A note on the asymptotic density-potential relation of a spiral galaxy with a finite thickness

Details A note on the asymptotic density-potential relation of a spiral galaxy with a finite thickness A note on the asymptotic density-potential relation of a spiral galaxy with a finite thickness

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cha%26a...7..186y&link_type=abstract

Chinese Astronomy and Astrophysics, Volume 7, Issue 3, p. 186-194.

Astronomy and Astrophysics

Astrophysics

Scientific paper

It is shown that the asymptotic σ1(r) and ψ1(r) relations can be derived very simply by using the method of double series expansion, where σ1, ψ1(r,0) and ψ1 are the surface density perturbation, the gravitational potential perturbation at the symmetric plane Z=0 and the average potential perturbation respectively. The results are accurate to the order of both m2(kr)-2 and k<|z|>, where m is the number of spiral arms, k is the radial wave number, r is the distance from the centre of the galaxy, and <|z|> is the average vertical distance of a star from the Symmetrie plane Z=0. Such an accuracy is usually sufficient for the discussion of spiral modes in a spiral galaxy of small but finite disk thickness. It is pointed out that ψ1(r,0)~(σ1(r) relation can be expressed in a unified form for different vertical density profiles if <|z|> is adopted as the thickness scale, and that ψ1(r,0)~(σ1(r) can be expressed in a unified form for different vertical density profiles if <|z-z|> the average vertical separation between two stars, is adopted as the thickness scale. Only the value of the ratio z/ is a functional of the vertical density profile. However, for the usual physically meaningful profiles, these values are very close to each other: It is sqrt(2) for the Gaussian profile, 1/Ln2 = 1.443 for the rmsech2(z/z1(r)) profile, and 1.5 for the exp[-z/z1(r)] profile.

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