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The Evolution and Death of Stars



Main idea: As stars age they gradually exhaust the nuclear fuel in their Nuclear Burning Cores
$\rightarrow$ amount of Energy ($E$) generated in core changes with time
$\rightarrow$stellar structure changes with time $\rightarrow$ stellar evolution
Stellar Evolution: change in stellar structure with time due to change in rate of $E$ generation inside star



How a star evolves depends on its Mass ($M$)
($M_{\rm Sun}$ = Mass of the Sun = $2 \times 10^{30}$ kilograms (Kg))
- Low Mass stars: $M < 0.4 M_{\rm Sun}$
- Intermediate Mass Stars: $0.4 < M < 11 < M_{\rm Sun}$ (so, the Sun is an Intermediate Mass star)
- High Mass stars: $M > 11 M_{\rm Sun}$



Note: Two important ideas for understanding stellar evolution:



Idea 1: Structure of star divided into two main parts:
A) Core: the Nuclear Burning Core where the nuclear fusion reactions and Energy ($E$) generation take place
- Significance: rate of $E$ generation in core determines star's structure
$\rightarrow$ exhaustion of nuclear fuel in core drives star's evolution
B) Envelope: the rest of the star -ie. the thick layers of gas around the core
- Significance: the state of the envelope determines the outward appearance of the star
$\rightarrow$ the Temperature ($T$) & Radius ($R$) of the envelope determine the star's color and Luminosity ($L$)
$\rightarrow$ determines the star's position in the Hertzsprung-Russell (H-R) diagram



Idea 2: Hydrostatic Equilibrium
- stars are always caught in the middle of a tug-of-war between two opposing forces:
Gravity: force pushing layers of stars inward toward center of star
- if Gravity were unchecked star would collapse in on itself under its own weight
Gas Pressure: force pushing layers of stars outward away from center of star
- Gas Pressure holds star up against gravity
- force of Gas Pressure depends on gas Temperature ($T$) - from Gas Law ( $P=\rho \times T$)
$\rightarrow$ Gas Pressure depends on an Energy ($E$) source heating the gas ($E$ source is nuclear fusion)
So: as long as Gravity and Gas Pressure are balanced, star is stable
$\rightarrow$ if rate of $E$ generation in star changes $\rightarrow$ Gas Pressure changes $\rightarrow$ stellar structure changes



Main Sequence (MS) life-time ($\tau$): time taken to exhaust Hydrogen (H) in Nuclear Burning Core
Most of a star's total life-time (about 90%) is spent on MS (ie. $\tau$ is 90% of total stellar life-time)
$\tau$ depends on Mass ($M$) of star:
- $M = 40 M_{\rm Sun} \rightarrow \tau= 1$ million years
- $M = 0.5 M_{\rm Sun} \rightarrow \tau= 56$ billion years
$\rightarrow$ More massive stars evolve more quickly than less massive stars



What happens when Hydrogen (H) in core is exhausted?



1) Intermediate Mass Stars ( $0.4 < M < 11 M_{\rm Sun}$):



General rule for Intermediate and High Mass Stars: As star evolves, stellar core and stellar envelope behave in opposite ways
ie. if core contracts and heats up $\rightarrow$ envelope expands and cools down
ie. if core expands and cools down $\rightarrow$ envelope contracts and heats up



By the time star reaches end of MS life-time ($\tau$):
- Nuclear Burning Core has been converted from Hydrogen (H) to Helium (He)
- star has He core



Changes in stellar core and envelope driven by exhaustion of nuclear fuel in core
- when all the H is fused to He, H fusion reaction stops
$\rightarrow$ heat source in core disappears $\rightarrow$ core Temperature ($T$) decreases
$\rightarrow$ core Gas Pressure ($P$) decreases (from Gas Law)
$\rightarrow$ core contracts under force of gravity (Hydrostatic Equilibrium)
$\rightarrow$ gas density ($\rho$) in core increases as core is compressed by gravity
$\rightarrow$ core Temperature $T$ increases (Gas Law)
$\rightarrow$ inner layers of envelope become hot enough to ignite H fusion
$\rightarrow$ Energy ($E$) generated by H fusion in a ``shell'' (Nuclear Burning Shell) around exhausted He core
ie. inner layers of envelope become part of Nuclear Burning Core



