PoS(CRF 2010)029 http://pos.sissa.it/ ce. the birth of the first stars in the entified in numerical simulations mall-scale dynamo during the for- amo is shown to provide additional compression of the field lines. We re resolved by at least 32 grid cells. in the presence of turbulence, initial as strong implications on the subse- een shown from cosmological hydro- c fields via small-scale dynamo action. chen, Germany 300 RA Leiden, the Netherlands; ut für Theoretische Astrophysik, ive Commons Attribution-NonCommercial-ShareAlike Licen , Robi Banerjee, Ralf S. Klessen ∗ [email protected] where the turbulent motions in theWe conclude central collapsing that core strong a magneticuniverse fields and discuss are implications generated for cosmic during evolution. dynamical simulations of primordial starquent formation. evolution, in This particular h on the generation of magneti find that the presence of the small-scale dynamo can only be id The ubiquity of turbulence in the primordial minihalos has b Using high-resolution numerical simulations, we showweak that seed magnetic fields are exponentiallymation amplified of by the the first s stars. The fieldamplification amplification over due what to is the dyn expected from pure gravitational Speaker. ∗ Copyright owned by the author(s) under the terms of the Creat c Cosmic Radiation Fields: Sources in theNovember early 9-12, Universe 2010 Desy, Germany Sharanya Sur Zentrum für Astronomie der Universität Heidelberg,Albert-Ueberle-Str. Instit 2, 69120 Heidelberg, Germany E-mail: Dominik R.G. Schleicher Leiden Observatory, Leiden University, P.O. Box 9513,ESO, NL-2 Karl-Schwarzschild-Strasse 2, 85748 Garching bei Mün The generation of strong magnetic fieldsformation during of the the first stars Christoph Federrath Ecole Normale Supérieure de Lyon, CRAL, 69364 Lyon, France

PoS(CRF 2010)029 . e 6 10 ∼ by 8, 16, J 10 [12]. λ Sharanya Sur ∼ z (IGM), consistent , reaching a peak value is a dimensionless time 6 τ of the first stars s been made in understanding tor of 10 ion of the collapsing core in our en from Figs. 2.2b and 2.2c. The lification of the baryon-dominated olds number and is thus related to ld on the formation process of the ored the possible role of magnetic urbulent, magnetized Bonnor-Ebert cosmological initial conditions and and their influence on later epochs urbulence is maintained on scales of resolution yields larger field amplifi- ed from pure flux-freezing. This in- anism at a redshift of onditions, the readers are referred to t star-forming cloud. This opens the ations where we resolve een previously addressed using semi- on of the first stars. We also discuss b). The radial infall motions dominate fields by a process commonly referred esults obtained from three-dimensional ditional amplification over compression f amplifying weak initial seed magnetic nsity has increased by a factor of sses like the Biermann battery [8] or the at the expense of the kinetic energy in the see Eq. 2 in [16]). As shown in Fig. 2.1b, e dynamo in these simulations requires a ecent FERMI observations [11] provide a ditions of our simulations motivated from all the way down to protostellar densities, ed from either cosmological processes like n of the first stars 2 12 as shown in Fig. 2.1a. Here, ∼ τ (see [13] for a review). In the context of the first stars and th G for the magnetic field strength in the intergalactic medium 15 − small-scale dynamo action Interestingly, hydrodynamical simulations starting from Over the course of the last decade, a great deal of progress ha We focus on the gravitational collapse and magnetic field amp and dominates the dynamics inside the core region as can be se J following the gravitational collapse of the primordialreveal gas the presence of turbulencepossibility in of amplifying the weak minihalos initial seed of magnetic the fields firs turbulent fluid motions, to eventually generate strong seed to as λ the physical processes governingof the structure birth formation of [1, thefields 2, primarily, first because 3, the stars 4, initial field 5]. strengthsinflation obtain and These phase studies transition [6, have 7] ign or astrophysical proce The generation of strong magnetic fields during the formatio 1. Motivation Weibel instability [9, 10] are highly uncertain.lower However, limit r of 10 with the predicted field strength from Biermann battery mech coordinate normalized in terms of the local free-fall time ( the field amplification is indeed stronger than what is expect dicates that the small-scale dynamo provides significant ad minimum resolution of 32 cells per Jeansthe length total (see velocity Fig. in 2.2 the envelope as shown in Fig. 2.2a. The t during the birth of the first stars. Capturing the small-scal first galaxies, dynamo amplification of smallanalytic seed fields models has [14]. b In thisnumerical contribution, simulations we aimed present at the exploring r thefields possibility through o small-scale dynamo actionthe during implications the of formati the dynamofirst generated stars random and magnetic their subsequent fie evolution. 