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The origin of filamentary star forming clouds in magnetized galaxies

The origin of filamentary star forming clouds in magnetized galaxies The Origin of Filamentary Star Forming Clouds in Magnetised Galaxies 1 1 2;3 1 Bastian Körtgen , Robi Banerjee , Ralph E. Pudritz and Wolfram Schmidt Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg, Germany Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4K1, Canada Origins Institute, McMaster University, Hamilton, ON L8S 4K1, Canada Released 2018 ABSTRACT Observations show that galaxies and their interstellar media are pervaded by strong magnetic fields with energies in the diffuse component being at least comparable to the thermal and even as large or larger than the turbulent energy. Such strong mag- netic fields prevent the formation of stars because patches of the interstellar medium are magnetically subcritical. Here we present the results from global numerical sim- ulations of strongly magnetised and self-gravitating galactic discs, which show that the buoyancy of the magnetic field due to the Parker instability leads at first to the formation of giant filamentary regions. These filamentary structures become gravita- tionally unstable and fragment into  10 M clouds that attract kpc long, coherent filamentary flows that build them into GMCs. Our results thus provide a solution to the long-standing problem of how the transition from sub- to supercritical regions in the interstellar medium proceeds. Key words: galaxies: evolution; galaxies: magnetic fields; galaxies: ISM; ISM: mag- netic fields; ISM: clouds; stars: formation 1 INTRODUCTION mediate the transition from sub- to supercritical conditions. It was soon pointed out that AD is not efficient enough to One of the most fundamental questions in astrophysics is trigger the transition (Osterbrock 1961; Vázquez-Semadeni how do stars form. Observations clearly show that this pro- et al. 2011). The problem of how magnetically supercriti- cess takes place in self-gravitating, turbulent, magnetized cal cloud cores form out of a magnetically subcritical, dif- filamentary molecular clouds (Blitz et al. 2007; Dobbs et al. fuse medium has remained a challenge ever since (see also 2014; André et al. 2014). However, the question of how more recent numerical studies on this issue, e.g. Vázquez- molecular clouds themselves arise is still largely unanswered. Semadeni et al. 2011; Körtgen & Banerjee 2015). A major obstacle to assembling dense star forming gas It is well known that an attractive potential solution from the diffuse interstellar medium is that magnetic fields is that magnetic fields are buoyant and will bubble out of dominate the energy budget within the latter (Beck 2001; sufficiently magnetized galactic disks, resulting in gas flow- Heiles & Troland 2005; Beck 2012). Star forming molecular ing back to the biplane and concentration into clouds, i.e. clouds, on the other hand, are known to have gravitational the Parker instability. The density increase in the magnetic energies that are typically a factor of 2-3 times greater than valleys is, for cases without self-gravity, only a factor of the magnetic energies (Crutcher et al. 2010; Crutcher 2012). 2, too small to provide the seeds for potential further This is often described by saying that diffuse Hi clouds are growth of molecular clouds (Kim et al. 2002). Parker insta- magnetically subcritical whereas the molecular cloud cores bility and subsequent cloud formation could be triggered by are supercritical (as measured by the ratio of the gravita- the passage of a compressive spiral wave however (Blitz & tional to magnetic energies = the mass to flux ratio, ). Shu 1980; Elmegreen 1982) . The inclusion of disk gravity Because magnetic energy scales with gravity, by assuming 5 lead to the formation of O(10 M ) Hi clouds by the Parker a finite mass reservoir and a nearly perfect conductivity of instability (Kim et al. 2002; Mouschovias et al. 2009). How- the interstellar medium, a magnetically subcritical medium ever, more attention has focused instead on magneto-jeans- will remain so no matter how it is compressed, and this will fragmentation (Kim et al. 2002). Although other processes prevent gravitational collapse. – such as cloud-cloud collisions and mergers (Tasker & Tan This problem was recognized over sixty years ago by 2009) and colliding warm neutral medium flows (Ballesteros- Mestel & Spitzer (1956). Their solution was that ambipo- Paredes et al. 1999; Vázquez-Semadeni et al. 2011) have lar diffusion (AD) in partially ionized gas might be able to Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 been simulated, these do not confront the question of mag- which takes into account old stars and dark matter and netized galaxies. Once a magnetically supercritical medium yields a flat rotation curve is established, the mass needed to assemble massive clouds v (R) = v p : (3) rot 0 could be collected by converging motions from a large mass 2 2 R + R reservoir. The necessary column density of such Hi con- 21 2 For our magnetised galactic disc model, we begin with an ini- nected regions is about 2  10 cm and would require a tial state in which the magnetic field is entirely toroidal. We catchment region of at least one kpc (Mestel 1985). scale the magnetic field strength with the gas density as B / In this work, we explore a major aspect of global Parker to achieve a constant ratio of thermal to magnetic energy instability in 3D galaxies that has been overlooked. Our sim- density ( ) throughout the disc (Beck 2015). Our fiducial ulations show that large scale Parker instabilities ranging value is = 0:25, which gives B (R = R )  30 G. The over many kpcs in a galactic disk can create kpc long fila- medium outside the disc is weakly magnetised and