ASTR 228: Chapter 18 - Advances in Stellar Astronomy After Newton

Chapter 18.

Advances in Stellar Astronomy After Newton

Latest Modification: December 8, 1997

18.1. History of Astrophysics

Sun assumed, since about 200 B.C., to be nearby star differing from other stars only in its distance
Until about a century ago, astronomers interest was in positions and motions of stars
Today astronomers interested in physical nature of stars - astrophysics
Two developments in understanding of light made astrophysics possible
- First, in late 1850s, invention of spectroscope by German chemist Robert Bunsen (1811-1899) and German physicist Gustav Kirchhoff (1824-1887)
- Spectroscope is device used to separate white light into its component colors
- Second, William Wollaston (1766-1828), English physicist, and Joseph Fraunhofer (1787-1826), German physicist, began investigation of colors emitted by various elements
Developments in spectroscopy of stars
- 1814, Fraunhofer labeled about 600 absorption lines in solar spectrum and identified elements responsible for some
- By 1830s recognition that each chemical element emits a specific set of colors that are peculiar to that element only; much like a person's fingerprints
- 1864, William Huggins (1824-1910), English astronomer, identified 9 elements in spectrum of bright star Aldebaran
- 1864, Norman Lockyer (1836-1920), English astronomer identified new element helium in solar spectrum
- 1869, Homer Lane (18??-18??), American meteorologist, made first estimate of Sun's surface temperature and density obtaining 30,000^o K and 0.00036 g/cm³
- 1860s, Kirchhoff formulated three empirical laws of spectroscopic analysis
- 1913, Ejnar Hertzsprung (1873-1967), Danish astronomer and Henry Russell (1877-1957), American astronomer, published independently Hertzsprung-Russell (or HR) diagram for stars
- Early 1920s to late 1930s, M. N. Saha (18??-19??), Indian physicist-astronomer, Henry Russell, B. Stromgren (19??-19??), Danish astronomer, and Subrahmanyan Chandrasekhar (1910-1995), Indian-American astronomer
  - Showed that hydrogen is dominant constituent of Sun and stars
  - Helium next most important element
  - Carbon, nitrogen, oxygen, iron present in minor amounts
  - All other elements present in trace amounts

18.2. Temperature and Luminosity of Stars

Temperature of stars
- Stars can be subdivided into 7 temperature groups call spectral classes on basis of appearance of absorption spectrum
- Spectral classes: O, B, A, F, G, K, M
- Temperature for O stars highest (40,000^o K) and for M stars lowest (3800^o K)
- Sun is G star; surface temperature of 6000^o K
- Survey of spectral types begun at Harvard College Observatory in 1884 ended in 1920, included 0.25 million stars
- Today spectral types or surface temperatures for about 1.0 million stars, most in our Galaxy
Distances of stars
- Main method for determining is parallax
- Units for measuring distance:
  - Distance Unit, Abbreviation, Equivalent To
  - parsec, pc, 3.3 ly
  - light year, ly, 206265 AU
  - astronomical unit, AU, 3 x 10¹³ km
- Today, we have distances for about 6000 stars
Luminosity or brightness of stars
- Hipparchus and Ptolemy graded apparent brightness of stars into 6 magnitude classes called apparent magnitudes
- 1st magnitude brightest and 6th magnitude just visible to naked-eye
- With distance apparent magnitudes can be turned into absolute magnitudes (inverse square law of light)
- Luminosity is brightness or absolute magnitude over all wavelengths
- Luminosity classes:
  - Luminosity Class, Designation, Radii
  - Supergiants, I, Largest
  - Bright Giants, II,
  - Red Giants, III,
  - Sub-Giants, IV,
  - Main Sequence, V,
  - White Dwarfs, VII, Smallest
- Sun is G-type main-sequence star
- Today have luminosities for about 1000 stars, most in our Galaxy

18.3. Hertzsprung-Russell Diagram

Plot of luminosity on vertical axis and surface temperature on horizontal axis for individual stars
Four identifiable regions on H-R diagram

Region	Spectral Type	Description of stars	Percent of stars
main sequence	O to M	bright-hot to faint-cool	90
red giants	F to M	bright-cool	<0.5
white dwarfs	B to F	faint-hot	10
blue supergiants	O to A	very bright-hot	0
red supergiants	G to M	very bright-cool	0

