3 Results

Figure: Velocity slices of Th2-A along the H$\alpha$ emission-line profile. The slices have a $\sim 20$kms$^{-1}$ width, the central velocity is given at the top of each slice, and the LSR systemic velocity is $v_{\rm sys}=-52$kms$^{-1}$. The color bar shows flux measurements in logarithm of $10^{-15}$ ergs${}^{-1}$cm${}^{-2}$spaxel${}^{-1}$ unit. Velocity channels are in kms${}^{-1}$ unit. The contours in the channel maps are the narrow-band H$\alpha$ emission in arbitrary unit obtained from the SHS. North is up and east is toward the left-hand side.

In Figure 2, we present the spatially resolved maps of the flux intensity, continuum, radial velocity and velocity dispersion of H$\alpha$ $\lambda$6563 for Th2-A, obtained by fitting a Gaussian curve to each spaxel of the IFU datacube using the MPFIT routine (Markwardt, 2009). The white/black contour lines in the maps depict the distribution of the H$\alpha$ emission obtained from the SuperCOSMOS H$\alpha$ Sky Survey (SHS; Parker et al., 2005), which can aid us in distinguishing the nebular border. We corrected the radial velocity for the motions of the Earth and Sun at the time of our observation by using the IRAF task rvcorrect, that results in the local standard of rest (LSR) radial velocity. We corrected the velocity dispersion for the instrumental width, the thermal broadening and the fine structure broadening. The instrumental width is obtained from the $[$OI $]\,\lambda$6300 night sky line, and is typically $\sigma_{\rm ins}\approx 18$kms$^{-1}$ at the chosen spectral resolution of $R \sim 7000$. The thermal broadening $\sigma_{\rm th}$ is obtained through the Boltzmann's equation $\sigma_{\rm th}= \sqrt{8.3\,T_e[{\rm kK}]/Z}$ [kms$^{-1}$], where $T_e$ is the electron temperature of the nebula and $Z$ is the atomic weight of the atom or ion. The fine structure broadening $\sigma_{\rm fs}$ in the hydrogen recombination lines is typically $\sigma_{\rm fs}\approx3$kms${}^{-1}$ for H$\alpha$ (Clegg et al., 1999).

As seen in Figure 2, the flux map shows a polygonal ring shape with low emission at the central region (also visible in the narrow-band H$\alpha$ image of Górny et al., 1999). However, the HST image shown in Fig. 1 does not show this morphology since it was taken using the wide-band F555W filter. The appearance of a prolate nebula viewed almost pole-on can become rectangular, when the density distribution along the shell decreases slightly with distance from the equator (see e.g. Akras & Steffen, 2012). The high values of velocity dispersion seen at the central region could be related to high-velocity point-symmetric outflows toward the axis of a prolate ellipsoid viewed pole-on, which is easily noticeable in the channel maps (see Fig. 3) and is discussed below (and later in Section 4).

The expansion velocity ( $v_{\rm exp}$) obtained from the half width at half maximum (HWHM) of the H$\alpha$ emission flux integrated over the entire nebula is $V_{\rm HWHM}=40\pm5$kms$^{-1}$, obtained from the corrected dispersion velocity, i.e. $V_{\rm HWHM}=({8\,{\rm ln (2)}})^{1/2}\sigma_{\rm corr}/2$. The obtained HWHM expansion velocity is higher than the peak-to-peak velocity of $2V_{\rm exp}=35$kms$^{-1}$ derived from the [OIII] emission line by Meatheringham et al. (1988). Note that the [OIII] emission typically occurs near inner regions of the nebula whose expansion velocity is lower than outer regions. However, measuring the expansion velocity by means of the HWHM method is not very fruitful for more detailed kinematic studies. The radiation-hydrodynamics models by Schönberner et al. (2010) showed that the HWHM velocities of volume-integrated line profiles always underestimate the true expansion velocity. The HWHM method is suitable for slowly expanding objects, but it does not reflects real expansion velocities of large spatially resolved objects.

Figure 3 shows the flux intensity maps of the H$\alpha$ emission line on a logarithmic scale observed in a sequence of 15 velocity channels with a resolution of $\sim 20$kms$^{-1}$, which can be used to identify different kinematic components of the nebula. The systemic velocity $v_{\rm sys}=-52$kms$^{-1}$ has been subtracted from the central velocity value given at the top of each channel. The stellar continuum map has also been subtracted from the flux intensity maps. While a prominent equatorial ring can be clearly seen in the $-30$ and $31$kms$^{-1}$ channels, a pair of collimated bipolar outflows can be identified in the $-71$ and $72$kms$^{-1}$ channels. This ring has a radius of $14\hbox{$^{\prime\prime}$}$ and a thickness of $9\hbox{$^{\prime\prime}$}$. Two different velocity components seen in the $-51$, $-30$, $31$ and $51$kms$^{-1}$ channels are consistent with front and back walls of a toroidal shell expanding with a velocity of $\sim 40$kms$^{-1}$. If we assume that this ring is a projection of a circle on the sky plane, the velocity channels correspond to a position angle (P.A.) of $-45^{\circ} \pm 5^{\circ}$ measured from the north toward the east in the equatorial coordinate system (ECS). A brightness discontinuity seen at the central region in both directions, from the $51$ to $72$ ($-51$ to $-71$)kms$^{-1}$ velocity slices, is related to an environment change of collimated point-symmetric outflows emerging from the dense shell. However, the dimensions of collimated bipolar outflows seen pole-on cannot be precisely determined, but their positions are approximately projected near the central star and inside the ring onto the sky plane. It is seen that the bipolar outflows reach a velocity of $\sim \pm 90$kms$^{-1}$ at the poles, and have similar brightness in the $-71$ and $72$ (also $-92$ and $93$)kms$^{-1}$ velocity slices.

Figure 4: SHAPE mesh model before rendering at two different orientations (inclination: 0$^{\circ }$ and 90$^{\circ }$), the best-fitting inclination, and the corresponding rendered image, respectively.