I.
Protostar
Stage (Note: color blocks = color of stage on color-coded evol. tracks)
A. Jean's Theory: gravity over pressure; at the critical density,
it predicts mass of initial collapsing gas cloud as a function of temperature
1. critical density = density of cloud at which the "self-gravity"
overcomes its internal pressure and a region in the cloud begins to collapse
together
2. total mass of collapsing region depends on the temperature, for
molecular clouds at ~10 K the mass is sufficient to produce several thousand
stars, consistent with observed galactic star clusters
3. subfragmentation = internal turbulence in the collapsing
region breaks the cloud into smaller collapsing clouds
B. Molecular Clouds reach critical density
1. supernova shock waves or other perturbations initiate collapse
of regions within a molecular cloud
2. free fall collapse of star cluster size mass which then subfragments
several times resulting in several thousand collapsing clouds with individual
stellar masses (from 0.1 to 100 solar masses)
C. protostar stage defined: "free-fall" collapse of an individual
stellar mass
1. stage begins with "free-fall" collapse of individual stellar mass
size clouds
2. stage ends when the "collapse" slows to a "contraction" as pressure
builds up in the core of what is now a self-gravitating ball of gas
3. this discussion has neglected certain details such as the dissociation
of the hydrogen molecules and the effects of magnetic fields on the collapsing
material
3. polar outflow (bipolar jetting) begins; the high spin rate and
almost totally convective nature of the central pre-MS star produces strong
magneto-hydrodynamical (MHD) effects on the material spiraling in from
the disk, ejecting it out along the axis of rotation of the star and allowing
the star to transfer some of its initial angular momentum to the disk
4. the jet material sometimes radiates light as it plows into the
surrounding interstellar medium, these glowing blobs of gas were called
Herbig-Haro objects after the astronomers who first catalogued them
1. brown dwarfs are considered to have a range of masses from 2 Mjupiter
< 80 Mjupiter ; however, some extra-solar planets that have
been discovered have masses in excess of 2 Mjupiter and are
not considered brown dwarfs; while the difference between brown dwarf and
super-planet is "fuzzy", perhaps we could say that brown dwarfs form at
the center of a proplyd and a super-planet forms in the disk itself around
a central body
2. in any case, the brown dwarf never initiates sustained nuclear fusion
in its core
C. stellar disruption? (> 100 Msun)
1. a pre-MS star with mass greater than ~100 solar masses is though to
initiate an extremely rapid, runaway fusion ignition of hydrogen in core
as it reaches the main-sequence stage
2. this hydrogen ignition is the equivalent of a gigantic hydrogen bomb
explosion which is thought to completely disrupt the star leaving nothing
behind (note: this is NOT a supernova explosion)
3. stellar disruption has never been observed and may be an extremely
rare or even non-existent event, it may be that unknown mechanisms could
limit the maximum size of collapsing gas clouds such that individual collapsing
gas clouds of the required size may never occur
You Tube video showing the range of star (and planet) sizes. Brown Dwarfs
could actually be smaller in diameter than Jupiter and White Dwarfs are about
the size of the Earth. Neutron Stars are only the size of a medium sized
asteroid (~10 km diam) and of course Black Holes are singularities (a "point" -
zero diameter) of infinite density, but the event horizon surrounding it would
be approximately 10 km in diameter or less.
