The interaction of planetary nebulae and their AGB progenitors with the interstellar medium
aa r X i v : . [ a s t r o - ph ] S e p Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 28 October 2018 (MN L A TEX style file v2.2)
The interaction of planetary nebulae and their AGBprogenitors with the interstellar medium
C. J. Wareing , ⋆ , Albert A. Zijlstra † , T. J. O’Brien ‡ Jodrell Bank Centre for Astrophysics, Alan Turing Building, The University of Manchester, Oxford Road,Manchester, M13 9PL, UK Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
ABSTRACT
Interaction with the Interstellar Medium (ISM) cannot be ignored in understand-ing planetary nebula (PN) evolution and shaping. In an effort to understand the rangeof shapes observed in the outer envelopes of PNe, we have run a comprehensive setof three-dimensional hydrodynamic simulations, from the beginning of the asymptoticgiant branch (AGB) superwind phase until the end of the post–AGB/PN phase. A’triple-wind’ model is used, including a slow AGB wind, fast post–AGB wind andthird wind reflecting the linear movement through the ISM. A wide range of stellarvelocities, mass-loss rates and ISM densities have been considered.We find ISM interaction strongly affects outer PN structures, with the dominantshaping occuring during the AGB phase. The simulations predict four stages of PN–ISM interaction whereby the PN is initially unaffected (1), then limb-brightened in thedirection of motion (2), then distorted with the star moving away from the geometriccentre (3) and finally so distorted that the object is no longer recognisable as a PNand may not be classed as such (4). Parsec-size shells around PN are predicted tobe common. The structure and brightness of ancient PNe is largely determined bythe ISM interaction, caused by rebrightening during the second stage; this effect mayaddress the current discrepancies in Galactic PN abundance. The majority of PNe willhave tail structures. Evidence for strong interaction is found for all known planetarynebulae in globular clusters.
Key words: hydrodynamics – planetary nebulae:general – stars: AGB and post-AGB– ISM: structure – stars: mass-loss.
Planetary nebulae (PNe) display a wide variety of shapesranging from round, which can be simply understood interms of the symmetric interacting stellar winds (ISW)model (Kwok 1982), through complex symmetrical shapes,such as hour-glasses and butterflies, to shapes which haveonly rotational point-symmetry. Many theories have beenintroduced to explain these complex shapes from adding anasymmetric slow wind to the ISW model (Kahn 1985; Balick1987) to involving the effects of binary central stars (Soker1996) and magnetic fields (Frank & Blackman 2004). Ob-servations of PNe have shown several cases where only theouter shell shows a departure from symmetry. In these cases, ⋆ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected] the cause of the asymmetries has been postulated to be aninteraction with the interstellar medium (ISM).Interaction with the ISM by PNe was first discussed byGurzadyan (1969) with an early theoretical study by Smith(1976) employing the ’snow-plough’ model of Oort (1951).Smith concluded that a nebula will fade away before any dis-ruption of the nebular shell becomes noticable. Isaacmann(1979) used the same approximation with higher relativevelocities to the ISM and ISM densities and concluded sim-ilarly.In contrast, Borkowski et al. (1990) found that manyPNe with large angular extent show signs of PN–ISM inter-action and that all nebulae containing central stars witha proper motion greater than 0.015 arcsec yr − do so.Soker et al. (1991) hydrodynamically modelled the inter-action revealing that the PN shell is first compressed inthe direction of motion and then in later stages this partof the shell is significantly decelerated with respect to thecentral star. Both conclude that the interaction with the c (cid:13) C. J. Wareing et al.
ISM becomes dominant when the density of the nebularshell has dropped below a certain critical limit, typically n H = 40 cm − for a PN in the Galactic plane. These low den-sities require large, evolved nebulae, in agreement with theobservational result of Borkowski et al. (1990). They notedthat their simple picture breaks down for high velocity PNein a low density environment. Here, a Rayleigh–Taylor (RT)instability develops, leading to shell fragmentation. Their2D hydrodynamic simulations started with the nebula shellalready formed but above their upper density limit for ISMinteraction to become apparent.The fragmentation predicted by Soker et al. (1991) wasdiscussed in more depth by Dgani & Soker (1994) and thenDgani & Soker (1998). In these papers, Dgani and Soker ap-plied theoretical results of hydrodynamic instabilities andfound that the RT instability can play an important rolein the shaping of the outer regions of a PN. They sug-gested these RT instabilities can cause fragmentation of thebow shock with Kelvin–Helmholtz instabilities also playing apart. Any fragmentation caused by these instabilities wouldonly be present if the relative velocity to the ISM of thecentral star was greater than 100 km s − .Villaver et al. (2003) (hereafter referred to as VGM)pointed out that the PN–ISM interaction had previouslybeen studied by considering the interaction after the neb-ular shell had formed. PNe are formed when a slow wind( ∼
10 km s − ) ejected during the preceding asymptotic gi-ant branch (AGB) phase of evolution is swept up into a denseshell by a fast wind ( ∼ km s − ) from the exposed, ioniz-ing hot white dwarf core. VGM performed 2D hydrodynamicsimulations and found that crucially the interaction beginsduring the AGB phase where the slow wind is shaped by theISM. The PN forms in this pre-shaped environment. Choos-ing a conservative relative velocity of the central star to theISM of 20 km s − and a low density of the surrounding ISMof n H = 0 . − , they discovered that the PN is brightenedon the upstream side of the nebular shell. They concludedthat PN–ISM interaction provides an adequate mechanismto explain the high rate of observed asymmetries in the ex-ternal shells of PNe. Further, stripping of mass downstreamduring the AGB phase provides a possible solution to theproblem of missing mass in PN whereby only a small fractionof the mass ejected during the AGB phase is inferred to bepresent during the post–AGB phase. Observational evidencefor the effect of the ISM on AGB wind stuctures, supportingVGM’s findings was found by Zijlstra & Weinberger (2002).VGM found that simple hydrodynamic simulations canreveal much information regarding the PN–ISM interaction.In order to investigate the interaction further, we have de-veloped a ’triple-wind’ model including an initial slow AGBwind, a subsequent fast post–AGB wind, and a third contin-uous wind reflecting the movement through