1	Astro 1050 Fri. Mar. 5, 2004 Today: More Ch. 10: The Deaths of Stars Homework #5 Extra Credit articles
2	Homework 5 solutions Q1. If a type G star like the sun expands to become a giant star with a radius 20 times larger, by what factor will its density decrease? Density = mass/volume Mass is the same, volume of sphere = 4/3 π R³ Radius increases by 20, R³ and the volume increases by 20³ = 8000, so density decreases by 8000 Q2. In an H-R Diagram, stars with the largest radius are found in the upper right of the diagram. (Fill in the blank.) Q3. The lifetime of high temperature main sequence O and B stars is much shorter than the lifetime of low temperature K and M stars. (Fill in the blank.)
3	Homework 5 solutions Q4. 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 Q5. If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.) d (pc) = 10 ^(m-M+5)/5 = 10^8.2 = 1.6x10⁸ pc x 1Mpc/10⁶pc = 160 Mpc Q6. 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
4	Homework 5 solutions Q7. Sunsets appear red for the same reason that some stars in space appear red -- they are both seen through dust particles. Why does this make them appear red? b. The dust scatters blue light more than red light, such that more of the red light passes directly though the dust. Q8. What do we see in the Orion nebula that indicates it is a region of new star formation? a. Hot O stars b. Herbig-Haro Objects c. Dust Disks around stars d. All of the Above e. None of the Above Q9. The Pleadies is an open star cluster not too far from us. It also represents a textbook example of a type of nebula. Which type is it? C. A reflection nebula
5	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 (e.g. Earth) Convection bringing in fuel from outer regions Mass loss from stellar wind, or mass gain from nearby star
6	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)
7	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.
8	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 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
9	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
10	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”
11	White Dwarfs
12	Simple Planetary Nebula IC 3568 from the Hubble Space Telescope
13	Complicated P-N in a Binary System M2-9 (from the Hubble Space Telescope)
14	A Gallery of P-N from Hubble
15	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
16	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
17	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
18	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
19	Supernova When the degenerate core of a star exceeds 1.4 M_Sun it collapses Type II: Massive star runs out of fuel after converting core to Fe Type I: White dwarf in binary, which receives mass from its companion (collapse ignites carbon burning). 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)
20	Supernova in Another Galaxy Supernova 1994D in NGC 4526
21	Tycho’s Supernova of 1572 Now seen by the Chandra X-ray Observatory as an expanding cloud.
22	The Crab Nebula – Supernova from 1050 AD Can see expansion between 1973 and 2001 Kitt Peak National Observatory Images
23	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
24	Spinning pulsar powers the Crab nebula Red: Ha Blue: “Synchrotron” emission from high speed electrons trapped in magnetic field