Transcript Chap. 02

Chap. 2 An Overview of
Stellar Evolution
Jan 28, 2009
Jie Zhang
Copyright ©
CSI661/ASTR530
Spring, 2009
Outline
•Basics (from “Universe” by Freedman & Kaufmann)
•Young Stellar Objects
•Zero-Age Main Sequence
•Leaving the Main Sequence
•Red Giants and Supergiants
•Helium Flash
•Later Phase and Advanced Phase
•Core Collapse and Nucleosynthesis
•Variable Stars
•Novae and Supernovae
•White dwarfs, neutron stars and black holes
•Binary Stars
Parallax
• The apparent displacement of a nearby object against a distant
fixed background from two different viewpoints.
Stellar Parallax
• The apparent position shift of a star as the Earth moves from
one side of its orbit to the other (the largest separation of two
viewpoints possibly from the Earth)
Stellar Parallax and Distance
1 pc = 3.26 ly
1 pc = 206,265 AU = 3.09 X 1013 km
• Distances to the nearer stars can be determined by
parallax, the apparent shift of a star against the
background stars observed as the Earth moves
along its orbit
Once a star’s distance is known …..
Luminosity and brightness
• A star’s luminosity (total light output), apparent brightness,
and distance from the Earth are related by the inversesquare law
• If any two of these quantities are known, the third can be
calculated
Luminosity, Brightness and Distance
• Many visible stars turn out to be more luminous than the
Sun
Magnitude Scale to Denote brightness
• Apparent magnitude
scale is a traditional way to
denote a star’s apparent
brightness (~ 200 B.C. by
Greek astronomer
Hipparchus)
• First magnitude, the
brightest
• Second magnitude, less
bright
• Sixth magnitude, the
dimmest one human naked
eyes see
Apparent Magnitude and Absolute Magnitude
• Apparent magnitude is a measure of a star’s apparent
brightness as seen from Earth
– the magnitude depends on the distance of the star
• Absolute magnitude is the apparent magnitude a star
would have if it were located exactly 10 parsecs from
Earth
– This magnitude is independent of the distance
– One way to denote the intrinsic luminosity of a star in
the unit of magnitude
• The Sun’s apparent magnitude is -26.7
• The Sun absolute magnitude is +4.8
A star’s color depends on its surface temperature
Wien’s Law
Photometry, Filters and Color Ratios
• Photometry measures the apparent brightness of a star
• Standard filters, such as U (Ultraviolet), B (Blue) and V
(Visual, yellow-green) filters,
• Color ratios of a star are the ratios of brightness values
obtained through different filters
• These ratios are a good measure of the star’s surface
temperature; this is an easy way to get temperature
Stellar Spectrum
• E.g., Balmer lines: Hydrogen lines of transition from higher
orbits to n=2 orbit; Hα (orbit 3 -> 2) at 656 nm
Classic Spectral Types
The spectral class and type of a star is directly related to
its surface temperature: O stars are the hottest and M
stars are the coolest
Classic Spectral Types
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O B A F G K
M
(Oh, Be A Fine Girl, Kiss Me!) (mnemonic)
Spectral type is directly related to temperature
From O to M, the temperature decreases
O type, the hottest, blue color, Temp ~ 25000 K
M type, the coolest, red color, Temp ~ 3000 K
Sub-classes, e.g. B0, B1…B9, A0, A1…A9
The Sun is a G2 type of star (temp. 5800 K)
Luminosity, Radius, and Surface Temperature
• Reminder: Stefan-Boltzmann law states that a blackbody
radiates electromagnetic waves with a total energy flux F
directly proportional to the fourth power of the Kelvin
temperature T of the object:
F = T4
Luminosity, Radius, and Surface Temperature
• A more luminous star could be due to
– Larger size (in radius)
– Higher Surface Temperature
• Example: The first magnitude reddish star Betelgeuse is
60,000 time more luminous than the Sun and has a surface
temperature of 3500 K, what is its radius (in unit of the solar
radius)?