the ISM. Em-ploying a parallel 3D hydrodynamic scheme developed byWareing (2005), we have understood the formation of theextreme PN Sh 2-188 (Wareing et al. 2006a) and the struc-ture around the AGB star R Hya (Wareing et al. 2006b).Sh 2-188 was thought to be a bright one-sided arc-likePN when new observations taken as part of the Isaac New-ton Group Photometric H α Survey of the Northern GalacticPlane (IPHAS) (Drew et al. 2005) revealed a faint ring-likecompletion of the arc and a tail stretching away in opposi-tion to the bright arc. Our model revealed this PN to be a strong PN–ISM interaction where the central star is mov-ing at 125 km s − in the direction of the bright arc relativeto the ISM and the nebular shell is interacting with a bowshock formed during the AGB phase between the slow windand the ISM. Recent IR observations of the AGB star R Hyaas part of the MIRIAD programme (Ueta et al. 2006) haverevealed the arc-like structure to the North West of the starto be a bow shock ahead of the star (Wareing et al. 2006b).The existence of this AGB wind bow shock has confirmedthe hypothesis that the major shaping effect for the PN–ISMinteraction occurs during the AGB phase of evolution.Using our model, we have now run a comprehensive setof 92 simulations equivalent to over 5 years of single CPUcomputation time investigating the PN–ISM interaction. Inthis paper, we discuss a representative set of these simula-tions and generalise the interaction into four distinct stages,indicating its effect on shaping and other PN characteris-tics. We apply our generalisation to a selection of PNe fromthe IAC Morphological Catalog of Northern Galactic Plan-etary Nebulae (Manchado et al. 1996) and find indicationsof interaction with the ISM in approximately 20 per cent ofobjects. The numerical scheme, CUBEMPI, used in our simulationsto solve the hydrodynamics equations employs a second-order Godunov solution due to Falle (1991). In recent years,variants of CUBEMPI have been used to shed light onnova explosions (Lloyd et al. 1997; Porter et al. 1998), ex-tragalactic jet-cloud interactions (Higgins et al. 1999) andmost recently PN (Mitchell 2007; Wareing et al. 2006a). Theversion of the scheme used here is posed in 3D cartesiancoordinates, fully parallel and includes the effect of radia-tive cooling due to the cooling curves of Raymond et al.(1976) above 10 K as the cooling curves extend no fur-ther. The parallelisation was developed using the MPI li-brary and involves slicing the numerical domain along anaxis and communicating relevant boundary data at the cor-rect points during a computational timestep. The paralleli-sation has been successfully tested for efficiency and scala-bility. The scheme itself has also been tested on a number ofstandard computational fluid dynamics problems and per-formed well on all tests. It has been further tested using as-trophysical problems which have highlighted its capabilityfor shock capturing, an important requirement for the mod-elling of PNe. The parallelisation and testing are detailed inWareing (2005)The numerical domain consists of a cubic grid, 200 cellsalong each axis, containing a total of 8 × uniformly-spaced cells. The grid is sliced ten times for parallelisa-tion purposes and distributed across ten processors of theCOBRA beowulf-type supercomputer at Jodrell Bank. Thislevel of parallel distribution is a comprimise between com-putational efficiency and availability of computational re-sources.In the ’triple-wind’ model, the simulation is performed (cid:13) , 000–000 GB/PN – ISM interaction in the frame of reference of the star, which is placed at cellcoordinates (50 , , cells centred on the star. The radius of thissource volume has been chosen by an experimental processbalancing production of the most spherical PN when mod-elling the stationary ISW model with spherically symmetricwinds (i.e. reducing the pixelation of the cartesian grid) andavoidance of interference with results of the simulation. Theconditions within the source volume are reset at the begin-ning of every computational timestep to drive the ejectionof the wind. The wind has been modelled with a sphericallysymmetric constant mass-loss rate ˙ M with constant velocity v and temperature T . Density in the source volume has beendefined by ˙ M/ (4 πvr ) where r is the physical radial distancefrom the central star. The other hydrodynamic variables areset accordingly. Simulation of movement through the ISM isachieved by flowing ISM material in at the ( x = 1) bound-ary with a velocity vector v x , v y , v z = (+ v ,0,0). The ISMdensity and temperature are constant. All other numericalboundaries have conditions allowing material to flow out ofthe domain freely. Gas pressures in the model are calculatedassuming an ideal gas equation of state. In our simulations, we have held the following parameter val-ues constant: for the slow AGB wind a velocity of v sw = 15km s − and a temperature of T sw = 10 K as the coolingcurves extend no further; for the fast post–AGB wind amass-loss rate of ˙ M fw = 5 × − M ⊙ yr − , a velocity of v fw = 1000 km s − and a temperature of T fw = 5 × K;and for the ISM a temperature of T ISM = 8000 K, character-istic of the warm intercloud medium (Burton 1988). Theseparameter values are typical of observations of PN condi-tions. In the model, the switch between the AGB wind andthe post–AGB wind is instantaneous and occurs after 5 × years of AGB evolution, typical of the duration of this phase.In view of the still considerable uncertainties on the detailedproperties and evolution of these winds, more detailed tem-poral variations have not been modelled. We have discussedthis further in later sections.In our simulations, we have varied three parameters:relative velocity of the star to the surrounding ISM v ISM ,slow wind mass-loss rate ˙ M sw and ISM density ρ ISM .Binney & Merrifield (1998) discussed v ISM of stars in theGalactic plane: typical thin disk stars resulting in a PN ap-pear to have a transverse variation on their galactic rota-tion velocity of 35 – 50 km s − ; thick disk stars, rarer inthe Galactic plane, have a typical range of 50 – 75 km s − ;halo objects can have a typical variation greater than 100km s − . Older stellar groups, such as PNe, are characterizedby larger velocity dispersions and asymmetric drift veloci-ties than are younger stellar groups. The average transversemotions of stars in the solar neighbourhood have been foundto be in the range of 20–40 km s − with the tail of the dis-tribution up to 130 km s − (Skuljan et al. 1999). For whitedwarfs an average velocity of 67 . ± . − has beenfound by Sanggak (1984). In terms of Galactic disk PNe,Borkowski et al. (1990) state 60 km s − as an average ve- locity. For Galactic Bulge PNe, velocities up to 200 km s − could be reasonably expected as these stars are dynamicallya much hotter