HW #7 Answers (Due 10/14)
1)Suppose you take a spectrum of a star and find that the hydrogen alpha absorption line has a wavelength of λ = 657 nm. When hydrogen is at rest the alpha line has a wavelength of λo = 656 nm. Find the velocity of the star. Is it coming toward us or moving away?
The Doppler velocity is given by the equation:
Where c is the speed of light and is the Doppler shift given by
So v = (3x108 m/s)*nm)/656 nm
v = 457,317 m/s or v = 457 km/s
Since the observed wavelength is longer than the rest wavelength, the star is moving toward us.
2)Using spectroscopy for a spectroscopic binary, explain how you can determine the period of the orbit.
For a spectroscopic binary the absorption features of the two stars are separated in the spectrum. This gives double the absorption lines. When one star is coming toward us and one star is moving away, the lines for the star that is approaching us are all blue shifted. The star that is moving away are all red shifted. As the stars orbit, the change positions and the star that was moving toward us is now moving away, and vice versa.
If you continue to observe the stars until the absorption lines are back to their original Doppler shift, then the stars will have completed one orbit. The time it takes to complete one orbit is the period of the orbit.
3)If star 1 in the binary has a velocity that is four times greater than star 2, how are the masses of star 1 and star 2 related. Explain.
The least massive star in the system will have a larger orbit than the massive star. They both have the same orbital period. So the less massive star has to move more rapidly in its orbit than the more massive star. If star #1 has four times the velocity of #2 then #2 has to have four times the mass of #1.
4)Explain why a star with high pressure on its surface can smear out the energy levels of the atoms and cause the absorption line to become very broad.
For an atom that is isolated, the jump between two energy levels is a very precise amount of energy. What determines how much energy is needed to jump energy levels is the force between the charges in the atom. This is why different elements have different energy levels. But for each type of element, the energy levels are exactly the same. That is, as long as the atom is isolated. In a star there are many atoms close to each other. If the pressure is high, the atoms are very close and each atom can feel the effect of the other charges around them. This perturbs the atom’s energy level a lit bit. In other words, a jump between energy levels is not very precise, but can take on a small spread of values. This allows the atoms to absorb energies of light (or wavelengths of light) which an isolated atom could not. When a star has a very high surface pressure, the effect is larger and the result is broader absorption lines. When the pressure is low, like in a supergiant star, the effect is less, and the absorption lines are narrow.
5)If we can determine the luminosity class of a star, and its surface temperature, how can we use these parameters to find its distance?
The H-R diagram works for all stars. It is a plot of luminosity vs. surface temperature. For a given temperature you can use the H-R diagram to see where a star would be located and then read off the luminosity. The only problem is that supergiants, giants and main sequence stars can have the same surface temperature, but very different luminosities. However, if you know the luminosity class, meaning you know if the star is a supergiant (I) and giant (III) or a main sequence star (V) then you can see where the surface temperature intersects the luminosity class and then read off the luminosity. Since B = L/4d2 you can then compute the distance of the star.