Detection of gravitational waves from accreting neutron stars (NSs) in our galaxy, due to ellipticity or internal oscillation, would be a breakthrough in our understanding of compact objects and explain the absence of NSs rotating near the break-up limit. Direct detection, however, poses a formidable challenge. Using the current data available on the properties of the accreting NSs in Low Mass X-Ray Binaries (LMXBs), we quantify the detectability for the known accreting NSs, considering various emission scenarios and taking into account the negative impact of parameter uncertainty on the data analysis process. Only a few of the persistently bright NSs accreting at rates near the Eddington limit are detectable by Advanced LIGO if they are emitting gravitational waves at a rate matching the torque from accretion. A larger fraction of the known population is detectable if the spin and orbital parameters are known in advance, especially with the narrow-band Advanced LIGO. We identify the most promising targets, and list specific actions that would lead to significant improvements in detection probability. These include astronomical observations (especially for unknown orbital periods), improvements in data analysis algorithms and capabilities, and further detector development.
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