Measuring the Properties of Stars

The textbook web resources for Chapter 12 are here.


Finding the Distance to a Star

Triangulation - using a right triangle in which we know the measurement of one side and the adjacent angle (besides the 90o angle) to find the distance of an object.

Parallax - a type of triangulation wherein we measure how much the star seems to move against the background stars.  The angle that the star moves is so small, it's measured in arc seconds (1/3600 of a degree).

The distance to stars, when using the parallax method, is measured in parsecs (parallax in arc seconds).  1 parsec (pc) = 3.26 light years

 

Finding Star Temperature

Wein's Law - the temperature of a star is equal to 3x106 / the wavelength at which the star radiated most strongly.  Since the wavelength determines the color, the color of a star is related to its temperature.

 

Finding Star Luminosity

Luminosity (L) - how much energy is radiated by the star/object each second.

Brightness (B) - how bright the star appears from Earth. 

The Inverse-Square Law explains that the farther away from an object you get, the lesser its brightness will be.  The formula for this is:

                      B = L / 4πd2

 Brightness = Luminosity / The surface area of a sphere with radius d (which represents the distance from the observer to the object).

 

Finding Star Radius

Note: If two stars have the same temperature, but one is more luminous than the other, then the brighter star has a larger surface area (it's bigger) than the dimmer star.

The Stefan-Boltzmann Law explains that the luminosity of a star depends on both its temperature and its radius: increasing either will make the star brighter.  The formula for this is:

                    L = 4πR2σT4

Luminosity = Surface area of star with radius R x σ x (Temperature T)4

So, if we know the luminosity and the temperature, we can calculate the size of the star.

 

Star Magnitude

Magnitude is a unit for measuring star brightness.  Brighter stars have smaller magnitudes, dimmer stars have larger magnitudes.

  - apparent magnitude - how bright a star looks to an observer.

  - absolute magnitude - how bright a star would look to an observer at a distance of 10 parsecs.

 

Star Spectra

A star's spectrum can tell us the star's composition, temperature, luminosity, velocity in space, and even its rotational speed.

Absorption lines in a star's spectrum are created when specific wavelengths of light are absorbed by atoms in the star.  Each element creates a unique set of absorption lines.  So, we can compare the lines in a star's spectrum to a catalogue of lines created by various elements, and use this to figure out the composition of the star.  In addition, the greater the quantity of an element in a star, the darker its absorption lines will be.

Absorption lines are affected by star temperature because...

  ...the wavelength absorbed by an atom depends on what energy level the

     atom's electrons are at (and which level they will be raised to).

  ...as stars get hotter, their electrons tend to move towards higher energy

     levels.

This means that hot stars will show different lines than cold stars, even if they are composed of the same material.  Thus, we have to take temperature into account when looking at star spectra.

 Stars are grouped into spectral classes based on the appearance of their spectral lines.  The spectral class indicates the star's temperature.  The basic classes are...

   O - Hotter than 25,000 K

   B - 11,000 - 25,000 K

   A - 7,500 - 11,000 K

   F - 6,000 - 7,500 K

   G - 5,000 - 6,000 K

   K - 3,500 - 5,000 K

   M - 2,200 - 3,500 K

  

Doppler Shift

When a star (or other light source) is moving away from an observer, the absorption lines in its spectrum shift towards the red end of the spectrum.  This is called a red shift.  A blue shift occurs when the lines move towards the blue/violet end of the spectrum, indicating that the star is moving towards the observer.  Blue shifts and red shifts can be used to calculate the speed at which stars are moving. 

 

Binary Stars - two stars that orbit each other.  About 40% of all known stars are binary (or triple, quadruple - even one group of six).  The star masses determine their gravitational forces, which determine their motions.  Thus, knowing their motions allows us to calculate their masses.

  1. Visual Binaries
    • You can see the two stars as separate, usually using a telescope.
  2. Spectroscopic Binaries
    • The stars are so close together that they can't be seen separately, even with a telescope.
    • Looking at their spectra shows a double set of lines: the lines red-shift and blue-shift as the stars orbit each other.
  3. Eclipsing Binaries
    • The plane of the stars' orbits appear flat to us, so the stars eclipse each other as they orbit.
    • This creates a dimming effect as we see the light from only one star while they are eclipsed.

Resources

Homework from the Text:

  • Read Chapter 12 (pg. 349-380).
  • Review Questions #2-6, 8-16 (pg. 381).