Download Stellar evolution – Part III of III - Inside Mines

Stellar evolution – Part III of III
The death of the stars (evolution out of the
Main Sequence)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Evolution in the Giant branch – the beginning of the end
Evidence for stellar evolution?
• How can we test our idea that stars
make a transition between a main
sequence star and a red giant?
• Transition too slow to observe in real
time
• Answer: look at star clusters where
stars all have approximately the same
age.
• Expectation: since more massive stars
evolve more quickly than less massive
ones, we should observe that the
upper end of the MS is missing in old
clusters
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Star clusters
• The “Jewel Box” star cluster – Kappa Crucis
Cluster (NGC 4755)
• Globular Cluster 47
Tucanae (“47 Tuc”)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Young clusters
NGC 2264
• Young cluster / still forming
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Older clusters
Pleiades
• Older cluster
• Apparition of a turnoff point
• Evidence of the evolution
of massive stars out of the
Main Sequence
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Old clusters
M64
• Very old cluster
• Turnoff point has moved to the
lower end of the Main
Sequence. Only the low mass /
low luminosity stars remain!
Method to date the age of star
clusters
• Location of the turnoff point
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Summary – evolution of a star cluster
Another example
The Hyades Star Cluster
(T~625 million years)
Time
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Evolution of individual stars depends on their mass
• Very low-mass stars (<0.4M☉) are completely convective
– H and He remain well mixed throughout the entire star
– No H shell burning.
– The He core never becomes hot enough to ignite He burning
à Late stage: red dwarf
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Evolution of individual stars depends on their mass
• Low / medium mass “Sun-like” stars (0.4M☉ to 4M☉) do develop a He core
– Expansion to red giant during H burning shell phase
– Ignition of He burning in the He core
– Formation of a degenerate C, O core, but not enough gravitational
pressure to ignite additional fusion reactions
à Late stage: white dwarf
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Evolution of individual stars depends on their mass
• High mass stars (4M☉ and higher)
– Same than before, but additional fusion reaction can occur
inside the core
– Explosive end - supernova
à Late stage: neutron star / black hole (depending on mass)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Red giant evolution & Helium burning
• H-burning shell keeps dumping He
onto the core.
• He core gets denser and hotter
until the next stage of nuclear
burning can begin in the core
• Ignition of He fusion to C
(“He flash” in low / medium
mass stars).
• He fusion through the
“triple-alpha process”:
4He + 4He → 8Be + g
8Be
+ 4He → 12C + g
Precise path on H-R diagram depends on the star mass
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Electron degeneracy pressure
• Prior to He burning ignition
(T~108K), the core collapses since
there is no outward pressure due
to thermonuclear reactions
Fermi energy
Electron energy
Fermi energy
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
• The collapse however eventually
slows down because of the
outward pressure produced when
electrons are forced to occupy
levels up to near the Fermi energy
• Temperature continues to increase
even as the core’s compression
slows down. Eventually, He
burning is ignited.
PHGN324: Stellar evolution (III)
Electron degeneracy pressure
From statistical physics*:
ℏ"
• Fermi energy is given by 𝜀& =
3𝜋 " 𝑛
2𝑚
"/!
where n is the number of electrons per unit of
volume and m the mass of the electron.
• For full ionization: 𝑛 =
𝑍 𝜌
𝐴 𝑚2
• The level of degeneracy is estimated by comparing the average thermal
!
energy of the electron " 𝑘𝑇 and the Fermi energy 𝜀& .
• Without further calculations, one can show that the electron pressure is:
3𝜋 "
𝑃=
5
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
"/!
ℏ"
𝑚5
𝑍 𝜌
𝐴 𝑚2
6/!
*See derivation
PHGN324: Stellar evolution (III)
Triple-alpha reaction to Carbon?
• Dense Helium core + Hydrogen
shell burning
• Why no 4He+p? 5Li is highly
unstable (lifetime ~ 10-22s).