population. Therefore, we have considered arange of v ISM from 0 km s − , testing the implementation ofthe triple-wind model and its ability to simulate a sphericalnebula, up to 200 km s − , in 25 km s − steps in order tofully cover the range of velocities of PN-forming stars in theGalaxy.The typical density of the ISM in the galactic plane isapproximately n H = ∼ − up to a scale height of 100 pcabove the plane where it then begins to drops off exponen-tially. We have used three constant values of ISM density n H = 2, 0.1 & 0.01 cm − to investigate this range. These densi-ties are comparable to that of the warm intercloud medium(Burton 1988).Mass-loss rates during the AGB phase of evolution varybetween 10 − – 10 − M ⊙ yr − with brief periods of enhancedmass-loss up to 10 − M ⊙ yr − . As we are using a constantmass-loss rate, we have not modelled mass-loss variations.We have used values of 10 − , 5 × − , 10 − & 5 × − M ⊙ yr − up to v ISM = 75 km s − . Above this velocity, wehave not used a mass-loss rate of 10 − M ⊙ yr − due to timeand computational constraints. In our initial test cases v ISM is set to zero. The forward shockdriven by the AGB wind is spherical and expands into ahomogeneous ISM. The shocked ISM material behind theforward shock is of relatively low density with the contactdiscontinuity and the reverse shock expanding sphericallysymmetrically outward. The unshocked AGB wind behindthe reverse shock is also spherically symmetric around thecentral star with an approximate 1/r distribution. After500 000 years, the fast post–AGB wind is introduced intothis distribution driving a shock which sweeps up the AGBwind material into an expanding shell. The shell has a rel-atively high density and a temperature on the scale of 10–20 000 K. The stromgren sphere around the central star en-compasses the shell indicating the material in the shell wouldbe ionized and observable as a PN. This method of PN for-mation is the result of interacting stellar winds and is thepremise of the ISW model.Next, we added the ISM velocity. We display and dis-cuss a representative set of five simulations covering variousparameter values which serve to illustrate the range of PNstructures formed in all our simulations. Table 1 shows theparameter values for these five simulations. The resultingPN structure is discussed for each case. In our online supple-mentary appendix, we have also included snapshots at theend of the AGB phase of evolution and parameter valuesfor our full set of simulations. We have performed calcula-tions to find the extent of the stromgren sphere during thePN phase and find that in all cases it extends beyond thesimulation domain.In the following figures, the results are illustrated byslices through the density data cubes at the position of thecentral star and parallel to the direction of motion. c (cid:13) , 000–000 C. J. Wareing et al.
Figure 1.
The results of case A: the panels show the gas density during the AGB and post–AGB phases. In panel (a), the simulationis 125 000 years into the AGB phase, panel (b) 250 000 years, panel (c) 375 000 years, panel (d) 500 000 years, panel (e) 15 000 yearsinto the post–AGB phase and in panel (f) 30 000 years. The position of the central star is marked by an asterisk. The colour scaling islogarithmic and the density is scaled in units of 10 − M ⊙ pc − where 25 000 is equivalent to n H = 1.0 cm − .c (cid:13)000
The results of case A: the panels show the gas density during the AGB and post–AGB phases. In panel (a), the simulationis 125 000 years into the AGB phase, panel (b) 250 000 years, panel (c) 375 000 years, panel (d) 500 000 years, panel (e) 15 000 yearsinto the post–AGB phase and in panel (f) 30 000 years. The position of the central star is marked by an asterisk. The colour scaling islogarithmic and the density is scaled in units of 10 − M ⊙ pc − where 25 000 is equivalent to n H = 1.0 cm − .c (cid:13)000 , 000–000 GB/PN – ISM interaction Table 1.
Input parameters for the five selected simulations dis-cussed in section 4. Column a) gives the simulation reference;column b) v ISM ; column c) the density of the surrounding ISM in n H cm − ; column d) the constant mass-loss rate during the AGBphase of evolution; and column e) the physical size of the gridalong one dimension of the numerical domain.a) b) c) d) e)case v ISM
ISM: n H ˙ M sw Grid(km s − ) (cm − ) (M ⊙ yr − ) (pc)A 25 0.01 5 × − × − × − − × − Figure 1 shows the result of case A. The central star has v ISM of 25 km s − . The AGB evolution is shown in the top fourpanels (a)–(d) with the post–AGB evolution in the bottomtwo panels (e) and (f). In panel (a), 125 000 years into theAGB phase, the shock has formed into a bow shock a shortdistance upstream of the central star with a tail connect-ing a short distance downstream of the central star. Overthe next three panels (b), (c) and (d), at 250 000, 375 000and 500 000 years respectively, the bow shock can be seen toexpand outwards from the central star and between panels(c) and (d) reach a stable position ahead of the star. Thiscan be understood in terms of a ram pressure balance be-tween the slow wind and the oncoming ISM. At this point,the bow shock is approximately 2.5 pc ahead of the centralstar. If we assume this is a strong shock, the temperature ofthe shocked material at the head of the bow shock shouldbe equal to (3/16) (m v ISM2 /k) where m is the particle massin the simulation and k the Boltzmann constant. Our sim-ulation is in agreement with this. The tail structure can beunderstood in terms of material being ram-pressure strippedfrom the head of the bow shock and cooling as it flows down-stream around the bow shock into the tail. It is clear thateven at this low speed, the ISM interaction strongly affectsthe shape of the AGB wind.The brightest phase of the PN evolution, typically 1–5 × yr into the post–AGB phase, is not shown. Panel (e)shows the phase 15 000 years into the post–AGB phase. Theexpanding (and now faint) shell of the PN is clear, inside andstill detached from the bow shock of shocked AGB wind ma-terial. The PN and the far older bow shock are at this timeseparate objects with the PN expanding within the bubbleof undisturbed AGB wind material; the ISM interaction hasyet to affect the PN. Observations would reveal an ancientsymmetric ring PN approximately 3.5 pc across. Deeper ob-servations may reveal the cooler material in the bow shockstructure surrounding the PN. In panel (f), 30 000 years intothe PN phase, the PN has now expanded far enough to in-teract with the AGB wind bow shock. The portion of thePN interacting with the bow shock now rebrightens via theinteraction of the bow shock and PN shell. The PN at thisstage is still circular, the rebrightening being the first andonly indication of an ISM interaction in this case.Figure 2 shows the temperature distribution of the PN Figure 2.
