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part2 - The Local Milky Way Color-Magnitude Diagram 15,630...

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The Local Milky Way Color-Magnitude Diagram Distances from Hipparcos trigonometric parallaxes 15,630 stars d < 100 pc Half of stars with M V > 10 are not detected. age differences ± ± ² ± ± ³ metallicity differences ± ±² ± ±³ red giants red clump Hertzsprung gap white dwarfs B0 A0 F0 G0 K0 M0 J.M. Lattimer AST 346, Galaxies, Part 2
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Local Stellar Luminosity Function Φ( M ) = number stars M V ± 1 / 2 volume over which seen Ψ( M ) = Φ MS ( M ) Θ ± τ gal τ MS ( M ) ² Θ( x ) = 1 if x 0 Θ( x ) = x if x > 0 τ gal 10 Gyr Hipparcos Reid et al. (2002) Dim stars hard to find; Bright stars are rare. Stars not uniformly distributed. Stars in binaries mistaken for brighter single stars. Wielen dip L V Φ( M V ) M Φ( M V ) total MS A, F K giants B, O J.M. Lattimer AST 346, Galaxies, Part 2
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Stellar Initial Mass Function ξ ( M )Δ( M )= number stars born with mass between M and M + Δ M Salpeter initial mass function ξ ( M ) = ξ 0 M ± ± M M ± ² - 2 . 35 Total number: R M u M ξ ( M ) d M = ξ 0 1 . 35 ± M ± M ² 1 . 35 ³ 1 - ± M M u ² 1 . 35 ´ Total mass: R M u M M ξ ( M ) d M = ξ 0 M ± 0 . 35 ± M ± M ² 0 . 35 ³ 1 - ± M M u ² 0 . 35 ´ Total luminosity: R M u M L ξ ( M ) d M = ξ 0 L ± 2 . 15 ± M u M ± ² 2 . 15 ³ 1 - ± M M u ² 2 . 15 ´ Pleiades cluster Salpeter mass function ξ ( M ) M ξ ( M ) J.M. Lattimer AST 346, Galaxies, Part 2
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Distances From Motions If V r and V t measured, and how they are related, we can find d . V t = μ d , μ ( marcsec / yr ) = V t ( km / s ) / (4 . 74 d ( kpc )) Example: Distance to Galactic center, if orbit edge-on and perpindicular 2 a = ( s / 1 arcsec )( d / 1 pc ) AU , P 2 a 3 = 4 π 2 G M BH V p (1 - e ) = V a (1+ e ) , V 2 p - V 2 a = 2 G M BH a - 1 ± (1 - e ) - 1 - (1 + e ) - 1 ² Galactic center ± ² 2 a = sd 6 ? J.M. Lattimer AST 346, Galaxies, Part 2
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Distances From Motions Example: Distance to supernova ring, if ring is circular t - = R (1 - sin i ) / c , t + = R (1 + sin i ) / c SN 1987a @ @ I Δ t = t A - t 0 = t - Δ t = t B - t 0 = t + Δ t = 0 - J.M. Lattimer AST 346, Galaxies, Part 2
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Spectroscopic and Photometric Parallax Assume stars of same spectral type and Z have equal L . Correct for dust reddening. Works to 10% for main sequence stars, 60% for K giants. Needs lots of observation time. Cheaper alternative is to estimate spectral type from color, other indicators determine dwarf/giant. Works best for clusters, where reddening is easier to determine. Photometric distances towards South Galactic pole
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part2 - The Local Milky Way Color-Magnitude Diagram 15,630...

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