R = 670 Rs (radius of the Sun)
A Supergiant star
Finding Key Properties of Nearby Stars
Hertzsprung-Russell (H-R) diagrams reveal
the patterns of stars
• The H-R diagram
is a graph plotting
the absolute
magnitudes of
stars against their
spectral types—or,
equivalently, their
luminosities
against surface
temperatures
• There are patterns
Hertzsprung-Russell (H-R) diagram
the patterns of stars
•The size can be denoted
(dotted lines)
0.001 Rs
To
1000 Rs
Hertzsprung-Russell (H-R) diagram
the patterns of stars
•Main Sequence: the band stretching
diagonally from top-left (high
luminosity and high surface
temperature) to bottom-right (low
luminosity and low surface
temperature)
– 90% stars in this band
– The Sun is one of main
sequence stars
– Hydrogen burning as energy
source
Hertzsprung-Russell (H-R) diagram
the patterns of stars
•Main Sequence
•Giants
– upper- right side
– Luminous (100 – 1000 Lsun)
– Cool (3000 to 6000 K)
– Large size (10 – 100 Rsun)
• Supergiants
– Most upper-right side
– Luminous (10000 - 100000 Lsun)
– Cool (3000 to 6000 K)
– Huge (1000 Rsun)
•White Dwarfs
– Lower-middle
– Dim (0.01 Ls)
– Hot (10000 K)
– Small (0.01 Rs)
A way to obtain the MASS of stars
Binary Star System
Period: ~ 80 days
Binary Stars
• Binary stars are two stars which are held in orbit
around each other by their mutual gravitational
attraction, are surprisingly common
• Visual binaries: those that can be resolved into
two distinct star images by a telescope
• Each of the two stars in a binary system moves
in an elliptical orbit about the center of mass of
the system
Binary Stars
•Each of the two stars in a binary system moves in
an elliptical orbit about the center of mass of the
system
Binary star systems: stellar masses
• The masses can be computed from measurements of the
orbital period and orbital size of the system
• The mass ratio of M1 and M2 is inversely proportional to
the distance of stars to the center of mass
• This formula is a generalized format of Kepler’s 3rd law
• When M1+M2 = 1 Msun, it reduces to
a3 = P2
Mass-Luminosity Relation for MainSequence Stars
• The greater the
mass of a mainsequence star, the
greater its
luminosity
Mass-Luminosity Relation for MainSequence Stars
• Masses from 0.2 MΘ
• to 60 MΘ
• The greater the mass
• The greater the
luminosity
• The greater the surface
temperature
• The greater the radius
Note: This is the end of the basics, which is
from “Universe” by Freedman & Kaufmann
Feb. 11, 2009 (continued)
(2.1) Young Stellar Objects
Four stages of star
formation
1. Form proto-star core
within molecular
cloud
2. Core grows from
surrounding rotating
disk
3. Bipolar flow along
rotation axis
4. New star clears away
the surrounding
nebular material
http://www.skyofplenty.com/wp-content/uploads/2008/09/esa__star_formation1.jpg
(2.1) Young Stellar Objects
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Energy source for a
proto-star is
gravitational potential
energy.
The contract life is
about 0.1% its
potential nuclear life
at the main sequence
Proto-stars are
convective
throughout, thus a
new star is chemically
homogeneous
Proto-star Evolution Track
(2.2) ZAMS
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Zero-age main sequence star: a star just ignites the
hydrogen fusion
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In practice, “zero-age” means that the star has changed
so little in radius, effective temperature and luminosity
– Means a few thousand years for a massive star
– Means 10 million years for the Sun
– Means 1 billion years for the least massive stars
(2.2.1) Main Sequence
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Two kinds of nuclear fusion converting H to He
1. pp-chain
– for stars less than 1.5 Msun
2. CNO cycle
• For stars more than 1.5 Msun, Tc > 1.8 X 107 K
• Fusion is much faster than PP-chain
• C, N, O act as catalysts
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Because of P=nKT=ρ/μ NAKT, number density decreases
Temperature must increase to maintain the pressure
Core must slowly contract and heat up
Faster energy generation, more luminous star
(2.2.2) Brown Dwarfs
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Proto-stars which never get hot enough to fuse hydrogen
to helium
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The brown dwarf/main sequence cut is about 0.085 Msun
(2.3) Post-main Sequence
< 0.05: No 2D fusion  “planet”
<0.085: No 1H Fusion  brown dwarf
=0.85: Hubble time scale
<1.50: PP chain, Helium flash, radiative core, He WD
<5.0: CNO cycle, no He flash, convective core, Carbon
WD
<8.0: planetary nebula, O, Ne, Mg WD
<25:
supernovae, neutron star
> 25: supernovae, black hole
Mass Cut versus star fate (also see Fig. 2.4)
(2.3.1) Cluster HR Diagram
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Stars in a cluster form at
nearly the same time
“TOP” turnoff point can be
used to determine the age of
a cluster
SGB: sub-giant branch
RGB: red-giant branch
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Horizontal Branch
