. They may contribute to thesingle-degenerate progenitors of type Ia SNe.

The radii of WDs are not too different from theEarth’s (about 10−2R�). Thus, the average densityis near 106 g cm−3.

WD structure and cooling

The structure of a WD approximately consists of two parts:I an isothermal degenerate electron core. Why is this a

reasonable assumption?I a thermal radiative envelope with negligible mass and energy

source.The internal energy source is primarily the thermal energy stored bythe ions (as the heat capacity of the electrons is negligible).Neglecting the mass and energy in the envelope, the total thermalenergy is

UI =3MkTc

2µImA, (1)

where Tc is the temperature of the core. The luminosity can beexpressed as

L = −dUI

dt(2)

and is determined by Tc and the WD mass M. This expression is tobe found.

In the radiative envelope,

dTdr

= − 34ac

κρ

T 3L

4πr2 ,

Replacing dr with the hydrostatic equation, using the Kramers’opacity, and integrate the equation from the surface, whereP = T = 0, inward, we have

P ∝(

ML

)1/2

T 17/4.

Reversing back to the density,

ρ ∝(

ML

)1/2

T 13/4,

which holds down to Rc , where the ideal electron pressure and thedegenerate electron pressure are the same:

ρ

µemAkT = K (ρ/µe)

5/3

where K is just a constant.

We further assume that there is no sudden jump in both density andtemperature across the radius. Eliminating ρ between the above twoequations, obtain

L/L�M/M�

≈ 9× 10−3(Tc/107K )7/2

Placing the above in Eq. 2 and then integrating it, we get

τcool ∝ (1/T 5/2c − 1/T 5/2

c,0 )

For Tc � Tc,0, we have

τcool = 2.5× 106 yr(

M/M�L/L�

)5/7

For example, about 2× 109 yrs would be required for the luminosity ofa 1M� WD to drop to 10−4L�.Afterward, the cooling can be accelerated by crystallization. The WDquickly becomes invisible.

Neutron stars and black holes

What end-product a massive star produces probably depends onmany factors (e.g., rotation, magnetic field, etc.). But its initial massand metallicity may play a major role:

Neutron stars are thestellar remnants ofmassive stars, withinitial mass mostly in therange of ∼ 10− 25M�.

The alternative stellarend-products of suchmassive stars are blackholes.

A. Heger et al. 2003, ApJ, 591, 288

Neutron stars

I The neutron degeneracypressure balances thegravity.

I Neutron stars, determinedby the stellar evolutionmodeling, are generally inthe mass range of∼ 1.2− 2.5M�.

I Observationally, theaverage mass of neutronstars in binary systems isof about 1.4M�.

A neutron star has a radius of ∼ 10 km, depending on the assumedexact equation of state, an issue of still much interest.The density is ∼ 3× 1014 g cm−3, comparable to the nuclear matterdensity.

Why don’t neutrons decay in a neutron star?

Neutron stars

I The neutron degeneracypressure balances thegravity.

I Neutron stars, determinedby the stellar evolutionmodeling, are generally inthe mass range of∼ 1.2− 2.5M�.

I Observationally, theaverage mass of neutronstars in binary systems isof about 1.4M�.

A neutron star has a radius of ∼ 10 km, depending on the assumedexact equation of state, an issue of still much interest.The density is ∼ 3× 1014 g cm−3, comparable to the nuclear matterdensity.Why don’t neutrons decay in a neutron star?

Neutron stars as pulsars

A newly born neutron star is expected to have fast rotation and strongmagnetic field. Such magnetized and fast rotating neutron starsexplain the presence of pulsars.

The life time of a pulsar is typicallyon the order of 107 years,depending on the magnetic field,which determines the spin-downrate.The exact evolution of themagnetic field in a young neutronstar is still very uncertain. But themagnetic field eventually decays.

Accretion neutron stars

A “dead” neutron star may become “alive” again in a binary system.The star may accrete matter from its companion and can be observedas an X-ray binary.

I The accretion leads to theangular momentum transferand the spin-up of theneutron star.

I As a result, the neutron starmay become a pulsar again,typically with a period of afew to a few tens of ms.

I Because of the weakness ofsuch an old neutron star, thespin rate is extremely stableand decreases very slowly.

Outline

Final evolution stages of high-mass stars

Stellar end-productsWhite dwarfsNeutron stars and black holes

SupernovaeCore-collapsed SNePair-Instability Supernovae (PISNe)Type Ia SNe

Review

Supernovae (SNe)

Basic types:I Type Ia: only metal lines; no hydrogen lines in its spectrum;

observed in all kinds of galaxies and regions inside a galaxy;rather uniform light curves.