a. hydrogen depleted in the core from the center out, produces a
"smooth" transition to shell "burning" of hydrogen at the end of the MS
stage
b. hot corona due to surface convection and resulting strong magnetic
"heat-pump" effect
B. high mass stars (hotter than ~F0)
1. CNO cycle (H to He); hydrogen fusion reaction which uses carbon, nitrogen
& oxygen as catalysis
2. convective core, radiative surface
a. H depleted evenly over entire core region, produces a "discontinuous"
transition to shell "burning" of hydrogen at the end of the MS stage; entire
core ceases hydrogen fusion before the star restructures itself and a thin
shell of hydrogen fusion begins
b. cool corona heated only by radiation from surface, no surface magnetic
effects to heat the corona
A. H to
He fusion moves to shell around H depleted core (He core)
1. low mass: smooth transition to thick H burning shell due to radiative
core of low mass stars; core H is depleted from the very center outward
so that H to He burning ceases first in the very center of the star and
the H depleted core (He core) slowly grows from the center leaving a thick
H to He burning shell
a. apparently larger core causes outer envelope to expand increasing
the surface area (less power per unit area at surface), surface temperature
cools and the star reddens
b. thick H to He shell quickly begins to produce as much power as
core H to He stage so star moves towards the right (cooler surface temperatures)
on the HR diagram without changing its luminosity by much
c. He core evolution becomes somewhat independent of outer layers
and the He core begins gravitational contraction, increasing the temperature
of the core and shell which increases the fusion rate in the shell, increasing
total power output; surface expands as total power output increases causing
the power per unit area to remain roughly constant (little change in surface
temperature) while the star moves dramatically upwards (higher luminosity)
on the HR diagram
2. high mass: discontinuous transition to thin H burning shell
due to convective core of high mass stars; core H burning ceases because
the convective nature of the core allows He to build up through out the
entire
core (not just primarily in the center of the core), when the H is
depleted in the entire core the H to He reactions cease and the star readjusts
its structure (pressure verses gravity) until a thin shell of H to He burning
begins just outside the He core
a. apparently larger core causes outer envelope to expand increasing
the surface area (less power per unit area at surface), surface temperature
dramatically cools and the star reddens
b. thin H to He shell at first produces slightly less power
than the core H to He stage so star moves towards the right (cooler surface
temperatures) and slightly lower (less luminosity) on the HR diagram
c. He core evolution becomes somewhat independent of outer layers
and the He core begins gravitational contraction, increasing the temperature
of the core and shell which increases the fusion rate in the shell, increasing
total power output; surface expands as total power output increases causing
the power per unit area to remain roughly constant (little change in surface
temperature) while the star moves upwards (higher luminosity) on the HR
diagram
B.
He core ignition (triple alpha process - He to Carbon)
1. low mass: He flash - He burning begins simultaneously throughout
entire core due to the isothermal nature of the degenerate electron gas
a. before He ignition, the core continues to contract until electrons
in the plasma are approximately as densely packed as electrons in an atom,
at this point a quantum mechanical effect called degeneracy pressure
becomes
a major component of the pressure in the star's core
b. electron degeneracy pressure: quantum mechanical effect
caused by the Pauli Exclusion Principle which states that no two electrons
can occupy exactly the same state: see page 457, The Cosmic Perspective,
Bennet, Donahue, Schneider, Voit (intro. astronomy textbook) [When the
"electron gas" in the core of a low mass star compresses to the same "number
density" of electrons as is found in an atomic nucleus - the Pauli Exclusion
Principle predicts (and of course we observe this to be true) that the electrons
will resist getting closer together and a quantum mechanical pressure results
called "electron degeneracy pressure".] Note: the Pauli Exclusion
Principle pertains to certain other particles such as neutrons; such that there
can be a "neutron degeneracy pressure" when neutrons are compacted to the same
density as in an atomic nucleus - see neutron stars below.