Range of Stellar Properties

Stellar Property	Range*
mass	10^-2 to 10⁺² M_sun
radius	10^-2 to 10⁺³ R_sun
mean density	10^-7 to 10⁺⁷ r_sun
luminosity	10^-5 to 10⁺⁵ L_sun
surface temperature	10⁺³ to 10⁺⁵ K
heavy-element mass abundance**	0.05 to 2.0 Z_sun
age	10⁺⁴ to 10⁺¹⁰ y

Observed numbers of stars in our Galaxy

.					Cumulative Percentage
Luminosity Class	Spectral Class	Typical Mass [M_sun]*	Typical Luminosity [L_sun]*	Number of Stars	Number	Mass	Luminosity
Supergiant (I & II)	O-M	?	50,000	~10⁵	~0	~0	~3
Red Giant (III)	F-M	~1.2	40	~2 x 10⁹	0.5	0.6	~41
Main Sequence (V)	O	~25	80,000	~10⁴	0.5	0.6	~42
.	B	5	200	300 x 10⁶	0.6	1.6	~70
.	A	1.7	6	3 x 10⁹	1.2	4.6	~79
.	F	1.2	1.4	12 x 10⁹	4.2	13.6	~87
.	G	0.9	0.6	26 x 10⁹	11.2	~27	~94
.	K	0.5	0.2	52 x 10⁹	~24	~42	~99
.	M	0.25	0.005	270 x 10⁹	~91	~80	~100
White Dwarf	B-F	~1.0	0.005	35 x 10⁹	~100	~100	~100
.	.	.	Total	400 x 10⁹	100	100	100

18.4. Why Stars Evolve

1869, Homer Lane, American meteorologist, wrote first paper on physical conditions inside Sun
Stars are self-gravitating, self-luminous spheres of hot gas
Life cycle of star is a battle with gravity (self-gravitation) to keep from squeezing star out of existence; three forces can counter gravity
- Kinetic pressure of hot gases (star must cool)
- Repulsion from Pauli exclusion principle for electrons
- Repulsion from Pauli exclusion principle for neutrons
Sun, model for stellar structure

Sun is model for physics of stars
Physical laws operating inside Sun and presumably other stars can be inferred

18.5. Physical Processes in Stars

Hydrostatic equilibrium - weight of overlaying layers balanced by pressure forces of hot gases pushing out
- Mathematical: weight of gas = pressure of hot gas
- Results: star neither expands or contracts
Thermal Equilibrium
- Thermal equilibrium - amount of energy produced inside equals amount radiated away as luminosity
- Because solar gases are almost totally ionized, behavior of nuclei and free electrons is simple, perfect gas
- Self-regulating mechanism
  - If too much energy produced, Sun heats up and expands
  - If too little energy produced, Sun cools down and contracts
Energy Generation
- Energy generation - Sun would cool at rate fast enough to measure, if Sun emitted radiant energy only because it is hot
  - Sun is not cooling significantly
  - Consequence, Sun has energy source that replaces energy loss in luminosity, thus keeping interior hot
- Thermonuclear Fusion
  - Thermonuclear fusion - fusion of small mass nuclei, primarily hydrogen nuclei, to form more massive nuclei, primarily helium, with resulting direct conversion of mass into energy by E = mc²
  - Mathematical form: 4¹H₁ => ⁴He₂ + g + n
    - ¹H₁ = hydrogen nucleus, i.e., proton
    - ⁴He₂ = helium nucleus, i.e., 2 protons + 2 neutrons
    - g = gamma-ray photon
    - n = neutrinos
- Hydrogen "Burning"
  - Proton-Proton Chain
    - ¹H₁ + ¹H₁ => ²H₁ + e⁺ + n
    - ²H₁ + ¹H₁ => ³He₂ + g
    - ³He₂ + ³He₂ => ⁴He₂ + 2¹H₁
  - Carbon-Nitrogen-Oxygen Cycle
    - ¹²C₆ + ¹H₁ => ¹³N₇^* + g
    - ...
    - ¹⁵N₇ + ¹H₁ => ¹²C₆ + ⁴He₂
Energy Transport
- Energy transport - movement by various physical processes of energy from deep interior to surface
- Energy liberated in deep interior is in form of relatively few high-energy gamma-ray photons
- Radiative transport - energy moves outward by absorption and re-emission by matter degrading to large number of low-energy visible photons
  - Opacity - resistence offered by matter to the movement of radiation through it
    - transparent <=> opaque
- Convective transport - hot gases rise, cooling, and sinking back down to be re-heated and rise again; cyclic movement of matter

