Galactic neutron stars are a promising source of gravitational waves in the analysis band of detectors such as LIGO and Virgo .
Previous searches for gravitational waves from neutron stars have focused on the detection of individual neutron stars , which are either nearby or highly non-spherical .
Here we consider the stochastic gravitational-wave signal arising from the ensemble of Galactic neutron stars .
Using a population synthesis model , we estimate the single-sigma sensitivity of current and planned gravitational-wave observatories to average neutron star ellipticity \epsilon as a function of the number of in-band Galactic neutron stars N _ { \text { tot } } .
For the plausible case of N _ { \text { tot } } \approx 53000 , and assuming one year of observation time with colocated initial LIGO detectors , we find it to be \sigma _ { \epsilon } = 2.1 \times 10 ^ { -7 } , which is comparable to current bounds on some nearby neutron stars .
( The current best 95 \% upper limits are \epsilon \lesssim 7 \times 10 ^ { -8 } . )
It is unclear if Advanced LIGO can significantly improve on this sensitivity using spatially separated detectors .
For the proposed Einstein Telescope , we estimate that \sigma _ { \epsilon } = 5.6 \times 10 ^ { -10 } .
Finally , we show that stochastic measurements can be combined with measurements of individual neutron stars in order to estimate the number of in-band Galactic neutron stars .
In this way , measurements of stochastic gravitational waves provide a complementary tool for studying Galactic neutron stars .