rather ments. Gas draining into such long magnetic valleys will ul- tenuous and thus does not exert any significant thermal or timately exceed the criterion for the gravitational fragmen- magnetic pressure on the disc. Our MHD simulations are tation of filaments. Subsequent flows along these filaments initially magnetically dominated, with a subcritical mass- towards these initial fragments result in the rapid growth to-magnetic flux ratio of = = 0:45, where the critical crit of massive GMCs. This addresses two crucial issues about 1=2 1=2 mass to flux ratio is  = 0:16= G  620 g s cm . crit star formation in magnetised galaxies, namely, how can star The simulations are non-isothermal and we follow the forming gas form out of an initial magnetically dominated recipe by Koyama & Inutsuka (2002) to heat and cool diffuse interstellar medium, and how do filamentary GMCs the gas in the disc. The form of the cooling curve al- arise as a consequence of this process? lows for a thermally unstable regime in the density range We adopt the simplest possible model of a galaxy that 1 6 n=cm 6 10. does not have a companion galaxy driving strong spiral The equations of ideal MHD are solved by using a arms. Under these conditions, galactic shear will ensure that HLL5R Riemann solver (e.g. Waagan et al. 2011) and the initial magnetic field is overwhelmingly toroidal in struc- the self-gravity is treated with a Barnes-Hut tree solver ture. We perform state of the art numerical simulations of (optimised for GPU Lukat & Banerjee 2016). We use an isolated, magnetized galaxy and present our results on outflow boundary conditions for the MHD and isolated the appearance and consequences of the Parker instability ones for the self-gravity. The root grid is at a resolu- in its initially subcritical interstellar medium. tion of x = 625 pc and we allow for five additional root refinement levels, thus giving a peak spatial resolution of x = 19:5 pc. The numerical grid is refined once the lo- min cal Jeans length is resolved with less than 32 grid cells and 2 NUMERICS AND INITIAL CONDITIONS derefined when it exceeds 64 cells. On the highest level of refinement, we incorporate an artificial pressure to ensure For our study of galaxy evolution we use the flash code that the Jeans length is refined with at least four grid cells. (v4.2.2, Dubey et al. 2008). The disc is initialised in the center of a cubic box 3 RESULTS with edge length of L = 40 kpc. The disc radius is set to R = 10 kpc. For both the hydrodynamic (HD) and mag- disc The global evolution of the galaxies is shown in Fig. 1 for netohydrodynamic (MHD) simulations, the initial gas den- two types of simulations - HD and MHD. As a reference sity of the galaxy is a function of radius R and height above case, we first consider a HD disc galaxy, which is depicted the midplane z. Following Tasker & Tan (2009) and taking in the upper row. The disc starts to fragment into rings at into account the Alfvén velocity, the initial density profile is around t = 100 Myr due to gravitational (Toomre) instabil- given as ity. The fragmentation is limited to the outer parts of the disc. At t = 200 Myr the rings have fragmented into individ- c 1 + ual objects (henceforth clouds). At this stage, gravitational (R; z) = sech : (1) and tidal interactions between clouds start to become dom- GQ H (R) H (R) inant, thereby inducing cloud-cloud collisions and mergers. 2 2 Here, Q is the effective Toomre parameter, = 2c =v e s a The latter is clear from the snapshot at time t = 300 Myr, the ratio of thermal to magnetic pressure,  the epicyclic where the number of clouds has been greatly reduced. frequency and H (R) = R (0:00885 + 0:01719R=R + The magnetised disc galaxy evolves quite differently. 0:00564(R=R ) ) the scale height at distance R from the The magnetic field is strong enough to suppress gravita- center and R = 8:5 kpc the solar distance. This realisation tional fragmentation of the disc which is readily seen at essentially yields a thin disc with H (R )  270 pc. For nu- t = 100 Myr, where the disc galaxy appears much smoother, merical reasons, we define the innermost and outer part as while its hydrodynamic counterpart has already started to being initially gravitationally stable and set Q = 20 for fragment. The surface density remains almost constant ex- radii R < 2 kpc and R > 8:5 kpc. Throughout the main disc cept for some small scale perturbations, which are indicative the initial value for Q is set at Q = 2. In addition to e e of a beginning instability. With time, the instability grows self-gravity we use a fixed, stationary external logarithmic and filaments of increased density, which extend both in the potential of the form azimuthal and radial direction, are formed. They are a few " !# kiloparsec long and the medium between the filaments shows 1 1 z 2 2 2 a decreased surface density. We also see that the spacing be- = v ln R + R + ; (2) ext 0 c 2 R q tween those filaments becomes smaller when looking at the Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 Figure 1. Column density maps of the simulated galaxies. Top: HD control disc in time steps of 100 Myr. Bottom: Same for the case with MHD, characterised by a low plasma- . The fragmentation pattern of the two discs (t=100 Myr for the HD case and t=200 Myr for the MHD disc) are significantly different. While in the HD case, the disc breaks up into ring-like structures as expected from classical perturbation theory, the MHD disc shows a pattern that is dominated by spurs which extent both in the azimuthal and radial direction. Movies of these two simulations can be found online. Figure 3. Zoom-in to selected areas of the disc for the reference run ( = 0:25), starting from the point of spur-formation in the outer parts of the disc. It is observed that the magnetic field lines