Galaxies and the Universe - Dynamics in Disk Galaxies

Galaxies and the Universe - Dynamics in Disk Galaxies -...

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1/15/12 Gala[ieV and Whe UniYeuVe - D\namicV in DiVk Gala[ieV 1/7 ZZZ.aVWu.Xa.edX/keel/gala[ieV/diVkd\n.hWml Dynamics in Disk Galaxies A detailed understanding of the internal working of galaxies must incorporate their dynamics - just how the gravitational potential and internal motions balance to give galaxies their forms. This is all from Newton's laws at work, but distributed masses can give results that violate intuitions honed on the inverse-square law. All of this is treated well and exhaustively by Binney and Tremaine. The key is that observable stars and gas move in response to the total potential of the mass. Major surprises have come from recent observations both of spirals and ellipticals. Disks Local densit\: Close to the disk plane, if we adopt a reference frame sharing the local rotational velocity, stellar motions consist mainly of small oscillations about the mean location (or guiding center) - shades of Ptolemaic astronomy! Radial, tangential, and vertical oscillations may occur, with the vertical frequency not in general matching the in-plane motion as it would for small perturbations to a Keplerian orbit (because galaxies have extended mass distributions). Small radial oscillations (epicycles) have an axial ratio 2:1 (tangential:radial extent - we'd have been in real trouble if Hipparchus had tried that for the planets instead of perfect circles). The epicyclic frequency is given by in which R g is the mean radius of the orbit's guiding center. Vertical oscillations through the disk plane are of particular interest, with an instantaneous period for a given ] -velocity set by the surface density within the region covered by the orbit. In the limit of a disk with infinitely thin mass profile, this case may be analyzed as simple harmonic motion, with the frequency Ȟ of ] -oscillations given by where Φ is the potential. For realistic cases, the oscillations are slower because the particle orbits do not sample the whole mass distribution. In the real Universe, the two frequencies will not be commensurate, leading to a three-dimensional space-filling trajectory within a roughly toroidal region for small excursions about the guiding center. The frequency is an easier quantity to work with than v ] , since various kinds of star have different scale heights, and scattering from molecular clouds should increase a population's scale height with time while the potential stays essentially unchanged. In the case of our galaxy, the surface density so measured is known as the Oort limit . This gives about 90 solar masses/parsec 2 within 700 pc of the plane, and implies a local density for matter of 0.15 solar masses per cubic parsec, which is slightly more than known stars and gas. A recent detailed analysis, including scale heights for various kinds of stars, is in Bahcall 1984 (ApJ 276, 169 and 287, 926). The need for invisible matter
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Galaxies and the Universe - Dynamics in Disk Galaxies -...

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