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H-shell burning
Helium core burning
AGB: Asymptotic Giant
Branch
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Helium shell burning
Variable stars caused RR
Lyrae
by thermal instability
Fig. 2.7. HR diagram of globular cluster M3
(2.3.1) Cluster HR Diagram
Fig. 2.8: theoretical HR for clusters
(2.4) Red Giants
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The stage that hydrogen shell burning ignites
The shell burning adds helium ash into the
core, causing the dormant core to contract
The shell burning causes the outer envelope to
expand and thus cooling, producing red giants
The hydrogen shell burning occurs via the
CNO cycle, the main source of N in the
universe
Chap. 2 (continued)
Feb.18, 2009
(2.5) Helium Flash
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Core contracts, and density increases
Core becomes degenerate, that is the electron
degeneracy pressure is larger than the gas thermal
pressure
 5/3
-2
Pe  1.004 10 ( )
dyne cm
e
13
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Degeneracy pressure is caused by the electron
momentum associated with the Heisenberg uncertainty
principle (ΔxΔp=ħ). It is also associated with Pauliexclusive principle
(2.5) Helium Flash
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Star M < 0.4 Msun
– core degenerate (ρ > 106 g cm-3)
– but low temperature (< 107 K)
– no further helium burning, produce helium white dwarf
Star M > 1.5 Msun
– core not degenerate (ρ < 106 g cm-3)
– but high temperature (> 108 K), ignite helium burning
– Peaceful transition to helium burning
Star 0.4 Msun < M < 1.5 Msun
– core degenerate (ρ < 106 g cm-3)
– and high temperature (> 108 K)
– helium flash: explosive helium burning
(2.5) Helium Flash
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For a degenerate gas, the ignition of helium burning will
heat the gas, but do not cause expand
The increased temperature makes the reaction go faster,
which further heats the gas, which makes the reaction
goes faster.
This cycle of explosive nuclear reaction continues until
temperature is high enough so that thermal pressure
exceeds degenerate pressure.
After helium flash, the core expands to a density about 103
g cm-3
It is mirrored by envelope contraction
Luminosity decreases, and effective temperature
increases; the star heads to the left in the HR diagram
(2.5) Helium Flash
Density Evolution for model
1 Msun, z=0.02
(2.5.1) Horizontal Branches (HB)
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Giant stars with
• Helium burning in the core
– Through triple-α reaction
– 34He  12C and 12C (4He, γ)16O
• Hydrogen burning in the surrounding shell through
CNO cycle
(2.5.2) Asymptotic Giant Branches
(AGB)
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When helium core is exhausted, HB star becomes
AGB
The C-O core contracts and heats up
Double shell burning
• Helium burning in the shell surrounding the
core
• Hydrogen burning in the shell surrounding He
shell
(2.5.2) AGB
Fig. 2.14. Double Shell Burning
(2.6) Later Phases, Initial Masses 6-10 Msun
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During the Giant star phases, a star may lose a large
fraction of mass through
– Super wind
– Pulsation
The blown-off envelope becomes planetary nebula (PN)
The residual core becomes a white dwarf
– Composition: Carbon-oxygen
– Mass: 0.55 – 1.3 Ms
– Radius: 10-2 Rsun, or the size of the Earth
– Energy source: residual heat of the atomic nuclei
• Luminosity: 10-5 Lsun
• Fading time: 1010 years
(2.6) Planetary Nebula
NGC 6543
IC 418
(2.6.1) White Dwarfs
Fig. 2.15. Color-Magnitude HR diagram
Chap. 2 (continued)
Apr. 8, 2009
(2.7) Advanced Evolution Phases, Initial
Masses Greater Than 6-10 Msun
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The core is composed of iron-peak elevemts
Silicon burning is taking place, adding to the iron core
Lighter elements are burning progressively in outer
layers
(2.8) Core Collapse and Nucleosynthesis
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The core collapses at about ρc=6 x 109 g cm-3 and Tc=8 x
109 K
The core collapses catastrophically
Inner core mass 1.2 Msun
Density from 109 to 1015 g cm-3
Dynamic time scale is only a few seconds
Forming neutron stars
Releasing 1053 ergs gravitational energy
– Most comes out in neutrinos
– 1% in kinetic energy
– 0.1% in visible light and other EM radiation
(2.11.2) Supernovae
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Further collapse is effectively halted by the very stiff
equation of state of nuclear matter
To convert 1 Ms iron core to all neutrons (binding energy
9 Mev/nucleon) requires 1052 ergs energy
As core material reaches the nuclear density, it
“bounces” and collide with informing material thus
forming a shock
Shock propagates outward lifting most or all of the
remainder of the star
(2.11.2) Supernovae
Crab Nebula – supernova in 1054 AD; a
pulsar or neutron star is at the center
Neutron Star or
Pulsar
Chap. 2 (to be continued)
End
of Chap. 2
Note: