MACHOs in a flattened halo

If massive compact halo objects (MACHOs) are detected in ongoing searches, then τ_SMC/τ_LMC, the ratio of the optical depths toward the Small and Large Magellanic Clouds, will be a robust indicator of the flattening of the Galactic dark matter halo. For a spherical halo, τ_SMC/τ_LMC is about 1.45, independent of details of the shape of the Galactic rotation curve, the assumed mass of the Galactic disk and spheroid, and the truncation distance (if any) of the dark halo. For an E6 halo (axis ratio c/a = 0.4), the ratio of optical depths is τ_SMC/τ_LMC ∼ 0.95, again independent of assumptions about Galactic parameters. This ratio can be measured with a precision as good as ∼10% depending on the typical mass of the MACHOs. If the halo is highly flattened (e.g., E6) and closely truncated (e.g., at twice the solar galactocentric radius), then the optical depth toward the LMC can be reduced by a factor of ∼2. For these extreme parameters, and the assumption of a heavy Galactic disk and spheroid, the upper limit of the MACHO mass range to which ongoing experiments are sensitive is reduced from O(10⁶) M_⊙ to O(10) M_⊙.