18.6. Stellar Evolutionary Models

Stellar model - mathematical model calculated as means of studying evolution of stars
Stellar model obtained by solving equations of stellar structure
Structure equations describe run of mass, pressure, temperature, and luminosity from center to surface
Stellar models suggest physical processes going on inside real stars
Sequence of stellar models calculated for different times in star's life show evolutionary tracks in H-R diagram
Stellar structure equations
Mass conservation - total mass equals sum of shell masses
Hydrostatic equilibrium - weight of overlying layer balanced by outward pressure of hot gases below
Energy conservation - luminosity equals sum of energy generation in each layer
Energy transport - energy moves from hot (high-energy density) region to cool (low-energy densty) region
Solve these equations for particular point in time
Result - stellar model

Radial Distance	Temperature (K)	Density (g/cm³)	Pressure (dynes/cm²)	Mass Fraction	Luminosity Fraction
0.00	_____	_____	_____	_____	_____
0.01	_____	_____	_____	_____	_____
0.02	_____	_____	_____	_____	_____
0.03	_____	_____	_____	_____	_____
...	...	...	...	...	...
0.97	_____	_____	_____	_____	_____
0.98	_____	_____	_____	_____	_____
0.99	_____	_____	_____	_____	_____
1.00	_____	_____	_____	_____	_____
...	...	...	...	Mass	Luminosity

18.7. Solar Interior Model

Radial Distance	Temperature (10⁶ K)	Density (g/cm³)	Mass Fraction	Luminosity Fraction
0.0	15.5	160	0.00	0.00
0.1	13.0	89	0.07	0.40
0.2	9.5	41	0.35	0.90
0.3	6.7	13	0.64	1.00
0.4	4.8	4	0.85	1.00
0.5	3.4	1	0.94	1.00
0.6	2.2	0.4	0.98	1.00
0.7	1.2	0.08	0.99	1.00
0.8	0.7	0.02	1.00	1.00
0.9	0.3	0.002	1.00	1.00
1.0	0.006	3 x 10^-7	1.00	1.00
...	...	...	Mass	Luminosity

18.8. Summary of Stellar Evolution

Protostar contracts from interstellar medium
Burns hydrogen on main sequence
Contracts, iniates helium burning as red giant
"Ash" of one nuclear-burning phase provides fuel for next burning phase
High-mass stars alternately contract/ignite new sources of thermonuclear burning
Shed outer layers and die
- Low-mass stars as white dwarfs
- High-mass stars as neutron stars
- Extreme high-mass stars as black holes

18.9. Birth of Stars

Stars born in giant molecular clouds composed of gas and dust (interstellar matter), which lie along spiral arms of our Galaxy
Giant molecular clouds
- Diameter: 60 to 300 light years
- Gas density: 10² to 10⁶ particles/cm³
- Mass: 10⁵ to 10⁶ M_sun of gas and dust
Collapse of giant molecular cloud initiated by
- Self-gravitation in growing density
- Squeezing by spiral-density waves or supernova shocks
Cloud fragments into smaller, denser bodies of 10³ to 10⁵ M_sun
These collapse into groups of young stars
If gravitational force unchecked, gravity would squeeze star down to nothing as star contracts
Force opposing gravity
- Gas pressure
- Radiation pressure
- Interstellar magnetic fields
Gas pressure holding up weight of overlying layers decreases due to loss of energy as star radiates in visible and infrared
Radiation from developing star hidden by surrounding gas and dust
Examples of birthplaces of stars
- Eagle nebula
- Orion nebula
- Young star cluster

18.10. Main Sequence

Contraction from interstellar medium leads star to zero-age main sequence where hydrogen burning is initiated
Main sequence compose of those stars and only those which are in hydrogen-burning phase of life
Stars remain on main sequence most of their lives for two reasons
- Large yield of energy per gram for hydrogen fusion
- Vast amount of hydrogen available
Time star spends on main sequence is proportional to mass divided by luminosity
- Mathematical form: t_{main sequence} a M/L
Mass loss at various periods of star's life may significantly alter course of subsequent evolution, since evolution is controlled by star's mass

18.11. Main-Sequence Evolution

Star replaces radiated energy through hydrogen "burning" and other thermonuclear fusion processes
Hydrogen burning
- Low-mass hydrogen nuclei fuse at very high temperatures, > 10⁶ K, 4¹H₁ => ⁴He₂ + energy
- End product heavier helium nuclei
- Plus energy by converting mass into energy according to Einstein's equation E = mc²
Hydrogen burning phase defines main-sequence phase of star's life (about 90% of total life span)