Also:
$\rightarrow$ H fusion reaction rate in shell is very fast due to higher $T$ in central region of star (see Stellar Structure chapter)
$\rightarrow$ rate of energy ($E$) generation in central region increases, becomes larger than rate of Main Sequence (MS) star
$\rightarrow$ envelope of star expands to increase star's Luminosity ($L$) (Conservation of Energy) (remember $L=R^2T^4$)
$\rightarrow$ Gas Pressure ($P$) in envelope decreases
$\rightarrow$ Temperature ($T$) of envelope decreases (Gas Law)
Note: agrees with General Rule above: contraction and heating of core leads to expansion and cooling of envelope



How does star's appearance change?


Star's Luminosity ($L$) has increased $\rightarrow$ star moves upward in H-R diagram to position above Main Sequence (MS)
AND: Star's envelope temperature ($T$) has decreased $\rightarrow$ star moves to the right of the MS in H-R diagram
$\rightarrow$ Star moves to upper right corner of H-R diagram $\rightarrow$ Star becomes a Red Giant (Luminosity Class III) star (see Stellar Properties chapter)
Reality check:
- star's envelope $T$ is reduced $\rightarrow$ cooler stars have redder color (from Black-body radiation law)
- star's envelope has expanded $\rightarrow$ star's Radius ($R$) is larger than $R$ of a MS star
$\rightarrow$ star has properties of a Red Giant



What happens next?



Nuclear Burning Core has no energy source
- core continues to contract and heat up
- eventually $T$ in core reaches $100$ million $^\circ$ K
$\rightarrow$He fusion reactions start (nuclear He burning ignited)
He fusion: 3He $\rightarrow$ Carbon (C) + Energy ($E$) - converts 3 Helium (He) nuclei into 1 Carbon (C) nucleus
- requires higher $T$ than H fusion $\rightarrow$ He fusion does not occur until He exhausted core contracts and heats up
He fusion provides new source of $E$ generation in core (ie. star has found a new ``fuel supply'')



Ignition of He fusion in core causes star to evolve in reverse - ie. changes that occurred when H was exhausted in core are reversed:
$\rightarrow$ Core gas pressure ($P$) increases due to new $E$ source in core
$\rightarrow$ core expands (Hydrostatic Equilibrium)
$\rightarrow$ core temperature ($T$) decreases (but not enough to stop He fusion!) (Gas Law)
$\rightarrow$ He fusion reaction rate in core and H fusion reaction rate in shell decrease
$\rightarrow$ Energy ($E$) generation rate decreases
$\rightarrow$ Envelope contracts to reduce star's Luminosity ($L$) (Conservation of Energy) (remember $L=R^2T^4$)
$\rightarrow$ Gas Pressure ($P$) in envelope increases
$\rightarrow$ envelope temperature ($T$) increases (Gas Law)
(remember rule about core and envelope behaving in opposite ways)



So: star moves to the left and downward in H-R Diagram (but it does NOT move all the way back to the MS!)
$\rightarrow$ star becomes a Horizontal Branch star - ie. an orange, yellow, or blue sub-Giant (Luminosity Class IV) or Giant (Luminosity Class III) star
Horizontal Branch (HB) stars: stars that get their Energy ($E$) from the nuclear fusion of Helium (He) in their Nuclear Burning Cores
- the Horizontal Branch (HB) is parallel to the Main Sequence (MS) in H-R diagram AND lies above the MS (ie. at higher $L$ than MS)
- the HB consists of sub-Giant and Giant stars; hottest HB stars are blue & coolest HB stars are orange
- these stars may also still have H fusion occurring in a shell around the He fusion core



What happens when the core Helium (He) is exhausted?



