The Effect of the Slit Configuration on the H₂ 1-0 S(1) to Br$\gamma$ Line Ratio of Spatially Resolved Planetary Nebulae

As the most abundant molecular species in planetary nebulae (PNe), the emission of H₂ is of great interest. Molecular hydrogen lines have been detected in the near infrared (IR) spectrum of more than 130 planetary nebulae (PNe) (e.g., Treffers et al., 1976; Isaacman, 1984; Kastner et al., 1996; Lumsden et al., 2001; Guerrero et al., 2000; Davis et al., 2003; Likkel et al., 2006; Ramos-Larios et al., 2017; Gledhill et al., 2018, see also Appendix A). Kastner et al. (1996) found a H₂ detection rate of 40 per cent. Recent deep imaging detections of H₂ in small structures in PNe indicate that this rate may be even higher (Fang et al., 2018; Akras et al., 2017, 2020a).

Most of the published H₂ spectroscopic observations of PNe uses narrow slits or small apertures¹¹1To simplify the text, only slit observations will be mentioned, but most of the discussion also applies or can be easily extended to observations with different shape apertures. including only part of the planetary nebula (see Table 2). Sometimes only extractions of the slit observation are considered. Often the authors focus on specific positions in the nebula, for example, obtaining a spectrum with a slit centred at the H₂ 1-0 S(1) line emission peak.

The position and width of the slit aperture during a observation have a great impact on the measured line fluxes and derived line ratios demonstrated by Fernandes et al. (2005), Gesicki et al. (2016), and Akras et al. (2020b) studies for optical atomic lines. Fernandes et al. (2005), for example, studied the effects of the nebular area covered by the slit on the atomic line ratios and derived quantities in H II regions. Their results showed that ratios of low to high-ionization lines are sensitive to this area. The ratios of [O II], [N II] and [S II] optical lines to H$\beta$ can be affected by up to 30% in relation to the ratio of the entire ionized nebula. The difference of the emitting regions of each of the lines (low-ionization lines are emitted in the outer layers of the nebula) is responsible for such high percentage. The effect of the slit configuration on atomic line ratios can be important when studying diagnostic diagrams or comparing observations to models as showed by Akras et al. (2020b).

It is therefore expected that the effect of the slit aperture and position can also be important for the H₂ line ratios to Br$\gamma$ as they are not produced in the same region. The H₂ 1-0 S(1)/Br$\gamma$ ratio (hereafter $R$(Br$\gamma$)) has been used in several studies of the molecular content of PNe, as proxies of the H₂ quantity (Aleman & Gruenwald, 2004, 2011) and assisting the diagnostic of the acting excitation mechanisms (Marquez-Lugo et al., 2015).

This paper studies the effect of the slit configuration on the $R$(Br$\gamma$) ratio, using observations available in the literature and numerical simulations to verify and quantify such effect. The observations used here are described in Sect. 2 and a table is given in Appendix A. The numerical simulations are described in Sect. 3. The results of the analysis of the slit configuration effect is presented in Section 4. Conclusions are summarised in Sect. 5.

For the present work, H₂ and Br$\gamma$ line fluxes and ratios from observations were compiled from the literature. The data collected is presented in Table 2 (see Appendix A). The table shows the $R$(Br$\gamma$) line ratios obtained from spectroscopic observations of PNe and information on the corresponding slit configuration. The table also includes a few other relevant characteristics of the PNe, which are used in the present analysis.

The slit centred at the nebular centre and positioned across the entire nebula (indicated as “centred” in Fig. 1) is the most typical PN observation configuration used for optical nebular analysis, i.e., for works focused on the ionized region. Although also used in studies of the H₂ component in extended objects, other common position in this case is the narrow slit positioned at the H₂ emission peak (indicated as “H₂ peak” in Fig 1). Observing the whole nebula is only possible for more compact and/or distant PNe. In Table 1, the observations are classified within four general slit configurations as follows:

• •

  Centred: the slit is positioned across the whole nebula passing by its centre;

• •

  H₂ peak: centred at the H₂ 1-0 S(1) emission peak;

• •

  Whole nebula: when the slit encompass the entire nebula;

• •

  Other: all other configurations that do not falls under the previous categories or the configuration is not clear from the paper description.