Similarly 4He+n leads to 5He which
is also highly unstable. No path to
A=5 nuclei.
• Similarly 4He+4He leads to 8Be
which is also unstable, although it
does have a longer lifetime (10-16s).
Production of A=8 nuclei needs to
be side-stepped quickly!
The A=5 and A=8 gaps
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The path to Carbon: the triple a reaction
• 3a reaction is a two-step process:
Lifetime of 8Be: ~10-16s!
4He
+ 4He → 8Be + g
8Be
+ 4He → 12C + g
• A case for the ”fined-tuned” Universe?
• 8Be lifetime long enough to allow
for another 4He capture before 8Be
system breaks apart again
• Existence of a resonance in 12C
(the “Hoyle” state) at the right
energy and with a significant gdecay partial decay width (Gg)
• 12C not destroyed through a fast
12C+a reaction à Otherwise, no
C-based life!
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The Hoyle state
The Hoyle state (7.656 MeV 0+)
• Above 8Be+a threshold
• Not too high in energy (otherwise the
star temperature would be too low for
the reaction to proceed through that
T~108K
state)
• Radiative capture (Grad) decay width
small, but not too small (Grad/G≈4x10-4)
• Right spin / parity
Reaction rate ∝ Grad exp(-Q3akT)
with Q3a ~ 380 keV and kT ~ 7 keV
From: S.Ekstrom et al., Astronomy and Astrophysics 514, A62 (2010)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
Fred Hoyle
(1915-2001)
PHGN324: Stellar evolution (III)
The fate of very low mass stars: red dwarfs
• Red dwarfs are small and relatively
cool stars on the lower end of the
Main Sequence. They will remain
there during their very long life
(>1012 years!)
• The most common type of stars in
the Milky Way - Proxima Centaury,
the closest star from the Sun is a red
dwarf.
Red dwarfs
• Convection mixes H throughout the
star, prolongs considerably the H
burning phase.
• Too small to ignite He burning
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The fate of low / medium mass (“Sun-like”) stars
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The fate of low / medium mass (“Sun-like”) stars
• The source of the star’s energy (He burning) is eventually exhausted inside
the core, which is now composed of carbon and oxygen
• The core begins to contract without outward thermal pressure of fusion
process. The contraction leads to further heating of the core.
• Similarly to the “hydrogen shell burning”, “helium shell burning” is ignited
around the core.
• A hotter core means that star expands in size, with a radius typically the orbit
of Earth and brightness roughly 100-1000 L☉. The giant stars suffer huge
energy loss rate, so they have short lives, and are very unstable
• As the outer layers cool, they become opaque, and the radiation from inside
the star blows away the outer layers. The loss of atmosphere is accelerated
once the hot carbon-oxygen core is exposed – a strong stellar wind blows all
the atmosphere away.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Formation of planetary nebulae
Mass loss
• Stars like our Sun are constantly losing
mass in a stellar wind (→ solar wind).
• The more massive the star, the stronger its
stellar wind.
Ejection of the outer layers / Formation of
planetary nebulae
• Remnants of stars with one to a few M☉
• Radii: R ~0.2 to 3 light years
• Expanding at ~10 to 20 km/s (measured by
Doppler shifts)
• Short lived phenomenon (a few 104 years –
see next slide)
• Planetary nebulae have nothing to do with
planets (name is a historical accident)!
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Formation of planetary nebulae
Stage 1: ejection of the star cold outer layers
• Slow wind from a red giant blows away cool, outer
layers of the star
Stage 2: formation of the planetary nebula
• UV light from hot, inner layers of the star excites the
cool gas and reveals the planetary nebula
Stage 3: fading away
• After a few 104 years, the shell is too large to be
illuminated by the star remnant, the planetary nebula
cools and fades away
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Planetary nebulae
Planetary nebulae are often asymmetric, possibly
due to:
• Stellar rotation
• Magnetic fields
• Dust disks around the stars
Note: the Sun may form a planetary nebula, but
uncertain (M☉ too small?)