Star evolves the same way it did after H exhaustion:



When He supply in core is exhausted:
- He fusion reaction stops $\rightarrow$ core Temperature decreases
$\rightarrow$ core Gas Pressure decreases (from Gas Law)
$\rightarrow$ core contracts and heats up AND envelope expands and cools
$\rightarrow$ star becomes a Red Giant again (an ``Asymptotic Giant Branch star'')
- see discussion of evolution after H exhaustion above for explanation



Stellar Mass-loss: each time High Mass star exhausts nuclear fuel supply in Nuclear Burning Core it becomes a Red Giant:
- star's envelope expands by a large amount
- extended envelope is only weakly attached to core by gravity
- some gas in envelope is ejected from star by pressure of radiation emitted by star (radiation pressure)
$\rightarrow$ radiation pressure drives a stellar wind whenever star becomes a Red Giant
$\rightarrow$ star loses some mass every time it becomes a Red Giant



Note: He burning life-time = time between ignition of He fusion and He exhaustion in core
- He burning life-time is much smaller than H burning life-time
- during H fusion, every 4 H nuclei produce only 1 He nucleus
$\rightarrow$ He nuclei exhausted more quickly that H nuclei



After core He exhaustion: Nuclear burning Core contracts and heats up
BUT: Core temperature ($T$) never reaches $600 000 000^\circ$ K $\rightarrow$ core never hot enough to ignite Carbon (C) fusion



Nuclear Burning Core continues to contract and heat up
$\rightarrow$ star's envelope continues to expand and cool down
- Envelope eventually expands until it becomes detached from core
$\rightarrow$ envelope gently ejected from core by radiation pressure
$\rightarrow$ envelope ejected in form of a stellar wind
$\rightarrow$ leads to shell (or bubble) of gas expanding into space around core



Stellar Wind: gentle flow of gas away from a star in all directions
- also called stellar Mass Loss



After envelope is ejected - Nuclear Burning Core is exposed
$\rightarrow$ exposed core is very hot $\rightarrow$ produces a fast stellar wind
Fast wind from exposed core collides with expanding envelope
$\rightarrow$ gives rise to complex gas structure, called Planetary Nebula (PN)



Planetary Nebula (PN):



Shell of ejected gas surrounding an exposed Nuclear Burning Core
- produced by Intermediate Mass star that loses its envelope after exhaustion of Helium (He) in Nuclear Burning Core
- ``Planetary Nebula'' is a misnomer - have nothing to do with planets - famous examples: Ring Nebula, Cat's Eye Nebula



PN can have complex shapes if:
- Star that loses envelope is companion in binary star system
- Star that loses envelope has a disk of gas around it



What happens to exposed Nuclear Burning Core?
- no nuclear fuel supply to heat gas $\rightarrow$ no source of gas pressure ($P$) $\rightarrow$ core cannot maintain Hydrostatic Equilibrium
- core contracts until Gas becomes electron ($e^-$) degenerate



Electron ($e^-$) Degenerate Gas: special state of gas when compressed to extremely high density ( $\rho = 3 \times 10^6$ grams/cm$^3$ (15 tons/teaspoon))
- gas has been squeezed to point where electrons ($e^-$) are packed together as closely as they can be
- a degenerate gas cannot be compressed any further - $e^-$'s would interfere with each other (due to Quantum effects (never mind!))
$\rightarrow$ star cannot contract any further
- a degenerate star is supported against the force of gravity (ie. maintains Hydrostatic Equilibrium) by electron ($e^-$) degeneracy pressure
$\rightarrow$ Gas Law does NOT apply to degenerate gas: can increase Gas Temperature ($T$), but Pressure ($P$) and density ($\rho$) do not change because Gas cannot be compressed any more



How does core's appearance change?



