This article reports a measurement of the proper motion of Leo II, a dwarf galaxy that is a likely satellite of the Milky Way, based on imaging with the Hubble Space Telescope and Wide Field Camera. 3. The measurement uses compact background galaxies as standards of rest in both channels of the camera for two distinct pointings of the telescope, as well as a QSO in one channel for each pointing, resulting in the weighted average of six measurements. The measured proper motion in the the equatorial coordinate system is (mu(alpha), mu(delta))= (-6.9 +/- 3.7, -8.7 +/- 3.9) mas century(-1) and in the Galactic coordinate system it is (mu(l), mu(b)) = (6.2 +/- 3.9, -9.2 +/- 3.7) mas. century(-1). The implied space velocity with respect to the Galactic center is (Pi, Theta, Z) =(-37 +/- 38, 117 +/- 43, 40 +/- 16) km s(-1) or, expressed in Galactocentric radial and tangential components, (V-r, V-tan) = (21.9 +/- 1.5, 127 +/- 42) km s(-1). The space velocity implies that the instantaneous orbital inclination is 68 degrees, with a 95% confidence interval of (66 degrees, 80 degrees). The measured motion supports the hypothesis that Leo. II, Leo. IV, Leo. V, Crater. 2, and the globular cluster Crater fell into the Milky Way as a group.

We conducted a large spectroscopic survey of 336 red giants in the direction of the Leo II dwarf galaxy using Hectochelle on the Multiple Mirror Telescope, and we conclude that 175 of them are members based on their radial velocities and surface gravities. Of this set, 40 stars have never before been observed spectroscopically. The systemic velocity of the dwarf is 78.3 +/- 0.6 km s(-1) with a velocity dispersion of 7.4 +/- 0.4 km s(-1). We identify one star beyond the tidal radius of Leo II but find no signatures of uniform rotation, kinematic asymmetries, or streams. The stars show a strong metallicity gradient of -1.53 +/- 0.10 dex kpc(-1) and have a mean metallicity of -1.70 +/- 0.02 dex. There is also evidence of two different chemodynamic populations, but the signal is weak. A larger sample of stars would be necessary to verify this feature.

We combine precision radial velocity data from four different published works of the stars in the Leo II dwarf spheroidal galaxy. This yields a data set that spans 19 years, has 14 different epochs of observation, and contains 372 unique red giant branch stars, 196 of which have repeat observations. Using this multi-epoch data set, we constrain the binary fraction for Leo II. We generate a suite of Monte Carlo simulations that test different binary fractions using Bayesian analysis and determine that the binary fraction for Leo II ranges from 0.30(-0.10)(+0.09) to 0.34(-0.11)(+0.11), depending on the distributions of binary orbital parameters assumed. This value is smaller than what has been found for the solar neighborhood (similar to 0.4-0.6) but falls within the wide range of values that have been inferred for other dwarf spheroidals (0.14-0.69). The distribution of orbital periods has the greatest impact on the binary fraction results. If the fraction we find in Leo II is present in low-mass ultra-faints, it can artificially inflate the velocity dispersion of those systems and cause them to appear more dark matter rich than in actuality. For a galaxy with an intrinsic dispersion of 1 km s(-1) and an observational sample of 100 stars, the dispersion can be increased by a factor of 1.5-2 for Leo II-like binary fractions or by a factor of three. for binary fractions on the higher end of what has been seen in other dwarf spheroidals.