Download Chapter 6: Stellar Evolution (part 2)

Chapter 6: Stellar Evolution (part 2): Stellar
end-products
Final evolution stages of high-mass stars
Stellar end-products
White dwarfs
Neutron stars and black holes
Supernovae
Core-collapsed SNe
Pair-Instability Supernovae (PISNe)
Type Ia SNe
Review
Outline
Final evolution stages of high-mass stars
Stellar end-products
White dwarfs
Neutron stars and black holes
Supernovae
Core-collapsed SNe
Pair-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 eventually
evolve to is still somewhat uncertain; they may just develop
degenerate O-Ne cores.
I
A star with mass above ∼ 11M will ignite and burn fuels
heavier than carbon until an Fe core is formed which collapses
and causes a supernova explosion.
I
For a star with mass & 15M , mass loss by the stellar wind
becomes important during all evolution phases, including the
MS.
Kippenhahn Diagram
Mass-loss of high-mass stars
For stars with masses & 30M ,
I
The mass loss time scale is shorter
than the MS timescale. The MS
evolutionary paths of such stars
converge toward that of a 30M star.
I
Mass-loss from Wolf-Rayet stars leads
to CNO products (helium and nitrogen)
exposed.
I
The evolutionary track in the H-R
diagram becomes nearly horizontal,
since the luminosity is already close to
the Eddington limit.
I
Electrons do not become degenerate
until the core consists of iron.
Mass-loss of high-mass stars
For stars with masses & 30M ,
I
The mass loss time scale is shorter
than the MS timescale. The MS
evolutionary paths of such stars
converge toward that of a 30M star.
I
Mass-loss from Wolf-Rayet stars leads
to CNO products (helium and nitrogen)
exposed.
I
The evolutionary track in the H-R
diagram becomes nearly horizontal,
since the luminosity is already close to
the Eddington limit.
I
Electrons do not become degenerate
until 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 nuclear
energy 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 stars
Mass loss plays an essential role in
regulating the evolution of very massive
stars.
I
WR stars are examples, following the
correlation: log[Ṁv∞ R 1/2 ] ∝ log[L].
Mass loss of high-mass stars
Mass loss plays an essential role in
regulating the evolution of very massive
stars.
I
WR stars are examples, following the
correlation: log[Ṁv∞ R 1/2 ] ∝ log[L].
I
How could Ṁ and vw be measured?
Mass loss of high-mass stars
Mass loss plays an essential role in
regulating the evolution of very massive
stars.
I
WR stars are examples, following the
correlation: log[Ṁv∞ R 1/2 ] ∝ log[L].
I
How could Ṁ and vw be measured?
I
In general, mass-loss rates during all
evolution phases increase with stellar
mass, resulting in timescales for mass
loss that are less that the nuclear
timescale 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 diminished
for metal-poor stars because the
mass-loss rates are generally lower at
low metallicity.
Kippenhahn diagram of the evolution of
a 60 M star at Z = 0.02 with mass
loss. Cross-hatched areas indicate
where nuclear burning occurs, and
curly symbols indicate convective
regions. See text for details. Figure
from Maeder & Meynet (1987).
Outline
Final evolution stages of high-mass stars
Stellar end-products
White dwarfs
Neutron stars and black holes
Supernovae
Core-collapsed SNe
Pair-Instability Supernovae (PISNe)
Type Ia SNe
Review
Stellar end-products
It is primarily the mass of a star that decides the outcome at the end
of the stellar evolution.
White dwarfs
WDs are the stellar end-products of relatively
low-mass stars. Observations show two peaks in
the mass distribution of WDs:
I
(Isolated) stars normally undergo the AGB
phase, accounting for most of the WDs
observed with their mass peaking at
0.67 ± 0.21 M (Zorotovic et al. 2011).
I
A helium white dwarf can theoretically be
made by mass transfer in a binary. But, many
He 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 selection
effects. We still don’t understand how CVs
evolve. They may contribute to the
single-degenerate progenitors of type Ia SNe.
White dwarfs
WDs are the stellar end-products of relatively
low-mass stars. Observations show two peaks in
the mass distribution of WDs:
I
(Isolated) stars normally undergo the AGB
phase, accounting for most of the WDs
observed with their mass peaking at
0.67 ± 0.21 M (Zorotovic et al. 2011).
