1	Astro 1050 Mon. Oct. 7, 2002 Today: Discuss HW #4 Finish Chapter 7 -- The Sun Start Ch. 8, Properties of Stars
2	Homework #4 Q1 The moon remains in Aries! Q2 1 kg of mass transformed into energy: E = mc² so E=1 kg x (3x10⁸m/s)² = 9x10¹⁶ J Q3 Sunspot brightness, use E = σT⁴ (T₁/T₂)⁴ = (5800/4200)⁴ = 3.6 times brighter Q4 Radio Wave same speed as Gamma Ray Q5 P. 123, flares up to a billion H-bombs so The Traitor dies like the dog he is!
3	Fusion Energy Released in Proton-Proton Chain Use E=mc² to do accounting Mass is a measure of the energy stored in a system Loss of mass from a system means release of energy from that system Compare mass of four ¹H to mass of one ⁴He 6.693 ´ 10^-27 kg - 6.645 ´ 10^-27kg = 0.048 ´ 10^-27 kg drop in mass E = mc² = 0.048 ´ 10^-27 kg ´ (3 ´ 10⁸ m/s)^{2 =} 0.43 ´ 10^-11 kg m²/s² = 0.43 ´ 10^-11 J (note == a Joule is just shorthand for kg m²/s²) So 4.3 ´ 10^-12 J of energy released This is huge compared to chemical energy: 2.2 ´10^-18 J to ionize hydrogen
4	How long will Sun’s fuel last? Luminosity of sun: 3.8 ´ 10²⁶ J/s H burned rate: H atoms available: Lifetime: In reality not all the atoms we start with are H, and only those near the center are available for fusion. The structure of the sun will change when about 10% of the above total have been used, so after about 10 billion years.
5	Testing solar fusion model Does lifetime of sun make sense? Oldest rocks on earth ~4 billion years old Oldest rocks in meteorites ~4.5 billion years old Other stars with higher/lower luminosity Causes for different luminosity Lifetimes of those stars Look for neutrinos from fusion Complicated story – due to neutrino properties Example of how astronomy presents “extreme” conditions
6	Neutrinos Generated by “weak” force during p⁺® n + e⁺ + n “Massless” particles which interact poorly with matter In that first respect, similar to photons Can pass through sun without being absorbed Same property makes them very hard to detect Davis experiment at Homestake Mine in Black Hills 100,000 gallon tank of C₂Cl₄ dry cleaning fluid in Cl nuclei n + n ® p⁺ + e^- so Cl (Z=17) becomes Ar (Z=18) Physically separate out the Ar, then wait for it to radioactively decay Saw only 1/3 the neutrinos predicted
7	Missing Neutrino Problem Lack of solar neutrinos confirmed by Kamiokande II detector in Japan. (Using different detection method) Possible explanation in terms of Neutrino physics 3 different types of Neutrinos: electron, muon, and tau neutrinos Sun generates and Cl detectors see only electron neutrinos Can electron neutrinos can change to another type on way here? These “neutrino oscillations” are possible if neutrino has non-zero mass Kamiokande II evidence of muon neutrinos becoming electron ones Read “Window on Science 7-2” on “scientific faith” Neutrino mass may have implications for “cosmology” Neutrinos also used to study supernova 1987A
8	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!
9	Distances to Stars Distance:
10	Parallax: Really just the small angle formula
11	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 Double distance – flux drops by 4 Triple distance – flux drops by 9
12	Inverse-square law for light:
13	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”
14	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
15	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
16	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
17	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)
18	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
19	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
20	Lines of constant R in the H-R diagram
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22	Different “types” of H-R diagrams
23	Luminosity Classes
24	Spectra of Different Luminosity Classes
25	Spectroscopic “Parallax”
26	What fundamental property of a star varies along the main sequence?
27	Masses of Binary stars
28	Masses of Binary stars
29	Masses of Binary stars
30	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
31	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
32	The Mass-Luminosity Relationship L = M^3.5
33	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