paper

The Minimum Total Mass of MACHOs and Halo Models of the Galaxy

arXiv:astro-ph/9610121 · doi:10.1086/310396

Abstract

If the density distribution ρ(r) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M_{min}^{ MACHO} of the MACHOs is 1.7\times 10^{10}\sol τ_{-6.7}^{ LMC} where τ_{-6.7}^{ LMC} is the optical depth (τ^{ LMC}) toward the Large Magellanic Cloud (LMC) in the unit of 2\times 10^{-7}. If ρ(r) is a decreasing function of r, it is proved that M_{min}^{ MACHO} is 5.6\times 10^{10}\sol τ_{-6.7}^{ LMC}. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also considered. It is found that M_{min}^{ MACHO} ranges from 5.6\times 10^{10}\sol τ_{-6.7}^{ LMC} to \sim 3 \times 10^{11}\sol τ_{-6.7}^{ LMC}. For general case, the minimal column density Σ_{min}^{ MACHO} of MACHOs is obtained as Σ_{min}^{ MACHO} =25 \sol { pc}^{-2}τ_{-6.7}^{ LMC}. If the clump of MACHOs exist only halfway between LMC and the sun, M_{min}^{ MACHO} is 1.5\times 10^9\sol. This shows that the total mass of MACHOs is smaller than 5 \times 10^{10}\sol , i.e. \sim 10\% of the mass of the halo inside LMC, either if the density distribution of MACHOs is unusual or τ^{ LMC}\ll 2\times 10^{-7}.

5 pages, 5 Encapsulated PostScript figures, Latex, Accepted for publication in Apj. Letters

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