Reading: Sections 1.1 - 1.4 of Sparke & Gallagher
The rules: Collaborative work is encouraged. This homework can be done in consultation with your fellow classmates, the AI, or the professor. However, everyone must submit their own solutions to get credit, and all help should be acknowledged (a single sentence mentioning the others in your study group is sufficient). Show your work. We will not give you credit if you do not first SET UP the problem and then show all intermediary steps. Also, neatness counts. Please make certain that your homework is legible and all pages are stapled together.
1. [14 pts] Consider a model star with an effective surface temperature of 28,000 K and a radius of 5.16 x 1011 cm. If the model star is at a distance of 180 pc from Earth, determine the following for the star: (a) Luminosity, (b) Absolute bolometric magnitude, (c) Apparent bolometric magnitude, (d) Distance modulus, (e) Radiant flux at the star's surface, (f) Radiant flux at Earth's surface (compare this with the solar constant), and (g) Peak wavelength.
2. [12 pts] (a) What are the colors (in B-V), luminosities (in solar luminosities or absolute magnitudes), surface temperatures, and spectral types of zero age main sequence stars of 3, 1, 0.8 Msun? (b) What are the major spectral features that distinguish them? (c) At what wavelength will the 3 Msun star radiate the most light? What about the 0.8 Msun star? [Note: part (a) is a literature question. While you do not need to show your work, you should cite the appropriate reference. NB: You may need to look beyond your textbook to find this information.]
3. [4 pts] Estimate the solar radius from its luminosity and effective temperature. Show that the acceleration of gravity, g, at the surface is about 30 times larger than that on Earth.
4. [12 pts] The red supergiant star Betelguese in the constellation Orion has Teff ~ 3500 K and a diameter of 0.045". Assuming its distance d=140 pc, what is its radius and luminosity? Betelguese has an apparent magnitude mV = 0 (after correcting for extinction) and V-K =5. Find its absolute magnitude in V and in K. What is the luminosity in V and K, compared to solar values?
5. [4 pts] Assuming that the Milky Way's luminosity L ~ 2 x 1010 Lsun, and making the very rough approximation that it is a sphere 8 kpc in diameter, what would be its effective temperature?
6. [4 pts] For approximately how many life cycles of a typical O5 star has the Sun been on the main sequence?