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Today:. Star sizes HR diagrams More info from spectra Mass: Mass and luminosity How do we measure mass? Binary stars. Stars come in various sizes. Let’s do a few calculations to get a feel for the range of stellar sizes:. Finding key properties of a nearby star.

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today
Today:
  • Star sizes
  • HR diagrams
  • More info from spectra
  • Mass:
    • Mass and luminosity
    • How do we measure mass?
  • Binary stars
stars come in various sizes
Stars come in various sizes

Let’s do a few calculations to get a feel for the range of stellar sizes:

understanding stellar data
Understanding stellar data
  • We have a huge pile of data about the stars. What do we need to do to understand it?
    • Make a graph!
  • What should we graph?
    • Two quantities differ substantially from star to star: temperature and luminosity.
  • If we make a graph relating these two quantities we can understand the relationship between L and T. As a bonus we also create a plot that helps us understand how stars form, evolve and die.
    • This is a really important graph, perhaps the most important in all astronomy!
hertzsprung russell diagrams
Hertzsprung-Russell diagrams
  • 1911: Ejnar Hertzsprung made a plot of absolute magnitude (luminosity) as a function of color (temperature).
  • 1913: Henry Norris Russell made a similar plot but used spectral class instead of color.
  • This plot is called a Hertzsprung-Russell or HR diagram.
more information in spectra
More information in spectra
  • Surface temperature largely determines which lines are prominent in a star’s spectrum.
    • Classifying stars by spectral type is equivalent to categorizing them by surface temperature.
    • Problem: 5800K surface temperature can mean a star is a white dwarf, a main-sequence star, a giant or even a supergiant…
  • It turns out that details in the spectrum of a star help us solve this problem.
    • Can determine type of star.
    • Can even be used to determine distance to star.
size from spectra
Size from spectra
  • Balmer lines are narrow in large, luminous supergiants and broad in small, less luminous main-sequence star.
    • Due to pressure broadening.
    • Higher density (small stars)=broad lines.
    • Lower density (large stars)=narrow lines
spectroscopic parallax
Spectroscopic parallax
  • A star’s spectral type and luminosity combined with info on the HR diagram allow us to estimate a star’s distance from Earth.
    • Also need inverse-square law.
    • Accurate to about 10% since HR diagrams consist of broad bands instead of narrow lines.
  • Let’s look at an example:
stellar mass
Stellar mass
  • Answer lies in energy source for stars:
    • Greater mass means higher pressure and temperature at center of stars leading to more rapid fusion and a greater energy output.
    • To maintain hydrostatic and thermal equilibrium in a more massive star, the star must have a larger radius and higher surface temperature.
  • This is what we see in the HR diagram.
how do we measure mass
How do we measure mass?
  • About half of all visible stars are parts of multiple star systems.
    • Typically pairs called binary stars.
    • These stars are gravitationally bound so we can use physics to describe their motions.
determining stellar masses
Determining stellar masses

In principle, if we can determine a and P we can calculate M1+M2. We want M1 and M2 separately however. How do we find that?

determining stellar masses1
Determining stellar masses
  • Binary stars orbit the center of mass of the system.
    • Balance point of kids on seesaw. Its position depends on the relative masses of the kids.
  • Understanding size of orbits around center of mass gives us M1/M2.
    • This, combined with the sum of the masses (and a little algebra) allows us to calculate the individual masses.
  • We won’t do this in class today, but you can on the homework for some extra credit.