In this figure we show the temperature profile (inKelvin) of the 30 000-year old PN shown in panel (f) of figure1 on the same slice through the numerical domain. shown in panel (f) of Figure 1, 30 000 years into the PNphase. Given our calculation that the Stromgren sphere ex-tends beyond the simulation domain, we assume that every-thing which is at 10 K or lower is photo-ionised and thateverything which has a temperature greater than 1 . × Kis collisionally ionised. Thus the material at the head of thebow shock appears to be collisionally ionised. Looking at thetail, the material is cooler and thus may be photo-ionised ifthe central star is still bright enough. This is the generalcase for the rest of our simulations where collisional ionisa-tion of material can be inferred at the head of the bow shockwith photo-heating/ionisation of the material stripped intothe tail.We define the previous phase where the PN was insidethe AGB wind bubble as the first stage of PN–ISM interac-tion. The second stage would begin with the first indicationof ISM interaction when the PN brightens in the direction ofmotion. This second stage will be responsible for rebright-ening of ancient PNe and including this effect in the projec-tion of current PN Galactic distributions may address thevery long visible life time of PNe implied by recent studies(Moe & De Marco 2006; Zijlstra & Pottasch 1991).The ISM interaction is clearly important even at theselow speeds, as it shapes the AGB wind long before the PNphase. The AGB wind forms a bow shock upstream of thecentral star with tails stretching downstream. The PN doesnot interact with the AGB wind bow shock until it has ex-panded enough to reach the bow shock, typically after 25–30 000 years. At that point, the enhanced density and tem-perature of the material in the region of interaction suggestsstrengthening of the emission from that area: rebrightening.The parameter values in this case are comparable to thoseused by VGM and we have found similar effects on the PNformed, supporting our triple-wind model and conclusions. c (cid:13) , 000–000 C. J. Wareing et al.
Figure 3.
The results of case B: the panels show the gas density during the post–AGB phase. In panel (a), the simulation is 5 000 yearsinto this phase, in panel (b) 10 000 years, in panel (c) 20 000 years and in panel (d) 30 000 years. The position of the central star ismarked by an asterisk. The colour scaling is logarithmic and the density is scaled in units of 10 − M ⊙ pc − where 2 . × is equivalentto n H = 100 cm − . In Figure 3 we show the results of case B during the post–AGB phase. We do not show the AGB phase as the structureformed during this phase is clear in panel (a), where the PNhas been expanding for 5000 years into the AGB wind bub-ble behind the bow shock. The central star is now movingat 50 km s − , an average v ISM for a PN-forming star. A bowshock has formed ahead of the central star during the AGBphase and stabilised at the point of ram pressure balance0.25 pc ahead of the central star. This is a much smallerstructure than in case A due to the increased ram pressure ofthe ISM. Further, the bow shock in this case is not smooth;instead there are indications of turbulent motion which canbe seen originating in the AGB phase as instabilities at thehead of the bow shock and moving back down the tail overtens of thousands of years. Note that the region between the forward shock and contact discontinuity is compressedupstream compared to the previous case. An investigationof the temperatures in this region shows that the material isfar hotter at ∼
30 000 K than in the previous case, in agree-ment with strong shock predictions, and therefore strongerradiative cooling can be inferred to be the cause of the for-ward shock compression. The PN is still inside the bubbleof undisturbed AGB wind material and as yet unaffected bythe ISM.In panel (b), 10 000 years into the PN phase, the PN hasreached the second stage of PN–ISM interaction wherebythe PN still appears circular but is now rebrightened at theinteraction with the AGB wind bow shock. The PN is alsorapidly entering a third stage where the geometric centreof the nebula, defined as the centre of the circular/ellipticalshape on the sky, is moving away from the central star. c (cid:13) , 000–000 GB/PN – ISM interaction After 20 000 years of PN evolution, the PN–ISM interac-tion has distorted the circular shape of the nebula as shownin panel (c). The central star appears displaced by a quar-ter of the diameter upstream of the geometric centre. Thehighest density and temperature regions have now movedaround the bow shock to the point where the tail stretchesaway from the PN shell. These regions can be interpretedas areas where the nebular shell and ISM have driven theAGB wind material away from the head of the bow shocktowards the tails. It is worth noting that at this time esti-mates of the nebular age via its observational dynamics (i.e.gas expansion velocity) would underestimate its true age.In panel (d), 30 000 years into the PN phase, the PN hasfurther departed from circular symmetry on the sky. Theregions of highest density and temperature are towards thehead of the fast wind bow shock which is now forming aheadof the star against the oncoming ISM. The nebular shell isstill progressing downstream though the undisturbed AGBwind bubble and causing the geometric centre of the nebulato deviate downstream. This stage of significant decelerationof the upstream shell was considered by Soker et al. (1991).At this typical v ISM , PN–ISM interaction has stronglyaffected the evolution of the PN. Rebrightening via interac-tion has occured at a much younger age of only a few thou-sand years and the shape of the PN has deviated stronglyfrom circularity on the sky. One sided brightening and/ordeviations from circular symmetry combined with an off-geometric-centre central star are clearly strong indicators ofPN–ISM interaction. Further, these indicators are not lim-ited to ancient or diffuse PNe. Such an interaction at thisaverage speed would indicate many PNe should display somecharacteristics of ISM interaction during their later life.
