The Collisions of HVCs with a Magnetized Gaseous Disk

THE COLLISIONS OF HVCs WITH A MAGNETIZED GASEOUS GALACTIC DISK4 Alfredo Santillán1,2 , José Franco2 , Marco Martos 2 and Jongsoo Kim3 ABSTRACT We present two-dimensional MHD numerical simulations for the interaction of high-velocity clouds with both magnetic and non-magnetic Galactic thick gaseous disks. For the magnetic models, the initial magnetic field is oriented parallel to the disk, and we consider two different field topologies (with and without tension effects): parallel and perpendicular to the plane of motion of the clouds. The impinging clouds move in oblique trajectories and fall toward the central disk with different initial velocities. The B-field lines are distorted and compressed during the collision, increasing the field pressure and tension. This prevents the cloud material from penetrating into the disk, and can even transform a high-velocity inflow into an outflow, moving away from the disk. The perturbation creates a complex, turbulent, pattern of MHD waves that are able to traverse the disk of the Galaxy, and induce oscillations on both sides of the plane. Thus, the magnetic field efficiently transmits the perturbation over a large volume, but also acts like a shield that inhibits the mass exchange between the halo and the disk. For the non-magnetized cases, we also uncover some novel features: the evolution of the shocked layer generates a tail that oscillates, creating vorticity and turbulent flows along its trajectory. Subject headings: interstellar matter —magnetohydrodynamics — high-velocity clouds 1 Cómputo Aplicado–DGSCA, Universidad Nacional Autónoma de México, A. P. 70-264, 04510 México D.F., México; Electronic mail: alfredo@astroscu.unam.mx 2 Instituto de Astronomı́a, Universidad Nacional Autónoma de México, A. P. 70-264, 04510 México D.F., México; Electronic mail: pepe@astroscu.unam.mx, marco@astroscu.unam.mx 3 Korea Astronomy Observatory, San 36-1, Hwaam-Dong, Yusong-Ku, Taejon 305-348, Korea; Electronic mail: jskim@hanul.issa.re.kr 4 To appear in The Astrophysical Journal, the April 20, 1999 issue, Vol. 515 –2– 1. INTRODUCTION High velocity clouds (HVC) are atomic HI cloud complexes located at high galactic latitudes, and moving with large velocities (| VLSR |≥ 90 km/s) that do not match a simple model of circular rotation for our Galaxy (see Mirabel 1981a, Bajaja et al. 1985, and Wakker & van Woerden 1997). The present data indicates an excess of negative-velocity (infall) HVC over positive-velocity HVC, but the interpretation for their origin and evolution is unclear because their distances and tangential motions are unknown. Limits to the location of some particular clouds indicate z-heigths of a few kiloparsecs (a recent detection of highly ionized HVCs indicates even larger distances, but the relationship between ionized and neutral HVCs is unclear; Sembach et al. 1998), setting a possible mass range of 105 -106 M⊙ for some of these complexes. Thus, a HVC complex moving with a speed of 100 km s−1 has a kinetic energy of about 1052−53 erg. This range of values (equivalent to that from an OB association in the disk) indicate that the bulk motion of the HVC system, and its interaction with the galactic disk, could represent a rich source of energy and momentum for the interstellar medium (ISM). Observational signatures for the interactions of HVCs with galactic disks have been claimed in our Galaxy and in some external galaxies. The best known examples are in complexes AC and H, both located near the anticenter region (Mirabel 1981b; Mirabel & Morras 1990; Tamanaha 1997; Morras et al. 1998), in the direction of the Draco Nebula (Kalberla et al. 1984; Hirth et al. 1985; Herbstmeier et al. 1996), in M101 (van der Hulst & Sancisi 1988), and in NGC 4631 (Rand & Stone 1996). These observations support the idea that HVC-galaxy collisions can have a significant influence on the structure and energetics of the gaseous disk. Previous 2-D and 3-D numerical simulations for collisions with non − magnetic (or weakly magnetic) and thin disks (e. g. Tenorio-Tagle et al. 1986,1987; Franco et al. 1988; Comerón & Torra 1992; Lepine & Duvert 1994; Rand & Stone 1996), indicate that the resulting ISM structures have sizes of several hundreds of parsecs, similar to those ascribed to multi-supernova remnants, or superbubbles, from OB associations. The colliding HVCs can sweep a great amount of disk mass in these non-magnetic models. The resulting shocked layer collects both the disk mass and the mass from the HVC, inducing the formation of massive gas structures far from the midplane (Franco 1986; Alfaro et al. 1991; Cabrera-Caño et al. 1996). Moreover, the fastest moving clouds can even drill holes through the whole gaseous disk, venting gas into the other side of the disk. Thus, for these thin disk cases, an efficient mass exchange can result from the interaction of the HVC system with the disk. The HVC-disk interactions, however, can have a radically different outcome in a disk that is thicker and more magnetized than assumed by these previous works (see Cox 1990 and Franco et al. 1995). The transition between the main gaseous disk and the halo is very broad and complex, with an intricate magnetic field structure and a number of extended gas components, including dusty high-z layers and the so-called ionized Reynolds layer (Hoyle & Ellis 1963; Reynolds 1989). Using the available data at the Solar neighborhood, Boulares & Cox (1990; hereafter BC) have incorporated the distended gas components, along with the vertical gradient of the magnetic –3– field, in a model for the thick disk of the Galaxy. They found that a time averaged hydrostatic support of the disk requires scaleheights of about 1 kpc for both the ionized Reynolds layer and the magnetic and cosmic ray pressures. These extended gas layers are not unique to our Galaxy, and recent observations indicate that they are probably common in spirals. Examples of diffuse ionized gas in external galaxies, that seem to be analogous to the Reynolds layer in our Galaxy, are the prominent Hα diffuse halos in NGC 891 and NGC 5775, and to a lesser extent in NGC 4302 (Rand 1995). In particular, NGC 891 reveals Hα emission extending up to 3 kpc above the midplane (Rand, Kulkarni & Hester 1990), along with other extraplanar structures such as worms (Dettmar 1990) and dusty filaments (Howk & Savage 1997). Also, the magnetic fields in edge-on galaxies can be traced for