Lecture 13
Measuring a Star's Properties

Key Concepts:

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

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

Stefan-Boltzmann Law

  • Making T larger makes each square meter of the star brighter
  • Making R larger increases the number of square meters
If the luminosity (L) and temperature (T) are known, the size (R) of a star can be deduced.

Stellar Spectra

Class Spectrum Color Temperature
O ionized and neutral helium, weakened hydrogen bluish above 31,000 K
B neutral helium, stronger hydrogen blue-white 9750-31,000 K
A strong hydrogen, ionized metals white 7100-9750 K
F weaker hydrogen, ionized metals yellowish white 5950-7100 K
G still weaker hydrogen, ionized and neutral metals yellowish 5250-5950 K
K weak hydrogen, neutral metals orange 3950-5250 K
M little or no hydrogen, neutral metals, molecules reddish 2000-3950 K
L no hydrogen, metallic hydrides, alkalai metals red-infrared 1500-2000 K
T methane bands infrared 1000 K

The visual colors are actually subtle and as much reflect where most of the light lies in the spectrum as the color a person would actually view. Classes A through G all look rather white to the eye.

Visual and Spectroscopic Binary

Quiz 13a

Eclipsing Binary

Hertzsprung-Russell Diagram

Quiz 13b

  • Spectral Type (ST) along the x-axis

  • Luminosity Class (LC) along the y-axis

  • Luminosity Class I: Supergiants

  • Luminosity Class II: Bright giants

  • Luminosity Class III: Giants

  • Luminosity Class IV: Subgiants

  • Luminosity Class V: Main Sequence

  • Our Sun is G2 V. Betelheuse is M5 V ( a red supergiant).

  • Look at the following table: Mv is the absolute magnitude, mv is the apparent magnitude, ST is the Spectral Type (ST) and LC is the Luminosity Class (LC)

  • Star............. Mv....... mv..... ST...... LC

    Aldebaran.... -0.2...... +0.9.... K5..... III
    Alpha Cen.... +4.4...... 0.0.... G2..... V
    Antares........ -4.5...... +0.9.... M1..... I
    Canopus...... -3.1...... -0.7.... F0..... II
    Formalhaut...+2.0...... +1.2.... A3..... V
    Regulus....... -0.6...... +1.4.... B7..... V
    Sirius......... +1.4...... -1.4.... A1..... V
    Spica.......... -3.6...... +0.9.... B1..... V

  • Which star appears brightest in our sky?

  • Which star appears faintest in our sky?

  • Which star has the greatest luminosity?

  • Which star has the least luminosity?

  • Which star has the highest surface temperature?

  • Which star has the lowest surface temperature?

  • Which star is the bluest?

  • Which star is most similar to our Sun?

  • WHich star is a red supergiant?

  • Which star has the largest radius?

  • Which star may have some molecules inits outer atmosphere?

  • Note that for a GIVEN star, its luminosity can only be increased/decreased by making its radius bigger/smaller or by making its temperature higher/lower. Just moving a star closer and farther away without changing the radius or temperature DOES NOT change its luminosity.

  • The absolute magnitude of a star is a measure of the star's luminosity or its "intrinsic brightness". Its the brightness of a star if it were placed at a distance of 10 parsecs. The apparent brightness of a star is the star's brightness as it appears in the sky and thus is related to how far away the star is.

  • If Regulus was suddenly moved to six times as far away, how would its luminosity and brightness change?

  • Luminosity stays the same because you are not altering its radius or temperature, but brightness decreases by a factor of 6x6 = 36.

  • If Regulus was suddenly moved to six times as far away, how would its absolute magnitude change?

  • No change

  • If Regulus was suddenly moved to six times as far away, how would its apparent magnitude change?

  • Its brightness changes by a factor of 36. Magnitude is a measure or scale of brightness such that a numerical change of 1 corresponds to a change in brightness by a factor of 2.512. 2.512 x 2.512 x2.512 x 2.512 is roughly 36 so this corresponds to a change in magnitude of 4.

  • Repeat the above three questions but instead Regulus is moved six times as close.

  • Stars A and B have apparent magnitudes 3 and 7. So what is the difference in their brightnesses?
  • A difference of four corresponds to a change in brightness by a factor of 2.512x2.512x2.512x2.512 = roughly 36.

  • If Regulus was made three times as large but kept at the same temperature, how would its luminosity change?

  • This uses the Stefan Boltzmann law - changing the radius by a factor y changes the luminosity by a factor yxy. Here we increase the radius by a factor 3 so the luminosity is increased by a factor of 9.

  • If Regulus was kept the same size but it was three times as hot, how would its luminosity change>

  • Increasing the temperature by a factor y increases the luminosity by a factor yxyxyxy. Here we increase the temperature by a factor 3, so its luminosity increases by factor 3x3x3x3 = 81.

  • Which of the following statements are true?

  • Two stars that look very different must be made up of different elements?

  • Sirius is the brightest star in the night sky, but if we moved it 10 times further away it would look only one-tenth as bright

  • Stars that look red-hot have hotter surface temperatures than stars that look blue

  • Some of the stars on the main sequence of the HR diagram are not converting hydrogebn to helium

  • The smallest, hottest stars are plotted in the lower-left hand portion of the HR diagram

  • The largest, coolest stars are plotted in the upper-left hand portion of the HR diagram

  • Star Clusters

    Open Clusters

    Globular Clusters

    • Main Sequence Turnoff: t(MS) ~ 10/L billion years

    Variable Stars

    Reading assignment for next lecture: Chapter 17 (p.544-p.571)