buckle, typical for the Parker instability (left). Near the valleys, where the field lines buckle down, gas motions along the field lines form filamentary structures. At later times, when the disc has partially fragmented into individual clouds, the magnetic field lines are still locally (preferentially in the outer parts) buckled. From the middle panel it is evident that the formed clouds are initially magnetically connected. At late times the B-field becomes highly distorted. regions near the center of the galaxy. At t = 300 Myr, the the field lines. Regions with vertically lifted field lines show spurs in the outer part of the disc have fragmented into a a decreased density in contrast to the areas with magnetic large number of clouds. These clouds appear to be connected valleys, where the density is increased. In the former regions, via filaments of high density, which are aligned in the same gas is pushed up and out of the disc by the rising field lines manner as the large scale spurs at earlier times. These re- and then flows back down along these towards the magnetic sults are still found even in simulations where we imposed valleys. The spacing of the valleys is observed to be around an initial turbulent velocity of  10 km s .  200 pc in the YZ-plane and  400 600 pc in the XZ- In Fig. 2 we show a density slice at t = 100 Myr in the plane (not shown), consistent with theoretical expectations, YZ-plane, centered at y = +5 kpc and x = z = 0, with the which give   H (R) and   (10 20)H (R) (see also YZ XZ magnetic field lines overplotted. The field lines are buoyant Kim et al. 2001). within 200 pc above/below the midplane and appear tangled Fig. 3 shows both the iso-surface maps of the density at larger distances due to turbulence caused by accretion of (n = 10 cm in red) and magnetic field lines (black) at min matter onto the disc (Klessen & Hennebelle 2010). The tan- three distinct stages of the magnetised disc. At t = 200 Myr, gling of the magnetic field is prominent in this plane as this the spurs are readily seen and magnetic field lines are per- (radial) component, which is initially zero, is much weaker turbed, being dragged by buoyant flows in the vertical di- compared to the toroidal field. rection. This topology of the magnetic field lines is a typical The density field is well correlated with the buoyancy of for the Parker instability, where field lines buckle up and Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 Figure 4. The Parker Instability in the disc at t = 200 Myr. Left: Face-on view of the mass-to-flux ratio shown in ’binary mode’ (supercritical equal to 1, red, and subcritical equal to -1, white). Right: Critical line-mass of the disc. The formed spurs are mag- netically supercritical and more prone to gravitational fragmen- Figure 2. Slice of density through the magnetised disc at tation as indicated by their lower critical line-mass. t = 100 Myr. The axes show the offset to the center of the re- gion, which is at y = +5 kpc and x = z = 0. Overlaid in white are magnetic field lines. The Parker instability is clearly seen in its -12 Beta0.25, t=100-200 Myr developed phase. The density enhancements correlate well with Beta10, t=232-332 Myr -13 the emergence of magnetic valleys. -14 -15 down in a vertically stratified disc. It is also seen that the Parker instability is most efficient in the outer parts of the -16 disc, whereas fragmentation of the inner part is suppressed -17 and the field is observed to be still rather unperturbed. We emphasize that the difference in these patterns is -18 due to the fact that the dynamical time of the Parker in- stability is shorter than that of the Toomre instability - we -19 1 10 deduce from our initial conditions that it is a factor of 2-3 Wavenumber k shorter, with t  90 100 Myr at 8 kpc. At later times, PI Figure 5. Azimuthal energy spectra of the vertical magnetic field t = 300 Myr, the magnetic field lines become even more component, which is used as a measure of the distortion of the perturbed, while the filaments have fragmented into clouds magnetic field. Different line styles depict different times (early: with initial masses  10 M . Even at this stage, the field solid, late: short-dashed). The last time step is chosen such that buoyancy can be clearly identified. Although the magnetic the disc is still in the phase of linear instability and this region is field becomes compressed in the magnetic valleys, the spurs hence representative for the entire disc. proceed to fragment into clouds. The reason for this is that gas flows coherently along the field, converges and accumu- lates in the magnetic valleys, which increases the line-mass The gravitational stability of filaments is mea- of the filaments (André et al. 2014). As the line-mass in- sured in terms of the critical gravitational line-mass 2 2 2 creases, then so too will be the mass-to-magnetic flux ratio (M=L) = 2  + v + c =G (Fiege & Pudritz 2000), crit rms A S since the inflow does not drag field into the filament which is which is shown in the right panel. The expression takes into contrary to the scenario suggested by Mestel (1985, see also account the sound and Alfvén speed as well as the RMS ve- Fig. 4). Thus, the inflow into the filament pushes the system locity. We see that the filamentary structures are far more towards higher line-mass and renders it magnetically super- prone to gravitational fragmentation than the diffuse gas - critical. At the same time, the filaments reveal low levels of these filamentary clouds are both magnetically and gravi- turbulence and thus the lowest threshold line-mass for grav- tationally supercritical. Interestingly, the critical line-mass itational fragmentation. It is further seen that these clouds appears to be rather constant along each spur and shows no are connected by the same