A uniformly valid asymptotic density-potential relation for spiral galaxies

Details A uniformly valid asymptotic density-potential relation for spiral galaxies A uniformly valid asymptotic density-potential relation for spiral galaxies

Sep 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cha%26a..13..250y&link_type=abstract

Chinese Astronomy and Astrophysics, Volume 13, Issue 3, p. 250-259.

Astronomy and Astrophysics

Astrophysics

Spiral Galaxies-Density Wave

Scientific paper

An asymptotic relation between density and potential perturbations which is uniformly valid for arbitrary pitch angle β for spiral galaxies with number of spiral arms m >= 2, is given. For small pitch angles (¦β¦<< 1), it is reduced to various known asymptotic relations. When ¦β¦is not small, this new result is suitable for discussing the open spiral waves forming barred spiral galaxies.
The final result is given by Eq. (5.40), where \̂gy1 and \̂gs1 are the complex amplitudes of the potential perturbation ψ1 and the density perturbation σ1 defined by Eqs. (5.32) and (5.33), respectively.
The region in the (-kr, m) plane where the present result is uniformly valid is given by Eq. (6.1) and shown in Fig. 2. In Eq. (6.1), k is the radial wave number and K is the total wave number.
When β = 0, Eq. (5.40) is reduced to Eq. (6.4), an asymptotic relation obtained by Shu (1970). When ¦β¦<< 1, Eq. (5.40) is reduced to Eq. (6.4), an equivalent form of Bertin and Mark's result (1979). When β = π/2, Eq. (5.40) is reduced to Eq. (6.5), an asymptotic relation for the ``open limit''. For the middle range of the pitch angle, neither the ``tightly wound limit'' result for ¦β¦<< 1 nor the ``open limit'' result for β ~ π/2 is valid, but the present result is still valid.
The pitch angle will be denoted by β throughout so as to leave i for the imaginary unit.

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