c. selected characteristics of degeneracy pressure: does not
depend on temperature of the gas as does regular "thermodynamic" pressure,
gas takes on characteristics of a "metal" such as incompressibility (takes
enormous pressures to compress the degenerate gas, the core behaves somewhat
like a hard sphere made of metal) and high thermal conduction (temperature
is "isothermal" throughout the degenerate gas)
2. high mass: smooth transition, radiation pressure prevents degenerate
electron gas in the core and He ignition begins at the very center of the
core and slowly spreads outward
C. post
He core ignition, surface temperature increases and star "moves" toward
the blue side of the HR diagram
1. low mass: rapid evolution toward blue side of HR diagram
with decreased luminosity; post He flash evolution is difficult to model
due to the rapid changes brought on by the He flash, therefore the resulting
luminosity and surface temperature is uncertain... stars with small heavy
element abundance's are thought to end up on the horizontal branch
- stars on the HB have a large range of colors, but an average luminosity
about 50 times greater than the Sun
2. high mass: rapid evolution toward blue side of HR diagram
with a slight decrease in luminosity begins a "blue loop" in the evolutionary
tracks of high mass stars
D. blue edge of the HB or
"loop": for both low and high mass stars, the core He fusion increases
after He ignition and the H shell fusion decreases - this results in a
slow increase in luminosity and a relatively stable surface temperature
defining the blue edge of the HB (low mass) or "blue loop" (high mass)
A. during the core He burning HR Diagram "loop" the star passes through
the "instability strip"
1. pulsation is driven by a "feed-back mechanism" in the He envelope
where ionization of the He envelope increases the opacity in that region
making the He envelope act like a "shutter" which traps the outgoing energy
from the core (increasing pressure) causing the star to expand, as the
star expands outward the temperature in the He envelope drops allowing
the gas to become neutral or "un-ionized" again, releasing the energy (lowering
the pressure) and allowing the star to contract; this mechanism "pumps"
the star once per pulsation cycle allowing the amplitude of the pulsation
to build up until dissipative forces limit the amplitude
2. the "instability strip" is the region in the HR Diagram where
the He envelope is at the correct depth in the structure of a He burning
star to drive stellar pulsation; for a given luminosity there is a range
of surface temperatures where the He envelope is at the correct depth to
drive stellar pulsation by the above mechanism, mapped out on the HR Diagram
the region is a narrow strip running roughly vertically through the region
of the diagram where core He burning is taking place in stars
a. for low mass stars where the Horizontal Branch runs through the
"instability strip" the pulsating stars are called: RR Lyrae stars
b. for high mass stars where the Blue Loop runs through the "instability
strip" the pulsating stars are called: Cepheid variable stars
C. during the AGB stage (see VI & VII below) unstable shell sources
may also drive periodic, semi-periodic, or irregular pulsation
VI.
Asymptotic
Giant Branch (2nd RG Stage) (this stage is mostly defined for low mass
stars and to a lesser extent those high mass stars which start off on the
MS with less than 8 solar masses and end their lives as white dwarfs)
A. He to C fusion moves to shell around He depleted core (low & high
mass stars)
1. apparently larger core causes outer envelope to expand increasing
the surface area (less power per unit area at surface), surface temperature
cools and the star reddens moving the star out of the "instability strip"
2. as in the first shell source, the (in this case C) core evolution
becomes somewhat independent of outer layers and the C core begins gravitational
contraction, increasing the temperature of the core and shell which increases
the fusion rate in the shell, increasing total power output; surface expands
as total power output increases causing the power per unit area to remain
roughly constant (little change in surface temperature) while the star
moves dramatically upwards (higher luminosity) on the HR diagram
3. luminosity becomes greater than 1st RG stage, star expands to
tremendous radius (~1.5 - 10 AU) (note: a 10 AU radius star's surface would
extend out to Saturn's orbit if it where located in our solar system)
