an approximate limit for NGC 6440 X-2, at a time when  found its X-ray luminosity to be $6\times10^{34}$ .

Discussion {#s:discuss}
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The discovery of millisecond pulsations [@Altamirano09] clearly identifies NGC 6440 X-2 as a neutron star LMXB system, and provides the orbital period of 57.3 minutes. The ultracompact nature of NGC 6440 X-2 confirms the trend [@Deutsch00] for globular clusters to have a higher fraction of ultracompact LMXBs than field systems, indicating a different formation mechanism [@Ivanova05]. However, it goes against the apparent trend [@Zurek09] for ultracompacts in globular clusters to have shorter periods than ultracompacts in the field. The lack of optical detections is not surprising, when the ultracompact orbit is considered. Using the relation between absolute magnitude, orbital period, and X-ray luminosity derived by @vanParadijs94, we predict $M_V=3.8$ and thus $V=21.8$ at peak. The scatter in this relation is about 1.5 magnitudes, and our optical observations all occurred during the outburst decays, so our limits on NGC 6440 X-2 are consistent with this relation.

NGC 6440 X-2’s outbursts are unusual among globular cluster LMXBs, both for the faintness of the outbursts (peak 0.5-10 keV $L_X=1.5\times10^{36}$  for the July outburst, $2.8\times10^{36}$  for the August outburst), but more importantly 