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MSU AST 308 - LECTURE NOTES

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1More about the game plan:• NOW… Kinematics of spiral galaxies• Rotation curves Î mass distribution [CO 24.3]• SKIP [CO 24.4 “The Galactic Center”]• Spiral structure [CO 25.3]• General properties of S and Irr galaxies [CO 25.2] • E galaxies [CO 25.4]• Midterm on Wednesday Oct. 3Homework 5= 2-3 spiral structure problems.Maybe something about E galaxies.Due Monday Oct 1. Homework 5 4Assigned on MondayDue Wednesday 26 NOTE: ALL OF THE SLIDES ARE ON THE COURSE WEB SITE AS PDF FILES, 2 SLIDES PER PAGE. www.pa.msu.edu/courses/ast308If outside shell:2The Milky Way’s Rotation CurveRadio dataTangent point methodYoung star clustersRotation curves in other galaxies• Vera Rubin & Kent Ford (late 1970’s)• Image tube spectrograph3Density as shown by flat rotation curves•dM(r)/dr~ constant• Unbounded mass distribution??• NFW profile• Predicted for Cold dark matter (CDM)• Actual derived dark matter profiles often slightly different than this• What is CDM? Coming later in course.[CO pg. 917]()20)/1(/)(ararr+=ρρHomework Assignment 5Due Monday Oct. 1•CO 2ndedition problems 25.13, 25.14, 15.16• Same as 1stedition problems 23.11, 23.12, 23.14• There may be one addition derivation-type problem having to do with the stellar velocities found in E galaxies. It depends on whether I cover that in class with enough lead time.4Spiral Structure[CO 25.3]Grand design (10%) Multi-arm (60%) Flocculent (30%)M51 M101 NGC 2841Inner rings Outer RingNGC 7096 M81 NGC 4340What causes spiral structure?• Winding up of arms• Due to differential rotation• Stochastic, Self-Propagating Star Formation• Chain-reaction star formation• SN shells Î shock fronts Î density enhancements Îstar formation Îmore SN• Differential rotation then winds these regions up into spiral patterns•Density Waves • Wave in gravitational potential• Orbital velocity of stars different than pattern speed• Stars, gas bunch up at position of spiral arms• Causes higher grav. potential• Unclear if self-sustaining or forced.50xxxxxxΩ=RvrotSpiral Arms & the Interstate Highway•Density wave• Spiral arms have higher density than space between arms• Excess gravitational attraction slows down gas, stars when they pass through spiral arm in course of their orbits.• Î spiral arms are a traffic jam6Retrograde Motion & Ptolemy’s Epicycles• Trying to place Earth at center.• Using only circular motions.• Led to very complicated system.Path of Mars, etc. as seen from EarthPtolemyAlexandria, 140ADEpicycles… the short form.For lurid details, see [CO 25.3 (23.3 1stEd.)]Define an effective potential:Taylor series expansion around position of minimum Φeff(circular orbit):Circular symmetry Î independent of φSeparate d2r/dt2into R, φ, z componentsÎ 3 equations.Conservation of specific angular momentumJZ= R2d φ/dtConservation of JZÎ acceleration inφdirection when rchanges.PtolemyAlexandria, 140AD(25.32-25.33)(25.17)(25.19-25.21)U = potential energyΦ = U/M(25.31)7Harmonic oscillation in R, φ, z about circular orbit(Epicycles)Ω = the rotation curve for Milky Way:Rm= R at min. ΦeffΩ = circular ang. vel.Orbits closed if: m (Ω - Ωlp) = nκIn inertial frame:Viewed from frame rotating with Ωlp:Two ways to line up closed elliptical orbits(as seen from frame rotating with Ωlp)2κ−Ω=ΩlpΩ=Ωlp32κ−Ω=Ωlp4κ−Ω=Ωlpn,m“local pattern speed”Angular velocity (Ωlp) ÎBasic nature of a density waveFrom: Toomre, Annual Review of Astronomy & Astrophysics, 1977 Vol. 15, 437.• At each Rm, stars’positions in epicycles are forced into a specific pattern by gravitational potential of spiral arm.• Sum of positions of stars at this Rmforms an ellipse rotating at pattern speed.• Spiral density pattern is sum of many ellipses, all rotating at same pattern speed.Pendulum example8Some Solar System Resonance PhenomenaAsteroid orbitsGaps in Saturn’s ringsLin & Shu’stheoryHydrodynamicsPerturbed form of collisionlessBoltzmann equation.“quite complicated”Milky WayAngular velocity (Ωlp) Î9Inner Lindblad Resonance (ILR)Co-rotation RadiusOuter Lindblad Resonance (OLR)Density wave theory interprets most spirals as 2-armed•4-armed pattern is n / m = 1 / 4• exists over a narrow range of radius.Î less likely to be seen.•Actual 4-armed spirals are superposition of two 2-armed patterns Important in all disk galaxiesDensity waves cannot propagate across ILR or OLRAngular velocity of ref. frame ÎSpiral Structure[CO 25.3]Grand design (10%) Multi-arm (60%) Flocculent (30%)M51 M101 NGC 2841Inner rings Outer RingNGC 7096 M81 NGC 434010M81 spiral structure at different wavelengthsUV: hot starsNear IR: late-type starsVisible: stars + obscuration21 cm: HIOld red population shows small but real spiral density enhancement.Passage of gas through spiral arms Calculated streamlines for gas11Response of gas to density waves• Simple pendulum model• Each pendulum = 1 gas cloud• For large amplitude forcing, pendulums collide.• Î shock fronts in spiral arms• HI map (right) shows velocity jumps at spiral arms.Orbits in Barred Spirals• Gas avoids “co-rotation” radius in barred potential.• Causes “Fig-8” shape in rotation curve.Kinematics of gas, in [NII][BM] Fig 4.60ROUND BULGE PEANUT-SHAPEDStable orbits (stars)Max. gas densityGas velocityGas densityMoviemovie12Bars appear to be easily excited instability in disksTrailing vs. leading spiralsWhich is the near side of the galaxy?13Molecular clouds on inner edges of armsCO contours over red imageCO contours over 21 cm mapSwing AmplificationWhile it is swing around, the spiral arm moves at about same angular speed as star. Automatically converts any leading spirals into much stronger trailing spirals.Position of (leading) spiral density enhancementEpicyclic orbit of starTime steps = ½ of crotation period at CR.14Spiral Structureof the Milky Way• Recent model• Lepine et al (2001)ApJ 546, 234.• Î mix of• 2-armed mode• 4-armed mode• Sun at ~ co-rotation radius.From HI (21 cm observations)assuming circular rotation.N-body simulationHard to measure, because we are inside it.Map of nearby young objectsSummary: Density Waves?• Evidence showing density waves do occur.• Old, red stars show spiral density perturbation.•


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