In Figure 4, we show the results of case C during the post–AGB phase. In panel (a), 5000 years into this phase, thePN already has passed through the first stage of interac-tion and the large higher density region on the upstreamside of the PN indicates it is now some way into the sec-ond stage. The stabilisation of the bow shock a shorterdistance of 0.18-pc upstream is responsible for this ear-lier interaction. Note that with v ISM = 75 km s − the bowshock is now seriously disrupted and instabilities noted inthe previous case are now forming cool, high-density spi-ralling vortices moving down the tail. The origin of thesevortices as vortex-shedding instabilities at the head of thebow shock and their effect on the local ISM are discussedelsewhere (Wareing, Zijlstra & O’Brien 2007). We find thevortices will affect almost all bow shock structures and PNewill interact with them at some point during their evolu-tion. A higher speed case carried out by VGM also revealedsimilar structures forming in the AGB wind bow shock(Szentgyorgyi et al. 2003).In panel (b), the upstream portion of the nebular shellhas been significantly decelerated causing the geometric cen-tre of the nebula to shift downstream. At this stage, 10 000years into the post–AGB phase, the regions of highest den-sity and temperature have again moved round the bow shockand the PN is in the third stage of PN–ISM interaction.In the third panel, 15 000 years into the post–AGBphase, the object is still recognisable as a PN, although the regions of highest density are in the tail of the bow shock.Finally, after 30 000 years of post–AGB evolution, the dens-est regions of the PN are indicative of the structure of thetail of the bow shock, including the effect of the vorticesmoving downstream. The thin fast wind bow shock is clearahead of the PN-forming star, although the star is no longeranywhere near the centre of the object. This would be anancient and probably very faint PN, but the PN–ISM inter-action would still cause many parts of it to rebrighten.In summary, the PN–ISM interaction is becoming moreimportant at higher v ISM : the bow shock is closer to the starcausing the PN to move through the stages of interactionmore quickly. PN–ISM interaction would be apparent at amuch earlier age even at this relatively average v ISM of 75km s − . In Figure 5 we show the results of case D, where the cen-tral star has v ISM = 100 km s − . A narrow confined bowshock has formed ahead of the star, with a tail stretchingfar downstream, as shown in panel (a), by the end of theAGB phase. This central star could be considered much likea speeding bullet and the high v ISM and high ISM densitycombined with the low mass-loss rate of the slow wind hasresulted in a much more confined bow shock. The ISM hasexerted a naturally stronger shaping influence due to greaterram pressure. Any instabilities at the head of the bow shockare either smoothed out by the oncoming ISM or flow outof the simulation before they have time to fully form.In panel (b), 1000 years into the PN phase, the PNhas very rapidly interacted with the bow shock and formeda fast wind bow shock further ahead of the central star,which can also be understood in terms of a ram pressurebalance. Interestingly, the highest densities are in the regionof the nebular shell which is moving downstream. In contrastto earlier cases, this portion of the shell is now closest tothe star. It has rapidly moved through the small bubble ofundisturbed AGB wind material and is now interacting withthe more dense shocked AGB wind material in the tail. Inpanel (c), after 2000 years, this effect is even more apparent.Over the course of the next few thousand years, the tail ofthe wide fast wind bow shock grows downstream and theremaining part of the nebular shell continues to move awayfrom the central star through the tail of older shocked AGBwind material.The PN formed in this case is very different to manyothers and characteristic of small and confined bow shocksthroughout our simulations. How observable the fast windbow shock would be remains an open question as whilst it ishot, it is also of low density. The PN in this case has rapidlymoved through the first three stages of PN–ISM interac-tion. We interpret the stage where the fast wind bow shockis forming and the remains of the nebular shell are fadingwhilst moving downstream as the fourth and final stage ofPN–ISM interaction. During this stage, it is difficult to rec-ognize the object, which would still be young enough to beobservable, as a PN. c (cid:13) , 000–000 C. J. Wareing et al.
Figure 4.
The results of case C: the panels show the gas density during the post–AGB phase. In panel (a), the simulation is 5000 yearsinto this phase, in panel (b) 10 000 years, in panel (c) 15 000 years and in panel (d) 30 000 years. The position of the central star ismarked by an asterisk. The colour scaling is logarithmic and the density is scaled in units of 10 − M ⊙ pc − where 2 . × is equivalentto n H = 100 cm − . The final case under discussion in this paper is case E, shownin Figure 6. In this case the central star has a high v ISM of125 km s − , a high ISM density and a high slow wind mass-loss rate. The bow shock structure is comparatively largebecause of the high mass-loss rate. Instabilities in the bowshock have caused multiple vortices to be shed downstreamwith an ensuing complex bow shock structure, as shown inpanel (a) at the end of the AGB phase. The PN–ISM in-teraction is almost immediately apparent and after 2000years, as shown in panel (b), the PN is mid-way throughthe second stage of interaction. The deceleration of the PNshell caused by the bow shock will soon cause the geometriccentre to shift downstream and the PN to enter the thirdstage of interaction. Observing a PN with a high-velocitycentral star and a faint completion of the nebular ring mov- ing downstream would indicate a young rather than old PN,even though the PN–ISM interaction is strongly apparent.In panel (c), 4000 years into the post–AGB phase, the dens-est regions of the PN have moved away from the head of thebow shock. The structure of the bow shock at the end ofthe AGB phase is having a very strong effect on the appear-ance of the PN – particularly the fact that the bow shockhad fallen back towards the central star having just shed avortex-causing instability downstream. In later stages (e.g.after 10 000 years shown in panel (d)) the vortices have be-come even more important for the evolution of the PN andare the regions of highest density. The object will eventuallyfade and look even less like a PN; faint objects serendipi-tiously discovered as part of Galactic surveys, e.g. IPHAS(Drew et al. 2005), may closely resemble this PN whilst notbe classified as such. Eventually, after the central star has c (cid:13) , 000–000 GB/PN – ISM interaction Figure 5.
The results of case D: the panels show the gas density during the post–AGB phase. In panel (a), the simulation at the endof the AGB phase, in panel (b) 1000 years into the post–AGB phase, in panel (c) 2000 years and in panel (d) 10 000 years. The positionof the central star is marked by an asterisk. The colour scaling is logarithmic and the density is scaled in units of 10 − M ⊙ pc − where2 . × is equivalent to n H = 100 cm − . turned off and there is no longer a wind supporting the bowshock, the nebula would be rapidly blown downstream andthe central star would move outside its nebula. How a PN will interact with the ISM is set during the AGBphase and VGM was the first to highlight this importantpoint. We have identified four stages of interaction whichwe call WZO 1–4. There is a phase of evolution where thePN is expanding within the bubble of undisturbed AGBwind material and this we define as the first stage of PN–ISM interaction, WZO 1. During this stage, a PN would beunaffected by the ISM interaction which is radially further from the central star. We suggest it would be possible duringthis stage to observe a faint arc around the PN, which wouldbe the AGB wind bow shock. In the case of a slow-movingstar with a large bow shock, this stage can last for the entirelifetime of the PN and it is unlikely a PN–ISM interactionwill ever be observed. However, if the central star is movingeven at average speed, the PN–ISM interaction can becomerapidly apparent, in some of our simulations after only athousand years. We show this stage in Figure 7(a).The characteristic of stage 1 is a shell of swept-upISM, up to a few pc away. This has been called a ’wall’(Zijlstra & Weinberger 2002). On sky images, this may alsoshow up an area of reduced emission around the PN, endingat the wall. Evidence for such cavities has been presentedby Evans et al. (2002) and Weinberger (2003).Stage WZO 2 is entered when the PN has expanded far c (cid:13) , 000–000 C. J. Wareing et al.