In Fig. 1, the illustration shows a round nebula, but the above classification is extended for all PNe morphologies. Bipolar PNe observations considered as centred are those with the slit across the equatorial region, perpendicular to the symmetry axis. In bipolar PNe, the waist region is usually a bright structure in H₂ emission (Kastner et al., 1996). This region shows a torus or barrel-like structure. For the purposes of this paper, what is of importance is the hydrogen species that are sampled by the slit (this will become clear further in the text.). It is then not difficult to see that using the slit across this torus/barrel is analogous to the centred position for elliptical PNe, despite the angle the bipolar is observed. For bipolar PNe, observations considered as H₂ peak are those where the slit samples a limited region around the wall of the torus, the wall of the lobes, or any known H₂ bright position.

To simulate the slit observations of the nebula, we use the Python²²2http://www.python.org library PyCloudy (version 0.9.6; Morisset, 2013). PyCloudy provides pseudo-3D simulations from cloudy one-dimensional models outputs. The library produces simulated line emission maps, which allow the simulation of slit observations in any configuration and the calculation of the corresponding line fluxes.

Numerical calculations of the H₂ and Br$\gamma$ emissivity in PNe were obtained with the photoionization code Cloudy (version 17.01; Ferland et al., 2017). Cloudy can simulate a photoionized nebula from the ionized to the neutral regions (photodissociation region, PDR) self-consistently. As shown in Aleman & Gruenwald (2004, 2011) and Aleman et al. (2011), this is very important for the calculation of the H₂ infrared emission, in special for the PNe with high-temperature central stars.

In the present models, the ionizing source emits as a blackbody, here described by its effective temperature ($T_{\textrm{eff}}$) and bolometric luminosity ($L_{\star}$). The gas is assumed to be spherically distributed. Models were calculated for two gas density ($n_{\textrm{H}}$) distributions: (i) uniform density and (ii) diffuse gas with a denser surrounding shell. For the first case, we studied density values from $n_{\textrm{H}}=$ 10³ to 10⁵ cm^-3. In the second case, the diffuse gas is assumed to have $n_{\textrm{H}}=$ 10³ cm^-3 and the shell $n_{\textrm{H}}=$ 10⁵ cm^-3. Shell models were simulated with different central star temperatures and shell distances from the central star. For each set of central star parameters, simulations with four different shell distances were studied. The position were set where H⁰/H = 10^-4, 10^-3, 10^-2, and 5$\times$10^-1. All simulations are done with solar abundance (Grevesse et al., 2010). Although different abundance sets may change the atomic line fluxes and therefore the gas cooling rates, such differences will not affect the conclusions of this paper. Dust is included in the models uniformly mixed with the gas. Aleman & Gruenwald (2004) showed that the dust composition in the regular dust model included in photoionization codes is not a significant factor for the H₂ emission (due to the similarities in the general behaviour of their opacities). On the other hand, dust size and density may greatly influence the H₂ emission (Aleman & Gruenwald, 2011). Here, Cloudy models with graphite dust and dust grain size distribution typical for the ISM were explored. Dust-to-gas ratios of 3$\times$10^-2 and 3$\times$10^-3 were studied (Stasińska & Szczerba, 1999). All the models were calculated assuming a 2 kpc distance, but this value has no effect on the present results, as they are based on distance-independent quantities.

For convenience, reference values are defined in Table 1. Unless stated otherwise the model parameters are the reference values listed in that table.

The present models simulate the physical conditions and emissivities along the PN radial outward direction from an inner radius of 10¹⁵ cm to a distance to the central star where the gas temperature decreases to $T_{\mathrm{F}}=$ 40 K. This value was chosen based on inspection of the H₂ emissivity radial profiles calculated with Cloudy and to reproduce well the observations. Such stop criterion guarantee the inclusion of most of the H₂ ro-vibrational lines 1-0 S(1) and 2-1 S(1) emitting region. Figure 2 provides an example of behaviour of the emissivities of such H₂ lines and Br$\gamma$ as a function of the gas temperature.

