ASTRONOMY AND ASTROPHYSICS. Numerical hydrodynamic simulations of molecular outflows driven by Hammer jets

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1 Astron. Astrophys. 343, (1999) Numerical hydrodynamic simulations of molecular outflows driven by Hammer jets ASTRONOMY AND ASTROPHYSICS Roland Völker 1, Michael D. Smith 2,1, Gerhard Suttner 1, and Harold W. Yorke 3,1 1 Astronomisches Institut der Universität Würzburg, Am Hubland, D Würzburg, Germany 2 Armagh Observatory, College Hill, Armagh BT61 9DG, Ireland 3 Jet Propulsion Laboratory, MS , 4800 Oak Grove Drive, Pasadena, CA 91109, USA (smith@star.arm.ac.uk; suttner@ voelker@ astro.uni-wuerzburg.de; yorke@lear.jpl.nasa.gov) Received 13 August 1998 / Accepted 15 December 1998 Abstract. Very young protostars eject collimated jets of molecular gas. Although the protostars themselves are hidden, some of their properties are revealed through the jet dynamics. We here model velocity shear, precession, pulsation and spray within dense jets injected into less-dense molecular clouds. We investigate the Hammer Jet, for which extreme velocity variations as well as strong ripping and spray actions are introduced. A three dimensional ZEUS-type hydrodynamics code, extended with molecular physics, is employed. Jet knots, previously shown to be compact in simulations of smoother jets, now appear as prominent bow shocks in H 2 and as bullets in CO emission lines. High proper motions are predicted in the jet. In the lobes we uncover wide tubular low-velocity CO structures with concave bases near the nozzle. Proper motion vectors in the lobes delineate a strong accelerated flow away from the head with some superimposed turbulent-like motions. The leading bow is gradually distorted by the hammer blows and breaks up into mini-bow segments. The H 2 emission line profiles are wide and twin-peaked over much of the leading bow. On comparison with the simulations, we identify observed outflows driven by various dynamical types of jet. Shear is essential to produce the jet bows, spray or precession to widen the outflows and hammer blows to generate knotty jets. We identify the proper motions of maser spots with the pattern speed of density peaks in the inner jet and shell. Key words: hydrodynamics shock waves ISM: clouds ISM: jets and outflows ISM: molecules radio lines: ISM 1. Introduction Molecular jets and outflows appear during a critical phase in the formation of a star in which the mass of an envelope accretes onto a growing protostellar core (e.g. André et al. 1993, Bachiller 1996, Padman et al. 1997). The jets may well be the agents which channel away excess angular momentum to allow the collapse to proceed (Shu et al. 1994, Bontemps et al. 1996). Send offprint requests to: M.D. Smith They may also promote the disruption and dispersal of the embedding cloud and so limit the eventual stellar mass (Velusamy & Langer 1998). Furthermore, the properties of the extended jets take on extra significance because the stars themselves are highly obscured even in the infrared (André et al. 1993). Thus surveys for outflows in the infrared can be used to locate the youngest protostars (Stanke et al. 1998). Ideally, we would like to detect or place useful constraints on the angular momentum and magnetic field in the outflow, since these quantities play crucial roles in the interaction between the accretion disk, magnetosphere and the wind (e.g. Camenzind 1997, Shu & Shang 1997, Ouyed et al. 1997). This is, however, not yet observationally feasible. Here, we ask: what other constraints on how an outflow must have formed, how it has developed and how it provides feedback on the environment in which it is created, can at present be derived? With this aim we develop the Würzburg molecular outflow model (Suttner et al. 1997, Smith et al. 1997a) to examine highly variable and non-uniform jets. Many qualitative properties of the earliest outflows from protostars have now been ascertained (Tables 1 and 2). These outflows are often driven by highly supersonic pulsed jets. They are well collimated and extremely long. Despite being deeply enshrouded by molecular gas, the warm shocked regions can be observed in the infrared H 2 lines, thus revealing the present impact regions. The cool accumulated material can be observed in the submillimetre CO lines, delineating the total swept-up and swept-out material. Some of the constraints imposed are quantified in Sect. 2. The theory of molecular jets is still being established. Our model involves three dimensional hydrodynamic calculations of supersonic molecular jets into molecular environments (Suttner et al. 1997). The ZEUS-type code encompasses the basic molecular characteristics: strong cooling, dissociation in fast shocks and reformation in dense dusty environments. It has so far proven to be remarkably successful, as signified by the number of ticks in the two tables. Nevertheless, the results suggest some extra dynamical input is required: we need to simulate more active jets to determine if bow-shaped jet knots and wider outflows are feasible. Specifically, we here investigate (1) hammer-like pulsations, (2) velocity shear, (3) directional

