Circumstellar density n_e at the radius of the shock R_p for AT 2023fhn and previous LFBOTs. The densities for ZTF 20 acigmel (Bright et al. 2022, Table 6) have been reduced by a factor ∼16 to align them with the equipartition ϵ_e = ϵ_B = 1/3 assumption used for all other measurements (for reference, see how Eq. (5) scales with ϵ_e and ϵ_B). As in Fig. 10, both AT 2023fhn epochs are shown, where the best constraints are from the epoch at 138 days. Other LBFOT results are from Ho et al. (2019; 2021, AT 2018cow), Ho et al. (2020, ZTF 18abvkwla), Coppejans et al. (2020, CSS161010), Bright et al. (2022, ZTF 20 acigmel, their fit to n_e(r) is adopted, shown as a red solid/dash line either side of a possible break) and Yao et al. (2022, AT 2020mrf). Lines of constant Ṁ are shown for v_w = 1000 km s⁻¹. Note that due to different assumptions in the modelling, the densities and/or mass loss rates derived between different authors and objects can differ by up to a factor 5 (DeMarchi et al. 2022).