3 Kinematics

Table 3: Kinematic parameters on the SuWt 2's ring and its central star.
Parameter Value
$ a=r$ (outer radius) &dotfill#dotfill; $ 45 \pm 4$ arcsec
$ b=r\cos i$ &dotfill#dotfill; $ 17 \pm 2$ arcsec
thickness &dotfill#dotfill; $ 13 \pm 2$ arcsec
PA &dotfill#dotfill; $ 48^{\circ} \pm 2^{\circ}$
GPA &dotfill#dotfill; $ 62^{\circ}16\hbox{$^\prime$}\pm 2^{\circ} $
inclination ($ i$) &dotfill#dotfill; $ 68^{\circ} \pm 2^{\circ}$
$ v_{\rm sys}$ (LSR) &dotfill#dotfill; $ -29.5\pm5$ kms$ {}^{-1}$
$ v_{\rm exp}$ &dotfill#dotfill; $ 28\pm 5$ kms$ {}^{-1}$

Figure: Flux intensity and radial velocity ( $ V_{\rm LSR}$) map in $ [$II$ ]$ $ \lambda $6584Å for Field 1 (see Table 1) of the PN SuWt 2. The white/black contour lines show the distribution of the narrow-band emission of H$ \alpha $ and [NII] in arbitrary unit taken with the ESO 3.6-m telescope. North is up and east is toward the left-hand side. Units are in kms$ {}^{-1}$.

Fig. 4 presents maps of the flux intensity and the local standard of rest (LSR) radial velocity derived from the Gaussian profile fits for the emission line $ [$II$ ]$ $ \lambda $6584Å. We transferred the observed velocity $ v_{\rm obs}$ to the LSR radial velocity $ v_{\rm lsr}$ by determining the radial velocities induced by the motions of the Earth and Sun using the IRAF/ASTUTIL task RVCORRECT. The emission-line profile is also resolved if its velocity dispersion is wider than the instrumental width $ \sigma_{\rm ins}$. The instrumental width can be derived from the $ [$I $ ]\,\lambda$5577Å and $ \lambda $6300Å night sky lines; it is typically $ \sigma_{\rm ins}\approx42$kms$ ^{-1}$ for $ R\sim3000$ and $ \sigma_{\rm ins}\approx19$kms$ ^{-1}$ for $ R\sim7000$. Fig. 4(right) shows the variation of the LSR radial velocity in the south-east side of the nebula. We see that the radial velocity decreases as moving anti-clockwise on the ellipse. It has a low value of about $ -70\pm30$kms$ ^{-1}$ on the west co-vertex of the ellipse, and a high value of $ -50\pm25$kms$ ^{-1}$ on the south vertex. This variation corresponds to the orientation of this nebula, namely the inclination and projected nebula on the plane of the sky. It obviously implies that the east side moves towards us, while the west side escapes from us.

Kinematic information of the ring and the central star is summarized in Table 3. Jones et al. (2010) implemented a morpho-kinematic model using the modelling program SHAPE (Steffen & López, 2006) based on the long-slit emission-line spectra at the high resolution of $ R\sim40\,000$, which is much higher than the moderate resolution of $ R\sim3000$ in our observations. They obtained the nebular expansion velocity of $ v_{\rm exp}=28$ kms$ {}^{-1}$ and the LSR systemic velocity of $ v_{\rm sys}=-29.5\pm5$ at the best-fitting inclination of $ i=68^{\circ} \pm 2^{\circ}$ between the line of sight and the nebular axisymmetry axis. We notice that the nebular axisymmetric axis has a position angle of $ {\rm PA}=48^{\circ}$ projected on to the plane of the sky, and measured from the north towards the east in the equatorial coordinate system (ECS). Transferring the PA in the ECS to the PA in the Galactic coordinate system yields the Galactic position angle of $ {\rm GPA}=62^{\circ}16\hbox{$^\prime$}$, which is the PA of the nebular axisymmetric axis projected on to the plane of the sky, measured from the North Galactic Pole (NGP; $ {\rm GPA}=0^{\circ}$) towards the Galactic east ( $ {\rm GPA}=90^{\circ}$). We notice an angle of $ -27^{\circ}44\hbox{$^\prime$}$ between the nebular axisymmetric axis projected onto the plane of the sky and the Galactic plane. Fig.5 shows the flux ratio map for the $ [$II$ ]$ doublet to the H$ \alpha $ recombination line emission. The shock criterion $ [$II$ ]$ $ \lambda \lambda $6716,6731/H $ \alpha\geq 0.5$ indicates the presence of a shock-ionization front in the ring. Therefore, the brightest south-east side of the nebula has a signature of an interaction with ISM.