I The spectra of Type II supernovae are dominated by H lines,while lines of Ca, O and Mg are also present. SNe II are nearlyalways found in recent massive star formation regions.

I Type Ib,c: Type Ib SNe have strong He lines in their spectra,which are lacking in Type Ic SNe. Similar to SNe II, they arefound in star-forming regions, and their late-time spectra are alsosimilar to Type II. A subclass of very bright Type Ic supernovae,known as hypernovae, may be associated with gamma-raybursts.

More physically, Type II and Type Ib,c together are called“core-collapsed” SNe.

Core-collapsed SNeTake the Fe core as an example. As the core collapses, instabilitiesoccur:

I Because of the high electron degeneracy of the gas, thetemperature rises unrestrained. In time, it becomes sufficientlyhigh for the photo-disintegration of iron nuclei: e.g.,

100MeV +5626 Fe→ 134

2He + 4n.

I The increase of the density forces the degenerate electrons toever-higher momentum state - hence higher energy states,exceeding the neutron-proton mass difference. Eventually, freeprotons capture free electrons and turn into neutrons.

I Not only does this process absorb energy, but it also reduces thenumber of particles.

I The rapid energy loss from neutrinos further deprives thethermal pressure support.

I The star contracting from a density of ∼ 109 g cm−3 and endingup with a neutron star with a size of ∼ 10 km, in which theneutron degeneracy pressure could be sufficient to stop thecollapsing.

Characteristics of CC SNe

The total gravitational energy release from the collapse is ∼ 3× 1053

ergs, more than enough to dissolve all the synthesized nuclearmaterials ∼ 2× 1052.But how a fraction of this energy may be used to drive the explosionis not clear.A few possibilities: 1) bouncing shock wave, 2) trapped neutrinos, and3) jets.

A few observational characteristics of CC SNe:I They are related to Pop I stars. Evidence for the core collapse:

pulsars and neutrinos (from SN1987A).I Eject more mass, but at slower speed than Ia SNe.I Slightly fainter. Light-curves are much less uniform.I Relatively easy to be picked up in radio and X-ray, usually at

later times than the visible light peak.

Characteristics of CC SNe

The total gravitational energy release from the collapse is ∼ 3× 1053

ergs, more than enough to dissolve all the synthesized nuclearmaterials ∼ 2× 1052.But how a fraction of this energy may be used to drive the explosionis not clear.A few possibilities: 1) bouncing shock wave, 2) trapped neutrinos, and3) jets.

A few observational characteristics of CC SNe:I They are related to Pop I stars. Evidence for the core collapse:

pulsars and neutrinos (from SN1987A).I Eject more mass, but at slower speed than Ia SNe.I Slightly fainter. Light-curves are much less uniform.I Relatively easy to be picked up in radio and X-ray, usually at

later times than the visible light peak.

SN1987A

First observed visually on Feb. 24, 1987 in the LMC. Kind of uniquelight-curve and intrinsically dimmer, compared with the “normal” TypeII SNe. Progenitor: B3 I blue supergiant (16-20 M�).

The key evidence for the corecollapse and the formation of aneutron star is the detection of theneutrinos about a quarter of a daybefore optical discovery. But theneutron star is so far not detected.

The explosion leads to thesynthesis of heavy elements in theejecta, chiefly 56Ni, which decaysinto 56Co and then to 56Fe.These decays give the majorenergy source that keeps theexpanding ejecta bright.

Pair-Instability Supernovae (PISNe)

The hotter a star’s core becomes, the higher energy the gamma raysit produces. When the mass of a star exceeds about 100M�, theproduced gamma rays become so energetic, their interaction withatomic nucleus can lead to the production of electron-position pairs.

The pair production decreases the distance that gamma rays travel inthe gas, which leads to an instability: as gamma ray travel distancedecreases, the temperature at the core increases, and this increasesthe generation of the nuclear energy and hence the gamma rayenergy and further decreases the distance that gammas can travel.

The consequence of the instability depends on the mass andmetallicity of a star:

I For a star in the mass range of ∼ 100− 130M�, the instabilitymost likely leads to partial collapse and pressure pulses. Thisprocess tends to eject parts of the outer layers of the star until itbecomes light enough to collapse in a normal SN.

Pair-Instability Supernovae (PISNe)

The hotter a star’s core becomes, the higher energy the gamma raysit produces. When the mass of a star exceeds about 100M�, theproduced gamma rays become so energetic, their interaction withatomic nucleus can lead to the production of electron-position pairs.