Figure 6.
The results of case E: the panels show the gas density during the post–AGB phase. In panel (a), the simulation at the endof the AGB phase and the beginning of the post–AGB phase, in panel (b) 2000 years into the post–AGB phase, in panel (c) 4000 yearsand in panel (d) 10 000 years. The position of the central star is marked by an asterisk. The colour scaling is logarithmic and the densityis scaled in units of 10 − M ⊙ pc − where 5 × is equivalent to n H = 200 cm − . enough to interact with the bow shock formed during theAGB phase of evolution. As the PN shock merges with theAGB wind bow shock, driving another shock through it, thedensity and temperature of the material increase accordinglyand strengthen the emission from this area. This is shown inFigure 7(b). If v ISM is predominantly in the plane of the sky,we would observe part of the nebular shell brighter than therest. If, however, v ISM is almost all along the line of sightto the PN, emision from the whole ring structure wouldstrengthen and it would be difficult to identify this PN asundergoing a PN–ISM interaction until later in its evolutionwhen distortions of the PN shell may reveal its true nature.This stage is relatively short lived and can be as short as athousand years or so in our simulations with the largest v ISM .During this stage the whole PN continues to appear circularon the sky, but as the central star moves away from the geometric centre of the nebula, caused by the decelerationof the nebular shell in the direction of motion, the PN entersthe third stage of PN–ISM interaction.The third stage of interaction, WZO 3, is defined by thegeometric centre of the nebula moving downstream awayfrom the central star as shown in Figure 7(c). The shiftof the geometric centre due to the deceleration of the PNshell in the direction of motion is guaranteed to occur andprovides a measurable effect of this interaction. During thisstage, and beginning during the second stage, it is difficultto estimate the age of the PN from its apparent diameter onthe sky. The AGB wind–ISM interaction has coccooned thePN inside the AGB wind bow shock and this considerablyinhibits the expansion of the PN shell during stages twoand three. Identification of the arc of nebular shell movingdownstream yet still inside the AGB wind bubble and the c (cid:13) , 000–000 GB/PN – ISM interaction PNshockbow direction of motion (a) (b)(c) (d)
Figure 7.
A simple illustration of the appearance of a PN duringthe four stages of PN–ISM interaction discussed in section 5.1.The direction of motion is to the left and thicker lines indicatethe brightest regions. Panel (a) illustrates stage WZO 1, (b) stageWZO 2), (c) stage WZO 3 and (d) stage WZO 4. The positionof letters (a), (b), (c) and (d) indicate the position of the centralstar at each stage. central star would provide an estimate of the radius of thePN if it had not been inhibited by the PN–ISM interaction.This radial distance could be used to dynamically estimatethe age of the PN. Interestingly, our simulations suggest thata secondary effect during this stage is that the regions ofhighest density and temperature move away from the head ofthe bow shock. This can be understood as the oncoming ISMsweeping the shocked PN material from the second stagetowards the tail of the nebula. This third stage can be open-ended and only in the higher v ISM cases is the PN affectedenough by the interaction to become completely unfamiliarand enter the fourth stage of interaction before it fades away.Even in the highest velocity cases, the third stage lasts atleast 10 000 years. It is possible that in the most extremecases, the PN shell will continue to appear circular as thenebula is swept downstream of the central star. Sh 2-68 isan example of a nebula where the central star is thought tohave deserted its PN (Kerber 2002).In the fourth and final stage of PN–ISM interaction,WZO 4, the PN no longer appears circular. The fast windhas formed a bow shock ahead of the star and the little re-maining AGB wind material in the vicinity of the star isbeing swept downstream with turbulent areas of high den-sity and temperature as shown in Figure 7(d). At this time,the observable structure may not be identified as a PN. Fur-ther, the central star appears to have long since left theseregions. Many objects such as this may exist and are proba-bly not classified as PNe, affecting estimates of the Galacticdistribution of PNe. Deep surveys in particular will be abeto uncover these objects.Our four stages of the interaction are summarised inTable 2. The first two stages are similar to the stages ofevolution suggested by Borkowski et al. (1990) from theirobservations of ancient PNe, although we find they can occurearlier in the PN evolution than considered in that work, dueto the pre-shaping during the AGB. Central stars of PNe which show evidence of interactionshould have a proper motion consistent with the observeddistortions across the plane of the sky if the nebula is closeenough and the central star is moving fast enough in theright direction to have an appreciable angular motion overtime. Borkowski et al. (1990) performed an investigation ofPNe with known large angular motion and revealed manyshow signs of being in WZO Stage 2.The largest value of proper motion of a central starmeasured via ground-based observations is 53 . ± . − . This is the proper motion of the central star of Sh 2-68Kerber (2002). The measurement has provided direct con-firmation of the process of the central star being displacedfrom the geometric centre of the nebula. The interaction with the ISM considerably alters the amountof mass within the observed nebula: the ram-pressure strip-ping of material downstream during the AGB phase removesmass from the circumstellar region. Our simulations showthat up to 90 per cent of the mass ejected from the starduring the AGB phase can be left downstream forming thetail behind the nebula. This effect may provide a solutionto the missing mass problem in PNe whereby only a smallfraction of the mass ejected during the AGB phase is ob-servationally inferred to be present during the post–AGBphase. Stellar evolution calculations predict that stars withinitial masses in the range of 1–5 M ⊙ will end as PN nucleiwith masses around 0.6 M ⊙ . Most of the mass is lost on theAGB phase and should be easily observable as ionized massduring the PN stage. However, observations of Galactic PNereveal on average only 0.2 M ⊙ of ionized gas. As the interac-tion progresses, the mass in the PN shell is increased duringmerger with the AGB wind bow shock, but this effect is min-imal when compared to the mass left downstream. At higherspeeds, the stripping effect is greater and more mass is lostdownstream. Our simulations clearly support VGM’s con-clusion that PN–ISM interaction at low speeds can providean explanation of the missing mass phenomenon. Further,we show that this effect is even more pronounced at highspeed.Recent observations of the Mira system containg theAGB star Mira A have revealed a comet-like tail of materialstretching 4 pc North away from the system (assuming adistance of 107 pc) and an arc-like structure in the South(Martin et al. 2007). Martin et al go on to comment thatthe space velocity of 130 km s − is in a direction consistentwith the comet-like tail being a ram-pressure-stripped tail ofmaterial behind a bow shock ahead of the system, therebyconfirming our postulation of tails of ram-pressure-strippedmaterial behind AGB stars. In reality, it is reasonable to expect the AGB wind to showan increasing mass-loss rate with time, whilst the post–AGBwind may increase in velocity over time. We have shown thatour current assumptions are sufficient to reproduce basicnebular structure and leave detailed temporal modelling toa future publication. c (cid:13) , 000–000 C. J. Wareing et al.