I
A helium white dwarf can theoretically be
made by mass transfer in a binary. But, many
He 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 selection
effects. We still don’t understand how CVs
evolve. They may contribute to the
single-degenerate progenitors of type Ia SNe.
The radii of WDs are not too different from the
Earth’s (about 10−2 R ). Thus, the average density
is 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?
a thermal radiative envelope with negligible mass and energy
source.
The internal energy source is primarily the thermal energy stored by
the ions (as the heat capacity of the electrons is negligible).
Neglecting the mass and energy in the envelope, the total thermal
energy is
3MkTc
,
(1)
UI =
2µI mA
I
where Tc is the temperature of the core. The luminosity can be
expressed as
dUI
L=−
(2)
dt
and is determined by Tc and the WD mass M. This expression is to
be found.
In the radiative envelope,
3 κρ L
dT
=−
,
dr
4ac T 3 4πr 2
Replacing dr with the hydrostatic equation, using the Kramers’
opacity, and integrate the equation from the surface, where
P = T = 0, inward, we have
P∝
M
L
1/2
M
L
1/2
T 17/4 .
Reversing back to the density,
ρ∝
T 13/4 ,
which holds down to Rc , where the ideal electron pressure and the
degenerate electron pressure are the same:
ρ
kT = K (ρ/µe )5/3
µe mA
where K is just a constant.
We further assume that there is no sudden jump in both density and
temperature across the radius. Eliminating ρ between the above two
equations, obtain
L/L
≈ 9 × 10−3 (Tc /107 K )7/2
M/M
Placing the above in Eq. 2 and then integrating it, we get
5/2
τcool ∝ (1/Tc
5/2
− 1/Tc,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 of
a 1M WD to drop to 10−4 L .
Afterward, the cooling can be accelerated by crystallization. The WD
quickly becomes invisible.
Neutron stars and black holes
What end-product a massive star produces probably depends on
many factors (e.g., rotation, magnetic field, etc.). But its initial mass
and metallicity may play a major role:
Neutron stars are the
stellar remnants of
massive stars, with
initial mass mostly in the
range of ∼ 10 − 25M .
The alternative stellar
end-products of such
massive stars are black
holes.
A. Heger et al. 2003, ApJ, 591, 288
Neutron stars
The neutron degeneracy
pressure balances the
gravity.
I Neutron stars, determined
by the stellar evolution
modeling, are generally in
the mass range of
∼ 1.2 − 2.5M .
I
Observationally, the
average mass of neutron
stars in binary systems is
of about 1.4M .
A neutron star has a radius of ∼ 10 km, depending on the assumed
exact equation of state, an issue of still much interest.
The density is ∼ 3 × 1014 g cm−3 , comparable to the nuclear matter
density.
I
Neutron stars
The neutron degeneracy
pressure balances the
gravity.
I Neutron stars, determined
by the stellar evolution
modeling, are generally in
the mass range of
∼ 1.2 − 2.5M .
I
Observationally, the
average mass of neutron
stars in binary systems is
of about 1.4M .
A neutron star has a radius of ∼ 10 km, depending on the assumed
exact equation of state, an issue of still much interest.
The density is ∼ 3 × 1014 g cm−3 , comparable to the nuclear matter
density.
Why don’t neutrons decay in a neutron star?
I
Neutron stars as pulsars
A newly born neutron star is expected to have fast rotation and strong
magnetic field. Such magnetized and fast rotating neutron stars
explain the presence of pulsars.
The life time of a pulsar is typically
on the order of 107 years,
depending on the magnetic field,
which determines the spin-down
rate.
The exact evolution of the
magnetic field in a young neutron
star is still very uncertain. But the
magnetic 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 observed
as an X-ray binary.
I
The accretion leads to the
angular momentum transfer
and the spin-up of the
neutron star.
I
As a result, the neutron star
may become a pulsar again,
typically with a period of a
few to a few tens of ms.
I
Because of the weakness of
such an old neutron star, the
spin rate is extremely stable
and decreases very slowly.
Outline
Final evolution stages of high-mass stars
Stellar end-products
White dwarfs
Neutron stars and black holes
Supernovae
Core-collapsed SNe
Pair-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 nearly
always 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 are
found in star-forming regions, and their late-time spectra are also
similar to Type II. A subclass of very bright Type Ic supernovae,
known as hypernovae, may be associated with gamma-ray
bursts.