magnetic field lines. The field significant variation with position in the disc with values of 3 4 1 itself stays buoyant thereby further allowing less dense ma- (M=L)  6 10 10 M pc . crit terial to flow to the magnetic valleys. When the disc has fully In order to identify the scale of the instability, in Fig. 5 fragmented at t = 400 Myr (rightmost panel), the magnetic we plot azimuthal energy spectra of the vertical B-field com- field becomes locally disordered as gravitational interactions ponent in a cubic region with an edge length of 2 kpc for two between the clouds take hold. initial magnetisations of the disc galaxy. In all simulations, We show in Fig. 4 the normalised mass-to-magnetic flux ra- the vertical magnetic field grows with time as indicated by tio = . It is depicted in ’binary mode’, where supercrit- the increase in the spectral energy. Particularly interesting is crit ical regions are shown in red and subcritical areas in white, the wavenumber at which the energy peaks, because it gives respectively. Note that the spurs appear as magnetically su- the characteristic length scale for the buoyancy of the field. percritical regions in the mass-to-flux ratio map. Regions, This wavenumber (normalised to the box size), k, can be where the magnetic field lines are lifted out of the disc ap- estimated to be at k  2 3. Note that the spectrum for the pear magnetically subcritical due to the greatly reduced gas weakly magnetised galaxy (initial plasma- = 10) peaks at a column density. larger wavenumber as this galaxy evolves almost like the hy- Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 E(k) drodynamical model. These wavenumbers give characteristic GCS Supercomputer SuperMUC at Leibniz Supercomput- scales of L = 0:7 1 kpc for the azimuthal perturbation, in ing Centre (www.lrz.de). good agreement with early theoretical studies (Parker 1966) and previous numerical simulations (Kim et al. 2001, 2002; Kim & Ostriker 2002). REFERENCES André P., Di Francesco J., Ward-Thompson D., Inutsuka S.-I., Pudritz R. E., Pineda J. E., 2014, Protostars and 4 DISCUSSION AND CONCLUSION Planets VI, pp 27–51 Our simulations show that gas accumulation along magnetic Ballesteros-Paredes J., Hartmann L., Vázquez-Semadeni field lines does not lead to the formation of GMCs directly. E., 1999, ApJ, 527, 285 Instead, kpc-scale coherent flows along buoyant magnetic Beck R., 2001, Space Science Reviews, 99, 243 field lines first lead to the formation of giant filaments by Beck R., 2012, Space Sci. Rev., 166, 215 converging in magnetic valleys. The mass reservoir provided Beck R., 2015, in Lazarian A., de Gouveia Dal Pino E. M., by this mechanism is sufficient to render the magnetic field Melioli C., eds, Astrophysics and Space Science Library magnetically supercritical. From an observational perspec- Vol. 407 of Astrophysics and Space Science Library, Mag- tive these filaments resemble the spur-like features that have netic Fields in Galaxies. p. 507 been noted in galaxies (Ho et al. 2009). We note also that Blitz L., Fukui Y., Kawamura A., Leroy A., Mizuno N., seven giant molecular filaments (GMFs) that have lengths Rosolowsky E., 2007, Protostars and Planets V, pp 81–96 4 5 on the order of 100 pc, total masses of 10 10 M exhibit- Blitz L., Shu F. H., 1980, ApJ, 238, 148 ing velocity coherence over their full length are observed in Crutcher R. M., 2012, ARA&A, 50, 29 the inter arm regions of our galaxy (termed ’Giant Molecular Crutcher R. M., Hakobian N., Troland T. H., 2010, MN- Filaments’, Ragan et al. 2014). In short, the filaments in our RAS, 402, L64 simulated discs are magnetically supercritical, have low lev- Dobbs C. L., Krumholz M. R., Ballesteros-Paredes J., Bo- els of turbulence, and have low critical mass per unit length. latto A. D., Fukui Y., Heyer M., Low M.-M. M., Ostriker Whereas the initial conditions of previous studies were mag- E. C., Vázquez-Semadeni E., 2014, Protostars and Planets netically supercritical (Kim et al. 2001, 2002; Mouschovias VI, pp 3–26 et al. 2009), we observe spur formation and fragmentation Dubey A., Fisher R., Graziani C., Jordan IV G. C., Lamb also for initially highly subcritical galaxies. D. Q., Reid L. B., Rich P., Sheeler D., Townsley D., Weide K., 2008, in Pogorelov N. V., Audit E., Zank G. P., We conclude that the Parker instability enables the for- eds, Numerical Modeling of Space Plasma Flows Vol. 385 mation of magnetically supercritical filaments out of an ini- of Astronomical Society of the Pacific Conference Series, tially subcritical diffuse interstellar medium. Hi flows into long magnetic valleys and produces filamentary clouds that Challenges of Extreme Computing using the FLASH code. undergo subsequent gravitational fragmentation. These frag- pp 145–+ ments are fed by flows in the filaments, resulting in the rapid Elmegreen B. G., 1982, ApJ, 253, 655 accumulation of GMC mass clouds. Our results provide a Fiege J. D., Pudritz R. E., 2000, MNRAS, 311, 85 solution to the question of how to form clouds out of a Heiles C., Troland T. H., 2005, ApJ, 624, 773 highly magnetically subcritical ISM, posed half a century Ho I.-T., Lim J., Dinh-V-Trung 2009, ApJ, 698, 1191 ago. We further emphasise that the behaviour uncovered by Kim J., Ryu D., Jones T. W., 2001, ApJ, 557, 464 our simulations is not merely a transient event based on ide- Kim W., Ostriker E. C., 2002, ApJ, 570, 132 alised initial conditions. While we cannot follow subsequent Kim W.-T., Ostriker E. C., Stone J. M., 2002, ApJ, 581, star formation in these simulations, it will have the effect of 1080 eventually dispersing the GMCs back into a diffuse medium. Klessen R. S., Hennebelle P., 2010, A&A, 520, A17 Galactic shear will rapidly comb out the fields and the cycle Körtgen B., Banerjee R., 2015, MNRAS, 451, 3340 will begin again. Koyama H., Inutsuka S.