PRECESSING JETS AND POINT-SYMMETRIC NEBULAE

Transcription

1 THE ASTROPHYSICAL JOURNAL, 447 : L49 L52, 1995 July The American Astronomical Society. All rights reserved. Printed in U.S.A. PRECESSING JETS AND POINT-SYMMETRIC NEBULAE J. A. CLIFFE, 1 A. FRANK, 1 M. LIVIO, 2 AND T. W. JONES 1 Received 1995 March 16; accepted 1995 April 15 ABSTRACT We present a model for the formation of point-symmetric nebulae that relies on the existence of a precessing jet interacting with the interstellar medium (ISM). Using three-dimensional numerical simulations, we investigate the basic gasdynamics inherent to the model. Through synthetic observations of our simulations we show that episodic precessing jets can reproduce the gross morphological structure of point-symmetric nebulae, i.e., a string of discrete clumps in an S-shaped intensity distribution. We also find that the bow shocks of the individual jet segments can merge into a single shock structure that envelops the entire complex of segments. The development of this enveloping shock allows the model to embrace nebulae consisting of discrete point-symmetric clumps as well as those bipolar objects that show nonuniform brightness distributions on their opposing lobes that are point symmetric through the nucleus. By demonstrating that these bipolar planetary nebulae can form from the same mechanism which produces the discrete point-symmetric nebulae, we can include them in the category of point-symmetric objects, thereby increasing their fractional occurrence in planetary nebulae by 75%. Subject headings: ISM: jets and outflows methods: numerical planetary nebulae: general 1. INTRODUCTION Point symmetry is becoming recognized as a characteristic common to many classes of astrophysical phenomena, particularly gaseous nebulae. Point-symmetric objects are defined as those whose morphological components are symmetrical with respect to reflection through a single point (rather than, for example, through a plane). Point symmetry occurs in a variety of astrophysical settings such as planetary nebulae (PNe; see Schwarz, Corradi, & Melnick 1992a), protonplanetary nebulae (Morris & Reipurth 1990), Herbig-Haro objects/herbig-haro jets (Marti, Rodriguez, & Reipurth 1993), young stellar objects (Scarrott, Draper, & Tadhunter 1993), SS 433 (Vermeulen 1993), and the outflows from active galactic nuclei (AGNs; e.g., Laing and Bridle 1987). The signature of point symmetry is often dramatic, as in the PNe Fleming 1 (Lopez, Meaburn, & Palmer 1993) and NGC 6543 (Harrington & Borkowski 1995). The literature concerning point symmetry in the environment of evolved stars has grown considerably in recent years. In several papers, observations of particular PNe with pointsymmetric morphologies have been discussed (e.g., Goodrich 1993; Morris & Reipurth 1990; Scarrott et al. 1993). In each case, the observed morphology has been explained through models that invoke mechanisms such as a binary companion or a strong stellar magnetic field. The general importance of point symmetry in PNe has also been recognized by Corradi & Schwarz (1994), who use morphological characteristics to divide PNe into five classes (Schwarz, Corradi, & Stanghellini 1992b) related, hopefully, by common underlying physical processes rather than simply by similar appearances. In their study of a large sample of PNe, Corradi & Schwarz find that point-symmetric PNe represent 4% of the total number of extended PNe. In view of the total number of PNe, this represents a large number of point-symmetric nebulae and therefore provides a compelling reason to attempt to understand the physics which leads to these morphologies. 1 University of Minnesota, 116 Church Street S. E., Minneapolis, MN Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD L49 Ideally, we would like to explain the observed characteristics common to the class of point-symmetric objects in terms of a common underlying physical mechanism. The clumps seen in point-symmetric PNe, for example, can be interpreted as arising from the periodic ejection of dense material by a precessing jet. Several investigators have proposed processes by which a jet could be collimated close to the nucleus of a planetary nebula (e.g., Soker 1990, 1991, 1992; Icke et al. 1992; Soker & Livio 1994; Goodrich 1991). In an application of this kind of scenario to a particular object, Lopez et al. (1993) proposed a simple ballistic model to explain the point-symmetric appearance of Fleming 1. With the exception of the work of Raga and collaborators (Raga, Canto, & Biro 1993; Raga & Biro 1993), no rigorous modeling of the evolution of a point-symmetric system has been attempted. In particular, no attempt has yet been made to use hydrodynamical models to study the full three-dimensional