Core's Radius ($R$) is smaller than value of $R$ that star's have on Main Sequence (MS)
$\rightarrow$ core's Luminosity ($L$) is smaller than $L$ of MS stars ($L=R^2T^4$ - see Stellar Properties chapter)
$\rightarrow$ core is smaller and fainter than MS star of same Temperature ($T$)
$\rightarrow$ core has becomes a Carbon-Oxygen White Dwarf (CO WD)



Carbon-Oxygen White Dwarfs (CO WD):
the exposed Nuclear Burning Core of an Intermediate Mass star ( $0.4 < M < 11 M_{\rm Sun}$) in which the Hydrogen (H) and Helium (He) have been converted to Carbon (C) and Oxygen (O) by nuclear fusion
- they are electron ($e^-$) degenerate
- composed mostly of Carbon (C) and Oxygen (O) (almost all H and He converted to C and O by fusion)
- WD's gradually cool - gradually shrink and become cooler and redder
- CO WD's often surrounded by Planetary Nebulae (PN) (see above)



2) High Mass Stars ( $M > 11 M_{\rm Sun}$):


High Mass stars go through the first two stages of nuclear burning that Intermediate Mass stars go through:
1) H fusion in Nuclear Burning Core ending with core H exhaustion
- star moves toward low Temperature (red color) side of H-R Diagram (see discussion of High Mass stars above)
2) He fusion in Nuclear Burning Core with H fusion in shell around core, ending in core He exhaustion


However, there are two major differences between how High and Intermediate Mass stars evolve during these two stages:


1) High Mass MS stars have large Luminosity ($L$) - see MS Mass-Luminosity Relation
$\rightarrow$ during H and He exhaustion in Nuclear Burning Core they do NOT become much brighter,
BUT they DO undergo a decrease in surface Temperature and become redder
$\rightarrow$ High Mass stars evolve along horizontal tracks from left to right in H-R diagram
2) Burning of nuclear fuel is much more rapid in High Mass stars than in Intermediate Mass stars (see MS Mass-Luminosity relation)
$\rightarrow$ High Mass stars pass through evolutionary stages much more rapidly ($\approx$100000's years instead of $\approx$ 100000000's years)
$\rightarrow$ High Mass stars finish He burning in Nuclear Burning Core while still evolving toward the Red Giant part of H-R diagram
$\rightarrow$ High Mass stars do NOT become Horizontal Bransh stars


What happens when the core Helium (He) is exhausted?


When Temperature ($T$) of contracting Core reaches $600 000 000^\circ$ K $\rightarrow$ ignition of Carbon (C) fusion in core
C fusion: C (6 protons ($p$)) $\rightarrow$ Magnesium (Mg, 12 $p$), Neon (Ne, 10 $p$), Oxygen (O, 8 $p$) + Energy ($E$)
- C is available in core because it was produced by He fusion (see above)
$\rightarrow$ ignition of C fusion causes core to expand and cool AND envelope to contract and heat up
- star becomes slightly less luminous and bluer again - becomes a yellow or blue Giant
- see discussion of evolution after H exhaustion above for explanation
He fusion continues in lower temperature shell around C burning core (see H shell fusion discussion above)
H fusion continues in even lower temperature shell around He burning shell


Final stages of High Mass Star's evolution:


Pattern of exhausting one supply of nuclear fuel then igniting another fuel supply is repeated several more times with heavier and heavier elements:



After Carbon (C) is exhausted in core:
- core contracts and heats up
$\rightarrow$ core $T$ becomes high enough to ignite fusion of Magnesium (Mg), Neon (Ne) & Oxygen (O)
- Mg, Ne, and O were produced in core by C fusion (see above)
Fusion reaction: Mg, Ne, and O $\rightarrow$ Silicon (Si, 14 protons ($p$)) & Sulfur (S, 16 $p$) + Energy ($E$)
C fusion continues in lower temperature shell around Mg, Ne & O burning core (see H shell fusion discussion above)
He fusion continues in even lower temperature shell around C burning shell
H fusion continues in even lower temperature shell around He burning shell



