1	Astro 1050 Mon. Oct. 21, 2002 Today: Review HW#6 Finish Ch. 9: Formation & Structure Start Chapter 10: The Deaths of Stars
2	Homework #6 Q1. The “Blade Runner Question.” A star that burns half the lifetime of the sun does not burn twice as bright. How bright (luminous) is it? Lifetime in solar units = M^-2.5 (solar m) 0.5 = M^-2.5 M^2.5 = 2 M = (2)^1/2.5 = 2^0.4= 1.3 solar masses L in solar units = M^3.5 (solar units) Luminosity = (1.3)^3.5 = 2.6 solar
3	Homework #6 Q2. Spectroscopic parallax. (Apparent) magnitude = 5.4 for an O6 V star. How far away is it? First need to get an absolute magnitude. Can estimate it several ways (H-R diagrams, mass-luminosity relation). I used M = -5.6. So: d (pc) = 10 ^(m-M+5)/5 = 10^3.2 = 1585 parsecs
4	Homework #6 Q3. Lava lamps display heat transport via CONVECTION. Q4. EGGs in the Eagle Nebula are Evaporating Gaseous Globules. Q5. Interstellar reddening occurs because dust preferentially scatters blue light, letting more of the red light through the cloud.
5	Lifetime on Main Sequence L µ M^3.5T µ fuel / L = M/M^{3.5 =} M^-2.5 Example: M=2 M_Sun L = 11.3 L_SunT =1/5.7 T_Sun
6	Width of Main Sequence – and Stellar Aging As star converts H to He you have more massive nuclei Pressure related to number of nuclei Gravity related to mass of nuclei Pressure would tend to drop unless something else happens Temperature must rise (slightly) to compensate Luminosity must rise (slightly) as heat leaks out faster
7	Orion Nebula: A Star-Forming Region Red light = Hydrogen emission Blue light = reflection nebula Dark lanes = dust Astronomy Picture of the Day: http://antwrp.gsfc.nasa.gov/apod
8	Protoplanetary Disks in the Orion Nebula Dusty disk seen in silhouette Central star visible at long wavelengths
9	Herbig-Haro objects: The angular momentum problem As clouds try to collapse angular momentum makes them spin faster A disk forms around the protostar Material is ejected along the rotation axis
10	Herbig-Haro 34 in Orion Jet along the axis visible as red Lobes at each end where jets run into surrounding gas clouds
11	Motion of Herbig-Haro 34 in Orion Can actually see the knots in the jet move with time In time jets, UV photons, supernova, will disrupt the stellar nursery
12	Chapter 9 Summary Interstellar Medium Types of Nebulae (emission, reflection, dark) Interstellar Reddening from dust Star formation Protostar Evolution on H-R Diagram Fusion (CNO cycle, etc.) Pressure-Temperature “Thermostat” Stellar Structure (hydrostatic equilibrium, etc.) Convection, radiation, and opacity Stellar Lifetimes
13	Chapter 10 – The Deaths of Stars What happens when the hydrogen runs out? Star once again tries to contract and heat up inside What might stop this? “Unusual” fusion energy sources Þ giant stars Hydrogen shell fusion Heavy element fusion Degenerate electron pressure Þ white dwarfs Loss of material from the star
14	Hydrogen Shell Burning Fusion stops in core when hydrogen runs out Star has core of He, but T too low for fusion there Heat loss makes star contract, T goes up in interior Before T in core reaches He ignition point -- Hydrogen above He core begins “shell burning” Shell burning changes the rules for structure Still need dense core to allow high T, P for fusion But high T on outside of core puts too much energy into outer parts of star Outer parts responds to input energy by expanding and cooling Star in effect separates into two parts Hot dense core where energy generation takes place Extended envelope which shields and insulates core
15	Expansion into a Red Giant For 5 M_Sun “red giant” Outer part swells to 75 R_Sun Inner core still contains most of mass Why is it red? Two equivalent ways to answer: Thick envelope insulates outside from hot core L µ R² T⁴ and L is not much greater (so far) R² is »(75/3)²=25² = 625 times larger T must decrease to compensate
16	HR Motion for other Mass Stars For higher mass (already luminous) stars Motion is more horizontal (to red) Hard to increase luminosity above already very high levels
17	Motion in the HR Diagram During H core burning (main sequence) L increases slowly as He accumulates in the core (and T_Core increases) During H shell burning At first R increases, T decreases L then increases slowly as more He accumulates in core (and T_Coreincreases) Eventually He ignites in the core During He core, H shell burning Moving some of E generation back into core shrinks size (and so raises T_Surface) Eventually He in core runs out leaving a C, O core inside the He region Core contracts and heats up till He ignites in shell outside C, O core During He shell, H shell burning At first R increases, T_Surface decreases L increases as more C,O accumulate and T_Core continues to increase