2 954 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets Table 1. Molecular Hydrogen signatures, typical examples and the successes (ticks) and failures (crosses) of the Suttner et al jet model Multiple Bows Complex Filamentation Wide Turbulent Jet L 1634: Davis et al. 1997a HH 90/91: Davis et al. 1994b HH 110: Davis et al. 1994b Cepheus A: Hartigan et al HH 2: Davis et al. 1994a Twin/single-peaked line Profiles Extremely Broad Profiles Constant Excitation L 1448: Davis & Smith 1996 DR 21: Garden et al Cepheus E: Eislöffel et al Cepheus E: Eislöffel 1997 HH 7-11: Carr 1993 L 1448: Davis & Smith 1995 Knots/mini-bows in jets Asymmetric Lobes High Proper Motions HH 111: Gredel & Reipurth 1993 L 1660: Davis et al. 1997a HH 46/47: Micono et al HH 212: Zinnecker et al L 1551: Davis et al HH 111: Coppin et al / / Table 2. Signatures of well-collimated CO bipolar outflows and the successes (ticks) and failures (crosses) of the Smith et al. jet model. NGC 2264G (Lada & Fich 1996) displays most of these signatures. Note that these are examples of a class of outflows. It is not clear how common counter-examples may prove. Collimation increases Red/blue lobe symmetry Power-law line profiles with Velocity (high-v) (γ = 1.3 to 2.0) Hubble Law Strong Forward Motion High-speed CO Bullets (velocity distance) IRAS : Bachiller et al High-speed CO Jets Tubular low-speed structure Helical appearance HH 211: Guilloteau et al HH 111: Nagar et al L 1157: Gueth et al v 0(0,t) v 0(R,t) velocity shear spray nozzle ψ precession pulsation Fig. 1. Nozzle geometry for the 3D simulations P P θ changes and (4) wide opening angles, and present their signatures, including line images, proper motions and spectroscopic properties. A comparison to other protostellar jet models was presented by Smith (1998). Frank et al. (1998) have also reviewed astrophysical jet simulations. In addition, three-dimensional hydromagnetic jets with atomic radiative cooling have now been presented by Cerqueira, de Gouveia Dal Pino & Herant (1997). Molecular jets are, however, particularly difficult to simulate numerically because of the high compression behind the stronglyradiative shocks. Nevertheless, Raga et al. (1995) managed to simulate an atomic jet drilling into a molecular cloud in 2D by employing an adaptive grid technique. Synthetic images from molecular emission lines have also been generated on assuming the shock physics across paraboloidal bow shocks (Smith 1991). We begin by placing the physical and dynamical properties studied here into their context. Radiative bow shocks driven by jets were analyzed by Raga (1988) through simulations in two dimensions. Complete outflows were simulated by Blondin, Fryxzell & Königl (1990). They demonstrated the formation of extended nose cones and disrupted, deformed bows. Gouveia Dal Pino & Benz (1993) and Stone & Norman (1994) stepped up the simulations to three-dimensions (3D) and found that the shell disrupted into knots and filaments but nose cones were absent. These findings were confirmed for strongly-radiative molecular fluids in full 3D in the work of Suttner et al. (1997). Jet structure could be generated by internal fluid instabilities, external triggers or source variations. Blondin et al. found that the reflecting pinch modes of the Kelvin-Helmholtz instability were suppressed in strongly-cooling jets. Similarly, Chernin et al. (1994) found that a low-density cocoon of gas shields high Mach number jets. The pulsation model has received most attention (e.g. Raga et al. 1990; Kim & Raga 1991; Hartigan &

3 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets 955 Fig. 2. The boundary condition for the jet velocity of model 3D-5: the central input velocity as a function of time (in years). Raymond 1993; Stone & Norman 1993; Biro & Raga 1994; Smith et al. 1997b). Note that non-periodic variations, which will be included here, have been considered by Raga (1992), who obtained some self-similar solutions for the separation of knots. Precession and directional variability of strongly cooling and ballistic jets were investigated by Raga et al. (1993), Biro, Raga & Canto (1995) and Cliffe et al. (1996), amongst others. Biro et al. demonstrated the proper motion vectors for density peaks in an adiabatic jet. Raga (1988) presented the proper motions from simulations of bow shocks driven by solid obstacles. Here we shall model the proper motions in strongly cooling jet-driven flows. Other topical questions concern molecule formation on the small-scale (e.g. Ruden, Glassgold & Shu 1990; Glassgold, Mamon & Huggins 1991) and the continued growth of the gigantic outflows (Bally & Devine 1994; Eislöffel & Mundt 1997; Reipurth et al. 1997). We intend to approach these themes with numerical simulations after the basic dynamical properties are established. 