Stellar Evolution: Parts of Chapters 12,13,15,16Stellar Evolution: Parts of Chapters 12,13,15,16 Stellar Evolution: Parts of Chapters 12,13,15,16Stellar Evolution: Parts of Chapters 12,13,15,16

Stars lose energy - hence they must evolve.Stars lose energy - hence they must evolve.

There are different time scales on which stars There are different time scales on which stars (Sun) evolve:(Sun) evolve:

(1) Nuclear time scale t(1) Nuclear time scale tnuclearnuclear = (0.007 x 0.1 x = (0.007 x 0.1 x

McMc22)/L ~ 10)/L ~ 1010 10 yryr

(2) Thermal time scale t(2) Thermal time scale tthermalthermal = (0.5GM = (0.5GM22/R)/L ~ 2 x /R)/L ~ 2 x

101077 yr yr

(3) Dynamical time scale t(3) Dynamical time scale tdynamical dynamical = remove pressure = remove pressure

- free fall time from surface to centre = - free fall time from surface to centre = (2R(2R33/GM)/GM)1/2 1/2 ~ 0.6 hour!~ 0.6 hour!

Stellar Evolution Stellar Evolution (Formation)(Formation) Stellar Evolution Stellar Evolution (Formation)(Formation)

Begins in clouds of gas and Begins in clouds of gas and dust called dust called dark nebulaedark nebulae. . Dark nebulae are observable Dark nebulae are observable since they block light from since they block light from background stars.background stars.

They have masses 20 - few 1000 They have masses 20 - few 1000 MMsun sun and sizes 1 pc - 100 pc.and sizes 1 pc - 100 pc.

Earlier stages of star Earlier stages of star formation exist as formation exist as Giant Giant Molecular Clouds Molecular Clouds Detected at radio wavelengthsDetected at radio wavelengths101033 - 10 - 1066 solar masses; sizes of solar masses; sizes of 20 pc - 100 pc; and T ~ 10K 20 pc - 100 pc; and T ~ 10K

Molecular emission of CO often Molecular emission of CO often detected at detected at = 2.6 mm = 2.6 mm

Star FormationStar Formation

INTERSTELLAR MOLECULES

Complexity Inorganic OrganicDiatomic H2 Hydrogen CH Methylidyne radical

HD Deuterizedhydrogen

CH+ Methylidyne ion

OH Hydroxyl radical CN Cyanogen radicalSiO Silicon monoxide CO Carbon monoxideSiS Silicon

monosulfideCS Carbon monosulfide

NS Nitrogen sulfideSO Sulfur monoxide

Triatomic H2O Water CCH Ethynyl radicalHDO Heavy water HCN Hydrogen cyanideN2H

+ protonatednitrogen

DCN Deuterium cyanide

H2S Hydrogen sulfide DCN Deuterium isosyanideSO2 sulfur dioxide HCO+ Formyl ion

HCO Formyl radicalOCS Carbonyl sulfide

4-atomic NH3 Ammonia H2CO FormaldehydeHNCO Isocyanic acidH2CS ThioformaldehydeHC2H AcetyleneC3N Cyanoethynyl radical

5-atomic H2CNH MethanimineH2NCN CyanamideHCOOH Formic acidHC3N Cyanoacetylene

6-atomic CH3OH Methyl alcoholCH3CN Methyl cyanideHCONH4 Formamide

7-atomic CH3NH2 MethylamineCH3C2H MethylacetyleneHCOCH3 AcetaldehydeH2CCHCN Vinyl cyanideHC5N Cyanodiacetylene

8-atomic HCOOCH3 Methyl formate

9-atomic (CH3)2O Dimethyl etherCH3CH2OH Ethyl alcoholHC7N cyanotriacetyleneCH3CH2CN Ethyl cyanide

Stellar Evolution Stellar Evolution (Formation)(Formation)Stellar Evolution Stellar Evolution (Formation)(Formation)

1028

Stellar Evolution Stellar Evolution (Formation)(Formation) Stellar Evolution Stellar Evolution (Formation)(Formation) Under what conditions will a cloud collapse to form a Under what conditions will a cloud collapse to form a star?star?