evolution of these systems or to address the question of how such a three-dimensional object would appear observationally. This latter point is particularly important. Corradi & Schwarz found a number of point-symmetric objects, such as Hb 5, that appeared to be primarily bipolar nebulae with secondary point symmetry. In these objects, the point symmetry manifests itself in an enhanced brightness distribution on opposing sides of the bipolar lobes, rather than in a string of discrete clumps. These kinds of objects are not easily explained by analytical models which invoke the episodic precessing jet scenario. There is, therefore, a real need for an exploration of the full time-dependent gasdynamics of the proposed models to ascertain their descriptive accuracy. In the present paper we report the first results of a program to study the evolution of episodic, precessing jets, through the use of three-dimensional hydrodynamical numerical simulations. By using a fully three-dimensional code, our results are not restricted by symmetry assumptions. Our goal in this Letter is to illustrate the basic hydrodynamics of episodic processing jets and to demonstrate that they can explain the basic observational characteristics of point-symmetric objects.

2 L50 CLIFFE ET AL. Vol COMPUTATIONAL METHOD AND INITIAL CONDITIONS In our investigation we have used a new three-dimensional numerical model based on the total variation diminishing (TVD) method (Harten 1983; Ryu et al. 1993). This code is designed to solve the Euler equations representing conservation of mass, momentum, and energy. For this first effort we do not include the effects of radiative cooling. Although these effects are probably important in determining the flow details, the influence of radiative losses should not alter the general morphology. We solve the Euler equations on a three-dimensional Cartesian computational grid with 128 zones on each side, implemented with continuous boundary conditions. The jet material was ejected from a circular wafer, three zones thick, of enhanced density at the bottom of the computational grid. The jet conditions are enforced at each time step within the wafer. The jet has constant, enhanced density (relative to the ambient ISM) through seven zones in the radial direction and a smooth (hyperbolic tangent) transition over three zones from the high jet density to the lower ISM density. The material in the jet has a velocity component of constant magnitude, with a direction vector that precesses in a cone about the z-axis. The velocity of the jet is episodic, so that the material is ejected for a time e and is quiescent for a time q. The free parameters in our simulations are therefore (i) the density contrast ( ) between the jet and ISM material, (ii) the precession period of the jet p, (iii) the ejection duration, e, (iv) the quiescent duration, q, and (v) the Mach number (M) of the flow relative to the sound speed in the ISM. The jet is assumed to be in pressure equilibrium with the ISM, which is a constant density medium. The physical parameters used for the model presented below have been chosen to match archtypical nebular values (ISM density, jet density, ISM sound speed, Mach number of jet). Thus, the simulation has parameters comparable to those found by Lopez et al. (1993) for Fleming 1. We note, however, that we are not attempting to model a specific object. Our input parameter values are size of computational domain, 5 pc; velocity of jet material, 148 km s 1 (Mach 10); density of ISM, 10 cm 3 ; density contrast, 100 jet:ism; precession period p yr; ejection duration e 0.13 p yr; quiescent duration q 0.03 p yr; cone half-angle 26. The simulation was run for yr. 3. RESULTS The results of the hydrodynamical simulation are shown in Figure 1 (Plate L9), in which we present a volume rendering of the gas density distribution at the end of the run. Though the relatively low resolution does not allow us to make inferences about the fine details and inner structure of the ejected material, gross morphological features should be reliable and are readily observable. As expected, we see several highdensity jet segments, which are arranged in a characteristic corkscrew-shaped string when viewed at an angle with respect to the y-z plane. By the end of the run, the first segment, which is almost off the grid, has been flattened and has begun to break up. The structure is qualitatively similar to that described by Raga & Biro (1993), in their modeling of an evolved, continuous jet, with time-dependent ejection velocity and direction. What we see, however, is that the individual bow shocks merge, forming a single structure that encloses the entire complex of clumps. This result was unexpected and has important observational