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tokens: into components which contribute significantly to the total density above z − , labelled Σ b 1 , and those which do not, e.g. are concentrated close to the disc plane below z − , labelled Σ b 0 . For this latter component, above z − the density is close enough to zero for the surface density to be considered constant. Hence, for z > z − , the total surface density is Σ( z ) = Σ b 0 + Σ b 1 ( z ) + 2ρ dm z , and equation ( 9 ) then becomes Note that the baryonic density shape inside z does not enter in the calculation of σ z ( z ); hence, there is no need to model the shapes of the baryonic components inside the z region where we have tracer data. Also note the term 2ρ dm ( h + z ) of equation ( 10 ) can be expressed as Σ dm ( z ) + Σ dm ( h ). Despite having a constant DM density to an infinite height, the contribution of this component to is finite. The term Σ dm ( h ) is a manifestation of the tracer density decaying exponentially with a scaleheight of h . Thus, the impact of the assumption of constant DM density is controlled by the scaleheight of the tracer population, with hotter populations reaching higher above the disc being affected more. 3.3 Tilt term At the midplane ( z = 0), a potential symmetric in z is separable up to second order (Binney Tremaine 2008 ), with the radial and vertical motions decoupling. Thus, at z = 0 the tilt term vanishes, though it may increase rapidly as z increases. Intuitively, the motion of the tracer stars can be viewed as a combination of oscillation around the disc, and orbital motion around the Galactic Centre; the tilt term can then be seen as a consequence of this orbital motion around the Galactic Centre. A star in an elliptic orbit around the Galactic Centre will on the part of its orbit where it is moving towards the Galactic Centre (i.e. has v R 0) typically also move towards the disc plane; hence, this star will for z > 0 have , and for z 0. Similarly, in the part of the orbit where the star moves away from the Galactic Centre (i.e. has v R > 0), it will typically also move away from the disc plane, again resulting in having the same sign as z . Hence, as , we arrive at the result that σ Rz carries the same sign as z . See Silverwood ( 2016 ) for further motivation on this result on the sign of σ Rz . The σ Rz data given in B15 has a sign error, as it is negative for positive z , and so as done in Silverwood et al. ( 2016 ) we apply a sign correction. We again assume symmetry above and below the disc plane, and for z > 0 we model the vertical profile of σ Rz using the functional form σ Rz = Az n , where A and n are fitted to the σ Rz data. For A ≥ 0 and n > 0, this model naturally encompasses the requirements that σ Rz ≥ 0 for z ≥ 0 and σ Rz = 0 for z = 0. The modelling σ Rz = Az n also fits the σ Rz data well, see Fig. 8 and Silverwood et al. ( 2016 ). The tilt term includes a radial derivative of ν and σ Rz , and so we must also model their radial behaviours. From Bovy et al. ( 2016 ), we see