Different stopping temperatures were tested. For $T_{\mathrm{F}}>$ 100 K (cut the nebula closer to the central star), a significant portion of the total nebular H₂ emission would have been ignored (unless the cloud is limited by matter). For models with $T_{\mathrm{F}}=$ 100 K, more than 70 % of the flux determined for the model with $T_{\mathrm{F}}=$ 40 K would have been ignored. For $T_{\mathrm{F}}=$ 60 K, the flux ignored is approximately 50-70 %. On the other hand, extending the nebula for very low $T_{\mathrm{F}}$, could produce an unrealistic large PN and the low line emissivity in such regions would not contribute much to the flux. For temperatures lower than 40 K, the H₂ 1-0 S(1) and 2-1 S(1) line emissivities decreases and affects very little the total calculated flux (Fig. 2). The difference in the fluxes found for $T_{\mathrm{F}}=$ 40 K and $T_{\mathrm{F}}=$ 20 K is less than a factor of two, which will not affect our conclusions.

The observation simulations were performed with PyCloudy, using a slit placed in two positions, centred and H₂ peak, as discussed in the previous section. Fig. 1 shows the configurations. The two slit apertures (white boxes) are positioned over a simulated PNe (reference model). The slit length is longer than the nebula size. For both cases, we study simulations where the slit width $w$ is varied from a small fraction of the nebula diameter up to a size that includes the whole nebula. The whole nebula configuration can therefore be understood as a special limit case of both of the configurations above, when the slit width is large enough to cover the entire nebula.

This paper presented the analysis of the slit configuration effect on the $R$(Br$\gamma$) ratio in PNe, using observations and numerical simulations. The main results are:

• •

  The H₂ 1-0 S(1) and Br$\gamma$ lines are produced in different regions in the nebula, and, therefore, the slit configuration used in the spectroscopic observations strongly affects the $R$(Br$\gamma$) ratio.

• •

  For round and ring-like PNe, $R$(Br$\gamma$) ratios obtained with a slit across the entire nebula passing by its centre (centred) provides similar values to those obtained by integrating the line flux over the whole nebula. Similar result is obtained for bipolar PNe when observing with the slit across the equatorial region, perpendicular to the main nebular axis (also considered here centred).

• •

  The $R$(Br$\gamma$) ratios derived from observations in the centred configuration or when the whole nebula is integrated reach only values up to 0.3. Values higher than this are only obtained when the slit is positioned at the H₂ peak positions.

• •

  The $R$(Br$\gamma$) ratio measured with the slit at the H₂ peak emission depends on the fraction of the nebula covered by the slit. The largest values of $R$(Br$\gamma$) are found when the slit covers a small fraction of the nebula.

• •

  When the slit configuration is taken into account, the simple photoionization models presented here can represent very well the range of values and the general behaviour of the observed $R$(Br$\gamma$).

• •

  The result above shows that the argument that shocks are needed to explain the higher values of $R$(Br$\gamma$) is not valid. Therefore, this ratio is not a good indicator of the H₂ excitation mechanism as suggested by Marquez-Lugo et al. (2015).

• •

  All the results showed here demonstrate the importance of considering the slit configuration in studies involving the $R$(Br$\gamma$) ratio.

It is important to notice that analogous results could be obtained for shock models if they produce similar H₂ and Br$\gamma$ emission distribution. It is not the aim of this work to defend photoprocesses over shocks as the dominant H₂ excitation mechanism in PNe. Here the focus is on geometrical effects and the intention is just to bring the attention to the effect of the slit configuration.

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The author is thankful to S. Akras and H. Monteiro for useful discussions and their suggestions to improve this manuscript. This research has made use of the NASA’s Astrophysics Data System and the SIMBAD database, operated at CDS, Strasbourg, France (Wenger et al., 2000). This work has also made use of the computing facilities available at the Laboratory of Computational Astrophysics of the Universidade Federal de Itajubá (LAC-UNIFEI). The LAC-UNIFEI is maintained with grants from CAPES, CNPq and FAPEMIG.

The data underlying this article are available in the article. Any additional information can be request to the Author.