Jeans (Sir James - 1902) Instability CriterionJeans (Sir James - 1902) Instability Criterion.. Assume a spherical cloud: Assume a spherical cloud:

      radius R       radius Rcc, uniform , uniform cc, ,

total mass Mtotal mass Mcc = 4/3 = 4/3 ccRRcc33,, speed sound cspeed sound css..

Compress region slightly. It takes time, tCompress region slightly. It takes time, tsoundsound = R = Rcc/c/css, for , for sound waves to cross region and attempt to re-establish sound waves to cross region and attempt to re-establish pressure balance.pressure balance.

At same time, gravity tries to contract system and does so on At same time, gravity tries to contract system and does so on free-fall time tfree-fall time tffff = 1/(G = 1/(G))1/21/2..

If sound crossing time is less than tIf sound crossing time is less than tffff, (t, (tsoundsound<t<tffff), pressure ), pressure wins and system bounces back to stable equilibrium, otherwise wins and system bounces back to stable equilibrium, otherwise gravity wins.gravity wins.

Thus, criterion for gravitational collapse is tThus, criterion for gravitational collapse is tffff < t < tsoundsound.. With some algebra we derive With some algebra we derive

MMJ J = c= c33ss/(G/(G3/23/21/21/2), ),

with cwith css = (P/ = (P/))1/2 1/2 and P = and P = kT/kT/mmHH we get we getMMJJ = (kT/ = (kT/mmHHG)G)3/23/2 x 1/ x 1/1/21/2

Stellar Evolution Stellar Evolution (Formation)(Formation) Stellar Evolution Stellar Evolution (Formation)(Formation)

Example: in the dense core of a typical giant Example: in the dense core of a typical giant molecular cloud:molecular cloud:T~ 10 K; T~ 10 K; ~ 3 x 10~ 3 x 10-17-17 kg/m kg/m33; ; ~ 2 for pure H~ 2 for pure H22 gas (X= 1, Y = Z = 0) gas (X= 1, Y = Z = 0) Thus MThus MJJ ~ 2 M ~ 2 Msunsun

The characteristic mass of these dense cores is The characteristic mass of these dense cores is ~ 10 M~ 10 Msunsun so they are unstable to so they are unstable to gravitational collapse - gravitational collapse - consistent with them consistent with them being sites of star formation.being sites of star formation.

Collapse could also be triggered by external Collapse could also be triggered by external pressure on cloud from, for example, a shock pressure on cloud from, for example, a shock wave from nearby supernova explosion.wave from nearby supernova explosion.

MMJJ = (kT/ = (kT/mmHHG)G)3/23/2 x 1/ x 1/1/21/2

Stellar Evolution Stellar Evolution (Formation)(Formation) Stellar Evolution Stellar Evolution (Formation)(Formation) In the collapsing cloud, energy is released by In the collapsing cloud, energy is released by gravitational contraction. The star shrinks and gravitational contraction. The star shrinks and begins to heat up. begins to heat up.

Similar to Fig 11.1

Contraction is originally on Contraction is originally on the dynamical timescale. the dynamical timescale. Eventually density increases Eventually density increases and so does opacity. A larger and so does opacity. A larger fraction of energy is fraction of energy is transformed into heat. transformed into heat. Pressure increases, raising Pressure increases, raising the resistance to the collapse the resistance to the collapse so the contraction slows. Tso the contraction slows. Teffeff rises with little change in R. rises with little change in R. Therefore, star moves to Therefore, star moves to higher L.higher L.

Eventually, the star’s core Eventually, the star’s core is hot enough for nuclear is hot enough for nuclear reactions. Star reaches reactions. Star reaches hydrostatic equilibrium, hydrostatic equilibrium, on on main sequence.main sequence.

Initially, radiation passes Initially, radiation passes right through star so that right through star so that TTeffeff stays nearly constant. stays nearly constant. Therefore, as R drops so does Therefore, as R drops so does L (L = 4L (L = 4RR22TTeffeff

4 4 ).).

Stellar Evolution Stellar Evolution (Pre Main Seq.)(Pre Main Seq.) Stellar Evolution Stellar Evolution (Pre Main Seq.)(Pre Main Seq.)

22H (from Big Bang) has very low H (from Big Bang) has very low abundance so the energy released abundance so the energy released from this reaction just slows from this reaction just slows the contraction rate a bit.the contraction rate a bit.