2. The Hammer jet model 2.1. Limitations Only the jet-driven outflow model is simulated here. Thus we assume that a collimated jet of gas is switched on and maintained. (The alternative model for collimated flows involves winds focussed on quite large scales (Barral & Cantó (1981)). This model for molecular jets has been developed and applied by Suttner et al. (1997) and Smith et al. (1997a). To summarize: (1) three-dimensional simulations are performed, (2) a hydrodynamic code is employed, (3) the jet and environment are initially fully molecular, (4) the jet is over-dense by a factor of 10, (5) the jet power is variable but non-evolving (i.e. no systematic long-term variation), (6) the environment is uniform in all parameters. Given these limitations, the ability to reproduce several observed features is encouraging. The conception followed here, presented in more detail by Smith (1998), is that the Class 0 phase is accompanied by dense molecular jets. The jets may also contain a high fraction of atomic hydrogen simply because molecule formation is not complete. During this phase large eruptions occur on time scales of years but the mass outflow over each 1000 years is held constant (some fraction of the accreting mass is ejected). This phase lasts a total of at least 10,000 years. In the following Class 1 phase the jet density is considerably lower and molecules cannot form within the jet; the environment has been swept away. In the Class 0 phase the jet possesses ballistic properties whereas in the Class 1 phase it interacts strongly with the cavity (e.g. through the growth of non-linear waves formed by the Kelvin-Helmholtz instability). We shall here assume the inflowing hydrogen gas to be 100% molecular. The shocks which form in the pulsed jets are strong enough near the nozzle to dissociate at least some of the molecules, leading to jet knots with a mixture of atomic and molecular gas. In sheared jets, the knots appear as bow shocks with hot atomic gas at the apices and warm molecular gas along the flanks. The calculations were carried out on a Cartesian grid that contains zones. The whole grid covers an integration domain of ( ) cm 3. A nozzle with radius R = cm was placed at the center of one side of the grid. We are limited by the grid resolution and the molecular cooling time scale to simulate on rather short time scales and length scales. Examples of small jet outflows include HH 211 ( cm), HH 24 ( cm and L 483 ( cm) (see Table 5 of Davis et al. 1997a). We compensate by considering quite rapid variations. Thus we find that the end of the grid is reached in typically 600 years. However, (1) the dynamics are controlled only by the fact that strong radiative cooling is present, and (2) the infrared structure is dominated by narrow shocked regions. Hence, provided that the chemistry does not introduce a further time scale, we believe that the flow patterns and resulting images should be scalable. Specifically, we find that molecule reformation is negligible during the simulation: the reformation time scale, assuming H 2 reforms on cool dust grains, is roughly /n s, where n is the atomic density. Hence, clumps of atomic gas of density 10 6 cm 3 would be converted to molecular clumps on a time scale of 3000 years. However, we actually find, because the atomic gas is formed in fast shocks through collisional dissociation of the molecules, instead of cooling and collapsing into clumps, the atomic gas simply fills a large low-density cavity. This gas then does not reassociate. Speeds in observed molecular jets range from 100 to 500 km s 1. This range is derived from proper motions of H S(1) knots (Micono et al. 1998, Coppin et al. 1998). Here we take the lower limit, consistent with our first goal of simulating the first stages in the outflow formation. Higher speeds of molecular jets were considered in two dimensional simulations by Suttner (1997). No noteworthy new structures were detected Precession Five three dimensional simulations have been performed (Table 3). These include two simulations previously analyzed by Suttner et al. (1997) and three new simulations. The first two simulations (3D-1 & 3D-2) were of uniform and low-amplitude pulsation jets with small precession angles. They are rediscussed here to contrast the new simulations. Furthermore, we have im-

4 956 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets Fig. 3. The density of H 2 molecules from models 3D-1 (upper) to 3D-5 (lower). Note the black edges where molecules are destroyed in fast shocks. The XY plane which includes the jet axis are displayed. Table 3. Parameter for the three dimensional calculations. Here n m is the ambient nucleon density. shear pulsation precession spray model n m/10 4 cm 3 n j/n m v j/km s 1 v 0(R)/v 0(0) v/v j P/yr θ P/yr ψ 3D o o 3D o o 3D o 46 0 o 3D o 36 2 o 3D o 26 2 o See Fig 2 for the input velocity. proved the technique to analyze the data (when making images we take advantage of all the information in the second-order calculations). Precession, or more appropriately, directional wandering, is suspected from the spatial structure of several molecular outflows including Cepheus E (Eislöffel et al. 1996), RNO 43 (Bence, Richer & Padman 1996), RNO 15-FIR (Davis et al. 1997b). Cliffe, Frank & Jones (1996) have studied the precession of heavy jets with numerical simulations, but with adiabatic equations of state. Hence, it is not clear that their conclusion, that precessing jets match better the morphology and momentum distribution of molecular outflows, is valid High-AMplitude Multiple ERuptions (HAMMER) We superimpose a strong sinusoidal perturbation onto the uniform jet velocity v j at the nozzle: ( ) 2π v 0 (0,t)=v j + v sin P t, (1)

