Dark Matter and Macho of the Galaxy

点击翻译按钮获取中文摘要

If the density distribution rho (gamma) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M^<MACHO>_ of the MACHOs is 1.7<of sun> 10^<10>M_<<of sun>>gamma^<LMC>_7 where gamma^<LMC>_7 is the optical depth (gamma^<LMC>) toward the Large Magellanic Cloud (LMC) in the unit of 2<of sun> 10^<-7>. If rho (gamma) is a decreasing function of gamma, it is proved that M^<MACHO>_ is 5.6<of sun> 10^<10>M_<<of sun>>gamma^<LMC>_7. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also considered. It is found that M^<MACHO>_ ranges from 5.6<of sun> 10^<10>M_<<of sun>>gamma^<LMC>_7 to-3<of sun> 10^<11>M_<<of sun>>gamma^<LMC>_7. For general case, the minimal column density SIGMA^<MACHO>_ of MACHOs is obtained as SIGMA^<MACHO>_ =25M_<<of sun>>pc^<-2>gamma^<LMC>_7. If the clump of MACHOs exist only halfway between LMC and the sun, M^<MACHO>_ is 1.5<of sun> 10^9M_<<of sun>>. This shows that the total mass of MACHOs is smaller than 5<of sun> 10^<10>M_<<of sun>>, i.e.-10% of the mass of the halo inside LMC,either if the density distribution of MACHOs is unusual or gamma^<LMC><<2<of sun> 10^<-7>.