Spectral Type	Temperature [K]	Luminosity [L_sun]	Mass [M_sun]	Main-Sequence Lifetime [yr]
O7	37,500^o	80,000	25	3 x 10⁶
B0	30,000^o	10,000	15	15 x 10⁶
A0	9,500^o	60	3.0	500 x 10⁶
F0	7,200^o	6	1.5	3 x 10⁹
G0	6,000^o	1	1.0	10 x 10⁹
K0	5,200^o	0.6	0.8	20 x 10⁹
M0	3,800^o	0.02	0.4	200 x 10⁹

18.12. Post Main-Sequence Evolution

How long H-burning lasts depends on star's mass
- High-mass stars <=> short main-sequence life
- Low-mass stars <=> long main-sequence life
H-burning moves star up away from main sequence, increasing radius slightly
Eventually, all H in energy-generating core transformed to He, i.e., end of H-burning
Too cool to ignite He-burning, so must contract and heat up to 120 x 10⁶ K

18.13. Helium "Burning"

Triple-Alpha Process
- ⁴He₂ + ⁴He₂ => ⁸Be₄
- ⁸Be₄ + ⁴He₂ => ¹²C₆ + g
Other Reaction Processes
- ¹²C₆ + ⁴He₂ => ¹⁶O₈ + g
- ¹⁴N₆ + ⁴He₂ => ¹⁸O₈ + e⁺ + g
For stars whose M < 2.3 M_sun, He-burning begins abruptly, consequence is runaway thermonuclear process, helium flash
Helium flash expands energy-generating core allowing He-burning in regulated fashion
During star's life, "ashes" of one nuclear-burning phase provide fuel for next burning phase
Summary of thermonuclear burning by mass of star

**Thermonuclear Burning by Mass**
MS Mass of Stars	Thermonuclear Burning Phases
M_star << M_sun	hydrogen
M_star < M_sun	hydrogen and possibly helium
M_star = M_sun	hydrogen and helium
M_star > M_sun	hydrogen, helium, carbon and possibly oxygen, neon, and silicon
M_star >> M_sun	hydrogen, helium, carbon, oxygen, neon, and silicon

Eventually, stars exhaust available nuclear
- Low-mass stars (< 2M_sun) end as white dwarfs (99% of all stars)
- High-mass stars (> 2M_sun) end as either a neutron star or black hole (1% or less of all stars)
Significance of H-R diagram clear several decades ago
- H-R diagram is a panorama portraying how stars evolve
- Star's position in diagram is a function of its mass, chemical composition, and current age
- Important point is that stars evolve, i.e., they are born, age, and eventually die
- Stars of our Galaxy are not same age as Galaxy, since some are young, or middle-aged, or old
Stellar evolution provides scheme whereby chemical elements in our Galaxy have evolved--a process called nucleosynthesis
- All stars convert some hydrogen to helium
- Whereas smaller number of stars convert helium into carbon
- Massive stars convert matter in stages from hydrogen to helium to carbon to oxygen and even to iron
- During supernova outburst by massive stars all elements beyond iron in periodic table made in minutes

18.14. Post-Giant Evolution

Star spends 10-25% of life as red giant in He-burning
After several hundred thousand years, low mass stars cease He-burning and expel hydrogen-rich envelope, a planetary nebula
Remnant of star contracts and heats so that surface temperature is 100,000o K which radiates ultraviolet photons that are absorbed by surrounding gaseous shell
Planetary Nebula
- Derives name from extended appearance, like Uranus, as seen in small telescope - has nothing to do with planet
- Properties
  - Number in our Galaxy: about 30,000
  - Typical size: about 1 ly
  - Expansion velocity of shell: 10-30 km/s
  - Typical lifetime: 10,000 to 50,000 years
- Some of expelled matter is chemically evolved, particulary carbon (15%) H-R Diagram, Post Giant

18.15. Death of Stars

Eventually, stars exhaust available nuclear
Depending on main-sequence mass, star undergoes a particular evolution to its death

Main-Sequence Mass	Death Sequence of Star
0.1 < M < 0.8 M_sun	spend entire life in H-burning and cool to white dwarf eventually
0.8 < M < 11 M_sun	go through red-giant phase and end as white dwarfs (99% of all stars)
11 < M < 50 M_sun	undergo supernova outburst and end as neutron star (1% or less of all stars)
M > 50 M_sun	undergo supernova outburst and end as black hole

