摘要
As an alternative gravitational theory to general relativity(GR),conformal gravity(CG)has recently been successfully veri/ed by observations of type Ia supernovae(SN Ia)and the rotation curves of spiral galaxies.The observations of galaxies only pertain to the non-relativistic form of gravity.In this context,within the framework of the Newtonian theory of gravity(the non-relativistic form of GR),dark matter(DM)is postulated to account for the observations.On the other hand,the non-relativistic form of CG predicts an additional potential:besides the Newtonian potential,there is a so-called linear potential term,characterized by the parameterγ*,as an alternative to DM in Newtonian gravity.To test CG in its non-relativistic form,much work has been done by/tting the predictions to the observations of circular velocity(rotation curves)for spiral galaxies.In this paper,we test CG with the observations from elliptical galaxies.Instead of the circular velocities for spiral galaxies,we use the velocity dispersion for elliptical galaxies.By replacing the Newtonian potential with that predicted by the nonrelativistic form of CG in the Hamiltonian,we directly extend the Jeans equation derived in Newtonian theory to that for CG.By comparing the results derived from the ellipticals with those from spirals,we/nd that the extra potential predicted by CG is not suf/cient to account for the observations of ellipticals.Furthermore,we discover a strong correlation betweenγ*and the stellar mass M*in dwarf spheroidal galaxies.This/nding implies that the variation inγ*violates a fundamental prediction of CG,which posits thatγ*should be a universal constant.
基金
supported by the National Natural Science Foundation of China(NSFC,grant No.11988101)
the K.C.Wong Education Foundation.