More physically, Type II and Type Ib,c together are called
“core-collapsed” SNe.
Core-collapsed SNe
Take the Fe core as an example. As the core collapses, instabilities
occur:
I Because of the high electron degeneracy of the gas, the
temperature rises unrestrained. In time, it becomes sufficiently
high for the photo-disintegration of iron nuclei: e.g.,
4
100MeV +56
26 Fe → 132 He + 4n.
The increase of the density forces the degenerate electrons to
ever-higher momentum state - hence higher energy states,
exceeding the neutron-proton mass difference. Eventually, free
protons capture free electrons and turn into neutrons.
I Not only does this process absorb energy, but it also reduces the
number of particles.
I The rapid energy loss from neutrinos further deprives the
thermal pressure support.
I The star contracting from a density of ∼ 109 g cm−3 and ending
up with a neutron star with a size of ∼ 10 km, in which the
neutron degeneracy pressure could be sufficient to stop the
collapsing.
I
Characteristics of CC SNe
The total gravitational energy release from the collapse is ∼ 3 × 1053
ergs, more than enough to dissolve all the synthesized nuclear
materials ∼ 2 × 1052 .
But how a fraction of this energy may be used to drive the explosion
is not clear.
A few possibilities: 1) bouncing shock wave, 2) trapped neutrinos, and
3) jets.
Characteristics of CC SNe
The total gravitational energy release from the collapse is ∼ 3 × 1053
ergs, more than enough to dissolve all the synthesized nuclear
materials ∼ 2 × 1052 .
But how a fraction of this energy may be used to drive the explosion
is not clear.
A few possibilities: 1) bouncing shock wave, 2) trapped neutrinos, and
3) 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 unique
light-curve and intrinsically dimmer, compared with the “normal” Type
II SNe. Progenitor: B3 I blue supergiant (16-20 M ).
The key evidence for the core
collapse and the formation of a
neutron star is the detection of the
neutrinos about a quarter of a day
before optical discovery. But the
neutron star is so far not detected.
The explosion leads to the
synthesis of heavy elements in the
ejecta, chiefly 56 Ni, which decays
into 56 Co and then to 56 Fe.
These decays give the major
energy source that keeps the
expanding ejecta bright.
Pair-Instability Supernovae (PISNe)
The hotter a star’s core becomes, the higher energy the gamma rays
it produces. When the mass of a star exceeds about 100M , the
produced gamma rays become so energetic, their interaction with
atomic nucleus can lead to the production of electron-position pairs.
Pair-Instability Supernovae (PISNe)
The hotter a star’s core becomes, the higher energy the gamma rays
it produces. When the mass of a star exceeds about 100M , the
produced gamma rays become so energetic, their interaction with
atomic nucleus can lead to the production of electron-position pairs.
The pair production decreases the distance that gamma rays travel in
the gas, which leads to an instability: as gamma ray travel distance
decreases, the temperature at the core increases, and this increases
the generation of the nuclear energy and hence the gamma ray
energy and further decreases the distance that gammas can travel.
Pair-Instability Supernovae (PISNe)
The hotter a star’s core becomes, the higher energy the gamma rays
it produces. When the mass of a star exceeds about 100M , the
produced gamma rays become so energetic, their interaction with
atomic nucleus can lead to the production of electron-position pairs.
The pair production decreases the distance that gamma rays travel in
the gas, which leads to an instability: as gamma ray travel distance
decreases, the temperature at the core increases, and this increases
the generation of the nuclear energy and hence the gamma ray
energy and further decreases the distance that gammas can travel.
The consequence of the instability depends on the mass and
metallicity of a star:
I
For a star in the mass range of ∼ 100 − 130M , the instability
most likely leads to partial collapse and pressure pulses. This
process tends to eject parts of the outer layers of the star until it
becomes light enough to collapse in a normal SN.
I
For a star in the mass range of ∼ 130 − 250M , the collapse
caused by the pair instability proceeds to allow runaway oxygen
and silicon burning of the star’s core, creating a thermonuclear
explosion, or a “hypernova”, a term that used to refer an
exceptionally energetic explosion with an inferred energy over
100 SNe.
I
A PISN may be distinguished from other SNe by its very long
duration to peak brightness, together with its brightness due to
the 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 core
masses), with low to moderate rotation rates.
I
In addition, stars formed by collision mergers having a metallicity
Z between 0.02 and 0.001 may also end their lives as PISNe if
their mass is in the appropriate range.
