1	Astro 1050 Mon. Oct. 13, 2002 Today: Chapter 8, Properties of Stars
2	Chapter 8: Properties of Stars How much energy do stars produce? How large are stars? How massive are stars? We will find a large range in properties!
3	Distances to Stars Distance:
4	Parallax: Really just the small angle formula
5	Intrinsic Brightness of Stars Apparent Brightness: How bright star appears to us Intrinsic Brightness: “Inherent” – corrected for distance How does brightness change with distance? Flux = energy per unit time per unit area: joule/sec/m² = watts/m² Example: 100 watt light bulb (assume this is 100 W of light energy) spread over 5 m² desk gives 20 Watts/m² Sun’s flux at the Earth Luminosity = 3.8 ´10²⁶ Watts It has spread out over sphere of radius 1 AU = 1.5 ´ 10¹¹ m Surface area of sphere = 4 p R² = 2.8 ´10²³ m² F_Sun = 3.8 ´10²⁶ Watts / 2.8´10²³ m² = 1,357 W/m² Inverse Square Law: Flux falls of as 1/distance²
6	Inverse-square law for light:
7	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”
8	Let’s work some examples: Problem from textbook: m_V M_V d (pc) P (arcsec) ___ 7 10 _______ 11 ___ 1000 _______ ___ -2 ____ 0.025 4 ___ ____ 0.040
9	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
10	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
11	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)
12	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 a G star 4 ´ as large as sun, expect L would be 4²=16 times as bright
13	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
14	Lines of constant R in the H-R diagram
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16	Different “types” of H-R diagrams
17	Luminosity Classes
18	Spectra of Different Luminosity Classes
19	Spectroscopic “Parallax”
20	What fundamental property of a star varies along the main sequence?
21	Masses of Binary stars
22	Masses of Binary stars
23	Masses of Binary stars
24	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
25	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
26	The Mass-Luminosity Relationship L = M^3.5
27	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