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Magnetohydrodynamic Simulations of Shock Interactions with Radiative Clouds P The Astrophysical Journal, 619:327–339, 2005 January 20 # 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A. MAGNETOHYDRODYNAMIC SIMULATIONS OF SHOCK INTERACTIONS WITH RADIATIVE CLOUDS P. Chris Fragile,1 Peter Anninos,1 Kyle Gustafson,2 and Stephen D. Murray1 Receivved 2004 June 2; accepted 2004 September 28 ABSTRACT We present results from two-dimensional numerical simulations of the interactions between magnetized shocks and radiative clouds. Our primary goal is to characterize the dynamical evolution of the shocked clouds. We perform runs in both the strong and weak magnetic field limits and consider three different field orientations. For the geometries considered, we generally find that magnetic fields external to, but concentrated near, the surface of the cloud suppress the growth of destructive hydrodynamic instabilities. External fields also increase the com- pression of the cloud by effectively acting as a confinement mechanism driven by the interstellar flow and local field stretching. This can have a dramatic effect on both the efficiency of radiative cooling, which tends to increase with increasing magnetic field strength, and on the size and distribution of condensed cooled fragments. In contrast, fields acting predominately internally to the cloud tend to resist compression, thereby inhibiting cooling. We observe that, even at modest strengths ( 0 P100), internal fields can completely suppress low-temperature (T <100 K) cooling in two-dimensional clouds. Subject headings: hydrodynamics — ISM: clouds — ISM: kinematics and dynamics — magnetic fields — MHD — shock waves 1. INTRODUCTION than 50% of the initial cloud mass cooling to below 100 K. The cold, dense fragments that form are presumably the precursors Shock waves are an important and common feature in both to active star-forming regions. interstellar (ISM) and intergalactic (IGM) media. They are trig- In the current work we consider the effects of dynamically gered by such energetic phenomena as jets, supernovas, cloud- important magnetic fields in radiative shock–cloud collisions. cloud collisions, and stellar winds and provide a means for Magnetic fields are known to be a pervasive element of the transferring energy from such events into the ambient gas. Since ISM and IGM and are often relevant in characterizing the local the ISM and IGM are generally inhomogeneous, an important and global dynamical behaviors of these media. In shock-cloud problem in astrophysics is understanding the interaction of these interactions, magnetic fields can act to suppress destructive hy- shocks with overdense clumps or clouds. A thorough review of this problem in the unmagnetized and nonradiative limits is pro- drodynamic instabilities by providing additional tension at the interface between the cloud and the postshock background gas vided by Klein et al. (1994). (Nittman 1981; Mac Low et al. 1994). Magnetic fields can also Of special interest to us is large-scale shock-induced star formation, particularly in the neighborhoods of extragalactic limit the growth of disruptive vortices that form in the wake of the cloud, again primarily because of tension in the magnetic radio jets. One of the first objects demonstrated to show a field lines as they are wound up within the vortices. Strong correlation between a radio jet and regions of active star for- external magnetic fields can also increase the compression of mation was the nearest radio galaxy, Centaurus A (e.g., Blanco the shocked cloud material, because of the increased external et al. 1975). Other examples have been found as the sensitiv- magnetic pressure. This compression enhances the radiative ef- ity and spatial resolution of radio and optical telescopes has ficiency of the cloud and allows additional cooling beyond that improved. For instance, ‘‘Minkowski’s Object’’ is a peculiar achievable without magnetic fields. However, strong internal small starburst system at the end of a radio jet emanating from magnetic fields can resist compression, thereby inhibiting cool- the elliptical galaxy NGC 541, located near the center of the ing of the cloud. In this paper we explore these competing cluster of galaxies A194 (van Breugel et al. 1985). Correlations between radio and optical emissions have also been observed effects and the general role of magnetic fields in radiative shock–cloud collisions. This paper also reports on the addition in the so-called alignment effect in distant (z > 0:6) radio gal- of magnetic fields to our astrophysical hydrodynamics code, axies (Chambers et al. 1987; McCarthy et al. 1987). Cosmos. We proceed in 2 by describing the models consid- These observations are most convincingly explained by x ered in this work. In 3 we describe our implementation of models in which shocks generated by the radio jet propagate x radiation MHD. Our results are presented in 4 and discussed through an inhomogeneous medium and trigger gravitational