several kpcs above the disk (Hummel & Beck 1995), and dusty filaments extending for more than 2 kpc above the plane of the host galaxy have been observed in NGC 253 and NGC 7331 (Sofue 1987). Some of these features are expected from the action of radiation pressure on dusty HI clouds (Franco et al. 1991), and from the spiral density wave (Martos & Cox 1998). Regardless of some poorly known ISM parameters (such as the distribution and filling factor of the hot gas), the existence of extended gas layers (neutral or ionized) might have far reaching consequences for the structure and overall stability of the gaseous disk. Any given parcel of gas located above the scaleheight of the thin disk weighs more than the same material placed within this disk. The inclusion of an extended gas layer, then, results in a disk model with a total interstellar pressure that is higher than the previously assumed thin disk values (this is in line with recent UV studies that indicate that the thermal pressure near the Sun can be a factor of 8 higher than previous estimates; Berghöfer et al. 1998). The non-thermal pressure gradients at high latitudes, along with the tension of magnetic lines, must play a crucial role in the overall support of these extended disk structures (BC; Zweibel 1995). The presence of a thick magnetic disk, then, should drastically alter the results obtained with purely hydrodynamic models, or models in which the gradients are concentrated in a thin disk with a scaleheight of about 150 pc. In this paper, we present two dimensional simulations of HVCs colliding with a thick disk, including both the purely hydrodynamic and the ideal magnetohydrodynamic regimes. Magnetized models are built from an isothermal gas distribution, in which magnetic support at high z-locations is crucial for the initial equilibrium state. The models have the field lines parallel to the galactic disk, but we consider two different line orientations: field lines lying in the plane of motion of the HVC, and field lines that are normal to this plane. The results with these orientations, along with those of the purely hydrodynamic cases, allow us to isolate the effects of field tension: for lines lying in the plane of motion, magnetic tension reverses the motion of HVC material and creates an outflow at late times. For the case when the field lines are perpendicular to the plane of motion, which have no tension effects, the magnetic pressure prevents the cloud material from reaching deep into the disk. Thus, in either case, the magnetic field does not allow any mass exchange with the halo. In contrast, the non-magnetic cases (which demand a hot halo for the initial equilibrium) evolve without resistance and allow mass mixing. The results for these –4– non-magnetic models confirm previous results, but some new features are uncovered here. Also, the resulting gas structures are now modified by the thicker and more pressurized nature of our models. The evolution of impinging HVCs, with a range of approaching angles and velocities, is followed with the MHD code ZEUS 3-D. The thick disk models are described in the next section. Section 3 deals with the numerical treatment of the problem. Section 4 presents our results, which are summarized and discussed in Section 5. 2. Magnetized Disk Models The magnetic disk model is plane-parallel. Two forms of pressure, thermal and magnetic, provide the support of the initial magnetohydrostatic equilibrium state against the gravitational field provided by the disk stars. Our model does not include cosmic-ray pressure. The density and gravitational acceleration functions are given by: − ρ(z) = ρ0 [0.6e z2 2(70pc)2 |z| − 400pc +0.1e − + 0.3e z2 2(135pc)2 |z| − 900pc + 0.03e and |z| − + 0.07e z2 2(135pc)2 (1) ] cm−3 |z| g(z) = 8 × 10−9 (1 − .52e− 325pc − .48e− 900pc ) cm s−2 , (2) where the midplane gas density is ρ0 = 2.24 × 10−24 g cm−3 . This density distribution adequately describes the observed gas z-structure in the solar vecinity, as discussed by BC. The functional form for the gravitational acceleration g is taken from Martos (1993), and provides a good fit to the data of Bienaymé, Robin & Crézé (1987). R The total pressure is given by p(z) = − zzext ρg dz, with the boundary condition p(zext =5 kpc)=0, and is numerically solved and set equal to the sum of the thermal, pt = n(z)kTef f , and magnetic, pb = B 2 (z)/8π, terms. The midplane values are taken from BC: total pressure p(0) = 2.7 × 10−12 dyn cm−2 (this is 20% higher than the thermal pressure value derived by Berghöfer et al. 1998), a magnetic field strength of B(0) = 5 µG, and an effective disk temperature of Tef f (0) = 10900 K. For simplicity, the magnetic model we adopt, which may be called a “warm” magnetic disk model, is defined by Tef f (z) = Tef f (0) (independent of z). Thus, the implicit sound speed of this warm model is similar to the observed velocity dispersion of the main HI cloud component, ∼ 8 km s−1 . The total magnetic field intensity at midplane adopted in this model includes contributions of the orderly (with a strength of ∼ 2 µG) and the dominant random component values (see Heiles 1996). This results in a moderate field value for a spiral galaxy, 5 µG, because an average total field strength of 19 µG has been derived for the disk of NGC 2276 (Hummel & Beck 1995). We assume magnetic field lines that are parallel to the midplane, as indicated by data near the plane (see Valleé 1997), in our initial magnetohydrostatic states. In the 2-D MHD regime, the adopted warm disk model is Parker unstable (Martos & Cox 1994) and, from a linear stability analysis for the undular mode, we have found that the minimum –5– growth time and the corresponding wavelength are 60 Myr and 3 kpc, respectively (Kim et al. 1999). The 2-D models indicate that the density enhancements become clearly apparent on timescales of the order of 100 Myr (Franco et al. 1995; Santillán et al. 1999). The instability can be triggered by a HVC collision (see Franco et al. 1995), but the HVC-disk interaction evolves in shorter timescales (the clouds are completely shocked in only a few Myr). Thus, given that the timescales for the two events are very different, here we do not discuss the appearance of the Parker instability, and a more complete description of the instability in a thick disk (i. e. the linear analyses and the nonlinear evolution) will be reported elsewhere (Kim et al. 1999; Santillán et al. 1999). These magnetic models reflect