1. The life history of a star depends primarily on its mass A little bit on its metallicity (Z) Sometimes influenced by nearby stars Low mass stars (M < 8M Sun ) live a long life and die slowly High mass stars (M > 8M Sun ) live fast and die violently The more massive a star is, the faster it does everything Stars form from cool clouds of gas called molecular clouds Gravity overcomes pressure, and several stars begin to form Usually get multiple stars in the same region, about the same age Called clusters Initially, the stars are all moving together at the same speed Lots of stars with low mass, few with large mass Lowest mass: about 0.08 M sun Highest mass: about 100 M sun

2. Molecular Clouds:

3. Stellar Evolution Molecular Clouds Protostar Main Sequence Star Red Giant star Horizontal Branch Asymptotic Giant Branch Planetary Nebula White Dwarf Protostar Main Sequence Star Supergiant Stages Type II Supernova Neutron Star or Black Hole Low Mass Stars M < 8 M Sun High Mass Stars M > 8 M Sun Stars are powered by nuclear fusion The combining of simple nuclei to make more complex ones Stages are defined by what is going on at the center

4. Main Sequence Stars: Introduction A Main Sequence Star is a star that is burning hydrogen to helium at its center This is nuclear burning, not combustion No oxygen We don’t care about the details This process is extremely efficient It can go for a long time During this stage, the structure of the star hardly changes Small increase in luminosity Spectral class stays almost the same Small motion upwards in the H-R diagram 4 1 H  4 He

5. Main Sequence Stars: Mass Dependance Everything about the star depends on mass Higher mass stars have: Larger radius Somewhat higher temperature Much higher luminosity TypeMass O560 B018 B55.9 A02.9 A52.0 F01.6 F51.3 G01.05 G5.92 K0.85 K5.74 M0.51 M5.21 M8.06 60 M Sun 1 M Sun 0.08 M Sun The main sequence is a band because Stars have variable metallicity Stars are different ages

6. Main Sequence Stars: Lifetime A star stays as a main sequence star until it runs out of hydrogen The amount of fuel is proportional to its mass: The rate it consumes fuel depends on its mass: How long it lasts depends on mass: Big Stars Die Fast The Sun lasts about 10 Gyr on main sequence

7. Giant Stars Molecular Clouds Protostar Main Sequence Star Red Giant star Horizontal Branch Asymptotic Giant Branch Planetary Nebula White Dwarf Protostar Main Sequence Star Supergiant Stages Type II Supernova Neutron Star or Black Hole Low Mass Stars M < 8 M Sun High Mass Stars M > 8 M Sun The stars run out of hydrogen to burn to helium Low mass stars burn helium to produce carbon and oxygen (Z = 6, 8) High mass stars also produce elements through iron (Z = 26) These produce much less energy than hydrogen The fuel is used faster and runs out faster All giant stages together last about 10% of the previous stages

8. Giant Stages: Movement on HR diagram Low mass stars get cooler and more luminous Up and right on the HR diagram High mass stars get cooler Right on the HR diagram The high mass stars move off from the main sequence first You can estimate the age of a cluster by which stars have left the main sequence The turn off point More about this later

9. Announcements 2/3 ASSIGNMENTS DayHomeworkRead TodayHwk. ECepheid Variable Stars, Type Ia Supernovae FridayHwk. FGeometric Distance Methods MondayHwk. GStandard Candle Distance Methods

10. Cepheid Variable Stars Not all stars are constant luminosity There is a region of the HR diagram where stars pulsate, called the instability strip Not Main Sequence stars The temperature, size, and luminosity all vary periodically Many Cepheids are extremely bright - much more luminous than typical main sequence stars We can see them far away, even in nearby galaxies One of the biggest motivations for the Hubble telescope was to study Cepheids in galaxies a few Mpc away

11. Cepheid Variable Stars

12. Bigger stars pulsate more slowly Bigger stars are more luminous There is a simple relationship between the period and the luminosity If you know the period, you know the luminosity If you measure the brightness, you can then get the distance P is period in days Complication – modified by metallicity Must be compensated for

13. Planetary Nebula Molecular Clouds Protostar Main Sequence Star Red Giant star Horizontal Branch Asymptotic Giant Branch Planetary Nebula White Dwarf Protostar Main Sequence Star Supergiant Stages Type II Supernova Neutron Star or Black Hole Low Mass Stars M < 8 M Sun High Mass Stars M > 8 M Sun Low Mass stars end their lives as planetary nebulas Outer layer is expelled from the star This mixes carbon/oxygen/helium back into interstellar space Inner super-hot layer gradually revealed This star is now radiating in the ultraviolet – visible luminosity is low But the ultraviolet light excites the atoms in the gas that has been expelled

