Joint probability density of the time and distance of closest approach for those stars that are predicted to pass within 2.5 pc of the Sun (listed in Table 3). The contour levels indicate regions enclosing 0.6, 0.9, and 0.99% cumulative probability (colour bar). The shape of each PDF is affected by the relative errors in the observational data of each star, particularly the errors on parallax and radial velocity.