5 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets 957 Fig. 4. The 1-0 S(1) H 2-emission images of models 3D-1 (top) to 3D-5 (bottom) taken from near the end of the runs. The fluxes were calculated by the method of Suttner et al. (1997). The XY projection is shown here. where v 0 (0,t) is the velocity in the center of the nozzle (r = 0). Hammer-type pulsations in the injection velocity are thus introduced in the three new models (Table 3. The variations are typically 90%. This causes the material to rapidly pile up into knots in the jet and produces bullet-type outflows (see Sect. 3) Shear and spray Jet shear (see Fig. 1) is quite plausible on theoretical grounds. Winds focussed by shocks may well have higher central velocities since the strength of the deflecting shock is angle-dependent. In extended disk-wind models the wind speed reflects the original Keplerian speed. In fast stellar winds asymmetries are related to the rotation of the star. Shear is difficult to detect but has been observed in the HH 47 jet (Hartigan et al. 1993). We apply a velocity variation over the cross section of the jet inflow: ) v 0 (r, t) = (1 r2 2R 2 v 0 (0,t). (2) Finally, the jet beam was forced to precess at the nozzle with a specified opening angle. The parameters used for the individual models are listed in Table Results Cross sections of the molecular density of all the models are displayed in Fig. 3. Note: The black tips are the regions where molecular destruction is complete. This occurs mainly at the locations of the strong shocks: at the leading edge and at the mini-bows along the shell. Low molecular densities also occur within the cavity, i.e. between the dense jet and the dense shell. High molecular densities are restricted to thin sheets where oblique shocks have swept up the gas. Knots of atomic gas are found along the jet axis, as molecules are destroyed as they enter the strong shock at the beginning of the jet. Downstream, the jet shocks weaken and the molecules survive (e.g. see Smith et al. 1997b). The introduction of a spray angle significantly widens the outflow shell and cavity as well as broadening the jet bow shocks. The cause of the rapid growth of mini-bows along the shell walls are the hammer blows from the jet. The blows accelerate the knots, which then grow via the Rayleigh-Taylor instability. This appears to intensify wave structures originally produced in the bow via the thin-shell instability (see Mac Low 1998). The jets propagate within low-density cavities, unaffected by the ambient medium.

6 958 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets Fig. 5. H S(1) line profiles from selected regions in the bow shock of model 3D-4. The projection angle is 60 to the line of sight. The abscissa runs from 20 to 80 km s 1, with the vertical dashed line at the rest velocity. The relative peak intensities are indicated. Fig. 6. H S(1) line profiles from selected regions in the bow shock of model 3D-4. The projection angle is 30 to the line of sight. The abscissa runs from 10 to 140 km s 1, with the vertical dashed line at the rest velocity. The infrared images (Fig. 4) bear little resemblance to the molecular distributions. The distributions of warm shocked molecules possess the following properties. A sequence of increasing jet brightness is produced, as expected. Without pulses (top box) the jet is invisible. With high variability (bottom box) an almost continuous infrared jet is generated. Jet shear is necessary to generate bow shocks in the jet in the 1-0 S(1) H 2 line. Pulsation alone (model 3D-2) is not sufficient. A complex emission structure is produced in the head region through high shear and hammer blows. Most of this emission arises from sheet structures confined to a disturbed bow-shell structure. Precession distorts the arrangement of bow shocks, which then appear slightly off-axis. Wave patterns are generated in and behind the main head. Close analysis reveals that they lie near the inner shell surface, generated by the Kelvin-Helmholtz instability due to relative fluid motions. High-resolution spectroscopy of the H 2 line provides a test for bow shock models. We present the line profiles for model 3D-4 in Figs. 5 and 6. These can be directly compared to those of model 3D-1 published by Suttner et al. (1997, Fig. 18). The hammer model leads to twin-peaked line profiles over an extended region (e.g. over the edge C, D, E & J). This is due to the shocked jet layers which reach the termination region and

7 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets 959 Fig. 7. The CO emission from the J=1-0rotational transition (i.e. 0-0 R(1)) of model 3D-4. Three radial velocity intervals are displayed. The angle between the jet axis and the line of sight is 60. Table 4. Total luminosities and excitation temperatures near the end of each simulation. The percentage of the total jet mechanical luminosity L m is given in parentheses; the model time of the simulation is in the final column. model H S(1) L/L 3D (0.5%) 3D (1.2%) 3D (0.8%) 3D (1.6%) 3D ( ) H S(1) L/L (0.06%) (0.13%) (0.18%) (0.23%) ( ) CO 0 0 R(1) L/L L m/l T ex/k t/yr (0.0008%) (0.0006%) (0.0002%) (0.0003%) ( ) are reshocked as they decelerate. In model 3D-1, the uniform jet, twin peaks were only generated very close to the bow apex. Note that the mini-bow structure C possesses the most complex line profiles, whereas Knots G& H are relatively narrow. Hence, Hammer Jets produce rather turbulent bow heads as will become evident when we study the kinematics below. The CO emission is dominated by a smooth tubular structure into which the ambient gas has been swept up over a considerable time. The CO submillimetre images for model 3D-4 is shown in Fig. 7. The jet bullets are present in CO but weak. A jet component and a bow component, however, can dominate in the high