The Butterfly
Nebula
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
What’s left behind: white dwarfs
Electron energy
• If the original star’s mass is less than
about 4 M☉, the core never reaches
temperatures high enough to ignite
fusion reactions using carbon and
oxygen as fuel.
• No more energy production. In the
absence of outward pressure, the star
contracts to a very compact object: a
white dwarf. The contraction
eventually stops because of the
pressure produced the “degenerate
electron pressure”.
• The core remains very hot for a long
time.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
What’s left behind: white dwarfs
• The radius of white dwarf star is about the radius
of Earth. The density of star ~ 106 g/cm3 (i.e. a
teaspoon of material on Earth would weigh the
same as a truck on a white dwarf)
Sirius B
• Mass of white dwarf must be less than 1.4 M☉
(Chandrasekhar limit). Any more massive and the
electron pressure won’t be able to resist the
gravitational collapse (see later...)
• White dwarfs are hot (T~ several 104K) and dim
(L~0.01L☉) and become dimmer as they cool
• Only visible with telescopes (e.g. Sirius B,
companion to bright star Sirius A, discovered
1863)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
Sirius A
PHGN324: Stellar evolution (III)
What’s left behind: white dwarfs
Low luminosity / high
temperature => white dwarfs
are found in the lower center /
left of the H-R diagram.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
Because they are
so small and so
hot, the cooling
can take billions
of years.
PHGN324: Stellar evolution (III)
The Chandrasekhar limit
• The more massive a white dwarf, the smaller it is.
• Pressure becomes larger, until electron degeneracy pressure can no longer hold up
against gravity.
White Dwarfs with more than ~1.4M☉ cannot exist
Chandrasekhar limit
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
A word of the Chandrasekhar limit
• From the differential equation of hydrostatic equilibrium assuming constant
density (which is unrealistic), the central pressure of a white dwarf on mass
MWD and Radius RWD is:
2
"
𝑃A ≈ 𝜋𝐺𝜌" 𝑅89
3
• By equalizing this pressure with the electron degeneracy pressure, one finds:
𝑅89
18𝜋 "
≈
10
"/!
ℏ"
G/!
𝐺𝑚5 𝑀89
𝑍 1
𝐴 𝑚2
6/!
!
• The important aspect of this equation is that 𝑀89 𝑅89
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, hence
𝑀89 𝑉89 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 as well.
à The larger the mass, the smaller the volume of the WD!
This is because the larger mass needs to be supported by a larger electron degeneracy
pressure. In order to achieve this increased pressure, the electrons need to be more
closely packed, hence the lower volume!
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
A word of the Chandrasekhar limit
• Assuming this equation holds, only an infinite mass can reduce the WD to a zero
volume star.
• However, as the electron density increases (r>109 kg.m-3), the velocity of the
confined electrons approach the speed of light due to the Heisenberg uncertainty
principle! Taking into account relativistic effects (which prevents the electron
velocity from reaching the speed of light), the electron degeneracy pressure cannot
be as large as predicted: the white dwarf is therefore smaller than predicted for a
given mass and zero volume is achieved for a finite mass of the white dwarf! That’s
the Chandrasekhar limit.
White Dwarfs with more than
~1.4M☉ cannot exist
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Mass transfer in binary systems
• In a binary system, each star controls a finite region of space, bounded by the Roche
Lobes (or Roche surfaces).
• Lagrange points = points of stability, where matter can remain without being pulled
towards one of the stars.
• Matter can flow over from one star to another through the Inner Lagrange Point L1.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Lagrange points
• The Lagrange points (see derivation) are
positions in an orbital configuration of two
large bodies where a small object affected
only by gravity can maintain a stable
position relative to the two large bodies.
ℓ"
𝑀"
𝑀G
ℓG
Reminder: a, distance M1 – M2
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
• A Lagrange point is a location in space
where the combined gravitational forces of
two large bodies equal the centrifugal
force felt by a much smaller third body.