consequences, as we will demonstrate below. In spite of the relatively low resolution of our simulations, the breakup of the first clump, apparent in Figure 1, probably reflects a real physical effect. Theoretical treatments of the shocked bullet problem (e.g., Jones, Kang, & Tregillis 1994) have shown that the timescale for the breakup of a spherical clump traversing an ambient medium is several times the interval for a transmitted shock to cross the clump; namely, t c 1/ 2 2 R, (1) u where is the density ratio between the clump and the ambient medium, R is the radius of the clump, and u is the clump velocity. For our model, the radius R can be replaced by the length of the jet sections L u e. Given the parameters used for our simulations, we find t c yr, which is of the same order as the time at which the density distribution in Figure 1 is displayed. High-resolution two-dimensional simulations performed by Jones et al. indicate that on longer timescales the jet segments will begin to fragment by the combination of Rayleigh-Taylor and Kelvin-Helmholtz instabilities. We expect that by 2 3 times this interval, the clumps would completely fragment. To compare the results of our simulations with observations of point-symmetric nebulae, we have generated simplified synthetic observations of our model. This was accomplished by first taking the three-dimensional density distributions from the simulations and then reflecting them through the midpoint of the jet base. As an approximation to the observed intensity distributions, we then integrated the square of these density distributions onto the plane of the sky, producing a crude approximation to the intensity distributions that would be observed from an optically thin, photoionized nebula. In Figure 2 (Plate L10) we present these intensity maps. The original three-dimensional model has been projected onto the sky at angles 20, 40,60, and 80 from the z-axis (cone axis). Figure 2 demonstrates that our models are successful in producing the characteristic S-shaped string of beads morphology seen in point-symmetric objects. Rotation about the cone axis does not change this result. Note also that the enveloping bow shock that surrounds the entire jet complex contributes an overall bipolar morphology to the intensity map. Our method for computing these synthetic observations actually underestimates the brightness of these bow shock bipolar lobes by ignoring shock-excited emission. If the emissivity produced by the bow shock were included, we expect that the bipolar lobes would be more visible in our intensity maps (Henney & Dyson 1992). 4. DISCUSSION AND CONCLUSION From the preliminary results of the work presented in the last section, it is clear that a precessing, episodic jet can, in principle, produce the string of discrete clumps in an S-shaped distribution characteristic of point-symmetric nebulae. The synthetic observations which we have presented are in good agreement with the gross morphological features seen in real observations of point-symmetric nebula. In addition, our results have revealed a new hydrodynamical feature in the development of a single, merged bow shock that envelops the individual jet sections. With respect to planetary nebulae, this is an important point because it allows the mechanism we have

3 No. 1, 1995 PRECESSING JETS AND POINT-SYMMETRIC NEBULAE L51 investigated to embrace both discrete point-symmetric objects as well as the rather enigmatic objects which appear as bipolar nebulae with nonuniform brightness distributions on their opposing lobes and are point symmetric through the nucleus. This effect of combining the bow shocks of the individual clumps undoubtedly depends on the particular values chosen for parameters such as the cone angle and the quiescent duration. We will explore in a later work the range of parameters that give this combined bipolar/point-symmetric morphology. In the particular case of Hb 5, however, which Schwartz et al. (1992a) identify as bipolar, it appears that the precessing jet and enveloping bow shock seen in our simulations could provide a good match to the observed pointsymmetric morphology. In general, scrutiny of published PN images reveals at least nine objects (He 2 36, He 2 141, IC 4642, IC 4663, NGC 6302, NGC 6309, NGC 2440, NGC 6537, and Hb 5) with this kind of bipolar/point symmetric symmetry (Corradi 1995). This brings the total number of point-symmetric PNe up to 21 and increases the fraction of occurrence in Corradi & Schwartz s sample to 7%. This increases the total fraction of point-symmetric PNe by a factor of In our model we have explicitly initiated the simulations with a well-formed precessing jet. In both PNe and young stellar objects the formation of the jet is likely to