radial velocity channels. Outflows generated by Hammer Jets (3D-3, 4&5)grow faster than the more uniform jet-driven outflows (see Column 7 of Table 4). The bow of model 3D-3 advances approximately 31% quicker than the 3D-1 bow. To explain this, the factors to consider are the extra momentum flow rate due to the pulsations, the lower average momentum flow due to the shear and the ballistic propagation of the jet core. Time and space integrations yield the result that the specific momentum flow rate in model 3D-3 is 12% higher than in model 3D-1, therefore not sufficient to explain the fast growth of model 3D-3. Hence, it is the ballistic motion of the jet core which is responsible. This is confirmed by inspecting Fig. 4, which shows a highly streamlined bow shock due to the fast jet core propagation. The spray jet model advances, of course, slower. The difference in advance speed between models 3D-3 and 3D-4 remains quite small, however, since the jets are still over-dense, and thus the advance speed U is only a weak function of the jet speed (note that the classical momentum balance yields U = v j /(1 + η) where η = n m /n j ). Note also that the advance speed and the excitation temperature are correlated. One may naively expect the presence of a greater quantity of hotter gas to lead to higher H 2 excitation (as measured by the 2-1 S(1)/1-0 S(1) ratio). This reasoning is not absolutely straightforward, however, since the excitation should depend on the ratio of warm and cool molecular gas which in turn depends on the bow shock shape or the spectrum of shocks produced in the turbulent wake, not on the absolute bow speed (since higher bow speeds only lead to more dissociation). We have previously found that the highest excitation is produced in the turbulent flanks rather than near the bow s leading edge (Suttner et al. 1997). We await a more detailed study of supersonic turbulence dissipation to shed light on this issue. The 1-0 S(1) luminosity is typically 1% of the available mechanical jet power (Column 2 of Table 4). Total H 2 luminosities

8 960 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets Fig. 8. A CO position-velocity diagram for model 3D-4. The line emission from the submillimetre rotational transition J=1-0 is displayed and, to ease comparison, the full bipolar outflow is simulated. The angle α is the angle between the jet direction and the sky plane. Fig. 9. A high-resolution one-dimensional study of proper motions from model 1D-3, as described in Table 5. At the time of 55.7 yr the jet has propagated out to cm. are typically 20 times higher (Smith 1995). Hence, about 20% of the power is radiated from hot molecular hydrogen gas. (Note that H 2 O cooling has not been included in these calculations and may well be a strong coolant of the warm gas.) There is also no clear trend of decreasing CO J = 1-0 flux with increasing activity in the models, although the CO flux is extremely low in the highly-variable 3D-5 simulation. Finally, we demonstrate the appearance of CO bullets on a position-velocity diagram. Fig 8 shows that a series of radial spikes are produced, which continue out to high velocities. This is superimposed on the Hubble-type low-velocity behaviour (i.e. the triangular contours) which dominated the position-velocity diagrams of the more uniform outflows (Smith et al. 1997a). 4. Kinematics Protostellar jets often contain numbers of well aligned knots. The origin of this phenomenon is still not fully understood. Individual knots possess high proper motions away from the jet source (Neckel & Staude 1987). This rules out jet models which assume that the knots are stationary shocks (Königl 1982). Two possible mechanisms are left to discuss. In the first scenario the knots are interpreted as crossing shock waves excited by Kelvin-Helmholtz instabilities that occur at the edge of the jet channel (Norman et al. 1982). The alternative model considers the knots to be the result of a time variable jet source (Kofman & Raga 1992). Efforts have been made to decide between these two models by examining the kinematic properties. In detailed studies Eislöffel and Mundt (1992, 1994, 1995) measured the proper motions of knots in several well known jet systems. From these optical observations they calculated the absolute values of the velocity of the pattern movement. This pattern speed v p is compared to the fluid speed v f derived from radial velocity measurements. The pattern speed v p is mostly observed to be lower. Fig. 10. The kinematics of the density peaks of model 3D-3. Note that the top panel displays the logarithm of the ratio of pattern to fluid speeds, shown individually below. The measured ratios ζ = v p /v f usually range from 0.4 to 1.0.In some of the jet systems the ζ-values increase with propagation distance. These results seem to be in agreement with models which describe the knots as running shock waves. However, the question remains as to the origin of the shocks. For this reason we investigated here the kinematics of our numerical jet models. During a calculation the positions of extrema of different variables were detected in several successive time steps. For numerical reasons these peaks cannot move further than a single grid cell spacing in one step. It is therefore a straightforward task to follow individual peaks and to determine the direction and the velocities of their motion.

