We introduce a likelihood analysis of multi-epoch stellar line-of-sight velocities to constrain the binary fractions and binary period distributions of dwarf spheroidal galaxies .
This method is applied to multi-epoch data from the Magellan/MMFS survey of the Carina , Fornax , Sculptor and Sextans dSph galaxies , after applying a model for the measurement errors that accounts for binary orbital motion .
We find that the Fornax , Sculptor , and Sextans dSphs are consistent with having binary populations similar to that of Milky Way field binaries to within 68 % confidence limits , whereas the Carina dSph is remarkably deficient in binaries with periods less than \sim 10 years .
If Carina is assumed to have a period distribution identical to that of the Milky Way field , its best-fit binary fraction is 0.14 ^ { +0.28 } _ { -0.05 } , and is constrained to be less than 0.5 at the 90 % confidence level ; thus it is unlikely to host a binary population identical to that of the Milky Way field .
By contrast , the best-fit binary fraction of the combined sample of all four galaxies is 0.46 ^ { +0.13 } _ { -0.09 } , consistent with that of Milky Way field binaries .
More generally , we infer probability distributions in binary fraction , mean orbital period , and dispersion of periods for each galaxy in the sample .
Looking ahead to future surveys , we show that the allowed parameter space of binary fraction and period distribution parameters in dSphs will be narrowed significantly by a large multi-epoch survey .
However , there is a degeneracy between the parameters that is unlikely to be broken unless the measurement error is of order \sim 0.1 km s ^ { -1 } or smaller , presently attainable only by a high-resolution spectrograph .