14. Hydrogen Helium Carbon/Oxygen Asymptotic Giant Ultraviolet Planetary Nebula White Dwarf

15. Ring Dumbbell Cat’s Eye Helix M2-9

16. Hourglass NGC 6751 Eskimo

17. Geometric Distance Methods: Radar Distancing Parallax Moving Cluster Method Light Echo Method Standard Candle Distance Methods: Spectroscopic Parallax Cluster Fitting Planetary Nebula Luminosity Function Cepheid Variable Stars Type Ia Supernovas Hubble’s Law Geometric distance methods rely on fundamental relationships between sizes, angles, etc. Standard Candle distance methods rely on objects that are believed to be consistently the same luminosity The methods are sometimes described as a ladder You have to use the low rungs to get the higher rungs Some rungs are sturdier than others

18. Radio waves move at the speed of light c If separation of two planets is d, then the time to see the signal is: Radar Distancing Can only be used within the solar system Reliability limited only by the accuracy with which we measure time Essentially no error This allows us to know the AU with high precision: d

19. Most astronomical objects are so far away, they look small Even though they aren’t! For such small objects, there is a simple relationship between size, distance, and angular size Small Angle Formula d s  An exact relation depends on the exact geometry An approximate relation does not Make sure angle is in radians For angles smaller than 1 degree, this works great

20. We use our two eyes to judge distances using a technique called parallax Parallax (1) p1p1 The difference between the angle seen by each of the eyes is called the parallax It is limited by baseline, how far apart the two points you measure from are You can use the orbit of the Earth as a baseline p2p2 p p

21. To understand what you will see, easiest to think of system as if Earth is still and star is moving in a circle: If you view it from the edge, it looks like a straight line If you view it from the bottom or top, it looks like a circle If you view it from an angle, it looks like an ellipse. Parallax (2) p  p sin  The angular semi-major axis of this ellipse is the parallax The other size depends on its ecliptic latitude  The actual size of the ellipse is 1 AU It’s really the Earth’s orbit We can determine distance: This combination is called a parallax-second or parsec

22. Proper Motion Why it’s not that simple: Actual paths of stars are more complicated Because the stars are also actually moving (relative to us)! The average motion over many years is causing the apparent position of the star to change If we know the distance, we can measure the tangential velocity

23. Sample Problem At right is plotted a star’s variation in position in the sky in x (red) and y (green) over a three year period in milliarcseconds. The red curve corresponds to the major axis of parallax. What is the: (a)Angular velocity of proper motion,  x and  y (b) Angular speed of proper motion  (c) Parallax in mas and distance in pc (d) Transverse speed v t

24. A cluster of stars is a group of stars born from a single cloud of gas It appears as a group of closely spaced stars In general, they will all be born with approximately the same velocity They are all moving together If the cluster is moving away from you, there will be a vanishing point where they appear to be converging to a vanishing point The vanishing point is where they end up at t =  It is the actual direction they are moving We don’t have to wait this long to see where they are going It’s where the projected paths intersect Now, for any given star, measure v r, , and  The Moving Cluster Method Vanishing point To vanishing point  v v r = vcos  v t = vsin 

25. Consider a very bright source of light that turns on suddenly Like a supernova The bright ring is probably a circle centered on the supernova It looks like an oval because it is probably tilted compared to our point of view We can determine angle of tilt from the shape The Light Echo Method SN 1987a Centered ring of gas Other gas rings? 2R2R 2R cos   The light from the supernova comes straight to us at the speed of light From the ring, it takes longer: From it must first go to the leading edge of the ring Then it must come from the leading edge to our eyes We can measure the difference in time d 2R2R

26. We can now find the actual size of the object The Light Echo Method (2) SN 1987a Centered ring of gas Other gas rings? We can also measure the angular size of the object Note many methods give distances only to very specific objects But many objects clearly are together Probably at comparable distances Measuring distance to one object gives you all such distances SN 1987a was in the Larger Magellenic Cloud

27. A Standard Candle is any object that is consistently the same luminosity The luminosity is normally converted to an absolute magnitude M We can generally measure the apparent magnitude m We can then determine the distance d: Standard Candles To use standard candles, we must: Establish that they are standard candles, i.e., show that they have consistently the same luminosity Calibrate the luminosity of one or a few representative members Determine its distance d by some other method Measure the brightness / apparent magnitude m Find M from our distance formulas Complications: There is often some spread in M: Either introduces error or must be compensated for Any dust between us and a source will change m Can be indirectly measured by comparing different filters

28. Uses main sequence stars These are 90% of all stars, so not a restriction Has nothing to do with parallax Study many nearby main sequence stars Get their distances by parallax Measure their apparent magnitudes m Deduce their absolute magnitudes M Make a Hertzsprung Russell Diagram Spectroscopic Parallax: Now, to measure the distance to any M.S. star: Measure the apparent magnitude m Measure the spectral class (color) Use H-R diagram to deduce the absolute magnitude M Find the distance using

29. Sample Problem: An F5 main sequence star has an apparent magnitude of m = 14.6. What is its distance?

30. Problems with Spectroscopic Parallax: Main sequence stars are not exceptionally bright You can’t see them at vast distances Must use other methods The main sequence is a band, not a line Metallicity varies signficantly Can be measured in the spectrum and compensated for Age varies significantly Difficult to compensate for with a single star Use clusters!