conditions in which the total pressure decreases more slowly than the density as z increases. At high z, the models mimic the expected dominance of non-thermal forms of pressure, and the effective signal speed is high. As a consequence, the compressibility of the plasma is effectively controlled by the magnetic term, and the medium is ”stiff“ and elastic (Martos & Cox 1998). The thermodynamic regime of the runs, isothermal or adiabatic, can only alter that character to a certain extent, but the assumed magnetic field geometry will certainly affect the response to any interaction (further details of the properties of this thick, magnetic model can be found in Martos 1993 and Martos & Cox 1994). The distinction between models with field lines in the plane of motion and perpendicular to the plane of motion, then, corresponds to whether the magnetic tension influences the dynamical evolution or not, respectively. Both types of magnetized models are inititated in equilibrium and with the same z-distribution for the total pressure. The total pressure distribution is shown in Figure 1a. The corresponding z-variations for the Alfvén and maximum magnetosonic (the quadratic sum of the Alfvén and sound velocities) wave speeds are shown in Figure 1b. The magnetosonic speed is the effective signal speed for compressional waves, and has a rapid increase inside the disk but varies slowly, from 50 to 60 km s−1 , in a wide z interval from 500 to 1500 pc. For completness, we have considered an additional third model representing a non-magnetic thick disk. This model maintains the same total pressure as in the previous magnetic models. Hence, hydrostatic equilibrium determines the temperature structure along the z-axis, R T (z) = zzext ρg dz/kn(z), with the density and gravity distributions described above. The resulting temperature and sound speed distributions are shown in Figure 1c. 3. Numerical Method The simulations are performed with the MHD code ZEUS-3D (version 4.2), which solves the three dimensional system of ideal MHD equations by finite differences on an Eulerian mesh (for a description of the code, see Stone & Norman 1992a, 1992b). The code can perform simulations in 3D but, due to computational restrictions, here we restrict the discussion only to two dimensional simulations. The effects of self-gravity and differential rotation of the Galaxy are not included in the present version. The role of self-gravity is not important at the densities considered here, but –6– the effects due to the shear of the galactic disk may be important during the evolution. When differential rotation is included, there are at least two effects that may prove to be significant for the HVC-disk collisions: first, the shear can cause distortions in the resulting gaseous structures (e. g. Olano 1982; Palǒus, Franco & Tenorio-Tagle 1990) and, second, it can trigger the appeareance of magneto-rotational instabilities (e. g. Chandrasekar 1960; Balbus & Hawley 1991; Foglizzo & Tagger 1994). In particular, the combined effects of the Parker and the magneto-rotational instabilities may lead to interesting results (Foglizzo & Tagger 1994). These instabilities have different dynamical effects on the plasma and magnetic field lines. The Parker instability distort the magnetic lines, generating a vertical component from an originally horizontal field and redistributing the gas in the disk. The magneto-rotational process stretches the field lines radially and generates internal torques, driving radial gas flows. Depending on the initial state, the instabilities may interfere constructively, with the vertical field lines from the Parker mechanism feeding back onto the magneto-rotational mechanism. In other cases, however, both processes operate in a stabilizing manner (Foglizzo & Tagger 1994). These issues are important and require detailed three dimensional studies with differential rotation that, unfortunately, are beyond our present capabilities. The 2-D results of the present paper cannot include the galactic shear, and the 2D computational domain lies in the plane defined by the azimuthal and vertical directions of the Galaxy. Our frame of reference is one in which the Galactic gas is at rest, and the origin of our 2D Cartesian grid is the local neighborhood. The coordinates (x, z) represent distances along and perpendicular to the midplane, respectively. The x-axis is anchored at a constant galactocentric radius (i. e. is quasi-azimuthal, defined by the tangent of the local field orientation in our Galaxy; see Heiles 1994 and Valleé 1997), and the motion of the HVC is always considered in the (x, z) plane. Two different setups for the magnetic field are considered: B parallel to the x-axis, in the plane of motion of the HVC, and B parallel to the y-axis, perpendicular to the plane of motion (and no deformation of the field is introduced by the dynamics of the gas). The y-direction is also defined in the midplane, but it would correspond to the galactocentric radial vector direction. For an efficient use of computer resources, we mostly worked with moderate resolutions of 200×200 zones, but verified that the results were not different from those obtained in runs with resolutions of 400×400 zones. We performed runs with a variety of different sizes but, for simplicity, the physical intervals of the simulations presented here are 3 kpc × 3 kpc (the z-axis runs from -1.5 kpc to 1.5 kpc). Thus, one zone has an extent of 15 pc per dimension, or better, with our linear zoning scaling. The boundary conditions are cyclic (periodic) in x, and free outflow in z. The evolution was computed in both the isothermal (γ = 1.01) and adiabatic (γ = 1.67) regimes, since explicit cooling or heating functions are not included in our numerical scheme. For simplicity, all infalling clouds were given the same dimensions, 210 × 105 pc (longer in the x direction), and they are threaded by the magnetic field strength corresponding to their initial –7– locations. We performed some runs with other cloud sizes but, except for the sizes of the initial pertubations, the results are similar to the ones described here. Since the evolution is followed on the x − z plane, and we have set the initial density of the clouds to n=1 cm−3 , the mass and energy densities of the models were 5.0 × 10−25 g cm−3 and 2.5 × 10−11 erg cm−3 (this would correspond 2 to a cloud mass and kinetic energy of 3.5 × 105 M⊙ and 3.5 × 1052 v100 erg, respectively, where −1 v100 