Table 2.
The four stages of PN–ISM interaction and their observable effects, as discussed in section 5.1 stage observable effects
WZO 1 PN as yet unaffected; faint bow shock may be observable.WZO 2 Brightening of PN shell in direction of motion.WZO 3 Geometric centre shifts away from central star,WZO 4 PN completely disrupted, central star is outside the PN.
In our models, we have not considered the intrinsicstructure of the PN; as initially discussed, PN display manyasymmetric shapes which cannot be explained in the contextof this model. The inclusion of time-variant AGB and post–AGB wind parameters, asymmetric winds and/or magneticfields may address this, but this is beyond this publication.In contrast to the studies of Dgani & Soker (1994) andDgani & Soker (1998), we have observed no fragmentationin our model above 100 km s − . In an effort to understandwhether grid resolution affects fragmentation, we have run ahigh resolution simulation on the head of the bow shock witheffectively 8 times higher resolution and found no evidenceof fragmentation. This disagreement could be attributed tothe simulations being of too low resolution to allow insta-bilities to fragment the bow shock in such a way as theoret-ically predicted. Soker et al. (1991) did not consider evolu-tion on the AGB which alters the structures considerably.Our simulations have not included the effect of magneticfield, neither as a scalar pressure nor a vector field. Magneticfields, if inclined to the direction of relative motion, breakthe cylindrical symmetry of the interaction process whichcan affect these instabilities and lead to the formation ofelongated structures. Huggins & Manley (2005) extends thesuggestion that filaments observed in PNe may be signaturesof an underlying magnetic field. We have demonstrated thatmagnetic fields are not necessary to explain asymmetries ob-served in slow-moving PNe. It is possible that the inclusionof a gravitational field in the hydrodynamic method mayfragment the bow shocks but this is also beyond the scopeof this work. Further, an inhomogeneous ISM could alter thestructure of the bow shock.In our simulations, we see instabilities forming at thehead of the AGB wind bow shock causing vortex shed-ding downstream. When the PN shell expands far enoughto interact with these vortices, typically during stage 3or 4, it is affected and the PN shell would be distortedand brightened accordingly. We have discussed the im-portance of these vortices for the local ISM elsewhere(Wareing, Zijlstra & O’Brien 2007). Inhomogeneities in theISM could be expected to seed more instabilities for vortices.Finally, we note that observability of such objects is de-pendent on the extent of the photoionisation and on excitedionisation lines. We have briefly examined the IAC Morphological Catalogof Northern Galactic Planetary Nebulae (Manchado et al.1996) and list in Table 3 the PNe which we suggest are inter- acting with the ISM, the stage of their PN–ISM interactionand their brief interaction characteristics.Of the approximately 130 well-resolved nebulae in thecatalogue, if we assume a random distribution of angles be-tween v ISM and the line of sight then approximately 15–20per cent of the nebulae will have their motion predominantlyin the plane of the sky. PN–ISM interaction is clear in caseswhere v ISM is in the plane of the sky and our brief inspectionof the catalogue has revealed 20 per cent show characteris-tics of PN–ISM interaction. The correlation between thesestatistics supports our finding that interaction is common,particularly amongst large and/or evolved PNe. A furtherstudy of our selected PNe may reveal angular motions of thecentral stars, which should be in the direction of the ISMinteraction.Considering the list of PNe given by Borkowski et al.(1990), we find that all of them are in the WZO 1 or WZO2 stages of PN–ISM interaction.
Galactic Bulge PNe have central stars with higher typical v ISM . Our simulations have shown that simulations withhigher typical v ISM are generally smaller and show signs ofstrong interaction at an earlier age, thus we would expectGalactic Bulge PNe to have such characteristics.
Three PNe are known in globular clusters. The PN in M15(K648) shows a strongly edge-brightened structure, remi-niscent of a WZO 2 interaction (Alves et al. 2000). The PNin M22 is known to be peculiar, strong in [O III] but ab-sent in H α : it is worth investigating the possible effect ofshock-excitation on its spectrum. Its structure shows a clearbow shock (Borkowski et al. 1993), with the star close tothe parabolic arc. This can be identified with a type WZO2 interaction. The tail is not seen.The final confirmed globular cluster PN (Jacoby et al.1997) is in the cluster NGC 6441. No previous high-resolution images have been published. We obtained an im-age taken with the VLT in [O III], background subtracted,courtesy of M. van Haas and L. Kaper. The image is shownin Fig. 8: it shows a clear edge brightening, with the bright-est region possibly split from the head of the bow shock.This is indicative for an early type WZO 3 interaction. Weconclude that all three globular cluster PNe are dominatedby ISM interaction.As globular clusters have been stripped of their inter-stellar gas and are moving at high velocities (up to 200km s − ) through the Galactic halo, we would expect to see c (cid:13) , 000–000 GB/PN – ISM interaction Table 3.
Nebulae displaying characteristics of ISM interaction from the IAC Morpohological Catalog of Northern Galactic Planetarynebulae (Manchado et al. 1996) discussed in Section 6.1Name Stage of CharecteristicsinteractionA 13 WZO 2 bow shock/PN interaction to the WestA 16 WZO 2 bow shock/PN interaction to the South-EastA 52 WZO 2 bow shock/PN interaction to the North-EastA 58 WZO 2 brightened on the Western side; may be a bow shock interactionA 59 WZO 2 bow shock/PN interaction to the NorthA 86 WZO 2 bow shock/PN interaction to the North-EastBa 1 WZO 1 faint bow shock structure outside PN to the North-WestDeHt 2 WZO 1 faint bow shock structure outside PN to the NorthDeHt 4 WZO 2 bow shock/PN interaction to the WestEGB 4 WZO 3/4 narrow, confined (fast wind?) bow shock to the SouthHe 2-428 WZO 2 bow shock/PN interaction to the SouthIC 4593 WZO 1 faint bow shock structure outside PN to the North-WestJn 1 WZO 3 bow shock/PN interaction with emission shifted downstreamK 2-2 WZO 3/4 structure may be a bow shock remnantK 4-5 WZO 3/4 structure may be remnant of a bow shock blown downstreamM 2-2 WZO 2 bow shock/PN interaction to the SouthM 2-40 WZO 1 faint bow shock structure outside PN to the EastM 2-44 WZO 1 faint bow shock structure outside PN to the South-WestNGC 6765 WZO 1 faint bow shock structure outside PN to the WestNGC 6853 WZO 1 faint bow shock structure outside PN to the North-WestNGC 6891 WZO 1 faint bow shock structure outside PN to the South-WestS 22 WZO 2 bow shock/PN interaction to the South-EastSd 1 WZO 2 bow shock/PN interaction to the North
Figure 8.
