Fallback in bipolar planetary nebulae?

The outflow structure, the Spiderweb and the outer structures observed in Hb 12 are delineated by forbidden [N II] (λ6584) and infrared [Fe II] (λ1.6435 μm) line emissions that all may be assumed to be related to shock heating and excitation. While the line emission associated with the outflow may be easily understood, the other line emission structures would suggest a non-outflow explanation. The existence of an accretion inflow close to the stellar surface would naturally result in an axisymmetric system of oblique shocks that guides the initially radial accretion inflow into the equatorial region and around the outflow structure as captured in the diagram of Figure 2. Hydrodynamically, an oblique shock stands under an angle with the flow direction and will thermalise part of the flow velocity component perpendicular to the shock, while leaving the parallel velocity component intact. Assuming that the underlying star has ceased its own shell burning activity and has no substantial stellar wind, the oblique shocks of the Outer Hourglass serve to decelerate and redirect the in-falling gas at large distances in order to guide the flow around the bipolar outflow regions and into the axisymmetric oblique shocks of the Spiderweb structure in the equatorial region. The very structured shock patterns observed around PN Hb 12 and other sources may thus be consistent with a hydrodynamic inflow pattern resulting from accretion, either spherical or from a distant companion star. While full hydrodynamical modelling of this inflow-outflow structure will be needed to further confirm this scenario, it will also provide a measure of the accretion rate, the strength of the oblique shocks and the actual scale size of the shock patterns (and indirectly the distance).

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The bipolar Inner Hourglass outflow structure in Hb 12 represents a prominent feature in the source with the base seen in forbidden [Fe II] line emission and the outline of the whole structure seen in the lower density tracing forbidden [N II] emission (Fig. 1). The observed structure clearly suggests a low power outflow expanding into a pressure gradient and energising a widening boundary layer as outlined by the [Fe II] and [N II] line emission (Kwok & Hsia 2007; Vaytet et al. 2009). The shape of the boundary of this hourglass outflow channel suggests consistency with a supersonic and accelerating fluid outflow from a simple DeLaval-like nozzle expanding into a circumstellar medium with a radial pressure profile p(r) ∝ r⁻² (using the formalism from Landau & Lifshitz 1959; Choudhuri 1998). The boundaries of this outflow are self-adjusting and are determined by the equilibrium between the internal pressure of the accelerating flow and the radially varying ambient pressure in the circumstellar envelope. The supersonic outflow along the polar axis starts at a narrowed throat formed in the atmosphere where the gas reaches a proton escape velocity equaling the local velocity of sound. If the 90 km s⁻¹ base velocity is indicative of the local escape velocity from a 1 M_⊙ star, then this Mach nozzle may form at a radius of about 10¹² cm and require a local temperature of 10⁵ K, which is higher than the effective surface temperature of 35 000 K (Hyung & Aller 1996). Our first order modelling of the case with a quadratic pressure gradient affirms that the flow accelerates early in the nozzle and may reach a final velocity of at least 2.5 times the sound velocity at the throat of the nozzle. Sustained operation of the nozzle outflow would require sustained replenishment of heated atmospheric material. Detailed modelling may provide an estimate of the power and the scale size of the outflow.

The boundary layer observed in Hb 12 and other sources will naturally develop around the outflow where the edges of the flow pattern are slowly decelerating because of energy and momentum being dissipated. This boundary layer of Hb 12 is very prominent with shock-tracer [Fe II] emission lines at the onset of the outflow and is seen in [N II] emission away from the star as the interaction becomes less intense (Clark et al. 2014). The velocities at the base of the Hb 12 outflow are estimated to be 90 ± 15 km s⁻¹ in the redshifted (north) and blueshifted (south) senses and consistent with the velocity estimate mentioned above. Similar bipolar structures and outflow velocities have been detected in the PNe MyCn 18 (V = ± 48 km s⁻¹) (Corradi & Schwarz 1993), in Mz 3 (V = 130 km s⁻¹) (Santander-García et al. 2004) and the Inner Hourglass structure of the symbiotic Mira Hen 2-104 (V = 50 km s⁻¹) (Corradi et al. 2001; Clyne et al. 2015).