is the cloud velocity in units of 100 km s , if we set the third dimension to the quadratic mean of the other two). We positioned the cloud centers at several selected heights, from 350 pc to 4050 pc, and made a series of runs with different incoming velocities and incident angles. The velocity range spanned was from 0 to 200 km s−1 (i. e. from free-fall to nearly the largest observed approaching velocity), and the angles were varied from 0◦ to 60◦ with the vertical (z) axis. Regardless of the initial position of the cloud, the entire cloud is shocked in less than 3 Myr. The evolution of the interaction is fast and takes place in a relatively small region (with dimensions of several dozens of cell sizes). Thus, the details of the early shock structure (which depend on the initial cloud conditions) are not resolved in our simulations (the interested reader can find a detailed discussion of high resolution simulations for cloud collisions in Klein & McKee 1994 and Mac Low et al. 1994), and we focus here only in the larger scale outcome of the impact (i. e. in structures of the order of a hundred pc or larger). A summary of the runs presented in this paper is given in Table 1. 4. 4.1. Results Non–magnetic thick disk As stated before, previously published calculations of HVC impacts have been performed with a thin Galactic disk model, and most of them are perpendicular collisions in the purely hydrodynamic regime. We start by comparing them with our results obtained with the non-magnetic disk model described above. This non-magnetic model requires a hotter halo and the thermal sound speed increases rapidly inside the main disk (see Figure 1c). Loosely speaking, the basic structures formed by the collisions are similar to those described in previous modeling. For instance, as found in earlier works, the sizes and shapes of the shocked layers in the disk resemble some of the HI supershells observed by Heiles (1984) in our Galaxy. There are, however, some clear differences with previous results, and they are mainly due to our more extended gas distributions (i. e. the structures formed at high z-locations are denser, better defined, and last longer than in the thin disk cases). Also, the resulting rear wakes are now completely formed and their morphologies and vorticities are clearly apparent. In particular, here we see one conspicuous structure, the tail, that has been either missed or disregarded in former studies (this is likey due to the fact that most previous models have located the HVC much closer to the midplane). The importance of this feature is better appreciated in (magnetic –8– and non-magnetic) oblique impacts, and may be one of the possible sources of turbulence in the Reynolds’ layer (see Benjamin 1998 and Tufte et al. 1998). 4.1.1. HVC with VHV C = 200 km s−1 , and θ = 0◦ Our first example is a purely hydrodynamic simulation of a collision perpendicular to the disk (impact angle θ = 0◦ ). The evolution is shown in the four snapshots displayed in Figure 2. The simulation is performed in the isothermal mode and the HVC center position is located at 1250 pc from midplane, with an initial velocity of 200 km s−1 . In all the following figures, the density is shown in logarithmic grayscale plots and the velocity field is indicated by arrows sized proportionally to the local speed. The first two snapshots show the initial conditions and the shock evolution at 3.2 Myr, respectively. The impact creates a strong galactic shock directed downwards, and a reverse shock that penetrates into the cloud. The galactic shock tends to move radially away from the location of impact, but momentum conservation keeps it strongest in the direction of motion of the impinging cloud. The lateral components of the shock, then, are milder and become a sonic perturbation in relatively short timescales (see Tenorio-Tagle et al. 1986 and Franco et al. 1988). The cloud has been completely shocked at the time of the second snapshot, and the lateral shocks have already disappeared. The cloud mass is locked in the shocked layer and, due to its supersonic motion, a vacuum is formed behind the layer. This rear vacuum begins to be filled up by material falling from higher locations, as well as from gas re-expanding from the shocked layer. This creates a pair of vortices, one at each side of the layer, and a plume, or tail, is formed at the central part of the rear wake. This is clearly seen in the third snapshot, at 9.5 Myr. At this time, the shocked layer is already collecting gas from the denser parts of the disk. The shock front decelerates as it penetrates into the disk, and reaches the midplane at about 13 Myr. After crossing the midplane, the shock accelerates in the decreasing density gradient, and blows out into the other side of the halo. The beginning of the blow out process is apparent in the last snapshot, at 19 Myr. The swirling motions of the rear wake, and the large extent (about 1 kpc) and shape of the shocked layer inside the disk are clearly displayed in this frame. A large fraction of the original cloud mass remains locked up in the shocked layer, and a small amount of it has re-expanded back into the rear wake and tail. In turn, the tail has expanded sideways and it has a density minimum at the central part. This minimum is promoted by the acceleration of the shock front after crossing the midplane. The size of the perturbed region has grown close to 2 kpc in this last snapshot. 4.1.2. HVC with VHV C = 200 km s−1 , and θ = 30◦ Figure 3 shows the hydrodynamical evolution for an oblique collision at θ = 30◦ . Again, the original cloud is located at 1250 pc from midplane, with 200 km s−1 , and the run is performed –9– in the isothermal mode. Now the cloud momentum has an important lateral component, which is conserved during the evolution because the gravitational force has only a z-component. The first two frames show the evolution of the shocked layer at 3.2 and 6.3 Myr, respectively. The initial cloud is again completely shocked in a relatively short timescale, before the first frame, and the vacuum left by the cloud motion is filled up by infalling material and by re-expansion of the shocked layer. The shapes of the interstellar structures are modified by the lateral velocity component, but the main features of the hydrodynamical evolution are similar to the ones described in the previous case. The motion of the shocked layer creates the rear wake (with vorticity and swirling motions), and