Summary of Stellar Proper/es Large range of Stellar Luminosi/es: 10 4 to 10 6 L sun Large range of Stellar Radii: 10 2 to 10 3 R sun Modest range of Stellar Temperatures: 3000 to >50,000 K Wide Range of Stellar Masses: 0.1 to ~50 M sun
Luminosity Radius Temperature Rela/on Stars are approximately black bodies. Stefan Boltzmann Law: energy/sec/area = σt 4 The area of a spherical star: area = 4πR 2 Predicted Stellar Luminosity (energy/sec): L = 4πR 2 σt 4
Example 1: 2 stars are the same size, (R A =R B ), but star A is 2 ho#er than star B (T A =2T B ): Therefore: star A is 16 brighter than star B
Example 2: 2 stars are the same temperature, (T A =T B ), but star A is 2 bigger than star B (R A =2R B ): Therefore: star A is 4 brighter than star B
Hertzsprung Russell Diagram Plot of Luminosity versus Temperature: es/mate T from Spectral Type es/mate L from apparent brightness & distance Done independently by: Eljnar Hertzsprung (1911) for star clusters Henry Norris Russell (1913) for nearby stars
Eljnar Hertzsprung Henry Norris Russell
H R Diagram 10 6 Supergiants Luminosity (L sun ) 10 4 10 2 1 10 2 Giants 10 4 White Dwarfs 40,000 20,000 10,000 5,000 2,500 Temperature (K)
Main Sequence Most nearby stars (85%), including the Sun, lie along a diagonal band called the Ranges of proper/es: L=10 2 to 10 6 L sun Main Sequence T=3000 to >50,0000 K R=0.1 to 10 R sun
Giants & Supergiants Two bands of stars brighter than Main Sequence stars of the same Temperature. Means they must be larger in radius. Giants R=10 100 R sun L=10 3 10 5 L sun T<5000 K Supergiants R>10 3 R sun L=10 5 10 6 L sun T=3000 50,000 K
White Dwarfs Stars on the lower lea of the H R Diagram fainter than Main Sequence stars of the same Temperature. Means they must be smaller in radius. L R T Rela/on predicts: R ~ 0.01 R sun (~ size of Earth!)
Hipparcos H-R Diagram 4902 single stars with distance errors of <5%
Luminosity Classifica/on Absorp/on lines are Pressure sensi4ve: Lines get broader as the pressure increases. Larger stars are puffier, which means lower pressure, so that Larger Stars have Narrower Lines. This gives us a way to assign a Luminosity Class to stars based solely on their spectra!
Luminosity Effects in Spectra
Luminosity Classes: Ia = Bright Supergiants Ib = Supergiants II = Bright Giants III = Giants IV = Subgiants V = Dwarfs = Main Sequence Stars
Spectral + Luminosity Classifica/on of Stars: Sun: G2v (G2 Main Sequence star) Winter Sky: Betelgeuse: M2 Ib (M2 Supergiant star) Rigel: B8 Ia (B8 Bright Supergiant star) Sirius: A1v (A1 Main Sequence star) Aldebaran: K5 III (K5 Giant star)
From Stellar Proper/es to Stellar Structure Any theory of stellar structure must explain the observed proper/es of stars. Seek clues in correla/ons among the observed proper/es, in par/cular: Mass Luminosity Radius Temperature
H R Diagram 10 6 Supergiants Luminosity (L sun ) 10 4 10 2 1 10 2 Giants 10 4 White Dwarfs 40,000 20,000 10,000 5,000 2,500 Temperature (K)
Main Sequence: Strong correla/on between Luminosity and Temperature. Holds for 85% of nearby stars including the sun All other stars differ in size: Giants & Supergiants: Very large radius, but same masses as M S stars White Dwarfs: Very compact stars: ~R earth but with ~M sun!
10 4 Luminosity (Lsun) 10 2 1 L M 3.5 10 2 0.01 0.1 1 10 100 Mass (M sun )
Mass Luminosity Rela/onship For Main Sequence stars: In words: More massive M-S stars are more luminous. Not true of Giants, Supergiants, or White Dwarfs.
10 4 Luminosity (Lsun) 10 2 1 L M 3.5 10 2 0.01 0.1 1 10 100 Mass (M sun )
Stellar Density Density = Mass Volume Main Sequence: small range of density Sun: ~1.6 g/cc O5v Star: ~0.005 g/cc M0v Star: ~5 g/cc Giants: 10 7 g/cc White Dwarfs: 10 5 g/cc
Interpre/ng the Observa/ons: Main Sequence Stars: Strong L T Rela/onship on H R Diagram Strong M L Rela/onship Implies they have similar internal structures & governing laws. Giants & White Dwarfs: Must have very different internal structures than Main Sequence stars of similar mass.
Laws of Stellar Structure I: The Gas Law Most stars obey the Perfect Gas Law: Pressure = Density Temperature In words: Compressing a gas results in higher P & T Expanding a gas results in lower P & T
Laws of Stellar Structure II: The Law of Gravity Stars are very massive & bound together by their Self Gravity. Gravita/onal binding increases as 1/R 2 In words: Compress a star, gravita/onal binding gets stronger. Expand a star, gravita/onal binding gets weaker.
Hydrosta/c Equilibrium Gravity wants to make a star contract. Pressure wants to make a star expand. Counteract each other: Gravity confines the gas against Pressure. Pressure supports the star against Gravity. Exact Balance = Hydrosta4c Equilibrium The star neither expands nor contracts.
Hydrosta/c Equilibrium Gravity Gas Pressure
Core Envelope Structure Outer layers press down on the inner layers. The deeper you go into a star, the greater the pressure. The Gas Law says: Consequences: More pressure= ho#er, denser gas hot, dense, compact CORE cooler, lower density, extended ENVELOPE
Core Envelope Structure Compact Core Extended Envelope
Example: The Sun Core: Radius = 0.25 R sun T = 15 Million K Density = 150 g/cc Envelope: Radius = R sun = 700,000 km T = 5800 K Density = 10 7 g/cc
The Essen/al Tension The Life of a star is a constant tug of war between Gravity & Pressure. Tip the internal balance either way, and it will change the star s outward appearance. Internal Changes have External Consequences
Summary: The Hertzsprung Russell (H R) Diagram Plot of Luminosity vs. Temperature for stars. Features: Main Sequence (most stars) Giant & Supergiant Branches White Dwarfs Luminosity Classifica/on Mass Luminosity Rela/onship
Summary: Observa/onal Clues to Stellar Structure: H R Diagram Mass Luminosity Rela/onship The Main Sequence is a sequence of Mass Equa/on of State for Stellar Interiors Perfect Gas Law Pressure = density temperature
Summary: Stars are held together by their self gravity Hydrosta/c Equilibrium Balance between Gravity & Pressure Core Envelope Structure of Stars Hot, dense, compact core cooler, low density, extended envelope
Ques/ons: Why don t stars have just any Luminosity and Temperature? Why is there a dis/nct Main Sequence? Answer: Parerns on the H R Diagram are telling us about the internal physics of stars.
Ques/ons How hot are the interiors of other stars? What would happen if gravity suddenly became stronger? What generates all the energy that keeps the star from collapsing?