Key Concepts:

1. What properties of stars can astronomers learn from stellar spectra?
2. How do astronomers measure masses of stars? Why is the studies of binary stars important in this regard?
3. What is Stefan-Boltzmann Law? What properties of stars does it reveal
4. What is the Hertzsprung-Russell Diagram?
5. How do astronomers use the H-R diagram to measure ages of star clusters?
6. How do astronomers use the H-R diagram to measure distances of star clusters?

Measuring Star's Properties

Quantity Method Distance parallax, standard candle Luminosity apparent brightness, distance, and inverse square law Size Stefan-Boltzmann law, eclipsing binary Composition spectral lines observed Temperature Wien's law Radial velocity Doppler shift of spectral lines Mass Modified Kepler's third law for binary stars Age Main Sequence Turn-off in an H-R diagram

Stellar Spectra

• spectrum: light separated and spread out by wavelength using a prism or a grating


• Wien's Law: deduce temperature of the stellar photosphere


• spectral lines
• atomic and molecular composition
• physical conditions of the gas (temperature, density)
• radial velocity (motion) from Doppler shift

Weighing Stars' Mass using Binary Stars

• Visual binary: a pair of stars that we can see distinctly orbiting each other
• Spectroscopic binary: a pair of stars orbiting each other, inferred by the Doppler shifts in their spectral lines
• Eclipsing binary: a pair of stars orbiting each other, inferred by the shadowing of each other by eclipse.
• Binaries can be used to measure the masses of stars using the Newton's version of Kepler's Law.

Visual Binary

Quiz 13A: weighing stars...

Weighing the Monster in the Heart of the Milky Way

• semi-major axis ~ 5 light days (about 850 AU)
• orbital period ~ 14 years
• BH mass = (850)³/(14)² ~ 3.2 million solar masses!

• period (P) and line-of-sight velocity (V = V₁+V₂) is measured directly
• semi-major axis (R) = (VP/2π) sini
• mass (M = m₁+m₂) = R³/P² (if R in AU and P in years as before).

Eclipsing Binary

• a special case of a binary star -- orbit seen nearly edge-on (i=0)
• light curve due to geometrical changes in light emitting regions
• geometrical information such as the shape and sizes can be derived

Stefan-Boltzmann Law

Making T larger makes each square meter of the star brighter Making R larger increases the number of square meters

__

Quiz 13B: The Giant Sun....

Hertzsprung-Russell Diagram

Quiz 13C:

Main Sequence most nearby stars (85%), including the Sun hydrogen-burning stars 3000-30,000 K 0.1 to 10 R(sun) Mass-Luminosity Relation: L ~ M3.5 Giants and Supergiants Brighter stars for the same temperature as MS 3000-30,000 K 10 to 1000 R(sun) example: Betelgeuse White Dwarfs faint stars for the same temperature as MS 5000-30,000 K 0.01 R(sun) HR diagram for the stars studied by Hipparcos satellite

Dating Stars' Age: Star Clusters

Open Cluster (M45)
Globular Cluster (M80) Main Sequence Turnoff: tMS ~ 10/L billion years The oldest globular clusters (M15, M68, M92) are about 13 billion years old.

Quiz 13D

Measuring Distance to Star Clusters using Main Sequence Fitting

• color = temperature
• magnitude = brightness
• absolute magnitude M = m - 5log(D/10pc)

Another Tool for Measuring Star's Distance: Variable Stars

• Pulsating variables
  • radius changes rhythmically, swelling and shrinking
  • temperature also changes
  • luminosity changes by a factor of 2 or 3
  • periods of a few days to years
  • appear along "instability strip" in H-R diagram
  • standard candles for distance determination (Miras, Cepheids)
  • movie of a Cepheid variable star in a nearby galaxy NGC 3370 made using the Hubble Space telescope
• Other types of variable stars

Reading assignment for next lecture: Units 55-58