-i., 2002, ApJ, 564, L97 Lukat G., Banerjee R., 2016, New A, 45, 14 ACKNOWLEDGEMENTS Mestel L., 1985, in Black D. C., Matthews M. S., eds, Pro- tostars and Planets II Magnetic fields. pp 320–339 We thank the referee for a timely and insightful report. We Mestel L., Spitzer Jr. L., 1956, MNRAS, 116, 503 further thank E. Vázquez-Semadeni, B. Elmegreen, and C. Mouschovias T. C., Kunz M. W., Christie D. A., 2009, McKee for discussions. BK and RB thank for funding via MNRAS, 397, 14 the DFG priority program 1573 ’The Physics of the Inter- Osterbrock D. E., 1961, ApJ, 134, 270 stellar Medium’ (BA 3706/3-2). Furthermore RB acknowl- Parker E. N., 1966, ApJ, 145, 811 edges additional funding from the DFG for this project Ragan S. E., Henning T., Tackenberg J., Beuther H., John- via the grant BA 3706/4-1. RB and WS are supported ston K. G., Kainulainen J., Linz H., 2014, A&A, 568, A73 by the DFG for the project via the grant BA 3706/15-1. Tasker E. J., Tan J. C., 2009, ApJ, 700, 358 The FLASH software was developed in part by the DOE Vázquez-Semadeni E., Banerjee R., Gómez G. C., Hen- NNSA ASC- and DOE Office of Science ASCR-supported nebelle P., Duffin D., Klessen R. S., 2011, MNRAS, 414, Flash Center for Computational Science at the University of Chicago. REP is supported by a Discovery grant from Waagan K., Federrath C., Klingenberg C., 2011, Journal NSERC - Canada. We thank the Gauss Centre for Su- of Computational Physics, 230, 3331 percomputing e.V. (www.gauss-centre.eu) for funding this project (ID: pr92pu) by providing computing time on the Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society Letters Oxford University Press

The origin of filamentary star forming clouds in magnetized galaxies

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Abstract

The Origin of Filamentary Star Forming Clouds in Magnetised Galaxies 1 1 2;3 1 Bastian Körtgen , Robi Banerjee , Ralph E. Pudritz and Wolfram Schmidt Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg, Germany Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4K1, Canada Origins Institute, McMaster University, Hamilton, ON L8S 4K1, Canada Released 2018 ABSTRACT Observations show that galaxies and their interstellar media are pervaded by strong magnetic fields with energies in the diffuse component being at least comparable to the thermal and even as large or larger than the turbulent energy. Such strong mag- netic fields prevent the formation of stars because patches of the interstellar medium are magnetically subcritical. Here we present the results from global numerical sim- ulations of strongly magnetised and self-gravitating galactic discs, which show that the buoyancy of the magnetic field due to the Parker instability leads at first to the formation of giant filamentary regions. These filamentary structures become gravita- tionally unstable and fragment into  10 M clouds that attract kpc long, coherent filamentary flows that build them into GMCs. Our results thus provide a solution to the long-standing problem of how the transition from sub- to supercritical regions in the interstellar medium proceeds. Key words: galaxies: evolution; galaxies: magnetic fields; galaxies: ISM; ISM: mag- netic fields; ISM: clouds; stars: formation 1 INTRODUCTION mediate the transition from sub- to supercritical conditions. It was soon pointed out that AD is not efficient enough to One of the most fundamental questions in astrophysics is trigger the transition (Osterbrock 1961; Vázquez-Semadeni how do stars form. Observations clearly show that this pro- et al. 2011). The problem of how magnetically supercriti- cess takes place in self-gravitating, turbulent, magnetized cal cloud cores form out of a magnetically subcritical, dif- filamentary molecular clouds (Blitz et al. 2007; Dobbs et al. fuse medium has remained a challenge ever since (see also 2014; André et al. 2014). However, the question of how more recent numerical studies on this issue, e.g. Vázquez- molecular clouds themselves arise is still largely unanswered. Semadeni et al. 2011; Körtgen & Banerjee 2015). A major obstacle to assembling dense star forming gas It is well known that an attractive potential solution from the diffuse interstellar medium is that magnetic fields is that magnetic fields are buoyant and will bubble out of dominate the energy budget within the latter (Beck 2001; sufficiently magnetized galactic disks, resulting in gas flow- Heiles & Troland 2005; Beck 2012). Star forming molecular ing back to the biplane and concentration into clouds, i.e. clouds, on the other hand, are known to have gravitational the Parker instability. The density increase in the magnetic energies that are typically a factor of 2-3 times greater than valleys is, for cases without self-gravity, only a factor of the magnetic energies (Crutcher et al. 2010; Crutcher 2012). 2, too small to provide the seeds for potential further This is often described by saying that diffuse Hi clouds are growth of molecular clouds (Kim et al. 2002). Parker insta- magnetically subcritical whereas the molecular cloud cores bility and subsequent cloud formation could be triggered by are supercritical (as measured by the ratio of the gravita- the passage of a compressive spiral wave however (Blitz & tional to magnetic energies = the mass to flux ratio, ). Shu 1980; Elmegreen 1982) . The inclusion of disk gravity Because magnetic energy scales with gravity, by assuming 5 lead to the formation of O(10 M ) Hi clouds by the Parker a finite mass reservoir and a nearly perfect conductivity of instability (Kim et al. 2002; Mouschovias et al. 2009). How- the interstellar medium, a magnetically subcritical medium ever, more attention has focused instead on magneto-jeans- will remain so no matter how it is compressed, and this will fragmentation (Kim et al. 2002). Although other processes