Mg, Ne & O fusion gives small amount of Energy ($E$)
$\rightarrow$ reaction rate must be large to generate enough $E$ to support star against gravity (Hydrostatic Equilibrium)
- number of Mg, Ne, and O in nucleus is small - eg. it takes 12 H nuclei to make one Mg nucleus with 12 $p$
$\rightarrow$ Mg, Ne & O fusion only lasts six months before Mg, Ne, and O are exhausted (remember: H fusion lasts millions of years in High Mass stars)
Generally: Stellar evolution speeds up as heavier nuclear fuels burned



After Mg, Ne and O are exhausted in core:
- core contracts & heats up
$\rightarrow$ core $T$ becomes high enough to ignite Silicon (Si) fusion
Fusion reaction: Si $\rightarrow$ Iron (Fe, 26 $p$) + Energy ($E$)
Mg, Ne & O fusion, C fusion, He fusion, and H fusion continue in progressively cooler shells around Si burning core
$\rightarrow$ stellar interior has ``onion'' structure - concentric spherical layers each supporting nuclear fusion of a different element
- Si fusion lasts one day before core Si is exhausted



After Silicon (Si) is exhausted in core:
- Nuclear Burning Core now converted entirely to Iron (Fe)
- Core contracts & heats up
Problem: Iron (Fe) is most stable element in Universe $\rightarrow$ Cannot fuse Fe to get Energy ($E$)
$\rightarrow$ No more nuclear fuel!
$\rightarrow$ No new source of Energy ($E$) to heat gas $\rightarrow$ No new source of Gas Pressure ($P$) to oppose Gravity




Core continues to contract $\rightarrow$ gas density ($\rho$) increases to very high values
- density ($\rho$) reaches high enough value for nuclear fission of Fe to start in core
- Nuclear Fission: larger nuclei breaking up into smaller nuclei - ie. opposite of nuclear fusion
- fission of Iron (Fe) absorbs Energy ($E$) (whereas fusion produces energy)
- Iron (Fe) fission reaction: Fe + $\gamma$ rays + electrons ($e^-$) + Energy ($E$) $\rightarrow$ smaller nuclei + neutrinos ($\nu$)



Fe fission removes Energy ($E$) from Nuclear Burning Core
$\rightarrow$ source of Gas Pressure ($P$) in core disappears
$\rightarrow$ inward force of Gravity suddenly unopposed
$\rightarrow$ Nuclear Burning Core suddenly implodes on itself (``implosion'' is opposite of explosion)
Note: time between Silicon (Si) exhaustion and collapse of core = 1/10 second
Nuclear Burning Core collapses into a Neutron Star OR Black Hole



Iron (Fe) fission in core produces very large number of neutrinos ($\nu$'s)
$\rightarrow$$\nu$'s abruptly heat envelope of star by large amount
$\rightarrow$ envelope violently ejected into space
$\rightarrow$ Type II Supernova (SN II) explosion


Note: Nuclear Burning Core and Envelope suffer opposite fates:
- the core implodes and the envelope explodes



Nuclear reactions in exploding envelope produce a form Nickel (Ni) that is radio-active ($^{56}$Ni = Ni with too many neutrons ($n$))
$\rightarrow$$^{56}$Ni radio-actively decays and heats ejected envelope
$\rightarrow$ ejected material is extremely bright (large Luminosity ($L$)) due to heating by decay of radio-active Ni
$\rightarrow$ Supernovae (SN) are extremely bright
- SN are the brightest astronomical objects known during first month after explosion; brighter than an entire galaxy


Example: SN 1987A in nearby galaxy Large Magellanic Cloud
- distance = $53 000$ parsecs (pc)
- Astronomers detected burst of neutrinos ($\nu$'s) from Fe fission in star's core before visible light from Supernova was detected



