We present proper motion measurements for more than 0.55 million main-sequence stars , by comparing astrometric positions of matched stars between the multi-band imaging datasets from the Hyper Suprime-Cam ( HSC ) Survey and the SDSS Stripe 82 .
In doing this we use 3 million galaxies to recalibrate the astrometry and set up a common reference frame between the two catalogues .
The exquisite depth and the nearly 12 years of time baseline between HSC and SDSS enable high-precision measurements of statistical proper motions for stars down to i \simeq 24 .
A validation of our method is demonstrated by the agreement with the Gaia proper motions , to the precision better than 0.1 mas yr ^ { -1 } .
To retain the precision , we make a correction of the subtle effects due to the differential chromatic refraction in the SDSS images based on the comparison with the Gaia proper motions against colour of stars , which is validated using the SDSS spectroscopic quasars .
Combining with the photometric distance estimates for individual stars based on the precise HSC photometry , we show a significant detection of the net proper motions for stars in each bin of distance out to 100 kpc .
The two-component tangential velocities after subtracting the apparent motions due to our own motion display rich phase-space structures including a clear signature of the Sagittarius stream in the halo region of distance range [ 10 , 35 ] kpc .
We also measure the tangential velocity dispersion in the distance range 5–20 kpc and find that the data are consistent with a constant isotropic dispersion of 80 \pm 10 ~ { } { km / s } .
More distant stars appear to have random motions with respect to the Galactic centre on average , but still indicates a possible coherent motion .
Our results demonstrate that wide-area ground-based imaging datasets for the same regions of the sky , with long time baseline , are powerful tools to measure the proper motions out to large distances .