prevent gravitational collapse. – such as cloud-cloud collisions and mergers (Tasker & Tan This problem was recognized over sixty years ago by 2009) and colliding warm neutral medium flows (Ballesteros- Mestel & Spitzer (1956). Their solution was that ambipo- Paredes et al. 1999; Vázquez-Semadeni et al. 2011) have lar diffusion (AD) in partially ionized gas might be able to Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 been simulated, these do not confront the question of mag- which takes into account old stars and dark matter and netized galaxies. Once a magnetically supercritical medium yields a flat rotation curve is established, the mass needed to assemble massive clouds v (R) = v p : (3) rot 0 could be collected by converging motions from a large mass 2 2 R + R reservoir. The necessary column density of such Hi con- 21 2 For our magnetised galactic disc model, we begin with an ini- nected regions is about 2  10 cm and would require a tial state in which the magnetic field is entirely toroidal. We catchment region of at least one kpc (Mestel 1985). scale the magnetic field strength with the gas density as B / In this work, we explore a major aspect of global Parker to achieve a constant ratio of thermal to magnetic energy instability in 3D galaxies that has been overlooked. Our sim- density ( ) throughout the disc (Beck 2015). Our fiducial ulations show that large scale Parker instabilities ranging value is = 0:25, which gives B (R = R )  30 G. The over many kpcs in a galactic disk can create kpc long fila- medium outside the disc is weakly magnetised and rather ments. Gas draining into such long magnetic valleys will ul- tenuous and thus does not exert any significant thermal or timately exceed the criterion for the gravitational fragmen- magnetic pressure on the disc. Our MHD simulations are tation of filaments. Subsequent flows along these filaments initially magnetically dominated, with a subcritical mass- towards these initial fragments result in the rapid growth to-magnetic flux ratio of = = 0:45, where the critical crit of massive GMCs. This addresses two crucial issues about 1=2 1=2 mass to flux ratio is  = 0:16= G  620 g s cm . crit star formation in magnetised galaxies, namely, how can star The simulations are non-isothermal and we follow the forming gas form out of an initial magnetically dominated recipe by Koyama & Inutsuka (2002) to heat and cool diffuse interstellar medium, and how do filamentary GMCs the gas in the disc. The form of the cooling curve al- arise as a consequence of this process? lows for a thermally unstable regime in the density range We adopt the simplest possible model of a galaxy that 1 6 n=cm 6 10. does not have a companion galaxy driving strong spiral The equations of ideal MHD are solved by using a arms. Under these conditions, galactic shear will ensure that HLL5R Riemann solver (e.g. Waagan et al. 2011) and the initial magnetic field is overwhelmingly toroidal in struc- the self-gravity is treated with a Barnes-Hut tree solver ture. We perform state of the art numerical simulations of (optimised for GPU Lukat & Banerjee 2016). We use an isolated, magnetized galaxy and present our results on outflow boundary conditions for the MHD and isolated the appearance and consequences of the Parker instability ones for the self-gravity. The root grid is at a resolu- in its initially subcritical interstellar medium. tion of x = 625 pc and we allow for five additional root refinement levels, thus giving a peak spatial resolution of x = 19:5 pc. The numerical grid is refined once the lo- min cal Jeans length is resolved with less than 32 grid cells and 2 NUMERICS AND INITIAL CONDITIONS derefined when it exceeds 64 cells. On the highest level of refinement, we incorporate an artificial pressure to ensure For our study of galaxy evolution we use the flash code that the Jeans length is refined with at least four grid cells. (v4.2.2, Dubey et al. 2008). The disc is initialised in the center of a cubic box 3 RESULTS with edge length of L = 40 kpc. The disc radius is set to R = 10 kpc. For both the hydrodynamic (HD) and mag- disc The global evolution of the galaxies is shown in Fig. 1 for netohydrodynamic (MHD) simulations, the initial gas den- two types of simulations - HD and MHD. As a reference sity of the galaxy is a function of radius R and height above case, we first consider a HD disc galaxy, which is depicted the midplane z. Following Tasker & Tan (2009) and taking in the upper row. The disc starts to fragment into rings at into account the Alfvén velocity, the initial density profile is around t = 100 Myr due to gravitational (Toomre) instabil- given as ity. The fragmentation is limited to the outer parts of the disc. At t = 200 Myr the rings have fragmented into individ- c 1 + ual objects (henceforth clouds). At this stage, gravitational (R; z) = sech : (1) and tidal interactions between clouds start to become dom- GQ H (R) H (R) inant, thereby inducing cloud-cloud collisions and mergers. 2 2 Here, Q is the effective Toomre parameter, = 2c =v e s a The latter is clear from the snapshot at time t = 300 Myr, the ratio of thermal to magnetic pressure,  the epicyclic where the number of clouds has been greatly reduced. frequency and H (R) = R (0:00885 + 0:01719R=R + The magnetised disc galaxy evolves quite differently. 