Type II Supernova (SN II):



Explosion of envelope of High Mass Star (Mass ($M$) $> 11 M_{\rm Sun}$)
- caused by implosion of Nuclear Burning Core after all elements have been fused into Iron (Fe)



During explosion:
Luminosity ($L$) increases by a factor of a billion
(SN more luminous than entire galaxy)
- takes few months for $L$ to decrease to ``normal'' levels
- ejected envelope has velocity ($v$) = $10 000$'s km/sec - gas ejected into space very rapidly



Type II Supernovae (SN II) leave behind two products:
1) Collapsed Nuclear Burning Core: Neutron Star OR Black Hole
2) Supernova remnant: shell of gas expanding into Interstellar Medium (ISM)



e.g. Crab Nebula - Nebula with diameter = 1.35 parsecs (4 Light Years (LY))
- Expanding with velocity ($v$) of $1400$ km/sec
- there is a Neutron Star near center of nebula
- due to Supernova seen by Chinese in 1054 AD



Cosmic significance of Supernova (SN):


- Universe originally composed of only two lightest elements: Hydrogen (H) & Helium (He)
-Stars are the ``factories'' in which all chemical elements heavier than Helium (He) were created
- there have been several generations of stars that have formed and exploded as SN since Universe was created
- High Mass stars turn H into nuclear products, ie. heavier elements (C, N, O, Mg, Si, S, Fe) produced by nuclear fusion in core
- some nuclear products mixed into star's envelope by convection; ie. envelope ``polluted'' by nuclear fusion products from star's core
- nuclear products ejected into Interstellar Medium (ISM) by Supernova (SN); ie. ISM ``polluted'' by nuclear fusion products of stars
$\rightarrow$ Next generation stars & planets that form from ISM incorporate heavier elements produced by earlier generation
$\rightarrow$ both Stars and Interstellar Medium (ISM) are becoming gradually more enriched in chemical elements heavier than Helium (He)



Intermediate Mass stars only go through the first two stages of nuclear burning that High Mass stars go through:
1) H fusion in Nuclear Burning Core ending with core H exhaustion
- star becomes Red Giant (see discussion of High Mass stars above)
2) He fusion in Nuclear Burning Core with H fusion in shell around core, ending in core He exhaustion
- star becomes a ``Horizontal Branch star'' - a blue, yellow, or orange sub-Giant or Giant (see discussion of High Mass stars above)



Low Mass Stars ( $M < 0.4 M_{\rm Sun}$):



In Low Mass Stars the Nuclear Burning Core and the Envelope change in the same way
(in Intermediate and High Mass stars the Core and Envelope change in opposite ways - see above)
- convection mixes gas throughout entire star (see ``Energy Transport mechanisms'' in Stellar Structure chapter)
- Gas in Nuclear Burning Core is mixed into Envelope
$\rightarrow$ Helium (He) produced my H fusion during Main Sequence (MS) life-time in core is mixed throughout entire star
- Gas in Envelope is mixed into Nuclear Burning Core
$\rightarrow$ Hydrogen (H) throughout entire star can be fused into He in core



So:Entire star (not just core) is converted to Helium during Main Sequence life-time
- due to convective mixing of star



Entire star evolves in the same way that the Nuclear burning Core of Intermediate Mass stars evolves
- as star converted to He by H fusion (4H $\rightarrow$ He) number of nuclei in star decreases
$\rightarrow$ Gas pressure decreases
$\rightarrow$ entire star contracts due to gravity (Hydrostatic Equilibrium)
$\rightarrow$ gas density ($\rho$) increases
$\rightarrow$ Temperature ($T$) increases (Gas Law)



As star contracts and heats up:
- Temperature ($T$) in core never reaches 100 million $^\circ$ K
$\rightarrow$ core $T$ never high enough to ignite Helium (He) fusion - ie. Star never finds another fuel supply after H exhaustion
- star contracts until gas becomes electron ($e^-$) degenerate - see discussion of electron degeneracy under Intermediate Mass Stars above



How does star's appearance change?



