Dynamics of Orbits and Local Gas Stability in a Lopsided Galaxy

Abstract

We study the dynamics of particles in closed orbits in a galactic disk perturbed by a lopsided halo potential. The underlying potential in a large fraction of spiral galaxies is now believed to have this form. The orbits are solved via Ðrst-order epicyclic theory, and the azimuthal variation in the e †ective surface density is obtained for an exponential disk. The results are obtained Ðrst for a Ñat rotation curve and then for a general power-law rotation curve. These are shown to be valid for both stars and gas in the inner (optical) region of a galaxy because both respond to the same lopsided potential and have comparable disk scale lengths. The results are applied to external lopsided galaxies. An orbit is shown to be elongated along the minimum in the lopsided potential. The net rotational velocity is highest at the minimum radial extent of the orbit. The perturbation parameter for the lop-sided potential is obtained as a function of the observed fractional amplitude of the m \ 1 azimuthal v lop , Fourier component of the surface brightness and the radius. The ellipticity of isophotes is shown to be higher by at least a factor of 4 compared to This explains why the phenomenon of lopsidedness is v lop. so commonly detected. It also means that even visually strongly lopsided galaxies have a fairly axisym-metric potential, with a small The e †ective disk surface density is highest along the maximum v lop \ 0.1. in the lopsided potential, and there is an underdense region in the opposite direction. The maximum increase in the surface density is high D35%È50%, for strongly lopsided galaxies. We obtain the local stability parameter in a lopsided galaxy and show that its values for gas are Q lop signiÐcantly lowered compared to the axisymmetric case in the overdense region. This is argued to result in an enhanced formation of massive stars which then result in H II regions. Thus we can naturally explain the observed azimuthal asymmetry in the distribution of molecular hydrogen gas and H II regions in the lopsided galaxies such as M101.