18	Expected Evolution of the HR Diagram for a Cluster A cluster consists of stars which all started to form at the same time (collapsing from the same fragmenting molecular cloud) Higher mass stars contract to main sequence before low mass ones reach it Higher mass stars are also the first to run out of H and leave the main sequence, becoming supergiants. As time continues, lower and lower mass stars move off the main sequence (at the moving “turn off point”) The original supergiants don’t live very long. The lower mass stars produce giants
19	Tests of Stellar Evolution using the HR Diagram Stellar evolution too slow to see changes in given cluster Can observe clusters and look for predicted patterns
20	Complications in Stellar Evolution Pressure forces other than thermal gas pressure Reminder: We’ve been assuming that when star loses energy it contracts and actually heats up. Clearly not all objects do this (eg. Earth) Convection bringing in fuel from outer regions Mass loss from stellar wind, or mass gain from nearby star
21	Pauli Exclusion Principle From quantum rules, electrons don’t like to be packed into a small space, either in atoms or in ionized gas At normal ionized gas densities, electrons are so spread out quantum rules don’t matter. As high enough ionized gas densities, quantum rules need to be considered, just has they have been in atoms Think of each “atom sized” region of space having a set of energy levels associated with it (although it is really more complicated)
22	Effect of Degenerate Electron Pressure Loss of energy does not reduce pressure Star does not contract in response to loss of energy Gravity not available as energy source to heat up star Electrons are already in lowest energy states allowed (equivalent to atoms in ground state) so no energy available there If there is no other energy source, as energy is lost nuclei move slower and temperature drops.
23	Degenerate Pressure Can End Fusion Degenerate Electron Pressure limits contraction and core temperature “Stars” with M < 0.08 M_Sun never burn H (brown dwarfs) Stars with M < 0.4 M_Sun never burn He (red dwarfs) Stars with M < 4 M_Sun never burn C (but do make red giants) Stars with M > 4 M_Sun do burn elements all the way to Fe What happens to these objects? Brown dwarfs never become bright – sort of like giant version of Jupiter Red dwarfs have such long lives none have yet exhausted H Red giants are related to white dwarfs Massive stars explode as supernova
24	Effects of Convection Energy can be moved by radiation or convection Convection in core brings in new fuel Cooler material more opaque making radiation harder and convection more likely Choice also depends on energy flux
25	Mass Loss from Giant Stars Envelope of red giant very loosely held Star is so big, gravity very weak at the surface Degenerate core makes nuclear “thermostat” sluggish Core doesn’t quickly expand and cool when fusion is to fast Energy can be generated in “thermal pulses” Low temperature opaque envelope can also “oscillate” Energy is transmitted in “pulses” as envelope expands and contracts Main cause of “Variable Stars”
26	White Dwarfs
27	Simple Planetary Nebula IC 3568 from the Hubble Space Telescope
28	Complicated P-N in a Binary System M2-9 (from the Hubble Space Telescope)
29	A Gallery of P-N from Hubble
30	Complications in Binary Systems Can move mass between stars 1^st (massive) star becomes red giant Its envelope transferred to other star Hot (white dwarf) core exposed 2^nd star becomes red giant Its envelope transferred to white dwarf Accretion disk around white dwarf Angular momentum doesn’t let material fall directly to white dwarf surface Recurrent nova explosions White dwarf hot enough for fusion, but no Hydrogen fuel New fuel comes in from companion Occasionally ignites explosively, blowing away remaining fuel