a. most of stellar mass of these expanded stars are still concentrated
near their core, which means their surface gravity is very weak and results
in a very low escape velocity at their surface
b. due to the low surface gravity these stars lose mass readily in
intense stellar winds which cause significant mass loss (especially for
high mass stars); this causes some higher mass stars to follow the same
latter stages of evolution as a low mass star, becoming PN stars and then
terminating as white dwarfs rather than exploding as a supernova (stars
on the MS with less than 8 solar masses)
c. the "slow" neutron capture process (s process - reactions that
take place slower than beta decay) results in small amounts of elements
heavier than iron and lighter than uranium being produced during a star's
AGB stage, these elements can be "dredged up" by convection and blown out
into the interstellar medium by the intense stellar winds described above
B. massive stars
may undergo several "blue loops" as core fusion of successively heavier
elements occurs
1. the main fusion reactions advance through the process of "alpha
capture" (since an alpha particle is the same thing as a helium nucleus,
this is sometimes referred to as "helium capture"): stellar
nucleosynthesis produces all of the elements heavier than He
2. for very massive stars several "blue loops" can occur as core
fusion of successively heavier elements left over from previous stages
occurs: carbon (C) to oxygen (O) & neon (Ne), and so on all the
way up to iron (Fe)
a. the final internal structure of a massive star has several fusion
shells: H -> He, He -> C, C -> O,O -> Ne,
Ne -> Si, Si -> Fe, with an Fe core; all these layers are
near the core where most of the mass of the star resides, outside the H
-> He shell source is an extended envelope of H of tremendous radius;
this layered structure is known as the "onion skin" model
b. the Fe in the core takes more energy to fuse than the fusion reaction
gives off, becoming an energy sink (absorbs energy) and allowing the pressure
to drop causing the core of the star to collapse which initiates a supernova
explosion (see transition stage below)
1. near the end of the AGB stage, shell sources "flicker" and die
as they gradually burn outward into less dense and lower temperature regions,
when the shell source "goes out" the star readjusts (contracts) and the
shell source can reignite re-establishing the pressure and causing a pulsation
of the star
a. these pulsation (sometimes called "thermal pulses") can gently
(non-explosively) eject large portions or even the entire outer envelope
of the star at the end of its life
b. at this point, energy production ends in the mostly carbon core
which is now supported by electron degeneracy pressure (no nuclear reactions
to produce pressure means the core contracts until the electrons are close
enough together for electron degeneracy pressure to arise); note:
the core must be less than 1.4 solar masses for electron degenerate pressure
to support the core against collapse; 1.4 solar masses is the mass of a
self-gravitating ball of electron degenerate gas at which the radius of
the ball of gas goes to zero, ie: electron degeneracy pressure fails
to support the gas against gravitational collapse, 1.4 solar masses is
called the Chandrasekhar limit for the astrophysicist who calculated this
limit
c. extremely hot surface of core revealed as outer layers expand
away and the star rapidly evolves toward the blue side of the HR Diagram
a. hot core (now called the planetary nebula central star) emits
UV photons which ionize the expanding shell of gas which becomes luminous
and is called a planetary nebula
b. this expanding shell of gas is "pinched off" at the waist by pre-existing
material in a disk around the star (some of this material results from
previous intense stellar winds from the star); this results in an "hour-glass"
or "dumb-bell" shape for the nebula; if seen from the side PNs have this
bi-lobed structure, but if viewed down the long axis they look like a ring
or helix of glowing gas
3. Type Ia supernova (binary star, explosion
powered by nuclear energy)
a. carbon-oxygen white dwarf (see VIII below) with red giant companion
b. mass transfer to white dwarf initiates catastrophic carbon "burning"
as the carbon core reaches 1.4 solar masses and collapses (ie: stellar
size fusion bomb) - total disruption of star, no neutron star left behind
B.
high mass stars (core mass greater than 1.4 solar masses = Chandrasekhar
limit)
1.