18.6. White Dwarfs

Central star of planetary nebula cools to become white dwarf
Gas in white dwarf is degenerate electron gas
- Degenerate gas - contraction has reduced available energy states to approximately number of free electrons; pressure no longer controlled by temperature
Mass-radius relation - larger the mass, the smaller the radius up to about 1.4 M_sun
- Chandrasekhar limit - no white dwarf can be stable if M_{white dwarf} > 1.4 M_sun
- M_{white dwarf} = 0.4 M_sun, R_{white dwarf} = 10,000 km = 0.015 R_sun
- M_{white dwarf} = 0.8 M_sun, R_{white dwarf} = 7,000 km = 0.010 R_sun
No correlation between spectral appearance and surface temperature or radius as for main sequence
Number of known white dwarfs is several thousand, some 400 studied spectroscopically
Estimated number of white dwarfs in our Galaxy is 35 billion
End state of old disk population of stars
Black dwarf - when thermal energy radiated away from white dwarf, takes billions of years

Comparison of Properties for White Dwarf,
Sirius B, with Earth and Sun
Property	Earth	Sirius B	Sun
Mass (M_sun)	3 x 10^-6	0.94	1.00
Radius (R_sun)	0.009	0.008	1.00
Luminosity (L_sun)	0.00	0.0028	1.00
Surface temperature (K)	287	27,000	5770
Mean density (g/cm³)	5.50	2.8 x 10⁶	1.41
Central temperature (K)	4200	2.2 x 10⁷	1.6 x 10⁷
Central density (g/cm³)	9.60	3.3 x 10⁷	160

18.17. High-Mass Star Evolution

Hydrogen exhaustion
Gravitational contraction in core and expansion in outer layers
- Gravitational potential energy converted to thermal energy and luminosity (surface)
- E_{gravitational} => E_thermal + L
High-mass stars evolve across HR diagram to giant and supergiant branch
- Time required < 10⁶ to 50 x 10⁶ years
11-50 M_sun star forms carbon-oxygen core producing neon and more oxygen
Oxygen-neon core contracts and heats until neon-burning reactions ignited
Cycle of contraction, heating, and ignition continues to core of iron-peak elements (26 protons & 30 neutrons)
Creating heavier elements takes up energy rather than releasing energy
Lighter elements burn in shells
Core grows until exceeds Chandrasekhar limit 1.4 Msun for white dwarf, then collapses
Conversion of gravitational potential energy to thermal energy during collapse
Iron-peak nuclei to decompose into helium nuclei that in turn decompose into neutrons
Core collapse produces degenerate-neutron sphere and Type II supernova outburst (Large Magellanic Cloud, 1987)

**Evolution of 25 Solar-Mass Star**
Stage	Central Temperature (K)	Central Density (g/cm³)	Time (years)
H-burning	4 x 10⁷	5 x 10⁶	7 x 10⁶
He-burning	2 x 10⁸	7 x 10⁸	5 x 10⁵
C-burning	6 x 10⁸	2 x 10¹¹	600
Ne-burning	1.2 x 10⁹	4 x 10¹²	1
O-burning	1.5 x 10⁹	1 x 10¹³	6 months
Si-burning	2.7 x 10⁹	3 x 10¹³	1 day
Core collapse	5.4 x 10⁹	3 x 10¹⁵	0.2 seconds
Core bounce	2.3 x 10¹⁰	4 x 10²⁰	10^-6 seconds
Explosive outburst	10⁹	varies	10 seconds

18.18. Supernova

Type II supernova
- 10-100 x 10⁹ L_sun (comparable to entire galaxy)
- Rapid rise to maximum brillance followed by gradual decrease over several weeks to months
- Frequency of about 1 every 50 years per galaxy
During outburst rapid evolution of chemical elements to fill out rest of periodic table
Examples

Crab nebula in Taurus
Gum nebula in Vela

18.19. Neutron Star

Neutron star - sphere of degenerate neutrons produced during core collapse in high-mass star followed by supernova outburst
Properties
- Mass: 2-3 M_sun
- Radius: < 10 km
- Density: 10¹⁴-10¹⁶ g/cm³
- Central temperature: 10¹⁰ K
Pulsar - rapidly spinning neutron star, emits high-intensity bursts of radio radiation

18.20. Nucleosynthesis

Nucleosynthesis - scheme for chemical evolution through stellar evolution
All stars convert hydrogen to helium
Smaller number convert helium into carbon
Massive stars convert in stages from hydrogen to helium to carbon to oxygen and even to iron
During supernova outburst by massive stars all elements beyond iron in periodic table made in minutes

Copyright 1995 J. C. Evans
Physics & Astronomy Department, George Mason University
Maintained by J. C. Evans; jevans@gmu.edu