VLT FORS1 image in [O III] of the PN in NGC 6441.Continuum has been subtracted. The edge brightening is indica-tive a PN–ISM shock. severe effects for these short-lived objects including rapidbrightening via interaction and destruction.
Observationally, the presence of asymmetries in the haloesof PNe has been found to be a relatively common fea-ture (Tweedy & Kwitter 1996; Guerrero et al. 1998). Theseasymmetries can be partially if not wholly attributed to in-teraction with the ISM. The high rate of asymmetries cannow be explained when the evolution through the AGBphase of the central star is considered. The simulations inthis work show that interaction is present at all evolutionarystages for all v ISM . Our comprehensive simulations have reinforced the re-sult of VGM that PN–ISM interaction is set during the AGBphase and affects central stars with typical v ISM , not justthose with extreme velocities. We have developed a modelwhich results in four stages of ISM interaction and inspec-tions of PNe support this four stage interpretation.PNe have been found to evolve more quickly throughthese stages the faster they move through the ISM. Theyhave also been found to be smaller for greater v ISM . Much oftheir mass ejected during the AGB phase has been strippeddownstream into the tail, providing a possible explanation ofthe missing mass problem observed in PNe, with evidence forsuch a tail found by Martin et al. (2007). The average speedresults of the model appear very similar to the recently dis-covered bow shock surrounding the Dumbbell Nebula whichhas an average v ISM (Meaburn et al. 2005) further support-ing our model.Our conclusions are in agreement with VGM using sim-ilar models. We have extended the study of the PN–ISMinteraction including the AGB phase to three dimensionsand higher v ISM where they were previously limited to twodimensions and low v ISM .PNe which show signs of ISM interaction are not nec-essarily ancient, nor require a high v ISM or magnetic fields.Interaction can become apparent at a young age via severalmethods and central stars with an average v ISM can showevidence of interaction in their nebulae, as commonly ob-served, and be displaced from the geometric centre of theirnebulae. None of the simulations have required a magneticfield to produce commonly observed effects, although thefragmentation of the bow shock in PNe as Sh 2-188 awaits afuller treatment of this interaction at higher resolutions in- c (cid:13) , 000–000 C. J. Wareing et al. volving inhomogeneous ISM and gravitational and magneticfield modelling to reasonably test the fragmentation theoriesof interacting PNe.
ACKNOWLEDGMENTS
This work was carried out as part of CJW’s STFC-fundedPhD project at Jodrell Bank under the supervision of TOBand as part of STFC rolling grant-funded post-doctoral re-search at the University of Manchester. The numerical com-putations were carried out using the Jodrell Bank Observa-tory COBRA supercomputer.
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APPENDIX A: APPENDIX 1
In figures 1–8, we show slices of the simulation domainthrough the position of the central star, parallel to the di-rection of motion at the end of the AGB phase of evolution.Each figure shows the set of simulations at a particular v ISM .In the accompanying tables 1–8, we list the parameter valuesfor each simulation. c (cid:13) , 000–000 GB/PN – ISM interaction Figure A1.
Snapshots at the end of the AGB phase of evolution for v ISM = 25 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A1. Table A1.
Input parameters for the PN–ISM simulations in figure A1: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − − × − − × − − × − − × − − × − (cid:13) , 000–000 C. J. Wareing et al.
Figure A2.
Snapshots at the end of the AGB phase of evolution for v ISM = 50 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A2. Table A2.
Input parameters for the PN–ISM simulations in figure A2: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − − × − − × − − × − − × − − × − (cid:13)000
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − − × − − × − − × − − × − − × − (cid:13)000 , 000–000 GB/PN – ISM interaction Figure A3.
Snapshots at the end of the AGB phase of evolution for v ISM = 75 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A3. The ’missing’ simulation in the bottomrow indicates the reduction in the mass-loss parameter range due to computational and time constraints. Table A3.
Input parameters for the PN–ISM simulations in figure A3: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − − × − − × − − × − − × − × − (cid:13) , 000–000 C. J. Wareing et al.
Figure A4.
Snapshots at the end of the AGB phase of evolution for v ISM = 100 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A4. Table A4.
Input parameters for the PN–ISM simulations in figure A4: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13)000
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13)000 , 000–000 GB/PN – ISM interaction Figure A5.
Snapshots at the end of the AGB phase of evolution for v ISM = 125 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A5. Table A5.
Input parameters for the PN–ISM simulations in figure A5: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13) , 000–000 C. J. Wareing et al.
Figure A6.
Snapshots at the end of the AGB phase of evolution for v ISM = 150 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A6. Table A6.
Input parameters for the PN–ISM simulations in figure A6: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13)000
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13)000 , 000–000 GB/PN – ISM interaction Figure A7.
Snapshots at the end of the AGB phase of evolution for v ISM = 175 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A7. Table A7.
Input parameters for the PN–ISM simulations in figure A7: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13) , 000–000 C. J. Wareing et al.
Figure A8.
Snapshots at the end of the AGB phase of evolution for v ISM = 200 km s − . mass-loss rate increases from left to right, ISMdensity decreases from top to bottom. Full details of each simulation can be found in table A8. Table A8.
Input parameters for the PN–ISM simulations in figure A8: column a) gives the mass-loss rate in the slow wind; column b)the density of the surronding ISM in n H cm − ; column c) the relative velocity of the central star; column d) the grid dimension alongone side. a) b) c) d)˙ M sw ρ ISM v ISM
Grid(M ⊙ yr − ) n H (cm − ) (km s − ) (pc)10 − × − × − − × − × − − × − × − (cid:13)000