you might as well be walkin' on the Sun Smash Mouth, Walkin' in the Sun

Assignments: Problem Set #3 due 11 February Read Chapter 24, sections 1 and 2 (pp. 380-385) for Monday's class

In Class: ----------- review: Annie Jump Cannon - classifying stellar spectra the sensible sequence was OBAFGKM, not ABCD... -> a connection between the blackbody properties and spectral line properties of stellar spectra Cannon's result made some sense in terms of temperature based on BB emission, but the patterns of spectral lines, and how they changed with spectral type was mysterious compositional differences? -- are hot stars deficient in H? -- are cool stars deficient in He? -- perhaps compositional differences are responsible for different temepratures (i.e., T determined by what fuel you've got) these are perfectly reasonable guesses, but they're WRONG it really took until the 1920's to understand the connection between temperature and spectral line emission ---------------- Meghnad Saha and the excitation levels of collections of atoms (STAIRCASE MODEL) there are a lot of choices for energy states for an atom - can be in the ground state -- lowest energy - can be in an excited state -- higher energy Saha noticed that if he knew the TEMPERATURE of a gas of atoms, he could predict, how many of the atoms would be in each energy state the higher the temperature, the larger fraction of the population would be in higher energy states recall that TEMPERATURE is average energy per particle, so maybe this makes sense - high T = high energy per particle one way to make an atom have high energy is to put it's electrons farther from the nucleus that's rasing the atom to a higher energy state The tricky part of this is that Saha looked at POPULATIONS of atoms, NOT just one atom his result is statistical, i.e., on average, the fraction of the population of atoms in each state can be determined from T Implications: as we've discussed, what energy state an atom is in determines what it can absorb or emit - in ground state, can't emit; can only absorb photons with energy equal to energy difference between ground state and some other acceptable state - in first excited state - can emit down to ground state (only one lower) - photon emitted has energy equal to difference in energy between first ex. state and ground state - can absorb, but only photons with energy equal to to energy difference betwen 1st ex. state and other acceptable states NOT THE SAME PHOTONS AS IF IT WERE IN GROUND STATE Saha tells us how many atoms of a population are in which state based on the temperature. (BOARD: 3 STAIRCASES) - really cold gas not much energy around everything in the ground state no emission nowhere for the atoms to go; no lower energy state absorption from ground state only no absorption of a photons whose energy is equal to the difference between states 2 and 3. Why" NO atoms in state 2. - warmer gas some atoms in ground state, some in higher energy levels emission: some atoms can emit and move to lower energy absorption: lots of choices available can make a transition from any state where there are at least some atoms - really hot gas very few or no atoms in ground state everything's excited lots of choices for emission get emission from states where there are at least some atoms; absorption: can't absorb from the ground state; no atoms in this state can absorb from higher states ---------------------- Cecilia Payne (1920's) understands the implications for stars: realizes that the brightness of an individual sppectral line depends not only on the amount of material there but also the temperature of the material Consider hydrogen and the prominent red H-alpha absorption line which was used as a major determinant in classification -- comes from a transition between the first and second excited states of H -- in order to see this absoprtion line, need a large fraction of H in first excited state -- so that the atoms in this state can "catch" the red photons and jump tot he second excited state -- if there aren't any atoms in the first excited state -- no absorption -- even if you have a ton of H How can you have H with no atoms in the first excited state? two ways: COLD -- all of the atoms in the ground state nothing in higher energy states don't see absorption (however, there is H absorption at other wavelengths) HOT -- all of the atoms in high energy states nothing in first excited state don't see absorption (again, though there might be absorption at other wavelengths MORAL: JUST CUZ YOU DON'T SEE ABSORPTION AT ONE H SPECTRAL LINE DOESN'T MEAN THERE'S NO HYDROGEN Payne figured out at which temperatures you would have a lots of your H in the first excited state: -- 5000 -- 10000 K -- at higher T, most of the H would be in higher energy states -- at lower T, most of the H would be in the ground state She looks at the BB temperature (from fitting the broad spectrum) of an A star: 7500 K -- noticed whopping H-alpha absorption -- this is consistent with having lots of H Looks at BB temp of an M star: 3000 K -- notices very little H-alpha absoprtion -- no H? -- not at all; it's just that the H is in the ground state Looks at BB temp of an O star: 30000 K -- very little H-alpha absorption -- no H? -- not at all; it's just that the H is too highly excited She does lots of calculations and realizes that when you factor in the temperatures of these star's surfaces, you need the same amount of H for any star CONCLUDES: stars very similar compositions, and are mostly H Can play the same game with He, C, N, Mg, Na (she did), and can show that the varied appearence of the spectral lines of nearly all stars can be explained by very similar elemental compositions and the effects of temperature on the atoms. Provided the physical understanding of the correlation between the broadband spectral characteristics and the spectral line appearence of stars. =========================================== 1. -- Stars are composed of 90% H, 10% He, and traces of other stuff. 2. -- The different spectral appearences are due mainly to differences in the temperatures of the stars. =========================================== One can determine the temperature of a star either from its broadband spectral characteristics ("color") or spectral line characteristics ("spectral type"). REALLY IMPORTANT: all stars are pretty much the same, except for temperature universal composition of the heavens Remaining piece of the puzzle: why do different stars have different temperatures? We'll get there, but first, let's figure out why they're hot at all. Now, let's look at the one star we can study close-up --- The Sun -------- The Sun is mainly a big ball of H (some He, too) as Cecelia Payne told us all stars are It's big - R(sun) = 100 R(earth) = 696000 km = 7.0 x 10^8 m often called solar radius It's massive - mass = 2.0 x 10^30 kg (really 1.9891) It's hot - visible layer (aka photosphere) has T = 5800 K - from BB fit to spectrum - from spectral type (G) determined from absoprtion lines Why is it so hot? - gravity - the Sun has a lot of mass - enormous gravity - wants to squich the Sun as small as possible - why doesn't the Sun get squished into a dot? - pressure support - as you squish a gas, it gets hotter - hotter --> higher T --> higher energy per particle - particles move faster - effectively push harder against each other and boundaries - pressure in interior of the Sun pushes against outer layers - inner layers push down because of gravity Attain an EQUILIBRIUM when - pushing down = pushing up - i.e., nothing moves (that's what equilibrium means) - if parts aren't in equilibrium - i.e., too cool - gravity wins - squishes material - material heats up - squishing continues until material is hot enough to push back with the same force - if too hot - thernmal pressure wins against gravity - layers expend - material cools off - exoansion continues until material cools enough that pressure reduces to be equal to force from gravity --> No matter what, you'll end up in equilibrium Makes for a simple prescription for the temperature inside the Sun - in the outer parts - not so much overlying - pushing down due to gravity is weak - don't need a laot of upward pressure - T doesn't need to be that high deeper in - more overlying material - more squishing due to gravity - need more upward pressure to counteract - need higher T very center - entire mass of Sun pushing down - lots of squishing due to gravity - need tons of upward pressure to counteract - need super high T Figured out by Eddington in the 1920s and 30s interior temperature has to be 10-20 million K outrageously hot