9 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets 961 Table 5. Parameters and resulting knot velocities of the one dimensional models. model n m/10 4 cm 3 n j/n m v j/km s 1 v/v j P/yr shape numeric v k /v j analytic v k /v j deviation 1D sinusoidal % 1D sinusoidal % 1D sinusoidal % 1D sawtooth % 1D sawtooth % 1D sawtooth % knots along the jet axis (upper panel). These material fragments expand with increasing distance from the source and form a complex structure of shock waves (Smith et al. 1997). The second panel displays the propagation velocities of density maxima and of extreme density gradients in comparison to the fluid motion. The one dimensional models (Table 5) show that the average pattern speed is always higher than the predicted knot velocity v k = P 0 ρ 0(t)v 2 0(t) dt P 0 ρ 0(t)v 0 (t) dt, (3) Fig. 11. The kinematics of the density peaks of model 3D-4. Note that the top panel displays the logarithm of the ratio of pattern to fluid speeds, shown individually below. where v 0 (t) and ρ 0 (t) are the time dependent velocity and density of the material ejected by the jet source. This equation is based on the assumption that at great distances from the origin the knots contain most of the mass and the momentum produced by the source during a period P. The systematic deviation between the numerical and the analytical results suggests that the method which is used to release the momentum onto the integration area contains numerical discrepancies. The ratios between pattern and fluid speed are all close to one, as one can expect from analytic studies of vertical shock waves (see Appendix). At the jet shocks where the gas overtakes the shock wave we find values less than one and, vice versa, we find values greater than one at the bows Three-dimensional density peaks Fig. 12. The relationship between the four speeds: pattern (p), fluid (f), radial (r) and tangential (t) One-dimensional proper motions We present here the first numerical simulations of proper motions in radiative jets. The proper motions of knots along the axis of a jet are the pattern speeds. Biro (1996) has studied the pattern speed of an isolated internal working surface. A numerical simulation demonstrated the deceleration due to the ambient medium. Full jet simulations have not reproduced this behaviour, probably because cocoon densities are extremely low (Stone & Norman 1993; Suttner et al. 1997). We begin with a one dimensional calculation, as shown in Fig. 9. The variation of the jet velocity produces periodic dense In the 3D-models the situation is different. Here we find that the measured points split up into a fast and a slow component. This separation can clearly be seen in Fig. 10. The individual plots display the absolute values of the calculated fluid and pattern velocities of the density peaks in model 3D-3 and the corresponding ratios. The low velocity component is formed from density maxima in the bow shock that surrounds the whole jet. The velocities range from only a few km s 1 in the region close to the origin up to about 100 km s 1 at the tip. Because the bow shock is oblique, only the normal component of the fluid speed is effected. Thus, one expects velocity ratios greater than one. In agreement with this idea, we find increasing ratios away from the apex. Whereas in the head region most of the values range from 1 to 5, in the wings, where the shock is quite oblique, ratios up to 40 are reached (as clarified in the Appendix). The high velocity component forms several groups which can be assigned to the pulses in the jet flow. The velocity in-

10 962 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets creases towards the tips of the pulses. Thus they behave like small bow shocks. The values range from 70 to 150 km s 1. The corresponding velocity ratios are close to 1, but exhibit a small variation (0.8 <ζ<1.4). However, we find greater variations in other models. The density peaks that belong to the jet knots in model 3D-5 (Fig. 11) possess ratios up to ζ =2. The kinematics of all models show in principle similar characteristics. The different velocities and ratios depend on the boundary condition for the jet inflow Infrared proper motions Using the method described above we studied the development of the emission structure of our models. Fig. 14 presents the motion of intensity peaks of model 3D-4, calculated from consecutive simulated H S(1) images. In the first plot an emission map is displayed that shows the jet at an orientation angle of α =30 o. The arrows illustrate the direction and the speed of the pattern motions v p calculated by reprojecting the measured tangential velocities v t onto the jet axis (Fig. 12). The lower captions reveal the corresponding absolute values of the pattern and fluid speeds and the resulting ratios. The required tangential v t velocities were taken from the model data. The measured kinematics are comparable to the motion of the density maxima. Within the knots high velocities ( km s 1 ) along the jet axis appear. As in the example above the ratios of pattern to fluid speed are close to one here