0:00564(R=R ) ) the scale height at distance R from the The magnetic field is strong enough to suppress gravita- center and R = 8:5 kpc the solar distance. This realisation tional fragmentation of the disc which is readily seen at essentially yields a thin disc with H (R )  270 pc. For nu- t = 100 Myr, where the disc galaxy appears much smoother, merical reasons, we define the innermost and outer part as while its hydrodynamic counterpart has already started to being initially gravitationally stable and set Q = 20 for fragment. The surface density remains almost constant ex- radii R < 2 kpc and R > 8:5 kpc. Throughout the main disc cept for some small scale perturbations, which are indicative the initial value for Q is set at Q = 2. In addition to e e of a beginning instability. With time, the instability grows self-gravity we use a fixed, stationary external logarithmic and filaments of increased density, which extend both in the potential of the form azimuthal and radial direction, are formed. They are a few " !# kiloparsec long and the medium between the filaments shows 1 1 z 2 2 2 a decreased surface density. We also see that the spacing be- = v ln R + R + ; (2) ext 0 c 2 R q tween those filaments becomes smaller when looking at the Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 Figure 1. Column density maps of the simulated galaxies. Top: HD control disc in time steps of 100 Myr. Bottom: Same for the case with MHD, characterised by a low plasma- . The fragmentation pattern of the two discs (t=100 Myr for the HD case and t=200 Myr for the MHD disc) are significantly different. While in the HD case, the disc breaks up into ring-like structures as expected from classical perturbation theory, the MHD disc shows a pattern that is dominated by spurs which extent both in the azimuthal and radial direction. Movies of these two simulations can be found online. Figure 3. Zoom-in to selected areas of the disc for the reference run ( = 0:25), starting from the point of spur-formation in the outer parts of the disc. It is observed that the magnetic field lines buckle, typical for the Parker instability (left). Near the valleys, where the field lines buckle down, gas motions along the field lines form filamentary structures. At later times, when the disc has partially fragmented into individual clouds, the magnetic field lines are still locally (preferentially in the outer parts) buckled. From the middle panel it is evident that the formed clouds are initially magnetically connected. At late times the B-field becomes highly distorted. regions near the center of the galaxy. At t = 300 Myr, the the field lines. Regions with vertically lifted field lines show spurs in the outer part of the disc have fragmented into a a decreased density in contrast to the areas with magnetic large number of clouds. These clouds appear to be connected valleys, where the density is increased. In the former regions, via filaments of high density, which are aligned in the same gas is pushed up and out of the disc by the rising field lines manner as the large scale spurs at earlier times. These re- and then flows back down along these towards the magnetic sults are still found even in simulations where we imposed valleys. The spacing of the valleys is observed to be around an initial turbulent velocity of  10 km s .  200 pc in the YZ-plane and  400 600 pc in the XZ- In Fig. 2 we show a density slice at t = 100 Myr in the plane (not shown), consistent with theoretical expectations, YZ-plane, centered at y = +5 kpc and x = z = 0, with the which give   H (R) and   (10 20)H (R) (see also YZ XZ magnetic field lines overplotted. The field lines are buoyant Kim et al. 2001). within 200 pc above/below the midplane and appear tangled Fig. 3 shows both the iso-surface maps of the density at larger distances due to turbulence caused by accretion of (n = 10 cm in red) and magnetic field lines (black) at min matter onto the disc (Klessen & Hennebelle 2010). The tan- three distinct stages of the magnetised disc. At t = 200 Myr, gling of the magnetic field is prominent in this plane as this the spurs are readily seen and magnetic field lines are per- (radial) component, which is initially zero, is much weaker turbed, being dragged by buoyant flows in the vertical di- compared to the toroidal field. rection. This topology of the magnetic field lines is a typical The density field is well correlated with the buoyancy of for the Parker instability, where field lines buckle up and Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 Figure 4. The Parker Instability in the disc at t = 200 Myr. Left: Face-on view of the mass-to-flux ratio shown in ’binary mode’ (supercritical equal to 1, red, and subcritical equal to -1, white). Right: Critical line-mass of the disc. The formed spurs are mag- netically supercritical and more prone to gravitational fragmen- Figure 2. Slice of density through the magnetised disc at tation as indicated by their lower critical line-mass. t = 100 Myr. The axes show the offset to the center of the re- gion, which is at y = +5 kpc and x = z = 0. Overlaid in white are magnetic field lines. The Parker instability is clearly seen in its -12 Beta0.25, t=100-200 Myr developed phase. The density enhancements correlate well with Beta10, t=232-332 Myr -13 the emergence of magnetic valleys. -14 -15 down in a vertically stratified disc. It is also seen that the Parker instability is most efficient in the outer parts of the -16 disc, whereas fragmentation of the inner part is suppressed -17 and the field is observed to be still rather unperturbed. We emphasize that the difference in these patterns is -18 due to the fact that the dynamical time of the Parker in- stability is shorter than that of the Toomre instability - we -19 1 10 deduce from our initial conditions that it is a factor of 2-3 Wavenumber k shorter, with t  90 100 Myr at 8 kpc. At later times, PI Figure 5. Azimuthal energy spectra of the vertical magnetic field t = 300 Myr, the magnetic field lines become even more component, which is used as a measure of the distortion of the perturbed, while the filaments have fragmented into clouds magnetic field. Different line styles depict different times (early: with initial masses  10 M . Even at this stage, the field solid, late: short-dashed). The last time step is