a tail that extends downstream to locations close to the point of impact. The tail is now denser and more conspicuous than in the previous case, and it has the appeareance of an elongated finger or cometary tail. There is a visible shock in the second frame (at 6.3 Myr), when the central tail is forming. The slower downward speeds, and the inclination of the structure, allows for the gas of the tail to catch up with the main body of the shocked layer. The velocity vectors within the structure are now larger, and clearly show the re-expansion into the rarefied regions. The shear between this faster flow and its surrounding medium is subject to Kelvin-Helmholtz instabilities (e. g. Shore 1992), but we cannot resolve the instability here. The oscillatory motion of the finger-like tail, is due to the combined effects of the vorticity of the rear flow and the unresolved instability. The prominence of this tail structure increases with both increasing HVC velocities and larger collision angles. The main shock crosses the midplane at about 13 Myr, and accelerates afterwards. As in the previous case, a density minimum is generated behind the accelerated layer. Given that the acceleration is promoted by the density gradient, is then directed along the z-axis and creates an elongation of the structure in this direction. This is clearly apparent in the third frame, at 22.2 Myr. Again, the shock front begins to blow out of the disk at about these times. The tail has also re-expanded at this time, and its vorticity and oscillations have created a chaotic velocity field along the trajectory of the interaction. The late times evolution displays a wealth of features, illustrated in the last snapshot at 47.7 Myr (to provide a better perspective, the midplane is now located in the middle of the frame). The central parts of the disk are distorted and compressed, with complex structures extending towards the impact zone. The disk scaleheight is altered on both sides of the plane, and the interphase between the upper and lower disk layers is marked but wavy, as in a water-air interphase. At the incoming side, there are rounded tongues, and some elongated structures breaking out from the disk, accompanied by a pair of vortices above. At the other side, the blow out expansion is clearly apparent and the front is reaching the lower edge of the grid. – 10 – 4.2. Magnetic disk with B parallel to the x-axis: the role of tension The rigidity and elasticity given to the disk by the magnetic field is better accentuated in 2D when the plane of motion of the HVC is parallel to the field lines, and the colliding gas distorts the initial field configuration. We illustrate the response of these deformed field lines with three representative cases. In these cases, the tension of the magnetic field dominates the evolution, and the results are completely different from those of the purely hydrodynamic cases. For the figures of these magnetic cases, where the densities and velocities are indicated as before, the B-field lines are now displayed with continuous lines. 4.2.1. HVC with VHV C = 200 km s−1 , and θ = 0◦ The first MHD simulation is illustrated in Figure 4. It corresponds to a collision perpendicular to the disk with cloud parameters identical to those of Figure 2 (cloud located at 1250 pc, with velocity 200 km s−1 and impact angle θ = 0◦ ), except that the simulation is now performed in the adiabatic mode. The initial shock is strong and has a magnetic Mach number close to 4, with a compression factor approaching 3 (a very strong shock has a compression factor of 4, as in the non-magnetic case). With these parameters, there are thermal shocks on both sides of the main shock front at the early evolutionary stages. The lateral and downward shocks, however, disappear in relatively short timescales, and the MHD waves begin to move ahead of the shocked layer. The first snapshot shows the expansion at t = 3.2 Myr after impact. A series of MHD waves are already driven in all directions, creating compressions and a round shell-like structure (the “bubble”) ahead of the shocked layer. The lateral disturbances are Alfvén waves moving along the field lines, and the disturbances in the z-direction are magnetosonic waves that compress the field lines. The initial shock fronts (in either direction) move faster than any of these waves, and are responsible for the strong deformation of the initial field configuration but, as stated before, the key parameter determining the outcome of this interaction is the downward distorsion of the magnetic field. During the first 7 Myr, a substantial fraction of the energy goes into the compression and tension of the distorted field lines (the second frame shows the evolution at 6.3 Myr). Also, the disk material that is inside (and above) the distorted sections slides down along the field lines, like in an inclined plane, and settles down at the location of the magnetic valleys. Thus, the distortions disrupt the local hydrostatic equilibrium, and there is a clear infall of material in the perturbed region. This creates a dense “head” of the perturbation moving towards the disk. The fast magnetosonic wave, moving in the upper disk layers at an average speed of 50 km s−1 , creates a strong perturbation as it enters into the denser parts of the disk (it becomes a very mild magnetic shock, that is apparent in the third frame, with a magnetic Mach number always close to unity) and crosses the midplane at t ∼ 12 Myr. At about 8 Myr, the energy stored in the magnetic field begins to be released as the field lines rebound, reversing the motion of the gas and – 11 – lifting the dense head (that has already penetrated a few hundred pc into the lower layers) back to the upper parts of the disk. Thus, as seen in the third and forth frames (9.5 and 15.9 Myr, respectively), a high-velocity outflow moving away from the disk is created. This is a novel result in which an incoming flow is forced to become an outflow by magnetic tension. At about 13 Myr, and later on, the compressional and Alfvén waves carry most of the available energy. The magnetosonic waves are able to perturb the other side of the halo, and the Alfvén waves continue to drive the expanding structure and create gas infall outside the location of the bubble. Thus, the resulting structure is characterized by rising motions inside the bubble (from the tensil restoring motion) and by lateral infall outside it. Figure 5 shows a run with