CSI661/ASTR530Spring, 2009

Chap. 2 An Overview of Stellar Evolution

Jan 28, 2009

Jie ZhangCopyright ©

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)

• 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

1 pc = 3.26 ly 1 pc = 206,265 AU = 3.09 X 1013 km

Stellar Parallax and Distance

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 inverse-square 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

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

Classic Spectral Types

• 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 revealthe 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

•The size can be denoted(dotted lines)0.001 Rs To 1000 Rs

Hertzsprung-Russell (H-R) diagramthe 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) diagramthe 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)

Hertzsprung-Russell (H-R) diagramthe patterns of stars

A way to obtain the MASS of starsBinary 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 Main-Sequence Stars

• The greater the mass of a main-sequence star, the greater its luminosity

• 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

Mass-Luminosity Relation for Main-Sequence Stars

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

• 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

• Zero-age main sequence star: a star just ignites the hydrogen fusion

• 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• 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

• 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

• Proto-stars which never get hot enough to fuse hydrogen to helium

• 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

Fig. 2.7. HR diagram of globular cluster M3

• 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

– H-shell burning

• Horizontal Branch– Helium core burning

• AGB: Asymptotic Giant Branch

– Helium shell burning

– Variable stars caused RR Lyrae

– by thermal instability

(2.3.1) Cluster HR Diagram

Fig. 2.8: theoretical HR for clusters

(2.4) Red Giants

• 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• Core contracts, and density increases• Core becomes degenerate, that is the electron

degeneracy pressure is larger than the gas thermal pressure

2-3/513 cm dyne )(10004.1e

Pe

• Degeneracy pressure is caused by the electron momentum associated with the Heisenberg uncertainty principle (ΔxΔp=ħ). It is also associated with Pauli-exclusive principle

(2.5) Helium Flash• 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• 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)• 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)

• 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

• 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 6543IC 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

• 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

• 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

• 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)

Endof Chap. 2

Note: