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The detection of a counter-rotating gaseous component is usually straightforward. Observationally, it may be addressed by looking at the opposite orientation of the ionized-gas emission lines and stellar absorption lines in 2-dimensional optical spectra (e.g., see Fig. 1 in Galletta 1987) or in position-velocity diagrams (e.g., see Fig. 1 in Bureau & Chung 2006). Moreover, the standard techniques adopted to derive the kinematics of gas and stars allow to measure differences of few km s-1 in their rotation velocities.

On the contrary, unveiling a counter-rotating stellar component is a more difficult task. It requires a detailed data analysis because the kinematics of two counter-rotating stellar populations are measured from the same absorption lines. X-shaped absorption lines are only observed when the two components are photometrically similar (see Figs. 2c and 2d in Rubin et al. 1992). However, a bimodal line-of-sight velocity distribution (LOSVD) is the signature of the presence of two counter-rotating components (see Fig. 2 in Rix et al. 1992). But, the detection of the LOSVD bimodality depends on both the galaxy properties (i.e., the fraction, dynamical status, and velocity of the retrograde stars with respect to the prograde ones) and instrumental setup (i.e., spectral sampling and resolution) of the spectroscopic observations. By analyzing synthetic spectra with a different fraction of counter-rotating stars, Kuijken et al. (1996) and Pizzella et al. (2004) set an upper limit of ~ 10% on the fraction of retrograde stars which can be detected in long-slit spectra of intermediate resolution (σinst ≃ 50 km s-1) obtained with a spatial resolution of FWHM ≃ 1" and a signal-to-noise ratio S/N ≥ 30 Å-1. Similar results were obtained by Coccato et al. (2013) for integral-field spectra.

The LOSVD is poorly reproduced by a Gauss-Hermite expansion (Gerhard 1993, van der Marel & Franx 1993) when the galaxy hosts a secondary kinematic component (Fabricius et al. 2012, Katkov et al. 2013). In addition, noise and aliasing features in the LOSVD can mimic what may be interpreted as a counter-rotating component. Therefore, the recovery and decomposition of parametric LOSVDs has to be performed with caution. Indeed, the counter-rotating bulge of the Sb NGC 7331 found by Prada et al. (1996) was proved by Bottema (1999) to be an artifact of the method adopted to measure the stellar kinematics. This seems also the case of the counter-rotating stellar disks of the Sb spiral NGC 7217. Fabricius et al. (in prep., but see also this volume) show that the stellar components of NGC 7217 are corotating in spite of what previously claimed by Merrifield & Kuijken (1994).

There is compelling evidence that the presence of two off-center and symmetric peaks in the stellar velocity dispersion in combination with zero velocity rotation measured along the galaxy major axis is indicative of two counter-rotating disks. This kinematic features are observed in the radial range where the two counter-rotating components have roughly the same luminosity and their LOSVDs are unresolved (Bertola et al. 1996, see Fig. 1, left panels). Recently, Krajnovic et al. (2011) have found 11 galaxies (including NGC 4550) with a double-peaked velocity dispersion in the volume-limited sample of 260 nearby early-type galaxies gathered by the ATLAS-3D project. They are interesting candidates for a further investigation to address the fraction of their counter-rotating stars.

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