Homework #2 - Peppy the Proton (Part 1)

due Monday July 15

Peppy the proton was formed about 0.000001 seconds after the Big Bang, as part of a proton - anti-proton pair. As the temperatures continued to drop, most protons annihilated with anti-protons and returned to energy, but Peppy was one of the lucky few who were not annihilated (a one in 1 billion chance ...lucky proton, eh?).

  1. What was happening in the universe that makes this the particular time when protons were created? That is, why couldn't it happen before this time, and why couldn't it after this time?
  2. Why were only form Hydrogen, Helium, and a bit of Lithium formed in the early Universe?

Time passed, and Peppy found that after a while, she had a companion - a little electron was orbiting around her. At this point, the temperature of the matter had dropped to about 3000 K - no longer hot enough to keep the matter ionized.

  1. What evidence do we have that this event, the creation of a neutral atom, occurred? Why isn't the radiation that we observe today characteristic of the 3000 K matter that emitted it? (Or is it)?

As she traveled through space, Peppy found herself drawn to an unstable and collapsing region of the Universe. This gigantic cloud of gas eventually collapsed to form a galaxy. After a few million years, Peppy got bored, so she invited about a trillion trillion trillion trillion billion (1057) of her closest friends over to form a high mass star. They formed a star of much higher mass than our Sun, so it burned itself out very quickly, eventually blowing itself up as a supernova.

  1. How long does a star live? There's a reasonably easy way to calculate this: A star lives (radiates energy) by converting Hydrogen atoms into Helium atoms. Each time the star turns 4 H atoms into 1 He atom, 0.7% of the mass of the H atoms is converted into energy (through E = mc2). A star will typically convert the inner 10% of its mass in this manner before other things happen that cause the star to blow up ( a supernova - for high mass stars) or become a planetary nebula/white dwarf (for low mass stars). So the total mass and efficiency rate of the fusion determine how much total energy the star has available. It radiates this energy away at a certain rate, which is called the luminosity, - by figuring out how long it takes to radiate away all of the available energy, you have calculated the lifetime of the star! Think of the star as having a certain reservoir of fuel (H atoms) and it burns some constant amount every second. To calculate how long the fuel will last, what must you do?

    [Units note: 1 erg = gm cm2 sec-2 = about the amount of energy used by a flea when it jumps. So, if you express masses in grams and the speed of light as 3x1010 cm/sec, the units of energy you get out will be ergs].

    Figure out the lifetimes for the following stars:
    
Name		Mass in Solar masses	Mass in grams	        Luminosity in erg/sec
Sun			1 		2 x 1033 		 4 x 1033 
Barnard's star		0.4		8 x 1032 	         6 x 1030
Nunki			10		2 x 1034 		 3 x 1036

The party was a little too hot for Peppy, so she stayed at the outer edges and kept her shape as a Hydrogen atom, but a lot of her friends were joined together to form heavier elements like Carbon, Oxygen, Silicon, Iron, and even heavier elements. Peppy's cousins, the Planck twins, could only get about a hundredth as many friends to form a star together, so they were still part of their star long after Peppy's party ended in a supernova.

  1. Given your answers to question 4, is it the more or less massive stars that are most important for chemically enriching the Universe? Remember that almost no elements more massive than Lithium are created in the early universe. Explain how a star like the sun (which is almost 0.4 % elements heavier than Helium) might come to exist.

  2. Suppose you found a star that was 15 billion years old. Given this age, is this a low- mass or high-mass star?. Could Earth-like planets form around this star? Why or why not? (Hint: Earth-like planets are made largely of oxygen, silicon, and iron)

The supernova blew Peppy back out into space, where she wandered around for many years until ...
(to be continued in future weeks ...)

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