2. Generation of strong magnetic fields during the formation inner parts of a collapsing primordial halo.the The cosmological initial con models of [1],sphere. [4] and For [15] more correspond details to on[16]. a the The t numerical efficiency of setup the and dynamohow initial process well c depends the on turbulent the motions Reyn arecation. resolved [17, We 18]. report results Higher obtained from five numerical simul 32, 64 and 128 cells.highest-resolution simulation at a Fig. time 1 when shows the a central snapshot de of the central reg Starting from a weak 1 nG field, the magnetic field grows by a fac of about 1 mG in the central core at PoS(CRF 2010)029 lation Sharanya Sur -plane, indicating radial xy e primordial minihalo can lead to sequences for our understanding smic evolution. Recent hydrody- centered on the position of the current g core at the time when the initial field J nce the dynamics in the protostellar he protostellar core of the first stars. he local Jeans length are resolved by s spectrum. To investigate the role of V ds can reduce the level of fragmenta- st stars. The small-scale dynamo only rowth phase. This will help us to gain of the primordial cloud, it is necessary t the infalling velocities are supersonic, urbulent dynamo action. We find in our nfluence this scenario provided they are on rate and change the disk morphology highly susceptible to fragmentation even 1 nG, is amplified to about 1mG strength I) [21, 22]. Self-gravitational instabilities ume ecent advances in the modeling of galactic ty component in the n of the first stars ∼ r core. The right image depicts the total magnetic 3 , showing the central region of our highest-resolution simu 6 10 ∼ Two-dimensional slices through the center of the collapsin In summary, we conclude that the ubiquity of turbulence in th The generation of strong magnetic fields has interesting con resolved by 128 cells). The circle indicates the control vol J λ ( infall in the outer regions and turbulent motions in the inne field amplitude and the local magnetic field direction. radial profile of the Mach number in Fig. 2.2d illustrates tha while inside the core, the velocities are subsonic. 3. Conclusions and Discussions the generation of strong magnetic fields byhighest the resolution small-scale simulation t that a weak seed field of star-forming clouds imply that thetion presence [20], of and magnetic by fiel doing somagnetic strongly fields influences in the influencing stellar the mas fragmentationto properties evolve our existing simulations beyondan the insight exponential on g the saturatedFurthermore, field small-scale strengths dynamo to generated be fieldsaccretion expected disk can in via t influe the magneto-rotational instabilityin (MR concert with the MRI can effectively decrease the accreti amplified to values close to equipartition. In particular, r in the central collapsing coreworks during in the formation simulations of in the whichat fir the least turbulent 32 motions cells. within t of how the first stars formnamical simulations and [19] how suggest they that the influence primordial subsequentfor gas co subsonic is turbulence. Magnetic fields can significantly i Figure 1: strength has increased by a factor of The generation of strong magnetic fields during the formatio density peak. The left image shows the density and the veloci PoS(CRF 2010)029 , i.e., l (panel v r v city (panel c) Sharanya Sur 4. olume as a function ∼ τ 12. The data are taken = e infall velocity, τ tions in a gravity-driven turbulent tional collapse of a magnetized gas derstanding of the complex interplay address these questions in more detail text of the first stars but also applies to cal Jeans length. Panel (a) shows the rms tudy that merits a careful analysis are - e Jeans radius at turbulence in a gravitationally collapsing ct flux freezing, (c) the evolution of the mean n of the first stars , showing the turbulent dynamo amplification by 3 / 2 m ρ / 4 rms B together with the rms fluctuations of the lateral velocity r v . The runaway collapse commences at about rms v (panel b), the radial profile of the rms value of the total velo r v , (b) the evolution of Evolution of the dynamical quantities in the central Jeans v rms B Time evolution of the the radial profile of the mean value of th and (d) the rms velocity m ρ , for five runs with different number of cells to resolve the lo τ a), the radial profile of the rms value of magnetic field strength and the Mach number (panel d). The vertical line indicates th Right (Fig. 2.2): of Figure 2: Left (Fig. 2.1): The generation of strong magnetic fields during the formatio [23]. The other interesting questions emanating from this s from our highest-resolution run. on what scales does the magneticcloud, field - grow what during is/are the the gravita system characteristic and driving scale(s) what of is thecore. ratio Addressing of these solenoidal questions to isof gravity, crucial compressible turbulence to and mo magnetic develop fields an notany un only turbulent, in magnetized the collapsing con system inin general. [24]. We dividing out the maximum possible amplificationdensity due to