• L1 plays a central role in close binary
systems. Distances from M1 and M2 to L1:
ℓG = 𝑎 0.500 − 0.227 logGO
𝑀"
𝑀G
ℓ" = 𝑎 0.500 + 0.227 logGO
𝑀"
𝑀G
PHGN324: Stellar evolution (III)
Exercise
Consider two stars (M1=10M☉ and M2=1M☉) separated by a=1AU. Calculate
the location of the inner Lagrange point L1 from the two stars.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
“Recycled” star evolution
• Binary stars are not identical, so their evolution
is not synchronized
• Depending on their proximity, mass transfer
between partners is possible, and this can
significantly alter the stars masses and affect
their stellar evolution.
• When the binary system is comprised of a
white dwarf (or a neutron star) and a giant,
nova explosions can occur if the hydrogen from
the giant’s outer layers can accrete on the white
dwarf (or neutron star)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
X-ray binaries
• Binary consisting of WD + MS or Red
Giant star => WD accretes matter
from the companion
X-ray
emission
• Angular momentum conservation =>
accreted matter forms a disk, called
accretion disk
• Matter in the accretion disk heats up
to ~1 million K => X-ray emission =>
“X-ray binary”
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
T ~ 106 K
PHGN324: Stellar evolution (III)
Nova explosions
• Hydrogen accreted through the accretion disk accumulates on the surface of the
WD, forming a very hot and dense layer of non-fusing hydrogen on the WD surface.
• Explosive onset of H fusion leads to a nova explosion. In many cases, the mass
transfer cycle resumes after a nova explosion → Cycle of repeating explosions every
few years to decades.
Evidence of multiple nova explosions
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The fate of high mass stars
• Unlike low mass stars, fusion continues after Helium exhausted, because
higher mass means higher temperature and pressure at stellar core
• Gravitational collapse contracts the core further and the temperature
soars to 600 million K, hot enough for carbon “burning” to ignite - fusion
with carbon as fuel
• Several nuclear reactions possible:
– 12C + 12C à 20Ne + 4He
– 12C + 12C à 24Mg + g
– 12C + 12C à 16O + 4He + 4He
• Eventually all carbon fuel is exhausted. Core collapses and “carbon shell
burning” ignites
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The fate of high mass stars
• If M > 9M☉, the gravitational collapse induces temperature in the core in excess of
109 K. As the temperature increases, more nuclear fusion reaction channels open
up leading to many different paths to produce heavier elements.
• T > 109 K: Neon burning
– 20Ne + 4He à 24Mg + g
– 20Ne + g à 16O + 4He
– Production of more O, Mg in core
Fusion limit (as a source of energy)
• T > 1.5 x 109 K: Oxygen burning
– 16O + 16O à 32S + g
– More reactions leads to Mg, S, P in the core
• T > 3 x 109 K: Silicon burning
– Hundreds of reactions leading up to Fe / Ni after which fusion reactions are
no longer exothermic.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The fate of high mass stars
• Each new stage leads to a smaller, denser and hotter core. The origin of the
“onion layer” of supergiant stars
• What happens when fusion reactions are no longer exothermic? Core collapse
~ 250 ms!
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Supernovae!
• Final stages of fusion in high-mass
stars (> 8-9 M☉), leading to the
formation of an iron core, happen
extremely rapidly: Si burning lasts
only for ~1 day
• Iron core ultimately collapses,
triggering an explosion that
destroys the star – Supernova
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Supernova – Type II
• The Iron core is likely more massive than the Chandrasekhar limit (1.4 M☉).
• Therefore the electron pressure cannot balance the gravitational collapse, which
occurs extremely quickly. Within 1/10th of a second, the collapse causes temperature
to soar to 5x109 K!
