Probing For Machos of Mass $10^{-15}M_\odot$-$10^{-7}M_\odot$ with Gamma-Ray Burst Parallax Spacecraft

Two spacecraft separated by $\sim 1\,\au$ and equipped with gamma-ray burst (GRB) detectors could detect or rule out a cosmological density of Massive Compact Halo Objects (MACHOs) in the mass range $10^{-15} M_{\odot}\lsim M \lsim 10^{-7} M_{\odot}$ provided that GRBs prove to be cosmological. Previously devised methods for detecting MACHOs have spanned the mass range $10^{-16} M_{\odot}\lsim M \lsim 10^{7} M_{\odot}$, but with a gap of several orders of magnitude near $10^{-9} M_{\odot}$. For MACHOs and sources both at a cosmological distance, the Einstein radius is $\sim 1\,\au\,(M/10^{-7} M_\odot)^{1/2}$. Hence, if a GRB lies within the Einstein ring of a MACHO of mass $M\lsim 10^{-7}M_\odot$ as seen by one detector, it will not lie in the Einstein ring as seen by a second detector $\sim 1\,\au$ away. This implies that if GRBs are measured to have significantly different fluxes by the two detectors, this would signal the presence of a MACHO $\lsim 10^{-7}M_\odot$. By the same token, if the two detectors measured similar fluxes for several hundred events a cosmological abundance of such low-mass MACHOs would be ruled out. The lower limit of sensitivity, $M\lsim 10^{-15}M_\odot$ is set by the finite size of the source. If low-mass MACHOs are detected, there are tests which can discriminate among events generated by MACHOs in the three mass ranges $M\lsim 10^{-12}\,M_\odot$, $10^{-12}\,M_\odot\lsim M\lsim 10^{-7}\,M_\odot$, and $M\gsim 10^{-7}\ M_\odot$. Further experiments would then be required to make more accurate mass measurements.