Other reactions:Other reactions: 66Li + p+ Li + p+ 33He + He + 44HeHe 77Li + p+ Li + p+ 2 2 44HeHe 1111B + p+ B + p+ 3 3 44HeHe

All abundances are low, so the All abundances are low, so the contraction rate is minimally contraction rate is minimally affected.affected.

For first few x 10For first few x 1044 years, years, the star contracts from the the star contracts from the interstellar medium and interstellar medium and radiates away gravitational radiates away gravitational energy.energy.By 10By 1066 years, the first years, the first nuclear reactions involving nuclear reactions involving light elements start: light elements start: eg p+ + eg p+ + 22H H 33He + He +

Stellar Evolution Stellar Evolution (Pre Main Seq.)(Pre Main Seq.) Stellar Evolution Stellar Evolution (Pre Main Seq.)(Pre Main Seq.)

Young Stars and Planet FormationYoung Stars and Planet Formation Young Stars and Planet FormationYoung Stars and Planet Formation

Stellar Evolution Stellar Evolution (Main Sequence)(Main Sequence) Stellar Evolution Stellar Evolution (Main Sequence)(Main Sequence) Life on Main Sequence (§ 13.1) - Life on Main Sequence (§ 13.1) -

Core H burning and hydrostatic equilibrium is the longest Core H burning and hydrostatic equilibrium is the longest lived stage in a star’s life. lived stage in a star’s life. HOW LONG DOES IT LAST?HOW LONG DOES IT LAST?

Mass - Luminosity relation Mass - Luminosity relation L L M M3.53.5

Energy produced by fusion E = Energy produced by fusion E = McMc2 2

M = mass destroyed = 0.007 x mass H fusedM = mass destroyed = 0.007 x mass H fusedMass of H available to fuse Mass of H available to fuse total mass star (0.1 based total mass star (0.1 based

on models)on models)Thus Thus M M M M E E M M or or E E M M

During main sequence stage, L ~ constant, thusDuring main sequence stage, L ~ constant, thusL = energy from fusion / MS lifetime = E/tL = energy from fusion / MS lifetime = E/tms ms or tor tms ms = E/L = M/M= E/L = M/M3.53.5 ttmsms = M = M-2.5-2.5

Thus,Thus, massive stars have shorter main sequence lifetimes than massive stars have shorter main sequence lifetimes than small mass stars.small mass stars.

In terms of Sun’s lifetime: In terms of Sun’s lifetime: ttmsms/t/tmsmssun = (M/Msun = (M/Msunsun))-2.5-2.5

Stellar Evolution Stellar Evolution (Main Sequence)(Main Sequence)Stellar Evolution Stellar Evolution (Main Sequence)(Main Sequence)

M/MM/Msunsun L/LL/Lsunsun t/tt/tsunsun t (yr)t (yr)

0.10.1 3 x 103 x 10-4-4 300300 3 x 103 x 101212 (> age (> age universe!!)universe!!)

11 11 11 10101010

55 ~300~300 0.020.02 2 x 102 x 1088

1010 ~3000~3000 0.0030.003 3 x 103 x 1077

3030 1.5 x 101.5 x 1055 2 x 102 x 10-4-4 2 x 102 x 1066

100100 101077 1010-5-5 101055 ( 100,000 yrs!)( 100,000 yrs!)

Low mass stars live for very long timesLow mass stars live for very long times

High mass stars are short-lived High mass stars are short-lived

Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters)Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters)

Star clusters are:Star clusters are:

Coeval (all Coeval (all stars same age) stars same age)

Same metal Same metal abundance abundance (formed from (formed from same gas cloud)same gas cloud)

Have a range in Have a range in masses in them masses in them (mass function)(mass function)

Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters) Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters) Many stars can condense from the same giant molecular cloud Many stars can condense from the same giant molecular cloud star star cluster.cluster.

