part5 - The Local Group and Galactic Evolution The Local...

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The Local Group and Galactic Evolution I The Local Group I Satellite Galaxies I Cepheid Variables I Tides and the Roche Limit I Local Spirals I Chemical Evolution I Dwarf Galaxies I Future of the Local Group J.M. Lattimer AST 346, Galaxies, Part 5
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The Local Group J.M. Lattimer AST 346, Galaxies, Part 5
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The Local Group J.M. Lattimer AST 346, Galaxies, Part 5
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The Local Group J.M. Lattimer AST 346, Galaxies, Part 5
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The Large Magellanic Cloud HI gas H α S Dor optical IR - 24 μ m = 10 or 8.5 kpc = = 7 or 6.0 kpc = Large Magellanic Cloud J.M. Lattimer AST 346, Galaxies, Part 5
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Bulge Large Magellanic Cloud J.M. Lattimer AST 346, Galaxies, Part 5
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Magellanic Clouds J.M. Lattimer AST 346, Galaxies, Part 5
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Cepheid Variables M V = - 3 . 525 log( P / d ) + 2 . 88( V - I c ) 0 - 2 . 80 - 1 . 05 A V J.M. Lattimer AST 346, Galaxies, Part 5
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Pulsational Frequency The Euler equation of motion for a surface layer of mass m and radius R m d 2 R dt 2 = - G M m R 2 - 1 ρ p r . Use V = 1 and - Vdp = pdV - pV = pdV = 4 π R 2 dr ( p = 0 at the top of the layer (surface) and V = 0 at the bottom). In equilibrium, one has G M m / R 2 0 = 4 π R 2 0 p 0 . With perturbation R R 0 + δ R ; p p 0 + δ p m d 2 ( R + δ R ) dt 2 = - G M m ( R + δ R ) 2 + 4 π ( R + δ R ) 2 ( p + δ p ) m d 2 δ R dt 2 = ± 2 G M m R 3 0 + 8 π R 0 p 0 ² δ R + 4 π R 2 0 δ p d 2 δ R dt 2 = G M R 3 0 (4 - 3 γ ) δ R We used pV γ = constant or pR 3 γ = constant or δ p / p 0 = - 3 γδ R / R 0 . This equation has a harmonic solution δ R = A sin ω t if γ > 4 / 3. ω = s (3 γ - 4) G M R 3 s G M R 3 0 ¯ ρ. J.M. Lattimer AST 346, Galaxies, Part 5
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Pulsational Instability An instability will occur if opacity increases with compression (temperature), which is not normally the case. Normal stellar opacity is of the Kramer’s type κ ρ T - 3 . 5 and ρ T 3 in adiabatic matter. Thus κ ρ - 1 / 6 and decreases upon compression. In a partial ionization zone, H H + + e - , He He + + e - , He + He ++ + e - , the temperature increases less because of the ionization energy sink. This is the key to the kappa mechanism. V I A B : opacity increases during compression I B C : heat absorbed Δ S BC = Δ Q BC / T hot I C D : opacity decreases during expansion I D A : heat released Δ S DA = Δ Q DA / T cold Δ Q BC + Δ Q DA = Δ S BC ( T hot - T cold ) / T hot > 0 J.M. Lattimer AST 346, Galaxies, Part 5
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Period-Luminosity Relation I log L = 3 . 5 log M + a I log L = 2 log R + 4 log T eff I log P = - 1 2 log M + 3 2 log R + b I log T eff ∼ - 1 20 log L I log P = ( 3 4 - 1 7 + 3 20 ) log L - 3 log T eff + b + a 7 I log P = 0 . 76 log L + b + a 7 I M V = - 2 . 5 0 . 76 log P + c = - 3 . 3 log P + c J.M. Lattimer AST 346, Galaxies, Part 5
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Dwarf Spheroidal Galaxies I At least as luminous as globular clusters I Surface brightness 1% of LMC I > 10 in Local Group I No young stars, no gas I Stars of a wide range of ages 3 - 10 Gyr I Low metallicities Z = 0 . 02 Z ± 3 Gyr 7 15 J.M. Lattimer AST 346, Galaxies, Part 5
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Galaxy Encounters I Weak or distant encounters I Flyby with associated tides I Satellite orbit decay due to dynamical friction I Tidal evaporation of orbiting satellite I Tidal or gravitational shocks I Strong or close encounters I Mergers I Global gravitational effects become important I
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part5 - The Local Group and Galactic Evolution The Local...

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