31. Clusters: A cluster of stars is a group of stars born from a single cloud of gas It appears as a group of closely spaced stars A cluster diagram is a Hertzsprung Russell diagram showing all the stars in a cluster Recall: Stars are “born” as Main Sequence Stars Massive stars are the hot luminous ones The most massive stars die first Over time, the cluster diagram will change:

32. The Sun 1 Million years old At 1 million years old: Some stars aren’t even main sequence yet The brightest stars, though rare, dominate the light O and B stars Blueish tint to the cluster

33. 10 Million Years At 10 million years old: Almost all stars are now main sequence Some of the heaviest are in their supergiant phases The transition determines the turnoff point Some of them have died B and A stars dominate Blue/white tint to cluster Turnoff

34. 30 Million Years At 30 million years old: More stars are supergiants Turnoff point has moved Mix of stars now White color to cluster Turnoff

35. 200 Million Years At 200 million years old: Red giants, horizontal branch, and asymptotic giants Turnoff point moved farther Yellow tint to cluster Turnoff

36. 2 Billion Years At 2 billion years old: G, K, M stars dominate Yellow/orange tint to cluster Turnoff

37. 10 Billion Years At 10 billion years old: K, M stars dominate Red tint to cluster Sun is about to turn off Turnoff

38. The turn off point: You can gauge the age of a collection of stars from the turn off point The color is also an indication Blueish: young Reddish: old

39. The turn off point: You can gauge the age of a collection of stars from the turn off point The color is also an indication Blueish: young Reddish: old

40. Cluster Fitting Spectroscopic parallax on steroids Applies to clusters of stars Many stars with similar composition and magnituded Plot the apparent magnitude vs. spectral type Measure composition – metallicity Build a computer model predicting what a set of stars would look like with this composition Plot the absolute magnitude vs. spectral type Age the computer generated stars until the graph has the same shape Turn off point tells you when to stop Compare the absolute magnitude of the result with the apparent magnitude of the actual cluster Find the distance from O5 B5 A5 F5 G5 K5 M5 m M m - M

41. Cluster Fitting Advantages More accurate than spectroscopic parallax Statistics of many stars helps eliminate errors Disadvantages Relies heavily on main sequence stars These stars are relatively dim Cannot be used beyond our galaxy

42. Planetary Nebula Luminosity Function Planetary nebulas come in a variety of luminosities But the distribution seems to be almost independent of where they come from Very little dependence on the metallicity The maximum luminosity can be determined from nearby planetary nebulae: Find an object with several (many?) planetary nebulas Make a histogram of number vs. apparent magnitude Fit to curve – determine maximum brightness m* Find the distance Advantages Can see these brighter objects at larger distances Disadvantages They aren’t that bright You can only get distance to large objects – like galaxies

43. Cepheid Variable Stars In their giant stages, certain stars begin to pulsate Known as Cepheid Variable Stars The bigger the star is, the slower its pulsation The bigger the star is, the more luminous it is There is a relationship between the period and the luminosity/absolute magnitude P is period in days Measure the period of a pulsating Cepheid variable star Use this formula to determine the maximum absolute magnitude M Measure its apparent magnitude m Determine the distance from

44. Cepheid Variable Stars Advantages Quite accurate method Bright, comparable to planetary nebulas You only need one Disadvantages Still somewhat rare stars – clusters or bigger only Metallicity changes the relationship Most stars near us (type I) have high metallicity Some stars have much lower metallicity Must be compensated for

45. Type Ia Supernovae All type Ia supernovae are approximately 1.4 M Sun white dwarfs that blow up the same way. They should all have the same maximum luminosity Find a type Ia supernovae where you want it Measure its maximum apparent brightness m Find the distance using: Disadvantages They aren’t really standard candles: There is a spread in the maximum magnitude There is an experimental correlation between how fast they fade and their maximum magnitude Can be used to compensate for this problem They are very rare – difficult to calibrate Advantages Quite accurate method Spectacularly bright Mixed: So far away, other effects become important Relativistic speeds, curvature of universe

46. Individual Conservation Laws: Sometimes, you can consider a star in isolation This only makes sense if the rest of the galaxy is (statistically) in a steady state Treat a single star as if it is reacting under the gravity of all the other stars “smoothed out” Fails if it undergoes a close encounter with another star Motion is governed by potential from the whole galaxy* Momentum is not conserved Energy is conserved* Angular momentum is harder: If the object is spherically symmetric, angular momentum is conserved* If it is axisymmetric, angular momentum around that axis is conserved* If it has no symmetry, angular momentum not conserved *Provided no close encounters