At a certain distance from the central star, bipolar outflows are expected to stagnate and produce lobes containing accumulated outflow and entrained material that are analogous to the radio lobes of extragalactic sources. The stagnation lobes in the low-power outflow of PN Hb 12 appear as multiple knots at a distance of 75'' (0.84 pc if at 2.24 kpc) that are emitting low-ionisation [N II] line emission (Vaytet et al. 2009). The velocities of these knots are at +275 (north) and -296 km s⁻¹, which are slightly higher than a few times the base velocity 90 km s⁻¹. Stagnation points have also been identified in the sources Hen 2-104 and the Rotten Egg Nebula (Corradi et al. 2001; Kwok & Hsia 2007).

The multiple coaxial rings in the walls of the hourglass outflow structures of Hb 12 are also seen as low-ionisation [N II] thermal emission (Kwok & Hsia 2007) and would result from energy dissipation in the boundary layer (see Fig. 1). These rings appear roughly equally spaced at approximately 850AU (if at 2.24 kpc) and may result from some axisymmetric Kelvin-Helmholtz-like instability resulting from the velocity gradients across the boundary layer. Alternatively, these rings could represent decelerating shocks only in the boundary layer as a result of the decreasing ambient pressure shaping the outflow. Similar rings are also prominent in the sources MyCn 18 (Sahai et al. 1999), M 2-9 (Kwok & Hsia 2007) and Hen 2-104 (Corradi et al. 2001).

The Outer Hourglass oblique shock structure appears as two axisymmetric elliptical surfaces that reach around the star and interconnect with the Inner Spiderweb at its outer edge (see Fig. 2). In PN Hb 12 only the base of the shock-related [Fe II] Outer Hourglass emission structures can be seen in (Fig. 1) but they are expected to extend towards the stagnation points in the outflows (Vaytet et al. 2009). The axisymmetric region between the boundary layer of the Inner Hourglass outflow and the Outer Hourglass shocks would also be filled with in-falling material that has been shock-heated and may show H₂ and [N II] tracer emission. All shock-related [N II] and H₂ emissions within the Outer Hourglass structure are expected to decrease in intensity away from the star because of decreasing densities and decreasing perpendicular velocities in the oblique shocks. While Hb 12 does not (yet) exhibit such emissions, the filamentary [N II] λ6583 emitting cloudlets in PN Hen 2-104 trace a very similar Outer Hourglass structure far beyond the Inner Hourglass outflow (Corradi et al. 2001; Corradi 2003; Kwok & Hsia 2007). Similar emissions are found in the Twin Jet Nebula M2-9 and PN Mz 3 (see Kwok & Hsia 2007; Clyne et al. 2015).

A long-slit velocity-position diagram taken along the major axis of the Hen 2-104 system demonstrates that the bipolar outflow has (accelerated) positive velocities in the north up to projected +90 km s⁻¹ and negative velocities in the south (Corradi & Schwarz 1993; Corradi et al. 2001). However, the diagram also features opposite velocities in the north as well as in the south that increase up to projected velocities of 30 km s⁻¹ at the edge of the Outer Hourglass structure. While the bipolar Inner Hourglass shows an outflow pattern, the filaments inside the Outer Hourglass of Hen 2-104 would indeed represent the expected inflowing accretion component.

The apparent shock structures in both the equatorial Spiderweb and the Outer Hourglass structures are consistent with a large scale hydrodynamic flow pattern leading towards the stellar core in Hb 12. The series of oblique shocks redirect and decelerate the accretion flow, raise the density and the temperature, and funnel the flow into the equatorial region. The shock nature of these structures may be supported by the detection of the shock tracer [Fe II] (λ1.6436 μm) emission, continuum (λ1.6 μm) and the H₂ (λ2.1214 μm) line emission (Hora & Latter 1996; Clark et al. 2014). The two tangential edge sections of this axisymmetric system of standing oblique shocks elucidate in great detail how the inflow is being guided onto an equatorial surface of the star (Fig. 2). The nearly face-on position of Hb 12 also displays the north-south symmetry in the Spiderweb, which indicates that the flow pattern near the star is the same above and below the equatorial plane. Incidentally, these oblique shocks work on the same principles as a diffuser (air intake) of a supersonic airplane. The inner Spiderweb and the Outer Hourglass form an interconnected oblique shock network that takes the initially spherical accretion flow, bypasses the region of the bipolar outflow, and brings it into the equatorial region of the star.

