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	Fig. 6 Left panel: polar paths of objects believed to be part of the E 3 stream. Right panel: close-up.
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Appendix A: Polar path technique analysis

Each Galactic globular cluster and satellite dwarf galaxy orbits the Galaxy in a plane including the object’s present position and the Galactic centre. This reference plane can be defined as the instantaneous orbital plane of the object. Following Lynden-Bell & Lynden-Bell (1995) we consider the geometric loci of all possible normals to the galactocentric radius-vector for a particular object. This defines the set of possible orbital poles for that object, globular cluster, or dwarf galaxy. We consider a system of galactic coordinates on the unit sphere (x² + y² + z² = 1) centred on the Galactic centre; the coordinates of any object in that system are given by (A.1)where l_g and b_g are the galactocentric (not the regular heliocentric) galactic longitude and latitude, respectively. The galactocentric radius-vectors for an object and its pole are perpendicular, therefore (A.2)Finding z(x,y) from Eq. (A.2), replacing it on the expression of the unit sphere, and reorganising we obtain

(A.3)If we now consider the Lambert azimuthal equal-area projection given by the expressions (A.4)with z = 1 − X² − Y², Eq. (A.3) can be rewritten as (A.5)This expression provides the positions of all the possible poles associated with the object. The intersection (if any) of polar paths gives the putative pole of a group of (perhaps) dynamically related objects. Once the pole has been found, its position on the sky relative to the Galactic centre is given by , see Eqs. (A.1) and (A.4). Polar paths of objects possibly associated with E 3 are shown in Fig. 6. For comparison, those of objects widely regarded as part of the Sagittarius stream, streams 8a and 8b in Table 2 of Lynden-Bell & Lynden-Bell (1995), are plotted in Fig. A.1.

	Fig. A.1 Left panel: polar paths of objects believed to be part of the Sagittarius stream, streams 8a and 8b in Table 2 of Lynden-Bell & Lynden-Bell (1995). Right panel: close-up.
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© ESO, 2015