• In the core, the trapped g-rays break up Fe nuclei into He nuclei (photodisintegration)
first, then even the He nuclei break apart. Eventually, the electrons and protons are
forced together to produce neutrons and neutrinos (e- + p à n + n - neutronization).
• Within a fraction of a second, the core density reaches nuclear density - 4 x 1014 g /
cm3 (= density inside nuclei) and can’t be compressed any more because nuclear
matter is uncompressible.
• The inner regions of the star falling towards the core and the core itself bounce off,
generating relativistic outward shock waves blowing the star apart
• The remaining nuclear density core is generally a neutron star, which in extreme case
can collapse further into a blackhole.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Exercise
• The mass of the proton is mp=1.673 x 10-27 kg. Assuming that the proton is a
sphere of radius rp=1.2 fm. Deduce the density of nuclear matter.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
SN1987A
• Ring due to SN ejecta
catching up with pre-SN
stellar wind; also
observable in X-rays
Unusual type II Supernova in the Large Magellanic Cloud in Feb. 1987
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
The story of the star behind SN1987a
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
SN1987A neutrinos
• Eighteen hours before SN 1987A was first seen at optical wavelengths, detectors on
Earth recorded neutrinos arriving from the direction of the supernova. The burst
dramatically exceeded the background of low-energy sporadic neutrinos normally
detected. Neutrinos are believed to play an important role in the dynamics of
supernovae.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Observation of supernovae
• During explosion, the star
luminosity can increase 108
times (20 magnitudes)
• The SN can be as bright as
an entire (small) galaxy
• Supernovae can easily be seen even in distant galaxies.
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Supernova Remnant (SNR)
• We may not be able to see the dense
core of the star that underwent
supernova
• However, the exploding outer layers
travelling at supersonic speeds may
collide with interstellar matter
causing gas there to glow
• Another type of nebula
Crab Nebula
SNR
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Supernova – Type I
• Recall binary systems comprising a
white dwarf and a red giant. What if the
accreting H brings the mass of the white
dwarf above the Chandrasekhar limit?
• The accreting H causes the white dwarf
to contract and kickstart C and O fusions
leading to another kind of supernova
(type I). SN I are generally brighter (they
have C and O fuel available in the white
dwarf) and have a different light curve.
• Nothing survives a Type I SN (e.g. no
neutron star)
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Type I and II supernovae light curves
Type II are usually about 2 magnitudes fainter than Type I supernovae
Core collapse of a massive
star: Type II Supernova
Accreting WD exceeding
the Chandrasekhar mass
limit: Type I Supernova.
Spectral differences:
• Type I: no hydrogen lines in the spectrum (WD – mostly C, O core)
• Type II: hydrogen lines in the spectrum
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Numerical simulations of supernova explosion
• The details of supernova explosions are highly
complex and not quite understood yet.
• Role of neutrinos?
• …
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Cosmic-ray acceleration in supernova shocks
• The shocks of supernova
remnants accelerate protons
and electrons to extremely
high, relativistic energies à
Cosmic Rays
• Also, in magnetic fields, the
relativistic electrons emit
synchrotron radiation, which
can be observed
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Stellar nucleosynthesis
• Landmark “B2FH” paper from
1957
• Paper suggests (correctly) that
the stars are responsible for
the nucleosynthesis of most
chemical elements beyond
Boron (Z=5) or so.
Produced in stars
• Measured abundance
of the chemical
elements on Earth
Production of heavier elements?
Fusion limit
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
PHGN324: Stellar evolution (III)
Stellar nucleosynthesis
A=5 & A=8 gaps
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
Fusion limit (as a source of energy)
PHGN324: Stellar evolution (III)
Rapid proton capture:
Explosive Nucleosynthesis
t(p/n)<<t(b+/-)
rp-process: Novae
Rapid neutron capture:
Other candidates: neutron star mergers…
Fred Sarazin ([email protected])
Physics Department, Colorado School of Mines
r-process: Supernovae?
PHGN324: Stellar evolution (III)