Massive stars reach main sequence first and evolve from it earlier Massive stars reach main sequence first and evolve from it earlier also (talso (tms ms M M-2.5-2.5))

As time advances, high mass tip of main sequence shortens and As time advances, high mass tip of main sequence shortens and evolved stars appear in upper right of H-R Diagram evolved stars appear in upper right of H-R Diagram

Position of main sequence turnoff Position of main sequence turnoff age of cluster age of cluster

Synthetic Clusters Synthetic Clusters Different AgeDifferent Age

Observed H-R Diagram compared to Observed H-R Diagram compared to theoretical isochrones - all theoretical isochrones - all

stars with same agestars with same age

young old

Evolved stars

Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters) Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters)

Real ClustersSynthetic Clusters

5 x 106 yr

3 x 107 yr

107 yr

108 yr

youngest

oldest

Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters)Stellar Evolution Stellar Evolution (Star Clusters)(Star Clusters)

Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun) Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun) How will the Sun die?How will the Sun die? Sun has enough H in its core to produce energy for Sun has enough H in its core to produce energy for about 10about 101010 yrs. (It is about halfway through its life yrs. (It is about halfway through its life now.)now.)

When the core’s H is exhausted, there will be no more When the core’s H is exhausted, there will be no more nuclear energy to heat the gas. Gravity will win over nuclear energy to heat the gas. Gravity will win over gas pressure and the core will collapse.gas pressure and the core will collapse.

Gravitational potential energy of the core will be Gravitational potential energy of the core will be converted to heat as it shrinks.converted to heat as it shrinks.

This new heat source will trigger new fusion This new heat source will trigger new fusion reactions:reactions:

(3-(3-) He + He + He ) He + He + He C and C + He C and C + He O O Outer layers of the Sun will expand because of extra Outer layers of the Sun will expand because of extra heat heat RED GIANTRED GIANT

Eventually, the surface gas will have enough kinetic Eventually, the surface gas will have enough kinetic energy to escape core’s gravity ( to form a planetary energy to escape core’s gravity ( to form a planetary nebula), leaving behind a “naked core” of C and O nebula), leaving behind a “naked core” of C and O WHITE DWARF.WHITE DWARF.

Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun)Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun)

Planetary nebulaePlanetary nebulae

Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun) Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun) When nuclear fuel is exhausted, the core will When nuclear fuel is exhausted, the core will contract again. Low mass stars never get hot contract again. Low mass stars never get hot enough for nuclear reactions beyond formation C, enough for nuclear reactions beyond formation C, O.O.

Core will shrink and electrons in core will be Core will shrink and electrons in core will be forced together.forced together.

Effects of Uncertainty Principle come into play Effects of Uncertainty Principle come into play when matter is compressed when matter is compressed xxp ~ p ~ hh- so there is - so there is zero-point energy (even at T = 0 K) zero-point energy (even at T = 0 K)

EEdegdeg = p = p22/2m = h-/2m = h-22/2m(/2m(x)x)22 which increases as size which increases as size decreases decreases

PPdegdeg = E = Edegdeg/V/V So for N particles in volume V, where particle So for N particles in volume V, where particle density n = N/V, density n = N/V, x = (V/N)x = (V/N)1/31/3

Hence PHence Pdegdeg = N/V(p = N/V(p22/2m) = N/V(/2m) = N/V(hh--22/2m) (N/V)/2m) (N/V)2/32/3 = ( = (hh--22/2m)n/2m)n5/35/3 so P so Pdegdeg 5/35/3

Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun) Stellar Evolution Stellar Evolution (Death of the Sun)(Death of the Sun) The pressure of the degenerate electrons can The pressure of the degenerate electrons can provide a pressure force provide a pressure force even at 0 K.even at 0 K.

PPdegdeg 5/3 5/3 (independent of T). NB P(independent of T). NB Pdegdeg not not T - T - perfect gas law breaks down.perfect gas law breaks down.

Recall that P Recall that P M M22/R/R44 and and M/R M/R33. With P . With P 5/3 5/3

wewe get:get: MM22/R/R44 (M/R (M/R33))5/35/3 R R M M-1/3-1/3 or or M M 1/V 1/V (Note how counter-intuitive this (Note how counter-intuitive this

relation is).relation is).

White DwarfsWhite Dwarfs

~ 10~ 1066 g/cm g/cm33; 10; 1055 K > T > 3000 K K > T > 3000 K Radiate away stored heat. Slowly approach 0 K.Radiate away stored heat. Slowly approach 0 K. If M > 1.4MIf M > 1.4Msunsun, gravity will exceed the pressure , gravity will exceed the pressure of the degenerate electrons and the white dwarf of the degenerate electrons and the white dwarf will collapse.will collapse.