Star contracts $\rightarrow$ Radius ($R$) decreases to below value of $R$ on Main Sequence (MS)
- star's Luminosity ($L$) decreases below MS value
$\rightarrow$ star is smaller and fainter than MS star of same Temperature ($T$)
$\rightarrow$ star has becomes a Helium White Dwarf (He WD)



Helium White Dwarfs (He WD): Low Mass stars ( $M < 0.4 M_{\rm Sun}$) that have exhausted Hydrogen (H) throughout entire star and contracted until they are electron ($e^-$) degenerate
- composed mostly of Helium (He) (almost all H converted to He by H fusion)



Evidence for Stellar Evolution from Star Clusters



Star cluster: Association of stars that formed at same time from collapse of same Giant Molecular Cloud (GMC) - see Star Formation chapter
- initially composed of stars of all Masses, Low, Intermediate and High Mass stars - ie. stars with $0.08 M_{\rm Sun} < M < 50 M_{\rm Sun}$
- more massive stars have shorter Main Sequence life-times ($\tau$) than less massive stars
$\rightarrow$ more massive stars in cluster evolve faster than less massive stars



Measure Temperature ($T$) or Color AND Luminosity ($L$) of cluster stars
- plot cluster stars on Hertzsprung-Russell (H-R) Diagram
- Main Sequence is a Mass sequence (see Stellar Properties chapter)
- AND: MS life-time ($\tau$) decreases with increasing Mass ($M$)
$\rightarrow$ for each cluster, pattern of stars on H-R diagram will depend on age of cluster



If cluster very young (age less than 100 million years):
- no stars have had chance to evolve beyond Main Sequence (MS)
$\rightarrow$All stars still on Main Sequence (MS) (OR are still proto-stars approaching Zero Age Main Sequence (ZAMS) - see Star Formation chapter)
If cluster is older: Stars near top of Main Sequence (MS) have become Giants or Supernovae (SN II)



Main Sequence Turn-off:
- point on H-R diagram that can be defined for each star cluster
- point on Main Sequence (MS) where:
-- less massive stars are still on MS
-- more massive stars are no longer on MS
- as star cluster ages, Main Sequence Turn-off moves down MS to lower mass stars as lower mass stars evolve off of MS
$\rightarrow$ location of Main Sequence Turn-off is a measure of star cluster's age eg. if star cluster is young $\rightarrow$ most stars still on MS $\rightarrow$ MS Turn-off near top of MS
if star cluster very old $\rightarrow$ only low mass stars still on MS $\rightarrow$ MS Turn-off near bottom of MS


Stellar Evolution in Binary Star Systems



Short Period Binary systems:
- binary system with companions separated by $\le$ few Astronomical Units (AU)
$\rightarrow$ system has a short orbital period - $P_{\rm orb} \le$ few months
(see Binary Stars section of Stellar Properties chapter)



Generally: companions have different masses, $M_{\rm A}$ and $M_{\rm B}$
E.g. If $M_{\rm A} > M_{\rm B}$:
- Companion A evolves off of Main Sequence (MS) before Companion B
- Companion A becomes a Red Giant while Companion B is still an MS (dwarf) star
- Companion A expands (Radius, $R_{\rm A}$, increases) when it becomes a Red Giant
- Companion B's gravity pulls gas from Companion A
$\rightarrow$ gas flows from envelope of Companion A onto Companion B (Mass transfer between Companions)
$\rightarrow$ Result of Mass transfer: Companion B can become more massive than Companion A ( $M_{\rm A} < M_{\rm B}$)



Mass transfer: the flow of gas from an enlarged Companion onto the other Companion in a short period binary star system
- results in binary star systems where $M_{\rm A} / M_{\rm B}$ differs from its original value



