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Lecture 12

Lecture 12 Stars.docx

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SCI 238
Mike Fich

Lecture 12 Stars Brightness depends on distance amount of light it actually emits e.g. Betelgeuse emits 5000x as much light as Procyon because it’s much farther away Brightness vs. luminosity • When we talk about how bright stars look in our sky, we are talking about apparent brightness. More specifically, we define the appar- ent brightness of any star in our sky as the amount of power (energy per second) reaching us per unit area. Depends on distance • inverse square law leads to a very simple and important formula re lating the apparent brightness, lumnosity, and distance of any light source. We will call it the inverse square law for light: 2 apparent brightness=luminosity/4pi * (distance) Because the standard units of luminosity are watts, the units of apparent brightness are watts per square meter. • When we talk about how bright stars are in an absolute sense, re- gardless of their distance, we are talking about luminosity—the total amount of power that a star emits into space. Doesn’t vary Magnitude and brightness examples: 1. a group of 20 identical stars are so close together that they appear to be one star. If each star has a brightness of 5.0 mag what is the brightness in magnitudes that is observed for the group? "m 20ag) - m (ma1) = -2.5 log (20 stars / 1 star) " m 20ag) - 5.0 = -2.5 log(20) = -2.5 " 1.30 = -3.25 " m 20ag) = 5.0 - 3.25 = 1.75 mag 2. stars A and B are identical except that B is three times further away than A. If mA= 2.5 mag what is m ?Bm - A = -B.5 log (b / bA)
 "Be are told that A and B are identical... but isAb =B ? "Yes, if the stars were at the same distance, but in this caseBd = 3A ... so... NO. "Remembering that brightness as d we then have b = 1/32 b = 1/9 b (or b 2 B A A A = 9b B and... m -m = -2.5 log (9) = -2.38 and finally, m = 2.38 + 2.5 = 4.88 mag A B B 3. absolute visual (V) magnitude of the Sun is 4.8.What is the absolute magnitude of a galaxy with 2x10 stars identical to the Sun? If it is at a 5 distance of 760 kiloparsecs (7.6x10 pc =760 kpc) what is its apparent magnitude? 
 8 Mgal – Msun = -2.5 log (2x10 /1) = -20.8 Mgal = Msun – 20.7 = -15.9 
 mgal- Mgal = 5 log (d/10) = 5 log (7.6x104) = 24.4 mgal = Mgal + 24.4 = 8.4 Hertzsprung-Russell (H-R) diagrams • The horizontal axis represents stellar surface temperature, which, as we’ve discussed, corresponds to spectral type. Temperature decreases from left to right because Hertzsprung and Russell based their dia- grams on the spectral sequence OBAFGKM. • The vertical axis represents stellar luminosity, in units of the Sun’s luminosity (LSun). Stellar luminosities span a wide range, so we keep the graph compact by making each tick mark represent a luminosity 10 times as large as the prior tick mark. • stars near the upper left are hot and luminous. Similarly, stars near the upper right are cool and luminous, stars near the lower right are cool and dim, and stars near the lower left are hot and dim. • star’s luminosity depends on both its surface temperature and its surface area or radius. If two stars have the same surface temperature, one can be more luminous than the other only if it is larger in size. Stellar radii therefore must increase as we go from the high-temperature, low- luminosity corner on the lower
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