We present the first asymmetric drift (AD) measurements for unresolved stellar populations of different characteristic ages above and below 1.5 Gyr. These measurements sample the age-velocity relation (AVR) in galaxy disks. In this first paper we develop two efficient algorithms to extract AD on a spaxel-by-spaxel basis from optical integral-field spectroscopic (IFS) data-cubes. The algorithms apply different spectral templates, one using simple stellar populations and the other a stellar library; their comparison allows us to assess systematic errors in derived multi-component velocities, such as template-mismatch. We test algorithm reliability using mock spectra and Monte Carlo Markov Chains on real data from the MaNGA survey in SDSS-IV. We quantify random and systematic errors in AD as a function of signal-to-noise and stellar population properties with the aim of applying this technique to large subsets of the MaNGA galaxy sample. As a demonstration of our methods, we apply them to an initial sample of seven galaxies with comparable stellar mass and color to the Milky Way. We find a wide range of distinct AD radial profiles for young and old stellar populations.
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