involve the presence of a disk or torus of gas surrounding the central star that will be collimated through either hydrodynamical means (e.g., Icke et al. 1992; Frank & Noreiga-Crespo 1994; Blandford 1993) or through MHD processes (Wardle & Koenigl 1993). In both cases the precession of the jet would be most easily explained in terms of the precession of the disk itself. A phenomenon of this type is observed, for example, in cataclysmic variables (e.g., Livio 1995) of the SU UMa type (e.g., Whitehurst 1988; Lubow 1991). For PNe, a promising model for the formation of the disk relies on the gravitational interactions of binary stars (Soker & Livio 1994). The binary model has also been proposed as a general mechanism to explain the toroidal density distributions in asymptotic giant branch (AGB) star winds which eventually lead to the shaping of all PN morphologies. Our results may be useful in establishing the applicability of the binary hypothesis. Observations of PNe which exhibit point symmetry show a single S-shaped string of high-emission clumps, rather than a zig-zag string that goes back and forth several times. If this result is not caused by an observational bias where the inner regions are not resolved, then it suggests that the lifetime of the blobs, that is, the jet segment crushing time ( c in eq. [1]), is of the same order as the precession period c 2 p yr. Note that c is determined by parameters inherent to the jet and that the values we have chosen can be considered reasonable for PNe. The velocity of the jet segments is certainly on the order of 100 km s 1, the observed morphology argues that length of the jet sections should be or cm, and the square root of the density contrast which appears in equation (1) guarantees that even 10 4 will increase the c by only an order of magnitude over what is found in our simulations. In the binary interaction model of disk formation, the relationship between the disk precession and binary rotation period ( b ) can be expressed as b p 3 4 q 1 q 1/ 2 R 3/ 2 disk a, (2) where q is the mass ratio, R disk is the disk radius, and a is the binary separation. For reasonable values of these quantities equation (2) shows that the disk (and jet) precession period will be approximately times longer than the binary period. Thus, our results would lead us to the prediction that b should be approximately 0.1 c to 0.01 c. In their study of PN progenitors with binary central stars, Yungelson, Tutukov, & Livio (1993) found a peak in the distribution of expected binary periods centered at b yr. This value is easily bracketed by the prediction of our model based on reasonable choices of parameters which determine the jet segment crushing time. We believe that the order of magnitude agreement between predictions of the jet precession period based on (1) the binary interaction model and (2) considerations of the jet segment crushing time might be considered circumstantial evidence for the hypothesis that binary interactions shape the outflows of AGB winds and lead to the production of jets. To establish this agreement more firmly, observations of the inner regions of point-symmetric nebulae are needed to determine the geometry of the flow close to the source. To conclude, our simulations indicate that precessing jets are a viable means of forming point-symmetric objects that are well matched to observed PNe both in terms of gross morphologies and observed kinematical parameters. These pointsymmetric systems appear to be quite common, and, therefore, their basic physics merits further study in an attempt to identify the exact relation between the hydrodynamical processes and observational characteristics. We would like to thank Arsen R. Hajian for his many insights into the observational consequence of these models. J. A. C., A. F., and T. W. J. were supported by NASA through grant NAGW-2548, by the NSF through grant AST , and by the University of Minnesota Supercomputer Institute. We are especially grateful to Dongsu Ryu for sharing the three-dimensional TVD code with us. Blandford, R. 1993, in Astrophysical Jets, ed. D. Burgarella, M. Livio, & C. P. O Dea (Cambridge: Cambridge Univ. Press), 15 Corradi, R. L. 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5 PLATE L9 FIG. 1. Logarithmic density profile in the simulation after yr. CLIFFE et al. (see 477, L50)

6 PLATE L10 FIG. 2. Synthetic images of log H intensity made by projecting the density squared (equivalent to assuming full ionization and constant temperature) on the sky for a line of sight at 20, 40, 60, and 80 from the cone axis. In our numerical model we have chosen a precession period that is of the same order ( p yr) as that deduced for the PN Fleming 1 (Lopez et al. 1993). CLIFFE et al. (see 447, L50)