Semi-detached binary: a binary star system in which the stars are connected by a stream of gas flowing from one Companion to the other
- binaries that are transferring mass are semi-detached



If $M_{\rm A} < 11 M_{\rm Sun}$ after Mass transfer:
- Companion A becomes White Dwarf (WD) star
- WD's a very dense (15 tons/teaspoon!): they are collapsed stars that are supported by electron degeneracy pressure (see WD discussion above)
$\rightarrow$ WD's have an extremely strong gravitational attraction
Later: Companion B evolves off the Main Sequence (MS) and becomes a Red Giant
- Companion A (now a WD) pulls gas from Companion B
$\rightarrow$ Hydrogen (H) gas from Companion B's envelope accumulates on surface of WD



X-ray Binaries:



Binary star system in which a White Dwarf (WD) star is gravitationally pulling gas from a Red Giant Companion
- Companions are revolving around Center of Mass of binary (see Binary Stars section of Stellar Properties chapter)
$\rightarrow$ gas from Red Giant spirals onto WD - forms a vortex around WD
$\rightarrow$ gas forms an accretion disk around WD



Accretion disk: a disk of gas revolving around a star that is gravitationally attracting the gas
- gas spirals down onto star through the accretion disk
- called an ``Accretion disk'' because the star is accreting gas through the disk
Gas in accretion disk is heated by friction
- disk Temperature ($T$) reaches millions degrees in inner disk
$\rightarrow$ disk emits X-rays (``X-ray binary'')



Novae:



Explosion that occurs in a binary star system in which mass is being transferred from a Red Giant Companion onto a White Dwarf (WD) Companion



A White Dwarf (WD) is an exhausted Nuclear Burning Core (see WD discussion above)
- transfer of Hydrogen (H) from Red Giant Companion supplies WD with fresh nuclear fuel!
- layer of H accumulates on surface of WD
- Temperature ($T$) and Gas Pressure ($P$) of H layer increases as more H accumulated until layer hot enough to start H fusion on surface of WD



WD has huge gravity $\rightarrow$ H layer on surface is compressed to the point of being electron degenerate (like WD itself) - see discussion of WD's above
$\rightarrow$ normal Gas Law ( $P=\rho \times T$) does not apply to a degenerate gas
$\rightarrow$ the thermo-static control of nuclear reaction rate that operates in stellar cores does not work on surface of WD
$\rightarrow$ when H fusion starts on surface of WD, it leads to a thermonuclear runaway
$\rightarrow$ detonates a nuclear explosion on surface of WD (like H fusion bomb) $\rightarrow$ Nova



During Nova:
- Star brightens by a factor of $\le$ million
- accumulated H layer on surface ejected into space by explosion
- ``Nova'' is Latin for ``New'' - Nova looks like new star appearing in sky
- Note: ``Supernovae'' (see High Mass Star evolution above) were discovered after Novae and are brighter than Novae)
- Nova fades in brightness over few months
- ejected layer of gas expands and cools $\rightarrow$ forms nebula around binary system



Note: Explosion does NOT destroy WD or companion
- Mass transfer can resume after Nova explosion
- Nova explosions can recur in same binary system!



Type I Supernovae (SN I):



Occur in binary systems similar to those of Nova explosions
- Red Giant transferring Mass onto a WD star
- WD accumulates Mass until its Mass ($M$) reaches about 1.5 $M_{\rm Sun}$
$\rightarrow$ WD becomes too massive to be supported by electron degeneracy pressure
- WD suddenly implodes (ie. collapses violently) under the force of gravity
- similar to implosion of Iron core at the end of a High Mass star's life (see High Mass star evolution discussion above)
- outer layers ejected violently into space - like Type II Supernovae (SN II)



Note: difference between Type I Supernovae (SN I) and Type II Supernovae (SN II)
- SN II's occur when the Nuclear Burning Core of a High Mass Star implodes
- SN I's occur when a WD in a mass transfer binary star system accumulates more mass than it can support

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