perfe the component perpendicular to PoS(CRF 2010)029 , , , 321 bility , 110 (2010) Sharanya Sur , Science, , 66–92, 2007 , 163–266 , L57–L60 331 , Science, 654 348 688 The intergalactic , 79–118 (2004) tellaren Raum (miteinem 42 . K are supported by the Generation of Magnetic Fields support via the priority pro- , Phys. Rep., , 533–541 (2004) The Biermann Battery in CDM Universe. I. The Effect of , Astrophys. J., greement No 229517. R. B is 37 Λ , Astrophys. J., tion of black holes, galaxies and d by the European Community’s . Li, ion g University funded by the German B. Mori, , 165 (1950) n Garching (Germany) via grant No. servations of the TeV blazar 5 ion Rate national Collaboration II under grant P- n of the first stars . Ghirlanda and P. Coppi, , Astronomische Nachrichten, 5 , L70–L74 (2010) , Ann. Revs. Astron. Astrophys., 406 Protostar Formation in the Early Universe The Formation of the First Star in the Universe Astrophysical magnetic fields and nonlinear dynamo theory The Formation of Population III Binaries from Cosmological Cosmological Magnetic Field Generation by the Weibel Insta Magnetic fields in the early Universe , 601 (2009) Population III Star Formation in a The First Stars 325 , Zeitschrift Naturforschung Teil A, , Journal of Korean Astronomical Society, , L57–L60 (2003) , Science, Magnetic fields in the early Universe , 1–209 (2005) , Mon. Not. Roy. Astr. Soc., 599 Über den Ursprung der Magnetfelder auf Sternen und im inters 417 , 93–98 (2002) Cosmological MHD Simulations of Population III Star Format (2008) Phys. Rep., 295 Anhang von A. Schlüter) Astrophys. J., in Cosmological Shocks magnetic field constrained by Fermi/Large Area Telescope ob 1ES0229+200 (2001) Formation Redshift and Environment on Protostellar Accret 669 (2008) Initial Conditions S. S thanks the German Science Foundation (DFG) for financial [1] T. Abel, G. L. Bryan and M. L. Norman, [2] V. Bromm and R. B. Larson, [3] B. O’Shea and M. L. Norman, [9] R. Schlickeiser and P. K. Shukla, [7] K. Subramanian, [6] D. Grasso and H. R. Rubinstein, [8] L. Biermann, [5] M. J. Turk, T. Abel and B. O’Shea, [4] N. Yoshida, K. Omukai and L. Hernquist, [13] A. Brandenburg and K. Subramanian, gram 1177 ’Witnesses of Cosmictheir History: environment’ (grant Formation and KL evolu 1358/10).Seventh Framework D. Programme R. (FP7/2007-2013) G.funded under S by is grant the supporte a Emmy-NoetherLandesstiftung grant Baden-Württemberg (DFG) via their BA program 3607/1. Inter LS-SPII/18. C. Computing time F at and the R.h1221 Leibniz-Rechenzentrum i and S partial support fromExcellence a Initiative is Frontier acknowledged. grant of Heidelber References The generation of strong magnetic fields during the formatio Acknowledgments [10] M. V. Medvedev, L. O. Silva, M. Fiore, R. A. Fonseca and W. [11] F. Tavecchio, G. Ghisellini, L. Foschini, G. Bonnoli, G [12] H. Xu, B. W. O’Shea, D. C. Collins, M. L. Norman, H. Li and S PoS(CRF 2010)029 , , ation. Is Sharanya Sur mordial Star , , 444–450 727 371 , L134–L138 (2010) The Generation of Strong A new Jeans resolution 721 , Astrophys. J., tars and galaxies. I. The ideal MHD Evolution of Self-Gravitating Magnetized Amplification of Interstellar Magnetic lence and Gravitational Instabilities II stars , 339–349 (2004) pplication to magnetic field amplification s, Gravitational fragmentation in turbulent , R. S. Klessen, R. Beck and M. Spaans, d R. S. Klessen, d R. S. Klessen, , Astrophys. J., 617 n of the first stars , 25–34 (2008) , Mon. Not. Roy. Astr. Soc., 477 6 Simulations of nonhelical hydromagnetic turbulence The Formation of the First Stars. I. The Primordial , Astrophys. J., , 23–51 (2002) 564 Magnetic processes in a collapsing dense core. II. Fragment , 401–413 (2004) , 115 (2010) , Astron. Astrophys., , Astrophys. J., accepted, arXiv:1102.0266 (2011) 603 522 Protostellar Disk Dynamos and Hydromagnetic Outflows in Pri On the first generation of stars , Astrophys. J., , 364–375 (2004) , 016308 (2004) 616 70 , Astrophys. J., , Astron. Astrophys., Phys. Rev. E, Fields by Supernova-driven Turbulence Star-forming Cloud doi:10.1088/0004-637X/727/2/110 (2011) there a fragmentation crisis? primordial gas and the initial mass function of Population I Magnetic Fields During the Formation of the First Stars Small-scale dynamo action during the formationlimit of the first s Formation (2006) Disks. II. Interaction between Magnetohydrodynamic Turbu Astrophys. J., criterion for (M)HD simulations of self-gravitating gas: A by gravity-driven turbulence [17] N. E. Haugen, A. Brandenburg and W. Dobler, [18] D. S. Balsara, J. Kim, M. -M. Mac Low and G. J. Mathews, [20] P. Hennebelle and R. Teyssier, [19] P. C. Clark, S. C. O Glover, R. S. Klessen and V. Bromm, The generation of strong magnetic fields during the formatio [14] D. R. G. Schleicher, R. Banerjee, S. Sur, T. G. Arshakian [16] S. Sur, D. R. G. Schleicher, R. Banerjee, C. Federrath an [21] J. Tan and E. Blackman, [15] V. Bromm, P. S. Coppi and R. B. Larson, [22] J. Silk and M. Langer, [23] S. Fromang, S. A. Balbus, C. Terquem and J. -P. DeVillier [24] C. Federrath, S. Sur, D. R. G. Schleicher, R. Banerjee an