Figure: Flux ratio maps of the $ [$II$ ]$ $ \lambda $6716+6731Å to the H$ \alpha $ recombination line emission.

The PPMXL catalogue3 (Roeser et al., 2010) reveals that the A-type stars of SuWt 2 move with the proper motion of $ v_l=D\mu_{l}\cos(b)=(-8.09\pm8.46)D$ kms$ ^{-1}$ and $ v_b=D\mu_{b}=(11.79\pm8.82) D$ kms$ ^{-1}$, where $ D$ is its distance in kpc. They correspond to the magnitude of $ v_{\mu}=(14.30 \pm 8.83) D$ kms$ ^{-1}$. Assuming a distance of $ D=2.3$kpc (Exter et al., 2010) and $ v_{\rm sys}=-29.5\pm5$kms$ ^{-1}$ (LSR; Jones et al., 2010), this PN moves in the Cartesian Galactocentric frame with peculiar (non-circular) velocity components of ($ U_s$,$ V_s$,$ W_s)=$( $ 35.4 \pm 18.4$, $ 11.0\pm13.7$, $ 33.18\pm26.4$)kms$ ^{-1}$, where $ U_s$ is towards the Galactic centre, $ V_s$ in the local direction of Galactic rotation, and $ W_s$ towards the NGP (see Reid et al., 2009, peculiar motion calculations in appendix). We see that SuWt 2 moves towards the NGP with $ W_s=33.18$kms$ ^{-1}$, and there is an interaction with ISM in the direction of its motion, i.e., the east-side of the nebula.

We notice a very small peculiar velocity ($ V_s=11$ kms$ ^{-1}$) in the local direction of Galactic rotation, so a kinematic distance may also be estimated as the Galactic latitude is a favorable one for such a determination. We used the FORTRAN code for the `revised' kinematic distance prescribed in Reid et al. (2009), and adopted the IAU standard parameters of the Milky Way, namely the distance to the Galactic centre $ R_0=8.5$ kpc and a circular rotation speed $ \Theta_0=220$ kms$ {}^{-1}$ for a flat rotation curve ( $ {\rm d}\Theta/{\rm d}R=0$), and the solar motion of $ {\rm U}_{\bigodot}=10.30$ kms$ {}^{-1}$, $ {\rm V}_{\bigodot}=15.3$ kms$ {}^{-1}$ and $ {\rm W}_{\bigodot}=7.7$ kms$ {}^{-1}$. The LSR systemic velocity of $ -29.5$ kms$ {}^{-1}$ (Jones et al., 2010) gives a kinematic distance of $ 2.26$ kpc, which is in quite good agreement with the distance of 2.3$ \pm$0.2 kpc found by Exter et al. (2010) based on an analysis of the double-lined eclipsing binary system. This distance implies that SuWt 2 is in the tangent of the Carina-Sagittarius spiral arm of the Galaxy ( $ l=311$$ \mbox{$.\!\!^\circ$}$0, $ b=2$$ \mbox{$.\!\!^\circ$}$$ 4$). Our adopted distance of 2.3 kpc means the ellipse's major radius of $ 45$arcsec corresponds to a ring radius of $ r=0.47\pm0.04$ pc. The expansion velocity of the ring then yields a dynamical age of $ \tau_{\rm dyn}=r/v_{\rm exp}=17500\pm 1560$ yr, which is defined as the radius divided by the constant expansion velocity. Nonetheless, the true age is more than the dynamical age, since the nebula expansion velocity is not constant through the nebula evolution. Dopita et al. (1996) estimated the true age typically around 1.5 of the dynamical age, so we get $ \tau_{\rm true}=26250\pm2330$ yr for SuWt2. If we take the asymptotic giant branch (AGB) expansion velocity of $ v_{\rm AGB}=v_{\rm exp}/2$ (Gesicki & Zijlstra, 2000), as the starting velocity of the new evolving PN, we also estimate the true age as $ \tau_{\rm true}=2r/(v_{\rm exp}+v_{\rm AGB})= 23360\pm 2080$ yr.

Ashkbiz Danehkar