Type
II supernova (single star, explosion powered by gravitational collapse)
a. due to the endothermic nature of Fe fusion (takes more energy
than the fusion releases) and photodisintegration of Fe (100 MeV gamma
ray photons are absorbed by Fe nuclei which then disintegrate into many
He nuclei and neutrons - a process which also is very endothermic) no pressure
is generated in the core and it collapses from the weight of the overlying
layers, slowed only briefly by electron degeneracy pressure that is quickly
overcome by the collapsing weight
b. as the electrons and nuclei are compressed even further, the electrons
react with the protons to produce neutrons and neutrinos in a process called
inverse beta decay; as the neutrons get squeezed closer together, they
(like electrons) obey the Pauli Exclusion Principle and a quantum mechanical
pressure called neutron degeneracy pressurebegins which halts the
collapse of the core
c. the neutron degenerate core behaves like a "perfect metal" and
cannot be compressed further by the infalling layers of the star which
creates an intense shock wave which propagates back outward through the
infalling layers of the star; this is known as the "core bounce"
d. the neutrinos from inverse beta decay are able to deposit vast
amounts of energy into the extremely dense material below the shock wave,
heating the material and causing intense convection which sustains the
shock wave allowing it to eject the outer layers from the star; the shock
wave heats and compress these layers as it passes through them causing
"rapid" neutron capture processes (r process - reactions that take place
faster than beta decay) producing those rare elements heavier than uranium
2. Type
Ib supernova (single star, powered by gravitation)
a. outer H envelope lost by intense stellar wind (Wolf-Rayet star)
b. same mechanism as Type II SN, but no H in spectra
1. as the Planetary Nebula dissipates, the PN central star which
is the left-over hot, but very small core held up by
electron degeneracy
pressure (no nuclear reactions) ends up on the lower left region of the
HR Diagram: faint but hot; this terminal state of a low mass star
is called a White Dwarf star; note: a White Dwarf star contains about
a solar mass of matter compressed into a ball the size of the Earth, a
million times more dense than a regular star
2. Black Dwarf? (white dwarf after much cooling, takes longer than
the present age of the universe)
3. Type Ia SN result in total disruption of the star
1. after a type II supernova explosion the surviving core of neutrons
held up by neutron degeneracy pressure
is called a Neutron Star; this ball
of neutrons is as dense as an atomic nucleus and in fact can be described
as a giant nucleus made up entirely of neutrons, typically there is more
than 1.4 solar masses compressed into the size of an asteroid (~10 km in
diameter) approximately 2 billion times more dense than a White Dwarf star
a. the neutron star has an intense magnetic field caused by "compression"
of any pre-existing stellar magnetic field
b. the neutron star is expected to have a very high rotation rate
caused by conservation of angular momentum as the mass of the rotating
precursor star is compressed into the neutron star
c. the high rotation rate and the intense magnetic field combine
to produce beams of electromagnetic energy which rotate around with the
spinning neutron star like light-house beams; if radio telescopes on Earth
can detect the radio pulses as the beam sweeps over the Earth, the spinning
neutron star is called a pulsar
2. Black Hole?
a. a collapsing core mass greater than 2.5 - 3.0 solar masses may
overcome even the neutron degeneracy pressure?
b. as far as we know, nothing can halt the collapse after it overcomes
the neutron degeneracy pressure and the core collapses to a point of infinite
density called a singularity
c. event horizon: radius from singularity where escape velocity =
c (c = speed of light = 3 x 108 m/s ); by Einstein's Theory
of Relativity, nothing can exceed the speed of light in a vacuum, so we
have no information about the condition inside the event horizon; note:
many movies and TV programs depict a black hole as "sucking" everything
near it down into its singularity, however, while there are relativistic
effects close to the event horizon, most objects outside the event horizon
would orbit or continue the same trajectory they would have around any
object of the black hole mass whether it was a black hole or not, it is
only if an object approaches closer than the event horizon that it would
never return; Comment: Dr. Jones actually knows someone who has fallen
into a black hole, click here for details!
d. stellar size black holes can be detected by the gravitational
effects on an accretion disk if the black hole is accompanied by a companion
star; eg: bipolar jets, high energy radiation as material is heated
by tidal forces as it approaches the event horizon, etc
(Note: color blocks = color of stage on color-coded evol. tracks)
(this stage is mostly defined for low mass
stars and to a lesser extent those high mass stars which start off on the
MS with less than 8 solar masses and end their lives as white dwarfs)
