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Physics 484/584 Homework 3

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Physics 484/584 Homework 3 Physics 484/584 Homework 3 Out: 2016 February 12 Due: 2016 February 19 2:30PM Pacific Standard Time 1. Parallax and Magnitudes Using the stellar database SIMBAD at http://simbad.harvard.edu/ : 1.1. (ALL) Determine the parallax for your favorite star (or if you don't have a favorite, you can use mine: Beta Librae, also known as Zubeneschamali). Go to either basic query or identifier query, and type your star's name in. 1.2. (ALL) How far away is your star in parsecs? Note that the units for the values given in SIMBAD are in milliarcseconds, mas. 1.3. (ALL) What is the apparent magnitude of your star in the visible? This is listed as `V' on SIMBAD in the \Fluxes" row. Could you see this star if you were out looking at the sky? 1.4. (PHYS 584 STUDENTS ONLY) Calculate your star's absolute magnitude. 1.5. (ALL) Look your star up on the stars website, http://stars.astro.illinois.edu/sow/sowlist.html. (hopefully it's there!). What's in- teresting and/or unusual about your star? 2. Blackbody Emission Imagine a solar-type star with R at 6000 Kelvin has a giant planet with the same radius as Jupiter's orbiting it with a semimajor axis a = 0:05 AU. These type of planets are variously called: 51-Peg planets, Hot Jupiters (as opposed to Very Hot Jupiters { no really, that's a class of even closer-in planets), Roasters, or close-in planets. Imagine that the planet is a blackbody, as we all did before we had thought about the problem very much. { 2 { 2.1. (ALL) What is the planet's equilibrium temperature if it is isothermal? 2.2. (PHYS 584 STUDENTS ONLY) Using any method you like, plot the planet's equilib- rium temperature as a function of incidence angle if it were NOT isothermal, i.e. if each point on the surface is separately in equilibrium. You may elect to use a spreadsheet program, graphing calculator, or other device for this problem. 2.3. (PHYS 484 STUDENTS ONLY) What would the planet's dayside equilibrium tem- perature be if heat transport were inefficient and the dayside and nightside were each just one single temperature? 2.4. (ALL) Using your result from 1.1 as the planet's real temperature, at what wavelength is the planet-to-star flux ratio maximized? 2.5. (ALL) Plot the blackbody emission curve Bλ from 0:3 µm to 10 µm for bodies of tem- perature 3000K and 3100K. At what wavelength is the 3000K body brighter per unit area than the 3100K body? 3. Blackbody Emission II (ALL) As they surveyed the sky from New Mexico, the Sloan Digital Sky Survey (SDSS) would take UVBRI photometry of giant swaths of the sky. When they found a source that was of interest, either something they were looking for or something unusual, they would follow up by taking a spectrum. When they found one weird object, they took its spectrum and it looked something akin to Figure 1. 3.1. (ALL) What might they be looking at? Assume that all objects involved are black- bodies. What temperature are the bodies in the spectrum? 3.2. (ALL) What are their relative radii? 3.3. (ALL) Say the cooler object is a red dwarf star (we'll talk more about these later), and so has a radius of about 0.3 R . How big is the other object? { 3 { 1.0 0.8 0.6 Flux (normalized) 0.4 0.2 0.1 1 10 Wavelength (Microns) Fig. 1.| As seen by the Sloan Digital Sky Survey (SDSS)..
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