to the circular speed from the disc. The central radial velocity dispersion is set to $90\,{\rm km}\,s^{-1}$, which yields a Toomre $Q$ parameter [@toomre1964] at $2.2\,R_d$ of $1.2$. For Model 2, $V_d^2/V_c^2 = 0.33$ at $2.2R_d$. In addition, the central radial velocity dispersion in the disc is decreased so that the Toomre $Q$ parameter at $2.2R_d$ is the same as in Model 1. The <span style="font-variant:small-caps;">galactics</span> parameters for the two models are given in Table \[tab:initialmodelparameters\].

  Parameter                                     Model 1   Model 2
  -------------------------------------------- --------- ---------
  $M_d$ \[$10^{10}\,M_\odot$\]                    3.9       2.3
  $R_d$ \[kpc\]                                   2.8       2.8
  $h$ \[kpc\]                                    0.44      0.44
  $R_t$ \[kpc\]                                   25        25
  $\delta R_t$ \[kpc\]                             3         3
  $\sigma_{R0}$ \[${\rm km}\,{\rm s}^{-1}$\]      90       56.3
  $M_h$ \[$10^{12}\,M_\odot$\]                    1.2       1.3
  $v_h$ \[${\rm km}\,{\rm s}^{-1}$\]              481       505
  $a_h$ \[kpc\]                                   43        43
  $M_b$ \[$10^{9}\,M_\odot$\]                     9.9      17.9
  $v_b$ \[${\rm km}\,{\rm s}^{-1}$\]              272       375
  $R_e$ \[kpc\]                                  0.64      0.64
  $n$                                            1.32      1.32
  $Q(2.2R_{d})$                                   1.2       1.2

  : Initial model parameters.[]{data-label="tab:initialmodelparameters"}

Disc mass; radial disc scale length; vertical disc scale height; truncation radius of the disc; truncation width of the disc; central radial velocity dispersion in the disc; halo mass; characteristic velocity scale of the halo; NFW halo scale length; bulge mass; characteristic velocity scale of the bulge; bulge effective radius; Sérsic 