期刊
ASTROPHYSICAL JOURNAL
卷 701, 期 2, 页码 1500-1505出版社
IOP PUBLISHING LTD
DOI: 10.1088/0004-637X/701/2/1500
关键词
dark matter; galaxies: halos; galaxies: kinematics and dynamics; stellar dynamics
资金
- Danish National Research Foundation
- STFC [PP/E00105X/1] Funding Source: UKRI
- Science and Technology Facilities Council [PP/E00105X/1] Funding Source: researchfish
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope. of the tracers must be given exactly by gamma = 2 beta, where beta is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
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