31	Is a star stable against catastrophic collapse? Imagine compressing a star slightly (without removing energy) Pressure goes up (trying to make star expand) Gravity also goes up (trying to make star collapse) Does pressure go up faster than gravity? If Yes: star is stable – it bounces back to original size If No: star is unstable – gravity makes it collapses Ordinary gas: P does go up fast – stable Non-relativistic degenerate gas: P does go up fast – stable Relativistic degenerate gas: P does not go up fast – unstable Relativistic: Mean are the electrons moving at close to the speed of light Non-relativistic degenerate gas: increasing r means not only more electrons, but faster electrons, which raises pressure a lot. Relativistic degenerate gas: increasing r can’t increase electron velocity (they are already going close to speed of light) so pressure doesn’t go up as much
32	Chandrasekhar Limit for White Dwarfs Add mass to an existing white dwarf Pressure (P) must increase to balance stronger gravity For degenerate matter, P depends only on density (r), not temperature, so must have higher density P vs. r rule such that higher mass star must actually have smaller radius to provide enough P As M_star ® 1.4 M_Sun v_electron ® c Requires much higher r to provide high enough P, so star must be much smaller. Strong gravity which goes with higher r makes this a losing game. For M ³ 1.4 M_Sun no increase in r can provide enough increase in P – star collapses
33	Implications for Stars Stars less massive than 1.4 M_Sun can end as white dwarfs Stars more massive than 1.4 M_Sun can end as white dwarfs, if they lose enough of their mass (during PN stage) that they end up with less than 1.4 M_Sun Stars whose degenerate cores grow more massive than 1.4 M_Sun will undergo a catastrophic core collapse: Neutron stars Supernova
34	Supernova When the degenerate core of a star exceeds 1.4 M_Sun it collapses Type II: Massive star where it runs out of fuel after converting core to Fe Type I: White dwarf in binary, which receives mass from its companion. Events: Star’s core begins to collapse Huge amounts of gravitational energy liberated Extreme densities allows weak force to convert matter to neutrons p⁺ + e^-® n + n Neutrinos (n) escape, carrying away much of energy, aiding collapse Collapsing outer part is heated, “bounces” off core, is ejected into space Light from very hot ejected matter makes supernova very bright Ejected matter contains heavy elements from fusion and neutron capture Core collapses into either: Neutron stars or Black Holes (Chapter 11)
35	Supernova in Another Galaxy Supernova 1994D in NGC 4526
36	Tycho’s Supernova of 1572 Now seen by the Chandra X-ray Observatory as an expanding cloud.
37	The Crab Nebula – Supernova from 1050 AD Can see expansion between 1973 and 2001 Kitt Peak National Observatory Images
38	What happens to the collapsing core? Neutron star (more in next chapter) Quantum rules also resist neutron packing Densities much higher than white dwarfs allowed R ~ 5 km r ~ 10¹⁴ gm/cm³ (similar to nucleus) M limit uncertain, ~2 or ~3 M_Sun before it collapses Spins very fast (by conservation of angular momentum) Trapped spinning magnetic field makes it: Act like a “lighthouse” beaming out E-M radiation (radio, light) pulsars Accelerates nearby charged particles
39	Spinning pulsar powers the Crab nebula Red: Ha Blue: “Synchrotron” emission from high speed electrons trapped in magnetic field
40	Review Chapters 7-10 Chapter 7: The Sun Atmospheric Structure Sunspots/Magnetic Phenomena Nuclear Fusion – proton-proton chain Solar Neutrino “Problem”
41	Review Chapters 7-10 Chapter 8: The Properties of Stars Distances to Stars Parallax and Parsecs Spectroscopic Parallax Intrinsic Brightness: Luminosity Absolute Magnitude Luminosity, Radius, and Temperature Hertzsprung-Russell (H-R) Diagram Luminosity Classes (e.g., Main Sequence, giant) Masses of Stars Binary Stars and Kepler’s Law Mass-Luminosity Relationship
42	Review Chapters 7-10 Ch. 9: The Formation & Structure of Stars Interstellar Medium Types of Nebulae (emission, reflection, dark) Interstellar Reddening from dust Star formation Protostar Evolution on H-R Diagram Fusion (CNO cycle, etc.) Pressure-Temperature “Thermostat” Stellar Structure (hydrostatic equilibrium, etc.) Convection, radiation, and opacity Stellar Lifetimes
43	Review Chapters 7-10 Ch. 10: The Deaths of Stars Evolution off the main sequence (=> giant) Star Cluster Evolution on H-R Diagram Degenerate Matter Planetary Nebulae and White Dwarfs Binary Star Evolution (Disks, Novae, etc.) Massive Star Evolution and Supernovae