the same initial parameters of the previous model, but now the evolution is isothermal. In this case, as expected, the shocked gas piles up in a thin dense shocked layer that carries the momentum of the cloud. Thus, now the compression and distortion of the field lines is more pronounced in the zones where the momentum of the dense shocked layer is concentrated, but the main evolutionary features are similar to the ones described in the previous case. The evolutionary times shown in Figure 5 are identical to those shown in Figure 4 (3.2, 6.3, 9.5, and 15.9 Myr). Comparison with Figure 4 illustrates that the deformation of the field lines is now more acute, leading to a sharp V-shaped form (almost a discontinuity) at 6.3 Myr. A thin, dense, vertical structure is formed from the material that slides down along the distorted field lines. The compressional wave also becomes a weak MHD shock as it enters into the disk, and the lateral expansions, driven by Alfvén waves, are similar to the ones described in the previous case (outflows in the central zones, and inflows in the external regions). Except for differences in details and timescales, cases initiated at other z locations and with different velocities behave in similar ways as the ones described in Figures 4 and 5: the field prevents the penetration of the cloud material into the disk and creates a net outflow at the late times evolution. For instance, an isothermal case started at z = 350 pc and with a speed of 100 km s−1 encounters a rapid tensional rebound at about t = 6 Myr. 4.2.2. HVC with VHV C = 200 km s−1 , and θ = 30◦ The oblique magnetic case is illustrated in Figure 6 by an isothermal collision with θ = 30◦ and 200 km s−1 , as in Figure 3. The galactic shock has an important lateral component, producing a strong compression in the x-direction, as seen in the first and second frames (3.2 and 6.3 Myr, respectively). Once again, the magnetic field rebounds but the lines tend to recover their original configuration in shorter timescales than in the perpendicular cases. The motion of the shocked layer is again reversed as the lines rebound (third frame at 15.9 Myr), and a series of prominent disk oscillations and MHD waves are apparent during most of the evolution. The horizontal component of the flow is maintained for a longer time (for instance, it has a velocity of 47 km s−1 at 20 Myr), and the patterns of the velocity fields and magnetic field distortions are completely – 12 – different to those of the perpendicular cases. As before, the Alfvén waves detach from the shocked layer, and create a region with infalling gas that surrounds the shocked structure. The magnetosonic waves also traverse the disk (becoming a weak MHD shock), and perturb the other side of the halo. The tail is again formed behind the shocked layer but the magnetic field now constraints the flows and quenches the vorticity. The dense head moves almost parallel to the plane after rebound. This creates a magnetic shear flow but the tension of the lines prevents the appeareance of Kelvin-Helmholtz instabilities (e. g. Frank et al. 1996; Malagoli et al. 1996; Jones et al. 1997). The asymmetries in the distorted lines produce two important effects in the tail. First, the downstream (right) field distortion has a larger extent, with a softer slope, than the one created upstream (left). Thus, there is more mass sliding down towards the tail from the downstream side. This provides additional momentum to the tail, and creates a large rarified region behind it, that is maintained for a long timescale (up to the end of the run). Second, the gas that slides down from the upstream side provides an effective (ram pressure) force that opposes to the motion of the tail. This is a Rayleigh-Taylor unstable situation (e. g. Shore 1992) but, as in the case of the Kelvin-Helmholtz instabilities, we cannot resolve the instability. The undular shape of the tail is long lived and is due to the unresolved instability. It is still present at the fourth frame, at 41.2 Myr (also note that the shape of the field lines are already distorted due to the Parker instability). In summary, a complex network of asymmetrical features is created, but the distorted tail moving almost parallel to the field lines is the most prominent structure of the run. Runs with other approaching angles and velocities generate the same type of features, but with logical differences. As the incident angle is increased, the asymmetries are increased: the lateral component of the velocity is increased and the downward penetration is reduced, but the lateral effects become more pronounced. The amplitude of the maximum distortion in the field lines is reduced accordingly, and line rebouncing occurs at earlier evolutionary times. For angles larger than θ ∼ 60◦ , the flow becomes almost parallel to the x-direction. Nonetheless, the lines oscillate due to the collision and the oscillations transmit MHD waves in all directions, creating perturbations that are weaker but similar to those described before. 4.3. Cases with B perpendicular to the x − z plane: the absence of tension In theses cases, the magnetic field lines are oriented along the y-axis (pointing outside of the figures). The lines preserve their straight alignment in the y direction as their footpoints are dragged along, in the x − z plane, by the flow motions. Thus, the lines are not distorted and there are no Alfvén waves in these case. Also, there are no tension effects, but the effects of magnetic pressure and field compression are certainly present. Thus, the cloud gas can travel longer paths and penetrate deeper into the disk. Also, the total pressure provides a very effective drag that slows down the flow faster than in the purely hydrodynamical case, and distorts the morphology – 13 – of the shocked layer. The evolution of these runs is intermediate to the previous non-magnetic and magnetic-with-tension cases. 