Strangers in the night exchanging glances Wond'ring in the night What were the chances we'd be sharing love Before the night was through. Frank Sinatra, Strangers in the Night

Assignments: Study for Friday's Exam! Review session tonight at 10pm in Olin 268

In Class: --------------------------------------------------------- review: H-R diagram: made with temperature and luminosity quantities inferred directly from observation yields Main Sequence correlation most stars on on a small part of the diagram TONS of low luminosity stars lower end of the MS is heavily populated fewer, but still lots of high luminosity stars upper end well-defined, but a little less populated star sizes most stars have sizes similar to the Sun 0.1 -- 10 x the Sun's size a few whackos very large, cool stars --> RED GIANTS very small, very hot stars --> WHITE DWARFS (ASIDE: MS stars are called "DWARFS" too) Note: be able to locate the positions of stars on the HR diagram by Friday WD, RG, (temp,lum), spectral type ------------------------------------------------------------- So far, we've been able to calculate the distance luminosity surface temperature size and even composition of stars, but one really important parameter has escaped us: MASS we know the sizes, but we don't know if they're very dense and therefore massive or fluffy, and therefore low in mass nothing we have measured so far allows us to characterize the masses of stars But mass is a really important quantity to determine for stars we've seen a glimpse of how a star generates it's luminosity by fusing H in to He a measurement of mass will tell us how much H a star has and therefore how much fuel it has which tells us something about how long they can continue to burn mass also determines how hot the centers of stars are (how squished the centers are) and that plays a role in how fast the H is fused So, to understand the evolution of stars, we really need to know something about their MASSES But how to measure mass? How do we know the mass of the Sun? - by its gravitational influence on the Earth (or any planet) the Sun's gravity "pulls" the Earth into a circular orbit the Earth's speed "pulls" the Earth away from the Sun without the Sun's gravity, the Earth would fly off into space without the Earth's orbital speed, it would crash into the Sun - like a ball on a string - ball wants to go straight - tension in string "pulls" the ball into a circle - as long as I pull, ball goes in a circle - if I let go, ball flies free - it is the BALANCE between the gravity of the Sun and the speed of the Earth that keeps us in a stable orbit around the Sun The Sun's pull can be characterized by Newton's theory of gravity: F = G M_sun M_earth --------------- R^2 where G is Newton's gravitational constant The Earth's pull outward can be characterized by a "centrifugal force": F = M_earth (v_earth)^2 ------------------- R Setting those forces equal and solving for M_sun: M_sun = (v_earth)^2 R ------------- G Therefore, if we know the speed of the Earth which we can get from it's oribtal period speed = distance/time = 2 pi R/period and we know the distance to the Sun which we can get via a number of means we can calcualte the Mass of the Sun M_sun = (30 x 10^3)^2 1.5 x 10^11 ------------------------- 6.67 x 10^-11 = 2.0 x 10^30 kg <-- It works Can we apply this process to other stars? Sure, just find a planet orbiting another star, and do the same thing Planets orbiting other stars???? - we really haven't found many (a few just recently) - planets are really faint - hard to see, especially next to a bright star - really limits this method Or does it? - can't find planets around other stars, but you sure can find stars - binary stars are everywhere - three out of every two stars in a binary - obervational result: no apriori expectation - it just seems that stars don't like to be lonely This is great - stars are bright - we can see both components - watch them orbit each other - if we can calculate the period and separation - we can get the masses of the stars A little trickier than the Earth-Sun game - we could cheat with the Earth-Sun calculation because the Earth is so much less massive than the Sun - Sun really doesn't get pulled around much by the Earth not so in a binary star system - since both members are stars, both are big - they pull each other around - both objects move about the CENTER OF MASS located somewhere between them - complicates things enough that you usually can only get the sum of the masses of the stars - sometimes that's enough Observing a binary system: visual binaries - can resolve both members - need to be pretty wide separation 1" is pretty good resolution at 10pc, 1" is 10 A.U. -- reasonable separation - about the separation between Sun and Saturn at 100pc, 1" is 100 A.U. -- large separation - 3x Sun-Pluto - periods of 1000 years - hard to measure orbits for even more distant binaries, can't resolve typical separations --> so you can measure some visual binaries spectroscopic binaries - too close together to be resolved as individual blobs - but you can detect their motion via the Doppler effect - at any time, one is appreoaching and one is receding - pattern of spectral lines for each star will be shifted - see two lines instead of one - absoprtion of approaching one will be at slightly higher than normal frequency - absoprtion of receding one will be at slightly lower than normal frequency - can calculate the line of sight velocities of both objects - can measure the period of orbit by measuring the time it takes for the pattern to repeat - velocity and period gives you enough info to characterize orbit (get seaparation) and measure masses However, Doppler only gives you line of sight velocity - what if the orbit is inclilned to your line of sight - measure smaller velocities - in the extreme, with orbit perpendicular to your line of sight measure zero velocity. - without knowing the INCLINATION of the orbit, can't be sure you have the right velocity - you have a lower limit to the velocity - must be at least as fast as what you;ve measured One remarkable special case: ECLIPSING BINARIES each star actually passes directly in front of its partner - brightness of pair dims a bit as eclipses occur requires nearly perfect alignment - you know what the inclination angle is : zero - can get the actual orbital velocity --> can get actual masses Binary stars are the only means for us to determine even indirectly the masses of stars - by looking at large numbers of Main Sequence binaries, we have developed a MASS-LUMINOSITY RELATION - all MS stars of a certain spectral type (or equivalently temperature) (or equivalently luminosity) appear to have the same mass - we haven't emasured all of them - just that of all the ones we've measured, the mass comes out the same - therefore, we extend this result to all MS stars of the same spectral type - see that more massive MS stars have higher luminosity - should make some sense - already found that bigger MS stars have higher luminosity - bigger <--> more massive; makes sense - and that hotter MS stars have higher luminosity - hotter <--> more massive; makes sense So now the picture for MS stars starts to make more sense 1) all mostly H 2a) differences in spectral type are caused by temperature differences 2b) differences in color are caused by temperature differences 3) hotter stars are: larger, more massive, and more luminous 4) cooler stars are: smaller, less massive, and less luminous