6.1.1 Density distribution

The dense torus used for the ring was developed from the higher spectral resolution kinematic model of Jones et al. (2010) and our plasma diagnostics (Section 4). Although the density cannot be more than the low-density limit of $ N_{\rm e}<100$cm$ ^{-3}$ due to the [S II] $ \lambda \lambda $6716/6731 line ratio of $ \gtrsim1.40$, it was slightly adjusted to produce the total H$ \beta $ Balmer intrinsic line flux $ I({\rm H}\beta)$ derived for the ring and interior structure or the H$ \beta $ luminosity $ L({\rm H}\beta)=4\pi\,D^2\,I({\rm H}\beta)$ at the specified distance $ D$. The three-dimensional density distribution used for the torus and interior structure is shown in Fig. 8. The central star is located in the centre of the torus. The torus has a radius of $ 38.1$arcsec from its centre to the centre of the tube (1 arcsec is equal to $ 1.12\times 10^{-2}$ pc based on the best-fitting photoionization models). The radius of the tube of the ring is $ 6.9$arcsec. The hydrogen number density of the torus is taken to be homogeneous and equal to $ N_{\rm H}=100$ cm$ {}^{-3}$. Smith et al. (2007) studied similar objects, including SuWt 2, and found that the ring itself can be a swept-up thin disc, and the interior of the ring is filled with a uniform equatorial disc. Therefore, inside the ring, there is a less dense oblate spheroid with a homogeneous density of 50 cm$ {}^{-3}$, a semimajor axis of $ 31.2$arcsec and a semiminor axis of $ 6.9$arcsec. The H number density of the oblate spheroid is chosen to match the total $ L({\rm H}\beta)$ and be a reasonable fit for H$ ^{2+}$/H$ ^{+}$ compared to the empirical results. The dimensions of the model were estimated from the kinematic model of Jones et al. (2010) with an adopted inclination of 68 $ {}^{\circ}$. The distance was estimated over a range 2.1-2.7 kpc, which corresponds to a reliable range based on the H$ \alpha $ surface brightness-radius relation of Frew & Parker (2006) and Frew (2008). The distance was allowed to vary to find the best-fitting model. The value of 2.3 kpc adopted in this work yielded the best match to the observed H$ \beta $ luminosity and it is also in very good agreement with Exter et al. (2010).

Ashkbiz Danehkar