Effect of a constant shift in the parallaxes of the stars (Δϖ =  − 0.029 mas) on the tilt angle γ, as measured in Galactocentric cylindrical coordinates for different types of intrinsic alignment. Left columns: intrinsic tilt angles γ₀ as a function of R and z. Middle columns: tilt angles γ₁ computed from the “observed” velocity moments. Right columns: Δγ = γ₁ − γ₀. Be aware of the different colourbar ranges. Top panels: we set the velocity covariances such that the input alignment is spherical. Bottom panels: the input alignment is cylindrical. Black contours denote regions where the tilt angle is not affected, i.e. Δγ = 0°. For spherical alignment this is expected to be the case on the line passing through the Galactic centre and the position of the Sun, thus along z ≈ 0 kpc, and on the circle that goes through the Galactic centre and the position of the Sun. For cylindrical alignment this is expected to occur at both z = z_⊙ ≈ 0 kpc and R = R_⊙.