Analysis of the molecular hydrogen emission in Hb 12 suggests that collisional processes would dominate over ultraviolet (UV) absorption for exciting the H₂ emission when the kinetic temperature T_k > 1000 K (Hora & Latter 1996). The temperature of free-falling material at a distance R from a star would be considerably high at T_ff = 1.08×10⁵ ${M}_{\odot }{R}_{{AU}}^{-1}\,{\rm{K}}$. This suggests that shock heating of the accreting material would completely dominate the excitation of H₂ inside a radius of about 100AU from the star.

In addition to PN Hb 12, evidence for similar Spiderweb structures has been found in bipolar PNe such as MyCn 18 (Bryce et al. 1997), Henize 2-104 (Corradi et al. 2001; Clyne et al. 2015), R Aqr (Corradi & Schwarz 1995), Mz 3 and M 2-9 (Clyne et al. 2015).

A final standing shock must exist above the equatorial stellar surface in order to further decelerate the (then) nearly radial flow pattern to a subsonic velocity and to let this inflow integrate with the stellar atmosphere and a possible circumstellar disk. Existing observational data of the H₂ and [Fe II] emissions in Hb 12 taken just north of the core, at the core and just south of the core provide evidence for this inflow inside the Spiderweb of Hb 12 (fig. 2 in Clark et al. 2014). At the 'northern edge' of the nuclear region and covering the edge of the Inner Hourglass, the shock tracer [Fe II] emission features a redshifted northern outflow with a (projected) velocity in the range of +30 to +60 km s⁻¹. However, there are also positive velocities in the [Fe II] and H₂ data south of the core at the edge of the Spiderweb in the range 0 to +30 km s⁻¹. Similarly, the blueshifted 'southern' outflow is seen south of the core in the [Fe II] data at −60 to −30 km s⁻¹, while the H₂ data also show emission north of the core at the Spiderweb structure in the range -30 to 0 km s⁻¹. While the strongly positive and negative velocity components in the [Fe II] data can be explained as being part of the bipolar outflow, the smaller velocity components in the same direction at opposite sides of the core do not fit the picture. A simple interpretation of these components would be that velocities in the same direction (positive or negative) at either (north and south) side of the tilted source indicate that one can represent an outflow and then the other is an inflow. This suggests that the observational data presented by Clark et al. (2014) represent an outflow-inflow velocity pattern that is consistent with an accretion scenario.

The accretion flow into an equatorial footprint may result in the formation of a thick disk/torus around the central star as a form of temporary mass storage before material transfers into the atmosphere of the star. Evidence for such an equatorial torus has indeed been found in Hb 12 using the bright He I (2.0585 μm) and Brγ (2.1655 μm) recombination line emission featuring a central cavity with a 0.2'' × 0.41'' (450×930 AU if at 2.24 kpc) inner torus structure (Clark et al. 2014). However, the observed velocity profile perpendicular to the symmetry axis indicates a rotation velocity of 90 km s⁻¹, which would suggest an orbital radius in the disk of only 0.22AU around one M_⊙ star (and an uncomfortable distance of only 2.2 pc to the observer).

The presence of a disk in a bipolar PN may also be confirmed by any maser activity to be detected at their central regions. OH (1665 MHz) and H₂O (22.12 GHz) maser features at the core region of the bipolar PN K 3-35 suggest a disk with an extent of 98 AU (if at 5 kpc) (Miranda et al. 2001). In addition, the OH and H₂O features at the core K 3-35 are redshifted relative to the OH (1667 MHz) maser components found in the bipolar outflows, which would further confirm inflow into the central region. OH and H₂O masers are also found in the core regions of other bipolar PNe (Gómez et al. 2008; Uscanga et al. 2014; Gómez et al. 2015). Similarly, the in-falling SiO (43 GHz) masers in the bipolar post-AGB pre-PN (Rotten Egg) OH 231.8+04.2 have been interpreted as being part of a torus (Sánchez-Contreras et al. 2002).