The pair production decreases the distance that gamma rays travel inthe gas, which leads to an instability: as gamma ray travel distancedecreases, the temperature at the core increases, and this increasesthe generation of the nuclear energy and hence the gamma rayenergy and further decreases the distance that gammas can travel.

The consequence of the instability depends on the mass andmetallicity of a star:

I For a star in the mass range of ∼ 100− 130M�, the instabilitymost likely leads to partial collapse and pressure pulses. Thisprocess tends to eject parts of the outer layers of the star until itbecomes light enough to collapse in a normal SN.

Pair-Instability Supernovae (PISNe)

The hotter a star’s core becomes, the higher energy the gamma raysit produces. When the mass of a star exceeds about 100M�, theproduced gamma rays become so energetic, their interaction withatomic nucleus can lead to the production of electron-position pairs.

The pair production decreases the distance that gamma rays travel inthe gas, which leads to an instability: as gamma ray travel distancedecreases, the temperature at the core increases, and this increasesthe generation of the nuclear energy and hence the gamma rayenergy and further decreases the distance that gammas can travel.

The consequence of the instability depends on the mass andmetallicity of a star:

I For a star in the mass range of ∼ 100− 130M�, the instabilitymost likely leads to partial collapse and pressure pulses. Thisprocess tends to eject parts of the outer layers of the star until itbecomes light enough to collapse in a normal SN.

I For a star in the mass range of ∼ 130− 250M�, the collapsecaused by the pair instability proceeds to allow runaway oxygenand silicon burning of the star’s core, creating a thermonuclearexplosion, or a “hypernova”, a term that used to refer anexceptionally energetic explosion with an inferred energy over100 SNe.

I A PISN may be distinguished from other SNe by its very longduration to peak brightness, together with its brightness due tothe production of much more radioactive Ni.

I The pair instability tends to happen in low metallicity stars (e.g.,Pop III stars, resulting in weak stellar winds and large coremasses), with low to moderate rotation rates.

I In addition, stars formed by collision mergers having a metallicityZ between 0.02 and 0.001 may also end their lives as PISNe iftheir mass is in the appropriate range.

I For a star in the mass range of & 250M�, a different reactionmechanism, photo-disintegration, results after collapse. Thisendothermic reaction (energy-absorbing) causes the star tocontinue collapse into a black hole rather than exploding due tothermonuclear reactions.

The Progenitor – SN Map

RedSupergiant

Type II-PSN 2003gd, SN 2004A, SN 2005cs, SN 2008bk

Blue Supergiant

SN 1987A(faint, slow)

?SN 1987A

Type IIn(dense CSM)

LBV(η Car) SN 2005gl

?

Type IIL/IIb(little H)

Late W-R(WN)

SN 1993J, SN 2008ax?

SN 2002ap, SN 2004gt, SN 2007gr (upper limits)

?

?Early W-R(WC/WO)

Type Ib(H, He)

MassiveBinaries

Type Ic (He)GRB/XRF

Based on Gal-Yam et al. 2007; updated

http://www.weizmann.ac.il/home/galyam/progenitors.html

Type Ia SNe

I The lack of hydrogens in the spectra of such SNe stronglyindicates that they result from the collapse of “undressed” cores(e.g., due to strong stellar winds and/or by transferring tocompanions).

I Energy source of Ia SN: explosive fusion of close to 1 M�carbon and oxygen to iron-peak elements, especially 56Ni. Theformation of each 56Ni from Carbon generates ∼ 8× 10−5 erg.Thus 1 M� would generate about 1052 erg, with a pretty to sparefor a SN.

I What causes this explosive burning?

The fuel must be degenerate at ignition, as in a “He-flash”.I Where do we expect to find this amount of carbon and oxygen?

A WD. But a WD with mass smaller than the Chandrasekharlimiting mass will just sit and cool off for the age of the Universe.

Type Ia SNe

I The lack of hydrogens in the spectra of such SNe stronglyindicates that they result from the collapse of “undressed” cores(e.g., due to strong stellar winds and/or by transferring tocompanions).

I Energy source of Ia SN: explosive fusion of close to 1 M�carbon and oxygen to iron-peak elements, especially 56Ni. Theformation of each 56Ni from Carbon generates ∼ 8× 10−5 erg.Thus 1 M� would generate about 1052 erg, with a pretty to sparefor a SN.

I What causes this explosive burning?The fuel must be degenerate at ignition, as in a “He-flash”.

I Where do we expect to find this amount of carbon and oxygen?

A WD. But a WD with mass smaller than the Chandrasekharlimiting mass will just sit and cool off for the age of the Universe.