but posses a certain variation. In the head region, however, one can find in addition lower velocities with strongly differing ratios. The values for ζ range from nearly zero up to 4. Owing to lack of emission in the wings of the bow shock far away from the jet apex, a low velocity component is not observed in the H S(1) line. To demonstrate the motion within the bow shocks of our numerical models, we displayed this region in a reference frame moving with the jet. Fig. 13 reveals the relative pattern velocities near the apex of model 3D-4. The average pattern speed of the jet has been subtracted. The knots posses the tendency to accelerate progressively away from the leading edge back towards the source. However, the flow pattern is more intricate, e.g. in a few cases motions towards the apex occur. These infrared models closely resemble the properties that are observed in the optical (Eislöffel et al. 1994). 5. Conclusions We have studied outflows driven by highly-variable Hammer Jets and compared them to relatively uniform jet-driven outflows. We have presented a range of observable infrared and submillimetre properties. Many results for uniform jets remain valid for Hammer Jets (e.g. CO line profile structures and the Hubble-type expansion law). Major new predictions, however, are as follows. Jet results. Long strings of knots, visible as CO bullets and H 2 knots, are generated in highly-variable jets. Continuous H 2 jets are not produced. H 2 bow shocks are produced when a velocity shear is present. The CO bullets can be identified spectroscopically on position-velocity diagrams. Bipolar Lobes. Hammer jets generate more complex filamentary infrared lobe structures. CO images are dominated by wider, tubular structures at low velocities. H 2 line profiles are often twin-peaked in the lobe, whereas for uniform jets twin-peaked profiles are located only immediately behind the bow apex. Proper Motions. We have presented detailed simulations of proper motions. Although done specifically for the H 2 infrared emission knots, the flow directions in the bows resemble the patterns produced in the optical studies (Eislöffel & Mundt 1992): some acceleration away from the head plus a turbulent component. The proper motions are very high in the jet, with the ratio of pattern to fluid speed close to unity. This model unites the bullet and jet driven scenarios. Smooth jets may well drive the HH 211 outflow, where no H 2 jet has been detected. In contrast, HH 111, with a long string of jet bows, would be hammer type. This does not imply that HH 111 possesses high-amplitude velocity variations in the visible jet jet shocks weaken rapidly with distance. The weakening is amply demonstrated in Fig. 9. Tubular CO structures, remarkably like those presented in Fig. 7, have been recently discovered in HH 111 (Nagar et al. 1997) and HH 211 (Guilloteau et al. 1997). The CO bullets in HH 111, are, however, found on a larger scale than the H 2 jet bows. This could imply that the most massive knots are formed downstream, perhaps involving the gradual accumulation of smaller bullets. Prominent gaps between the inner knots and the driving source are found on the infrared H 2 images of HH 111 and HH 212. In the present model 3D-5, we have uncovered striking gaps. Fig. 15 displays the outflow at a time of 414 years, towards the end of a low period in the jet power. This gap has disappeared 50 years later, as displayed in Fig. 4. This is an alternative interpretation for the gaps; high extinction of the inner infrared jets due to a dense core around the protostar is expected. Proper motion studies in the near infrared are now just possible (Noriega-Crespo et al. 1997, see also Table 1). High speeds directed roughly along the jet axis are indeed being found in the jets. Proper motions traced by atomic line emission, however, lead to pattern/fluid speed ratios which are often well under unity and variable along the jet axis (Eislöffel & Mundt 1992, 1995). We predict that dense molecular/atomic jets will have pattern/fluid speed ratios near unity. Light pressure-confined jets, in contrast, are susceptible to the Kelvin-Helmholtz instability and modes can grow locally rather than being rapidly advected. High resolution infrared spectroscopy along jets and within bow shocks should begin to reveal new features. The high-speed jet should be detected just where it impacts the bow region through the high-velocity bump in the 1-0 S(1) line profile (see Figs. 5 and 6). Masers in outflows probably correspond to shockcompressed layers, edge-on to the observer. Maser observations