chosen such that buoyancy can be clearly identified. Although the magnetic the disc is still in the phase of linear instability and this region is field becomes compressed in the magnetic valleys, the spurs hence representative for the entire disc. proceed to fragment into clouds. The reason for this is that gas flows coherently along the field, converges and accumu- lates in the magnetic valleys, which increases the line-mass The gravitational stability of filaments is mea- of the filaments (André et al. 2014). As the line-mass in- sured in terms of the critical gravitational line-mass 2 2 2 creases, then so too will be the mass-to-magnetic flux ratio (M=L) = 2  + v + c =G (Fiege & Pudritz 2000), crit rms A S since the inflow does not drag field into the filament which is which is shown in the right panel. The expression takes into contrary to the scenario suggested by Mestel (1985, see also account the sound and Alfvén speed as well as the RMS ve- Fig. 4). Thus, the inflow into the filament pushes the system locity. We see that the filamentary structures are far more towards higher line-mass and renders it magnetically super- prone to gravitational fragmentation than the diffuse gas - critical. At the same time, the filaments reveal low levels of these filamentary clouds are both magnetically and gravi- turbulence and thus the lowest threshold line-mass for grav- tationally supercritical. Interestingly, the critical line-mass itational fragmentation. It is further seen that these clouds appears to be rather constant along each spur and shows no are connected by the same magnetic field lines. The field significant variation with position in the disc with values of 3 4 1 itself stays buoyant thereby further allowing less dense ma- (M=L)  6 10 10 M pc . crit terial to flow to the magnetic valleys. When the disc has fully In order to identify the scale of the instability, in Fig. 5 fragmented at t = 400 Myr (rightmost panel), the magnetic we plot azimuthal energy spectra of the vertical B-field com- field becomes locally disordered as gravitational interactions ponent in a cubic region with an edge length of 2 kpc for two between the clouds take hold. initial magnetisations of the disc galaxy. In all simulations, We show in Fig. 4 the normalised mass-to-magnetic flux ra- the vertical magnetic field grows with time as indicated by tio = . It is depicted in ’binary mode’, where supercrit- the increase in the spectral energy. Particularly interesting is crit ical regions are shown in red and subcritical areas in white, the wavenumber at which the energy peaks, because it gives respectively. Note that the spurs appear as magnetically su- the characteristic length scale for the buoyancy of the field. percritical regions in the mass-to-flux ratio map. Regions, This wavenumber (normalised to the box size), k, can be where the magnetic field lines are lifted out of the disc ap- estimated to be at k  2 3. Note that the spectrum for the pear magnetically subcritical due to the greatly reduced gas weakly magnetised galaxy (initial plasma- = 10) peaks at a column density. larger wavenumber as this galaxy evolves almost like the hy- Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018 E(k) drodynamical model. 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W., 2001, ApJ, 557, 464 our simulations is not merely a transient event based on ide- Kim W., Ostriker E. C., 2002, ApJ, 570, 132 alised initial conditions. While we cannot follow subsequent Kim W.-T., Ostriker E. C., Stone J. M., 2002, ApJ, 581, star formation in these simulations, it will have the effect of 1080 eventually dispersing the GMCs back into a diffuse medium. Klessen R. S., Hennebelle P., 2010, A&A, 520, A17 Galactic shear will rapidly comb out the fields and the cycle Körtgen B., Banerjee R., 2015, MNRAS, 451, 3340 will begin again. Koyama H., Inutsuka S.-i., 2002, ApJ, 564, L97 Lukat G., Banerjee R., 2016, New A, 45, 14 ACKNOWLEDGEMENTS Mestel L., 1985, in Black D. C., Matthews M. S., eds, Pro- tostars and Planets II Magnetic fields. pp 320–339 We thank the referee for a timely and insightful report. We Mestel L., Spitzer Jr. L., 1956, MNRAS, 116, 503 further thank E. Vázquez-Semadeni, B. Elmegreen, and C. Mouschovias T. C., Kunz M. W., Christie D. A., 2009, McKee for discussions. BK and RB thank for funding via MNRAS, 397, 14 the DFG priority program 1573 ’The Physics of the Inter- Osterbrock D. E., 1961, ApJ, 134, 270 stellar Medium’ (BA 3706/3-2). Furthermore RB acknowl- Parker E. N., 1966, ApJ, 145, 811 edges additional funding from the DFG for this project Ragan S. E., Henning T., Tackenberg J., Beuther H., John- via the grant BA 3706/4-1. RB and WS are supported ston K. G., Kainulainen J., Linz H., 2014, A&A, 568, A73 by the DFG for the project via the grant BA 3706/15-1. Tasker E. J., Tan J. C., 2009, ApJ, 700, 358 The FLASH software was developed in part by the DOE Vázquez-Semadeni E., Banerjee R., Gómez G. C., Hen- NNSA ASC- and DOE Office of Science ASCR-supported nebelle P., Duffin D., Klessen R. S., 2011, MNRAS, 414, Flash Center for Computational Science at the University of Chicago. REP is supported by a Discovery grant from Waagan K., Federrath C., Klingenberg C., 2011, Journal NSERC - Canada. We thank the Gauss Centre for Su- of Computational Physics, 230, 3331 percomputing e.V. (www.gauss-centre.eu) for funding this project (ID: pr92pu) by providing computing time on the Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly094/5004868 by Ed 'DeepDyve' Gillespie user on 08 June 2018

Journal

Monthly Notices of the Royal Astronomical Society Letters – Oxford University Press

Published: May 25, 2018

Keywords: stars: formation; ISM: clouds; ISM: magnetic fields; galaxies: evolution; galaxies: ISM; galaxies: magnetic fields

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