1	Astro 1050 Wed. Oct. 9, 2002 Today: Chapter 8, Properties of Stars Please bring calculators to class
2	Inverse-square law for light:
3	Correcting Magnitudes for Distance To correct intensity or flux for distance, use Inverse Square Law Up to now we have used “apparent magnitudes” m_v Define absolute magnitude M_v as magnitude star would have if it were at a distance of 10 pc. This gives us a way to correct Magnitude for distance, or find distance if we know absolute magnitude Note: the book writes m_v and M_v: The “V” stands for “Visual” Later we’ll consider magnitudes in other colors like “B=Blue” “U=Ultraviolet”
4	Let’s work some examples: Problem #4: m_V M_V d (pc) P (arcsec) ___ 7 10 _______ 11 ___ 1000 _______ ___ -2 ____ 0.025 4 ___ ____ 0.040
5	Let’s work some examples: Problem #4: m M_V d (pc) P (arcsec) 7 7 10 0.1 11 1 1000 0.001 1 -2 40 0.025 4 2 25 0.040
6	How to recognize patterns in data What patterns matter for people – and how do we recognize them? Weight and Height are easy to measure Knowing how they are related gives insight into health A given weight tends to go with a given height Weight either very high or very low compared to trend ARE important Plot weight vs. height and look for deviations from simple line Example of cars from the book Note “main sequence” of cars Weight plotted backwards Just make main sequence a line which goes down rather than up Points off main sequence are “unusual” cars
7	Stars: Patterns of L, T, R The Hertzsprung-Russsell (H-R) diagram Plot L vs. backwards T. (We can find R given L and T)
8	How are L, T, and R related? L = area ´sT⁴ = 4 p R² sT⁴ Stars can be intrinsically bright because of either large R or large T Use ratio equations to simplify above equation (Note book’s symbol for Sun is circle with dot inside) Example: Assume T is different but size is same A star is ~ 2 ´ as hot as sun, expect L is 2⁴= 16 times as bright M star is ~1/2 as hot as sun, expect L is 2^-4= 1/16 as bright B star is ~ 4 ´ as hot as sun, expect L is 4⁴= 256 times as bright Example: Assume T same but size is different If you have a G star 4 ´ as large as sun, expect L would be 4²=16 times as bright
9	L, T, R, and the H-R diagram L = 4 p R² sT⁴ The main sequence consists very roughly of similar size stars The giants, supergiants, and white dwarfs are much larger or smaller
10	Lines of constant R in the H-R diagram
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12	Different “types” of H-R diagrams
13	Luminosity Classes
14	Spectra of Different Luminosity Classes
15	Spectroscopic “Parallax”
16	What fundamental property of a star varies along the main sequence?
17	Masses of Binary stars
18	Masses of Binary stars
19	Masses of Binary stars
20	Measuring a and P of binaries Two types of binary stars Visual binaries: See separate stars a large, P long Can’t directly measure component of a along line of sight Spectroscopic binaries: See Doppler shifts in spectra a small, P short Can’t directly measure component of a in plane of sky If star is visual and spectroscopic binary get get full set of information and then get M
21	Masses and the HR Diagram Main Sequence position: M: 0.5 M_Sun G: 1 M_Sun B: 40 M_sun Luminosity Class Must be controlled by something else
22	The Mass-Luminosity Relationship L = M^3.5
23	Eclipsing Binary Stars System seen “edge-on” Stars pass in front of each other Brightness drops when either is hidden Used to measure: size of stars (relative to orbit) relative “surface brightness” area hidden is same for both eclipses drop bigger when hotter star hidden tells us system is edge on useful for spectroscopic binaries