The shock-heated material in the disk around the stellar core will contribute to emission of the source in addition to the ongoing or enhanced shell burning possibly triggered by the accreted material. The estimated effective surface temperature of Hb 12 is 35 000 K based on modelling of the observed emission lines (Hyung & Aller 1996), which suggests an early O-star classification and would indicate an early stage in PNe evolutionary models (Perinotto et al. 2004; Werner & Herwig 2006).

Considering that bipolar PNe do not (yet) exhibit the shell-like characteristics of spherical and elliptical PNe, the possibility should be considered that the bipolar activity is driven by accretion in sources such as Hb 12. For early-type PNe the material may be accreted from a circumstellar cocoon/envelope or a large circumbinary disk that was formed during the later stages of post-AGB evolution (Perinotto et al. 2004; Herwig 2005; Akashi & Soker 2008). Simulations indicate that depending on the mass of the underlying star, such envelopes/shells may exist at distances ranging from a few to 10×10¹⁷ cm and have particle densities ranging from 20 to a few hundred cm⁻³ (Perinotto et al. 2004; Chen et al. 2016). During the early evolutionary PN phases lasting a few 10⁴ yr, the free-fall timescale t_ff = R^3/2/(2GM)^−1/2 suggests that material within a radius of R = 0.22×10¹⁷ cm can fall back onto the star.

An accretion model that most adequately describes sub-Eddington accretion from a (distant) surrounding medium is the Bondi-Hoyle spherical accretion model (Bondi 1952; Mestel 1954). Because the luminosity of the source is not sufficient to halt the spherical accretion, the inflow is spherical until close to the stellar surface, where the polar outflow and the equatorial inflow regions compete for space. Assuming a uniform surrounding medium, a spherical accretion rate may be expressed for the temperature limited case with γ = 3/2 as (Bondi 1952) ${\dot{M}}_{\mathrm{acc}}=2\pi \alpha ({{GM}}_{\mathrm{st}}^{2}{({V}^{2}+{c}_{s}^{2})}^{-3/2}{\rho }_{\mathrm{ism}})=3.5\times {10}^{-9}{M}_{\mathrm{st}}^{2}\,{n}_{100}\,{T}_{10}^{-3/2}\,{M}_{\odot }\,{\mathrm{yr}}^{-1},$ where M_st is the stellar mass assumed to be 1 M_⊙, V is the spatial velocity of the star and is assumed to be zero, c_s is the speed of sound that depends on the temperature of the surrounding medium expressed in units of T₁₀ = 10 K and ρ_ism is the particle mass density of the medium far from the star expressed in units of n₁₀₀ = 100 cm⁻³. The factor α is between 1 and 2 depending on environmental conditions and a value of 1.5 is adopted here. The accretion rate favours higher stellar mass, higher gas densities and lower temperatures. The luminosity resulting from the estimated accretion rate may be estimated as ${L}_{\mathrm{acc}}={\dot{M}}_{\mathrm{acc}}{{GM}}_{\mathrm{st}}/{R}_{\mathrm{st}}=2.9\times {10}^{33}{M}_{1}^{3}\,{n}_{100}\,{T}_{10}^{-3/2}\,{R}_{10}^{-1}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$,where the stellar radius R_st is expressed in units of 10¹⁰ cm.

An estimate of the luminosity of Hb 12 may follow from the estimated effective surface temperature of 35 000K based on modelling of the observed emission lines (Hyung & Aller 1996), which results in a (minimum) blackbody luminosity for a stellar core with an effective radius 10¹¹ cm to be L_bb = 8.8 ×10³⁶ erg s⁻¹. This value is less than the Eddington luminosity L_Edd = 1.2 ×10³⁸ M₁ ergs⁻¹, which would verify that sub-Eddington accretion is possible for PN Hb 12. Assuming some reasonable parameters for the surrounding environment, a scenario with spherical accretion from fallback of circumstellar material could account for part of the apparent luminosity of the star and result in driving the outflow activity of Hb 12.