Dark Matter and Macho of the Galaxy

如果MACHO的密度分布Rho(Gamma)相对于银河系中心是球对称的，则MACHO的最小总质量为太阳的1.7倍，单位为太阳的大麦哲伦云(LMC)，单位为太阳。10^&lt；-7；如果Rho(Gamma)是伽马的递减函数，则证明了SUN&gt；10&gt；10&gt；M；&lt；的M^&lt；mano&gt；_是5.6&lt；。结果表明，SUN&GT；10&GT；10&GT；MMC&gt；_7~-3&lt；SUN&GT；10^&lt；10&gt；MMC&gt；_7~-3&lt；SUN&GT；10^&lt；10&gt；10&gt；MMC&gt；MMC&gt；_7的最小柱密度为Sigma；如果MACHO丛仅存在于LMC和太阳的中间，则M^&lt；是太阳的1.5M；。这表明，无论是MACHO的密度分布异常，还是如果SUN&GT；10^&lt；10&lt；2&lt；的密度分布不正常，MACHO的总质量都小于SUN&GT；10^&lt；10&gt；M_&lt；&lt；即LMC内晕质量的-10%。

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>.