x further in 5. collapse in relatively overdense regions, leading to a burst of x star formation (Begelman & Cioffi 1989; De Young 1989; Rees 2. MODELS 1989). In a recent study (Fragile et al. 2004), we investigated a key component of such models: the radiative shock–induced Models of shock-induced star formation are generally built collapse of intergalactic clouds. For moderate cloud densities upon the assumption of an inhomogeneous two-phase medium (k1cmÀ3) and shock Mach numbers (P20), we found that consisting of warm or cold dense clouds or clumps embedded cooling processes can be highly efficient and result in more in a hot, tenuous background medium. Following Rees (1989), Begelman & Cioffi (1989), and McCarthy (1993), we assume 7 1 a background temperature Tb; i ¼ 10 K and density nb; i ¼ University of California, Lawrence Livermore National Laboratory, Liver- À3 more, CA 94550. 0:01 cm . In this work we restrict ourselves to modeling iso- 2 4 Department of Physics, University of Missouri, Columbia, MO 65201. lated clouds. Each cloud has an initial temperature Tcl; i ¼ 10 K, 327 328 FRAGILE ET AL. Vol. 619 appropriate for warm, ionized gas. Assuming pressure equilib- TABLE 1 Model Parameters rium between the two phases, the density of the cloud is ncl; i ¼ À3 3 (Tb; i=Tcl; i)nb; i ¼ nb; i ¼10 cm , where ¼ 10 is the density a ratio between the cloud and background gases. A planar shock Run Resolution 0 Field Component Cooling ; 3 À1 of velocity vsh; b ¼ 3:7 10 km s (M ¼ 10, where M is the A.................................. 200 1 ... No Mach number, measured in the background gas) is set up to C.................................. 200 1 ... Yes propagate across this cloud. This background shock triggers a BZ4A........................... 200 4 Bz No secondary, compressive shock of velocity BZ4C........................... 200 4 Bz Yes BY4A .......................... 200 4 By No 1=2 BY4C .......................... 200 4 By Yes nb; i vsh; b BX4A .......................... 200 4 Bx No vsh; cl ’ vsh; b ¼ 1=2 ð1Þ ncl; i BX4C .......................... 200 4 Bx Yes BZ1C........................... 200 1 Bz Yes BZ100C....................... 200 100 B Yes inside the cloud. z BY100C ...................... 200 100 By Yes We require the clouds in these models to be large enough not BX1C .......................... 200 1 Bx Yes to be destroyed by the shock prior to the onset of cooling. This BY4C(L)..................... 100 4 By Yes is equivalent to requiring tcool Ttcc or qs ¼ kcool=Rcl T1, BY4C(L1)................... 100 4 By Yes where BY4C(L2)................... 100 4 By Yes a 1:5k T Initial number of zones per cloud radius. t B cl; ps ð2Þ cool (n )Ã(T ) cl; ps Fitt & Alexander 1993). As in Fragile et al. (2004), our models are two-dimensional, in Cartesian geometry. In this geometry, is the cooling time, we consider three different field orientations: (1) parallel to both the planar shock front and the cylindrical cloud (Bz), Rcl 1=2 Rcl tcc ¼ ’ ð3Þ (2) parallel to the shock front but perpendicular to the cloud (By), vsh; cl vsh; b and (3) perpendicular to the shock front and the cloud (Bx). For the strong shocks considered here, Bz and By are enhanced by is the cloud-compression or cloud-destruction timescale, qs about a factor of ( þ 1)=( À 1) ¼ 4(fora ¼ 5=3gas)inthe is the cooling parameter, and kcool vsh; cl tcool is the cooling postshock region, whereas Bx is continuous across the shock. length. Provided tcool Ttcc (or qs T1), the shock is radiative We also consider runs with and without radiative cooling active and the postshock gas loses much of its internal energy during for each of the field orientations. Together, these runs facili- compression. If radiative losses significantly outpace compres- tate an easy comparison of results with various magnetic field sive heating, an initial compressive shock can trigger runaway configurations and atomic processes using a single numeri- cooling to very low temperatures (Mellema et al. 2002; Fragile cal scheme. The various runs and physical parameters of each et al. 2004). If, however, tcool > tcc (or qs > 1), the shock- shock-cloud simulation considered in this study are summa- heated gas does not have time to cool before it is diffused into rized in Table 1. the background gas (Klein et al. 1994). Approximating the For the strong magnetic field cases we distinguish between À19 À1=2 3 À1 cooling function as à ¼ 1:33 ; 10 T ergs cm s (Kahn what we consider primarily internal fields (Bz component) 1976), the restriction on the cloud radius becomes and what we consider primarily external fields (Bx and By components), differentiated by the regions where their effects À2 4 À1 are greatest. We make this distinction based on the fact that Rcl À4 vsh; b ncl; i k1:2 ; 10 : the Bz field component, being parallel to the cylindrical cloud, 100 pc 103 103 km sÀ1 1 cmÀ3 plays no role other than to modify the total effective pressure ð4Þ (there are no gradients in the z-direction, so the B =: terms in eqs.
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