The phenomenon of counter-rotation is:
intrinsic when the two kinematically decoupled components are rotating in opposite directions around the same rotation axis and, therefore, their vectors of angular momentum are antiparallel;
apparent if the two kinematically decoupled components rotate around skewed rotation axes and the line of sight lies in between them so that the vectors of angular momentum are projected antiparallel onto the sky plane.
Observationally, the intrinsic or apparent nature of counter-rotation may be addressed in not edge-on galaxies by analyzing their full velocity field as mapped with multi-slit or integral-field spectroscopy.
As far as the counter-rotating components are concerned, counter-rotation occurs in a variety of forms:
gas-versus-stars counter-rotation (also known as gaseous counter-rotation) is observed when the gaseous disk counter-rotates with respect to the stellar body of the galaxy. This is the case of the SB0/SBa NGC 4546 in which the rotation of the ionized, molecular, and atomic gas (≈ 108 M⊙) has similar amplitude but opposite direction with respect to the stars (Galletta 1987, Bettoni et al. 1991, Sage & Galletta 1994).
stars-versus-stars counter-rotation (also known as stellar counter-rotation) occurs when two stellar components counter-rotate. Usually the more massive component is labeled as the prograde one. The E7/S0 NGC 4550 hosts two cospatial counter-rotating stellar disks, one of them is corotating with the gaseous disk (Rubin et al. 1992, Johnston et al. 2013, Coccato et al. 2013). The two stellar disks have similar luminosities, sizes, and masses (Rix et al. 1992) although one is thicker than the other (Cappellari et al. 2007). The bulge (e.g., NGC 524; Katkov et al. 2011), a secondary bar (e.g., NGC 2950; Corsini et al. 2003a, Maciejewski 2006), or some of the stars in a bar (Bettoni 1989, Bettoni & Galletta 1997) are other examples of counter-rotating stellar components.
gas-versus-gas counter-rotation is reported when two gaseous disks counter-rotate. The S0 NGC 7332 possesses two apposed disks of ionized gas rotating in opposite sense with respect to each other. The gaseous material (≈ 105 M⊙) displays non-circular motions indicating it has not reached equilibrium (Fisher et al. 1994, Plana & Boulesteix 1996).
Finally, counter-rotation in disk galaxies is detected in:
the inner regions of the galaxy. For example, the Sa NGC 3593 (Fig. 1) is composed by a small bulge, a main stellar disk which contains ~ 80% of the stars (1.2 × 1010 M⊙) and a secondary counter-rotating stellar disk (Bertola et al. 1996, Coccato et al. 2013). The latter dominates the kinematics in the inner kpc and corotates with the disk of ionized and molecular gas (Corsini et al. 1998, García-Burillo et al. 2000).
the outer regions of the galaxy. The Sab NGC 4826 (M64) contains two counter-rotating nested disks of ionized, molecular and neutral gas extending out ~ 1 and ~ 11 kpc, respectively (Braun et al. 1992, Braun et al. 1994, Rubin 1994a, Walterbos et al. 1994). They have similar masses (≈ 108 M⊙) and are both coplanar to the stellar disk. Stars corotate with the inner gas. Beyond the dust lane which marks transition between the two gaseous disks, only a small fraction of stars (5%) corotate with the outer gas (Rix et al. 1995).
overall the galaxy, as for the Sa NGC 3626. This is the first spiral galaxy where the gaseous component (≈ 109 M⊙) was observed to counter-rotate at all radii with respect to the stars (Ciri et al. 1995, García-Burillo et al. 1998, Haynes et al. 2000, Sil'chenko et al. 2010).
Figure 1. The inner stellar counter-rotation and overall gaseous counter-rotation of the Sa NGC 3593. Left panels: Velocity (top panel) and velocity dispersion (bottom panel) radial profiles measured along the major axis of NGC 3593 for the stellar (open circles) and ionized-gas component (filled circles). Right panels: Photometric decomposition of NGC 3593 (top panel). The surface-brightness radial profile measured along the major axis (crosses) is decomposed into the contribution of a bulge (dot-dashed line), a smaller-scale disk (short-dashed line), and a larger-scale disk (long-dashed line). The sum of the three component is given by the continuous line. Mass model of NGC 3593 (bottom panel). The contribution of the smaller-scale disk (short-dashed line) and larger-scale disk (long-dashed line) to the total circular velocity (continuous line) is shown with the observed ionized-gas velocity curve (filled circles). The contribution of the bulge is neglected. From Bertola et al. (1996).