11 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets 963 Fig. 13. Proper motions and fluid speeds in the bow shock of the 3D-4 simulation of the emission from the 1-0 S(1) H 2 line as seen in the XYplane. Fig D 4Bow Fig. 14. Proper motions and fluid speeds in the 3D-4 simulation of the emission from the 1-0 S(1) H 2 line, as seen in the XZ-plane. Fig. 15. The hydrocode simulation of a pulsating and outbursting jet, model 3D-5, demonstrates (at 414 years) a gap followed by complex knot structures. The infrared H S(1) emission is displayed. provide constraints on both proper motions and radial velocities (Gwinn, Moran & Reid 1992). Mac Low et al. (1994) tested the proposal that masers could be identified with density peaks within a jet-driven outflow. The simulated pattern speeds of the density peaks shown here in Fig. 11 are indeed strikingly similar to those observed for maser proper motions in the W49N outflow (Gwinn et al. 1992). This is the first direct comparison for the bullet model (since Mac Low et al. (1994) investigated the instantaneous velocities i.e. the fluid speeds, not the proper motions). On small scales, hypersonic turbulence is inferred from the observed maser properties (Gwinn 1994). Confirmation will

12 964 R. Völker et al.: Simulations of molecular outflows driven by Hammer jets require higher resolution simulations to resolve hypersonic jetdriven turbulence within the dense layers. Several problems listed in Tables 1 and 2 remain to be solved. We have made no detailed attempt to model the excitation of the hydrogen molecules or other molecular species. A physical description of supersonic turbulence in jets is still lacking although one means to generate it by fluid instabilities is there (e.g. Rossi et al. 1997; Stone et al. 1997; Downes & Ray 1998). The magnetic field has also been ignored. Ambipolar diffusion may be important in molecular jets, heating the gas even in uniform jets. Evolution in the spray angle and the jet velocity should be modeled since outflow ages and protostellar formation ages are comparable. Finally, we return to the initial goal: what can we now say about the protostar itself? First, the ejected material is consistent with a simple hydrodynamic flow: laminar and center-filled rather than shell-type. There is some evidence for moderate shear and spray being introduced, either at the source or during the propagation through the first cm. Small variations in the ejection direction are also consistent. The outburst time scale is given by the inter-knot spacing divided by the knots velocity. Outbursts must generate jet powers which vary by high factors. Jets with multiple time scales for the power variations (see model 3D-5) generate a fuller jet structure. These variations could arise from the thermal instabilities in accretion disks thought to be responsible for FU Ori objects (Bell & Lin 1994). Note, however, that we have here specifically modeled velocity variations, holding the density fixed. An accretion disk instability would probably lead to variations in both parameters. More work is necessary to specifically identify FUor outburst signatures with jet structures and thus to establish the inflow-outflow connection in the earliest protostars. Acknowledgements. We sincerely thank C. Davis, J. Eislöffel, M.-M. Mac Low and H. Zinnecker for helpful discussions. We also thank the DFG for financial support. The calculations were performed on CRAY computers at the LRZ München, at the HLRZ Jülich, and at the Rechenzentrum der Universität Würzburg. Appendix We here develop the basic relation between the propagation speed v s of the shock wave and the velocity v g of the deflected gas. For this purpose we assume an oblique shock that runs into a steady medium. Fig. A1 shows the shock propagating along the x-axis in a frame which is moving with the shock wave. The unshocked gas moves towards the shock front and is deflected away from the x-axis when it penetrates the discontinuity. On the surface of the shock front the jump conditions for the hydrodynamical variables have to be satisfied. In this case the mass flux ρv n through the shock front is continuous and the tangential component of the gas velocity v t is preserved. ρ 1 v 1 e n = ρ 2 v 2 e n, (A.1) v 1 e t = v 2 e t. (A.2) v = v - v 2 g s ρ 2 ρ 1 y e t φ e n shock wave v 1 = - v s Fig. A1. Oblique shock running into a steady medium Solving for the velocity component of the compressed gas, we obtain v x2 = v x1 [1 (1 β 2 ) sin 2 φ ], (A.3) v y2 = v x1 (1 β 2 ) sin φ cos φ, (A.4) where ρ2 β =. (A.5) ρ 1 In a stationary frame we have to take into account the motion of the shock wave. v x1 = v s, (A.6) v x2 = v xg v s, (A.7) v y2 = v yg. (A.8) This transformation allows us to derive an equation for the ratio ζ of the velocity of the shock wave v s and the velocity of the deflected gas v g. ζ = v s 1 = v g (1 β 2 ) sin φ. (A.9) Note that β is a function of the normal component of the Mach number of the inflowing gas. In strong shocks the deflected gas is so strongly compressed that β far exceeds unity. Thus, v s v g for vertical shock waves (φ =90 o ). For oblique shocks (φ <90 o ) the ratio ζ increases with decreasing φ. References André P., Ward-Thompspon D., Barsony M., 1993, ApJ 406, 122 Bachiller R., Martin-Pintado J., Plansas P., 1991, A&A 251, 639 Bachiller R., 1996, ARA&A 34, 111 Bally J., Devine D., 1994, ApJ 428, L65 Barral J.F., Cantó J., 1981, Rev.Mex. Astron. Astrofis. 5, 101 Bell K.R., Lin D.N.C., 1994, ApJ 427, 987 Bence S.J., Richer J.S., Padman R., 1996, MNRAS 279, 866 x

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