A sharp transition between inner and outer density slopes creates a bump in the distribution function that drives a growing l=1 dipole mode, dislodging the cusp and producing a long-lived sloshing soliton.
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The Dipole Instability in Gravitational $N$-body Systems: A Natural Explanation for Lopsidedness and Off-Centered Nuclei in Galaxies
A sharp transition between inner and outer density slopes creates a bump in the distribution function that drives a growing l=1 dipole mode, dislodging the cusp and producing a long-lived sloshing soliton.