Type Ia SNe

I The lack of hydrogens in the spectra of such SNe stronglyindicates that they result from the collapse of “undressed” cores(e.g., due to strong stellar winds and/or by transferring tocompanions).

I Energy source of Ia SN: explosive fusion of close to 1 M�carbon and oxygen to iron-peak elements, especially 56Ni. Theformation of each 56Ni from Carbon generates ∼ 8× 10−5 erg.Thus 1 M� would generate about 1052 erg, with a pretty to sparefor a SN.

I What causes this explosive burning?The fuel must be degenerate at ignition, as in a “He-flash”.

I Where do we expect to find this amount of carbon and oxygen?A WD. But a WD with mass smaller than the Chandrasekharlimiting mass will just sit and cool off for the age of the Universe.

How to make a WD add mass?I Merging two WDs (double degenerate scenario):

I accounting for the absence of hydrogen.I But there may not be enough of them with enough masses

and tight enough to merge over the age of the Universe.I Also how could the explosion of a WD merger be a

standard candle?

I Accretion (single-degenerate scenario):I A natural process that leads to an explosion at the

Chandrasekhar limit.I But, physically most of the accreted materials is fused to

carbon and oxygen during nova and possibly ejected. So allthese need to lead to the increase of the WD mass.

I The accumulated X-ray emission from such accretingsources, as observed from nearby galaxies, seems to be farless than required by this scenario.

I The missing of the running-away companion stars in Ia SNremnants also casts doubts on the the scenario.

Is a neutron star expected? Typically not. But a leftover WD is apossibility, if the explosion is only partial and off-center.

How to make a WD add mass?I Merging two WDs (double degenerate scenario):

I accounting for the absence of hydrogen.I But there may not be enough of them with enough masses

and tight enough to merge over the age of the Universe.I Also how could the explosion of a WD merger be a

standard candle?I Accretion (single-degenerate scenario):

I A natural process that leads to an explosion at theChandrasekhar limit.

I But, physically most of the accreted materials is fused tocarbon and oxygen during nova and possibly ejected. So allthese need to lead to the increase of the WD mass.

I The accumulated X-ray emission from such accretingsources, as observed from nearby galaxies, seems to be farless than required by this scenario.

I The missing of the running-away companion stars in Ia SNremnants also casts doubts on the the scenario.

Is a neutron star expected? Typically not. But a leftover WD is apossibility, if the explosion is only partial and off-center.

How to make a WD add mass?I Merging two WDs (double degenerate scenario):

I accounting for the absence of hydrogen.I But there may not be enough of them with enough masses

and tight enough to merge over the age of the Universe.I Also how could the explosion of a WD merger be a

standard candle?I Accretion (single-degenerate scenario):

I A natural process that leads to an explosion at theChandrasekhar limit.

I But, physically most of the accreted materials is fused tocarbon and oxygen during nova and possibly ejected. So allthese need to lead to the increase of the WD mass.

I The accumulated X-ray emission from such accretingsources, as observed from nearby galaxies, seems to be farless than required by this scenario.

I The missing of the running-away companion stars in Ia SNremnants also casts doubts on the the scenario.

Is a neutron star expected? Typically not. But a leftover WD is apossibility, if the explosion is only partial and off-center.

Outline

Final evolution stages of high-mass stars

Stellar end-productsWhite dwarfsNeutron stars and black holes

SupernovaeCore-collapsed SNePair-Instability Supernovae (PISNe)Type Ia SNe

Review

Review

1. What is the internal energy source of a white dwarf that keeps itbright? Why is the interior close to be isothermal?

2. What are the main differences of the post-MS evolution ofmassive stars (≥ 10M�) from that of lower mass ones?

3. In an HR diagram, name the nuclear burning states along theevolutionary tracks for low and high mass stars, separately.

4. How do massive stars end their lives? Why do the coreseventually collapse?

5. How do neutron stars form? Why don’t the neutrons decay inneutron stars?

6. What are the key observational signatures that distinguish Type Iand Type II supernovae? Why are Type Ib,c supernovae alsobelieved to arise from the collapse of massive stars?

7. What is a pair-instability supernova? Why is it proposed to berelated to Pop III stars?

Review (cont.)

9. What is the energy source that keeps a supernova bright for∼ 102 days or longer?

10. Why do most stars show absorption lines? What kinds of starstend to have emission lines?

11. How might one estimate the rate of supernova explosions in agalaxy?

12. Can you roughly estimate the “waiting time” for a supernovaexplosion within, say, 50 light-years of the Sun?