Simple discs with flat roatation curves

Details Simple discs with flat roatation curves Simple discs with flat roatation curves

Sep 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993mnras.264..353e&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Vol. 264, 353-374 (1993)

Astronomy and Astrophysics

Astronomy

24

Scientific paper

The aim of this paper is to understand why the squared axial ratio of the velocity ellipse, σphi_^2^/σ_R_^2^, of old disc stars in the Galaxy is less than 1/2. To this end, two infinitesimally thin steady-state axisymmetric discs with asymptotically flat circular velocity curves are presented. The first model - which we designate the Rybicki disc has surface density decaying inversely with radius. The second model is Freeman's exponential disc, which is immersed in the gravity field of the halo simulated by Mestel's potential. For both discs, we provide an infinite family of simple distribution functions, which form a sequence of increasing pressure support. In the Rybicki disc, the stellar streaming velocity increases outwards with radius, which typically causes σphi_^2^/σ_R_^2^ to be greater than 1/2. For our exponential disc distribution functions, the stellar streaming velocity declines outwards with radius, which typically causes σphi^2^/σ_R_^2^ to be less than 1/2. Our exponential disc distribution functions have the property that σ_R_^2^ decays only inversely with galactocentric radius R. If the diminution is faster, the ratio σphi_^2^/σ_R_^2^ rises above 1/2 at the Sun as the mean streaming velocity declines only in the inner disk. To investigate this, exponential discs with exponentially falling radial velocity dispersion are built. These are in conflict with the observations on the axial ratio, even allowing for a mismatch in the photometric and kinematic scalelengths. There are a number of possible resolutions of the contradiction: (1) the galactic disc is not in a steady state or is non-axisymmetric; (2) the circular velocity curve is locally declining; (3) the description of all stellar populations by a single distribution function is invalid; (4) the radial velocity dispersion does not drop off exponentially fast, but much more slowly; (5) the sampling of moving clusters and transient associations of stars creates a biased data set.

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