Stellar Evolution Stellar Evolution (Death Massive Star)(Death Massive Star) Stellar Evolution Stellar Evolution (Death Massive Star)(Death Massive Star) Gravity strong enough to squeeze C-O core until T rises Gravity strong enough to squeeze C-O core until T rises high enough to fuse C.high enough to fuse C.

C C Ne, Mg and O, and briefly stabilizes star until C Ne, Mg and O, and briefly stabilizes star until C used up.used up.

Again, core collapses. EAgain, core collapses. Egravgrav turned into more heat turned into more heat core core hot enough fuse Ne.hot enough fuse Ne.

Ne Ne O, Mg and cycle repeats with O O, Mg and cycle repeats with O Si, S, Ph then Si Si, S, Ph then Si Fe then Fe Fe then Fe ?? ??

Fe most strongly bound nucleus. Its formation consumes Fe most strongly bound nucleus. Its formation consumes energy. By this time, energy. By this time, > 10 > 1099 g/cm g/cm33, T > 3 x 10, T > 3 x 1099 K. K.

Now get Now get 5656Fe + Fe + 13 13 44He + 4n - what kind of nuclear He + 4n - what kind of nuclear reaction is this? (reaction is this? ( here ~ 100 Mev and further drains here ~ 100 Mev and further drains thermal energy of core).thermal energy of core).

Star collapses rapidly, T continues to rise, star almost Star collapses rapidly, T continues to rise, star almost in free-fall in free-fall 44He He 2p + 2n eventually p + e- 2p + 2n eventually p + e- n n + +

Two possible outcomes - n degeneracy stops collapse Two possible outcomes - n degeneracy stops collapse (neutron star)(neutron star) or complete gravitational collapse or complete gravitational collapse (black (black hole).hole).

Stellar Evolution Stellar Evolution (Death Massive Star)(Death Massive Star) Stellar Evolution Stellar Evolution (Death Massive Star)(Death Massive Star) The final 1.4 second:The final 1.4 second: Sudden core collapse. T soars to > 5 x 10Sudden core collapse. T soars to > 5 x 1099 K, K, reaches 4 x 10reaches 4 x 1014 14 g/cmg/cm33 (thimble = mass of a mountain!), (thimble = mass of a mountain!), intense flood of neutrinos emitted.intense flood of neutrinos emitted.

Pressure forces electrons to combine with protons to Pressure forces electrons to combine with protons to make neutrons - core composed entirely of neutrons. make neutrons - core composed entirely of neutrons.

Superdense matter in core stops contracting abruptly Superdense matter in core stops contracting abruptly - but layers above still plunging inward at 10-15% - but layers above still plunging inward at 10-15% speed of light. This material hits core and speed of light. This material hits core and “bounces”.“bounces”.

Shock wave rebounds throughout star, ripping away Shock wave rebounds throughout star, ripping away outer envelope and most of star’s mass ejected outer envelope and most of star’s mass ejected (>90%).(>90%).

SUPERNOVASUPERNOVA

In next second a SN can release as much energy In next second a SN can release as much energy (mostly neutrinos) as Sun does in 10(mostly neutrinos) as Sun does in 101010 years. years.

SupernovaeSupernovaeSupernovaeSupernovae

Neutron Stars / PulsarsNeutron Stars / PulsarsNeutron Stars / PulsarsNeutron Stars / Pulsars Masses ~ 1.4 Msun - presence made known as Masses ~ 1.4 Msun - presence made known as PULSARSPULSARS Size ~ 10 kmSize ~ 10 km                 

Model of pulsar

Radio pulsar period Radio pulsar period 0.714 s0.714 s Distribution of periods

Black HolesBlack HolesBlack HolesBlack Holes Escape velocity > speed light VEscape velocity > speed light Vescesc = (2GM/R) = (2GM/R)1/21/2 > c > c R < 2GM/c R < 2GM/c22..

R is called Schwarzschild Radius and defines the R is called Schwarzschild Radius and defines the event horizon.event horizon.

For example with M = 10 MFor example with M = 10 Msunsun R < 30 km. R < 30 km. For Earth to be a black hole R < 1 cm!For Earth to be a black hole R < 1 cm! Presence of black holes is suggested in binary Presence of black holes is suggested in binary systems - high mass dark component and x-ray source. systems - high mass dark component and x-ray source.