To Circularize or Not To Circularize?—Orbital Evolution of Satellite Galaxies

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Abstract
We investigate the orbital evolution of satellite galaxies using numerical simulations. It has long been believed that orbits suffer circularization due to dynamical friction from the galactic halo during orbital decay. This circularization was confirmed by numerous simulations in which dynamical friction was added as an external force. However, some of the recent N-body simulations have demonstrated that circularization is much slower than expected from approximate calculations. We find that the dominant reason for this discrepancy is the assumption that the Coulomb logarithm log Λ is constant, which has been used in practically all recent calculations. Since the size of the satellite is relatively large, an accurate determination of the outer cutoff radius is crucial to obtaining a good estimate for the dynamical friction. An excellent agreement between N-body simulations and approximate calculations is observed when the outer cutoff radius is taken to be the distance of the satellite to the center of the galaxy. When the satellite is at the perigalacticon, the distance to the center is smaller, and therefore log Λ becomes smaller. As a result, the dynamical friction becomes less effective. We apply our result to the Large Magellanic Cloud (LMC). We find that the expected lifetime of the LMC is twice as long as that which would be predicted with previous calculations. Previous studies predict that the LMC will merge into the Milky Way after 7 Gyr, while we find that the merging will take place 14 Gyr from now. Our result suggests that generally, satellites formed around a galaxy have longer lifetimes than previous estimates.
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