4.3.1. HVC with VHV C = 200 km s−1 , and θ = 0◦ Figure 7 shows a model with the same cloud parameters as those of Figures 2 and 5 (isothermal evolution with 200 km s−1 directed along the z-axis, and the HVC is located at 1250 pc). The early times evolution resembles the one of the purely hydrodynamical case described in section 4.1.1. The shocked layer collects the gas and aquires a bow-shock form. The vacuum left behind the shocked layer creates a swirling gas inflow, and a pair of vortices are apparent behind the shocked layer during most of the simulation. As before, a tail moving behind the shocked layer is created, and the differences with the non-magnetic case begin to be apparent when the decelerating shocked layer reaches the velocity of the effective signal speed (at about 2 Myr). After this moment, the precursor compressional perturbation begins to move ahead of the shocked layer (it is already apparent, and located some 100 pc ahead of the shocked layer, in the first frame at 3.2 Myr). As in the previous magnetic cases, the layer and its precursor wave sink into the disk (second frame at 6.3 Myr), and the precursor magnetosonic wave becomes a new magnetic shock wave that creates a second shocked layer. Due to the lack of tension, the new MHD shock in this case is stronger than in the previous magnetic cases (with a magnetic Mach number ranging increasing from 1 to almost 3, as it penetrates into the central regions). The resulting new shocked layer collects only disk material, and is clearly present in the third frame at 9.5 Myr. This shocked disk layer is the one that actually penetrates into the central parts of the disk, and excites the excites the magnetosonic perturbation that goes into the other side of the halo (last frame at 19 Myr). The final fate of the first shocked layer, on the other hand, which is the one that contains the gas from the impinging cloud, is controlled by the magnetic pressure. The gas is forced to re-expand by the compressed magnetic lines that have had accumulated in the space between the two shocked layers, and it goes back to high z-locations. Again, then, the cloud material cannot penetrate into the disk. 4.3.2. HVC with VHV C = 200 km s−1 , and θ = 30◦ Figure 8 shows a model with θ = 30◦ and the same parameters as in Figures 4 and 6. The evolution follows the same basic features that were described in these previous models: a wake with swirling motions and a tail are created behind the shocked layer, and a second shock front appears when the compressional wave begins to penetrate the denser parts of the disk (first and second frames at 3.2 and 9.5 Myr, respectively). Again, the structure and evolution of the tail plays an important role in the evolution. The gas of the tail catches up with the main body of the shocked layer, and a prominent and elongated, finger-like, flow structure is created. As in – 14 – the previous non-magnetic case of Figure 4, the flow is subject to Kelvin-Helmholtz instabilities, and the oscillatory motion of the structure (clearly apparent in the third frame at 19 Myr) is due to vorticity and the unresolved instability. Similarly, the prominence of the finger-like structure increases with both increasing approaching velocities and larger collision angles. In the case of the second shocked layer, there is one important difference with respect to the previous perpendicular case: the two shocked layers are not aligned. The snapshot at 19 Myr shows that the new shock is directed along the z-axis. This is due to the fact that the density gradient is directed along this same axis. Thus, the second shocked layer moves perpendicular to the plane of the disk, and the relative orientation between the two layers is sensitive to the approaching angle of the cloud. The strength of this second shock increases with increasing cloud velocities, but decreases with increasing collision angles. Again, as in all previous magnetic cases, the cloud material is unable to penetrate into the disk. The late times evolution of the tail is almost identical to the one of the non-magnetic case in Figure 3. The rounded (almost circular) tongues and vortices extending along the trajectory toward the impact region (last frame at 41.2 Myr), are long lived (up to the end of the run). 5. Discussion and Conclusions We have presented simulations of HVCs collisions, at different incidence angles and velocities, with magnetic and non-magnetic models of the Galactic thick disk. In general terms, the structures formed in the non-magnetic cases are similar to those discussed in previous studies, but some novel features are uncovered here: the motion of the shocked layer creates a rear wake, with vorticity, and a conspicuous tail. In oblique collisions, the tail becomes more prominent and aquires an oscillatory motion that leads to a highly chaotic, turbulent, velocity field along the trajectory of the interaction. Also, in contrast with thin disk results, where the perturbed region has dimensions similar to those of the original HVC, the resulting structures are larger and better delineated. The response of a magnetized thick disk, on the other hand, reveals new aspects of the interaction. Such a disk, with a strong magnetic support at high-z, also has important consequences for processes such as SN and superbubble evolution (e. g. Slavin & Cox 1993; Tomisaka 1994, 1998). In contrast with non-magnetic HVC-disk interactions, the cloud now encounters substantial resistance through its evolution in the halo and cannot merge with the gaseous disk. The results with a magnetic field indicate that the perturbed volume is certainly much larger than that of the non-magnetic counterparts. Moreover, if the disk is Parker unstable, as it is the case of our warm magnetic model, the collisions are able to excite different oscillation modes in the disk and the halo, and do trigger the Parker instability (see Franco et al. 1995 and Santillán et al. 1998). With a B-field in the x-direction, the MHD waves propagate in all directions but any gas flow towards the disk is drastically quenched. The tension effectively stops – 15 – the shocked gas, and reverses the motion of the flow, preventing any penetration of the original HVC mass into the disk and creating gas motions, with velocities in the range of 40 to 60 km s−1 , away from the disk. Thus, at least for this restricted field geometry, the magnetic field represents an effective shield that prevents any direct mass exchange between the halo and the disk. For a B-field perpendicular to the plane of motion, the strength of the shock also decreases rapidly but the compressional waves now have a more direct effect on the central disk. The results for this field topology, which has magnetic pressure but behaves in a tensionless manner, are intermediate to the non-magnetic cases and the ones with magnetic tension. The shocked layer can move deeper into the disk, but the buildup of magnetic pressure in the compressed gas eventually stops the motion of the