I
For a star in the mass range of & 250M , a different reaction
mechanism, photo-disintegration, results after collapse. This
endothermic reaction (energy-absorbing) causes the star to
continue collapse into a black hole rather than exploding due to
thermonuclear reactions.
The Progenitor – SN Map
Red
Supergiant
Type II-P
SN 2003gd, SN 2004A,
SN 2005cs, SN 2008bk
Blue
Supergiant
?
LBV
(η Car)
?
SN 1987A
(faint, slow)
SN 1987A
Type IIn
(dense CSM)
SN 2005gl
Type IIL/IIb
(little H)
Late W-R
(WN)
SN 1993J, SN 2008ax?
Early W-R
(WC/WO)
Massive
Binaries
Type Ib
(H, He)
?
?
Type Ic (He)
GRB/XRF
SN 2002ap, SN 2004gt,
SN 2007gr (upper limits)
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 strongly
indicates that they result from the collapse of “undressed” cores
(e.g., due to strong stellar winds and/or by transferring to
companions).
I
Energy source of Ia SN: explosive fusion of close to 1 M
carbon and oxygen to iron-peak elements, especially 56 Ni. The
formation of each 56 Ni from Carbon generates ∼ 8 × 10−5 erg.
Thus 1 M would generate about 1052 erg, with a pretty to spare
for a SN.
I
What causes this explosive burning?
Type Ia SNe
I
The lack of hydrogens in the spectra of such SNe strongly
indicates that they result from the collapse of “undressed” cores
(e.g., due to strong stellar winds and/or by transferring to
companions).
I
Energy source of Ia SN: explosive fusion of close to 1 M
carbon and oxygen to iron-peak elements, especially 56 Ni. The
formation of each 56 Ni from Carbon generates ∼ 8 × 10−5 erg.
Thus 1 M would generate about 1052 erg, with a pretty to spare
for 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?
Type Ia SNe
I
The lack of hydrogens in the spectra of such SNe strongly
indicates that they result from the collapse of “undressed” cores
(e.g., due to strong stellar winds and/or by transferring to
companions).
I
Energy source of Ia SN: explosive fusion of close to 1 M
carbon and oxygen to iron-peak elements, especially 56 Ni. The
formation of each 56 Ni from Carbon generates ∼ 8 × 10−5 erg.
Thus 1 M would generate about 1052 erg, with a pretty to spare
for 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 Chandrasekhar
limiting 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?
How to make a WD add mass?
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 all
these need to lead to the increase of the WD mass.
I The accumulated X-ray emission from such accreting
sources, as observed from nearby galaxies, seems to be far
less than required by this scenario.
I The missing of the running-away companion stars in Ia SN
remnants also casts doubts on the the scenario.
I
How to make a WD add mass?
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 all
these need to lead to the increase of the WD mass.
I The accumulated X-ray emission from such accreting
sources, as observed from nearby galaxies, seems to be far
less than required by this scenario.
I The missing of the running-away companion stars in Ia SN
remnants also casts doubts on the the scenario.
I
Is a neutron star expected? Typically not. But a leftover WD is a
possibility, if the explosion is only partial and off-center.
Outline
Final evolution stages of high-mass stars
Stellar end-products
White dwarfs
Neutron stars and black holes
Supernovae
Core-collapsed SNe
Pair-Instability Supernovae (PISNe)
Type Ia SNe
Review
Review
1. What is the internal energy source of a white dwarf that keeps it
bright? Why is the interior close to be isothermal?
2. What are the main differences of the post-MS evolution of
massive stars (≥ 10M ) from that of lower mass ones?
3. In an HR diagram, name the nuclear burning states along the
evolutionary tracks for low and high mass stars, separately.
4. How do massive stars end their lives? Why do the cores
eventually collapse?
5. How do neutron stars form? Why don’t the neutrons decay in
neutron stars?
6. What are the key observational signatures that distinguish Type I
and Type II supernovae? Why are Type Ib,c supernovae also
believed to arise from the collapse of massive stars?
7. What is a pair-instability supernova? Why is it proposed to be
related 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 stars
tend to have emission lines?
11. How might one estimate the rate of supernova explosions in a
galaxy?
12. Can you roughly estimate the “waiting time” for a supernova
explosion within, say, 50 light-years of the Sun?