The Death Throes of a Star The future of the sun? Very likely!! A star just about identical

1. The Death Throes of a Star The future of the sun? Very likely!! A star just about identical to our sun is seen after it has thrown off a planetary nebula. It is in the process of collapsing to a white dwarf...all of its hydrogen and helium fuel has been “burned” and it is, essentially, dead. It will continue to give off heat and light for millions, if not billions of years, but it is no longer a star.

2. Notes 64 - Optional Topic E - Astrophysics* ------------------------------------------------------------------------------ E.2.1 Stellar Fusion • Nuclear fusion is the main energy source of stars; • Sol is a red dwarf star with an interior temperature of only 1.6 x 107 K; • At this temperature, the proton-proton cycle* of nuclear fusion which converts hydrogen into helium occurs: 2 [1H1 +1H1 ----> 1H2 + +1e0 + neutrino + 0.4 MeV]; 2 [1H1 + 1H2 ----> 2He3 + 5.5 MeV]; 2He3 + 2He3 ----> 2He4 + 2[ 1H1 ] + 12.9 MeV; [*NOTE - Proposed by Hans Bethe, 1930's, for which he won the Nobel Prize]

3. The result of these reactions is 24.7 MeV of energy released per cycle; • In other, more massive stars, nuclear fusion occurs which produces elements up through and including Fe-56. In Sol, 685 MTon* (6.85 x 1011 kg) of matter is converted into energy each second by the nuclear fusion of H into He. (*Note: 685,000,000 tons represents 685 fully loaded Nimitz Class USN aircraft carriers being changed into energy each second!!)

4. E.2.2 Equilibrium in a Stable Star • In a stable star, the outward pressure exerted by the nuclear fusion is balanced by the inward pressure exerted by gravity. • An object with 80% of the sun’s mass (or 8x the mass of Jupiter) will not have a sufficient gravitational force to compress the hydrogen to the proper temperature and pressure to initiate fusion...the resulting hydrogen-rich object is called a brown dwarf.

5. E.2.3 Stellar Luminosity Luminosity (L) - total energy emitted by a star per second; or, its power; measured in watts (W) or J s-1; LSol= 3.9 x 1026 W;

6. E.2.4 Apparent Brightness; Apparent Brightness (b) - light intensity is indirectly proportional to the square of the distance between the source and the observer; or, light intensity is directly proportional to the inverse square of the distance between the source and the observer. Units are Wm-2; b = L / (4 π d2) where L is luminosity and d is distance to the star; 4 π d2 = area of sphere at d from star; - b is in units of W m-2 and gives the luminosity over a sphere around the luminous object at a radius of d; Apparent Brightness and Luminosity http://zebu.uoregon.edu/~soper/Light/luminosity.html

7. Sample Problem: What is the apparent brightness of the sun as seen from earth? Given: Unknown: Equation: d = I A U=1.5x108 km; L=3.9x1026 W

8. E.2.5 The Stefan-Boltzmann Law All objects above absolute zero... A. emit radiaton at all wavelengths; B. emit radiation in proportion to their temp (higer temperatrure bodies emit more radiation than lower temperature bodies; C. emit more radiation at one specific wavelength than any other (peak radiation); D. have a peak radiation that is determined by temp; higher temp produce peak radiation at higher frequencies;

9. - The luminosity of a star (L) is directly related to its temperature. However, high temperature bodies do not emit radiation at only one wavelength. Different bodies each have their own radiation spectrum. • Stefan-Boltzmann Law - the luminosity of a star (L) is directly proportional to the product of its surface area, A (4 π r2), and T4 (the fourth power of its surface temperature); - To change from a proportionality to an equality, a constant, σ (lower case Greek letter, sigma), the Stefan-Boltzmann constant, is added; σ = 5.67 x 10-8 W m-2 T-4; L = σ A T4 ; The Stefan-Boltzmann Law can also be written: L = σ 4 π r2 T4 - Stefan-Boltzmann Law allows us to estimate the size of stars for which we know luminosity (L) and temperature (T in K): r = √(L / 4 πσ T4) Lα T4 ; Lα A BLACKBODY RADIATION http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm

10. E.2.6 Wien’s Displacement Law • Wien’s Displacement Law predictsthe wavelength and at which a luminous object will emit the largest fraction of its radiation; λmax = constant / T ... where T= Kelvin temp; constant = 2.9×10−3 (meter)(Kelvin) The higher the Kelvin temperature, the shorter the wavelength at which the largest fraction of the radiation is emitted (ie., the “bluer” the radiation); thus the progression from red to blue as surface temperatures of stars increase.

11. Combination Problem: [constant = 2.9×10−3 Km] The λmax= 960. nm for the star Betelgeuse, and its luminosity is 10,000 times greater than Sol’s. Estimate (A) the surface temperature [Wien] and (B) the radius of Betelgeuse [S-B]. A. Given: Unknown: Equation: B. Given: Unknown: Equation: (Hint - find LSol / LBetel w/S-B Law)