layer and forces its re-expansion. The compressional waves, however, are transformed into a new secondary shock front that penetrates into the disk. This creates a more complex double shocked layer structure that lasts over several million of years. The interaction of the new shock front with the inner disk layers alters visibly the structure of the disk at large scales. Here again, however, the cloud material cannot penetrate very deep into the disk. The uniformity and symmetry of the disk and field modeled here are obvious idealizations. At high z, a likely vertical component of the field should modify the gas transport, and field line wandering would probably make the fluid more viscous than modeled here. Thus, one might suspect that our results would be altered in a 3D simulation. For instance, as suggested by the referee, the field lines in the disk would split apart and let the cloud to go through with much less resistance. Thus, our conclusions about bouncing clouds cannot be conclusive and this issue requires a 3D verification. Due to the stochastic nature of the Galactic magnetic field (Parker 1979), however, we anticipate that some aspects of the behavior found in the two magnetic field topologies considered here are bound to be present in more realistic 3-D cases. In particular, it is hard to imagine a situation in which a cloud would not have to fight magnetic tension from tangled and compressed field lines. Thus, at least in some cases, a thick disk containing a bulky bundle of tangled lines could act as an effective shield against material penetration into the innermost layers of the disk. Also, as stated before, the combined effects of the Parker and magneto-rotational instabilities require three dimensional studies with differential rotation. We are already making test runs with additional field morphologies and, also, 3-D cases with a moderate resolution. The results are encouraging, and a detailed analysis will be presented elsewhere (Martos et al. 1999). Summarizing, the magnetic field provides an adequate coupling for the energy and momentum exchange between the disk and the halo, but inhibits the mass exchange. The interactions can create strong MHD perturbations, with a turbulent network of flows and vertical gas structures. Thus, the interstellar B-field topology plays a paramount role in the final outcome of the interaction with colliding clouds, and further studies with a magnetized disk will shed more light on the origin and fate of the HVC system. We are grateful to Bruce Elemgreen, the referee, and Steve Shore, the editor, for useful comments and suggestions. We also thank M. Norman, M. MacLow and R. Fielder for continued – 16 – consultory on Zeus. JF acknowledges useful, and heated, discussions with Bob Benjamin and Bill Wall during the Interstellar Turbulence conference, in Puebla, Mexico. AS thanks Victor Godoy and Juan Lopez for their help with the visualization. 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Carramiñana, Cambridge: Cambridge University, in press van der Hulst, T. & Sancisi, R. 1988, AJ, 95, 1354 Valleé, J.P. 1997, in Fundamental of Cosmic Physics 19, 1. Wakker, B. P., & van Woerden, H. 1997, ARA&A, 35, 217. Zweibel, E.G. 1995, in The Physics of the Interstellar Medium and Intergalactic Medium, ASP Conference Series, Vol. 80, ed. Ferrara, McKee, Heiles & Shapiro, 524 This preprint was prepared with the AAS LATEX macros v4.0. – 20 – Table 1. Parameters of the 2-D and 2.5-D runs Case Evolution ~ B Direction vcloud (km s−1 ) θ (degrees) 1 2 3 4 5 6 7 Isothermal Isothermal Isothermal Adiabatic Isothermal Isothermal Isothermal x x x y y 200 200 200 200 200 200 200 0 30 0 0 30 0 30 – 21 – Fig. 1.— The frames show the z–distributions for: (a) the total pressure, (b) the Alfvén and maximum magnetosonic speeds for the magnetic disk, and (c) the temperatures and sound speed for the non–magnetic disk. Fig. 2.— Perpendicular collision (non–magnetic disk, and isothermal evolution). The sequence shows the density (gray logarithmic scale), and velocity field (indicated by arrows), at four selected times (0, 3.2, 9.5 and 19 Myr). The maximum velocity values are 200, 166, 77 and 47 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks in the frames is 500 pc. Fig. 3.— Oblique collision (non–magnetic disk, and isothermal evolution). The sequence shows the density (gray logarithmic scale), and velocity field (arrows), at four selected times: 3.2, 6.3, 22.2 and 47.7 Myr. The maximum velocity values are 176, 113, 32 and 26 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks is 500 pc. Fig. 4.— Perpendicular collision (magnetic disk, B parallel to the x–axis, and adiabatic evolution). The sequence shows the density (gray logarithmic scale), velocity fields (arrows), and magnetic fields (lines), at four selected times: 3.2, 6.3, 9.5 and 15.9 Myr. The maximum velocity values are 128, 71, 84 and 77 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks is 500 pc. Fig. 5.— Perpendicular collision (magnetic disk, B parallel to the x–axis, and isothermal evolution). The sequence shows the density (gray logarithmic scale), velocity field (arrows), and magnetic fields (lines), at four selected times: 3.2, 6.3, 9.5 and 15.9 Myr. The maximum velocity values are 137, 72, 95 and 50 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks is 500 pc. Fig. 6.— Oblique collision (magnetic disk, B parallel to the x–axis, and isothermal evolution). The sequence shows the density (gray logarithmic scale), velocity field (arrows), and magnetic field (lines), at four selected times: 3.2, 6.3, 15.9 and 41.2 Myr. The maximum velocity values are 149, 82, 49 and 48 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks is 500 pc. Fig. 7.— Perpendicular collision (magnetic disk, B parallel to the y–axis, and isothermal evolution). The sequence shows the density (gray logarithmic scale), and velocity field (arrows), at four selected times: 3.2, 6.3, 9.5 and 19 Myr. The maximum velocity values are 160, 126, 96 and 78 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks is 500 pc. – 22 – Fig. 8.— Oblique collision (magnetic disk, B parallel to the y–axis, and isothermal evolution). The sequence shows the density (gray logarithmic scale), and velocity field (arrows), at four selected times: 3.2, 9.5, 19 and 41.2 Myr. The maximum velocity values are 173, 80, 56 and 38 km s−1 , respectively. The midplane is located at z = 0 kpc. The distance between tick marks is 500 pc.