Hideki Maki Department of Physics, Rikkyo University Dissipation of Magnetic Flux in Primordial Clouds Hideki Maki Department of Physics, Rikkyo University Collaborator: Hajime Susa (Rikkyo University) * This work was partly supported by the “Rikkyo University Special Found for Research”. September 3-4 2003 Mini workshop @ Niigata

Importance of the First Star’s Mass Of course, its own is one of the interesting things. Influence on the reionization of the universe Massive stars → strong UV → earlier reionization Heavy elements pollution Massive stars → production of heavy elements WMAP QSO absorption lines The mass of first stars affects the formation of objects after the first star forming. September 3-4 2003 Mini workshop @ Niigata

Mini workshop @ Niigata Mass of First Stars Star formation Fragments of high dense gas that are the parent of star are formed. Mass accretes to the core that is formed at the center of the fragment. envelope CDM density perturebation mass accretion stellar core fragments mass of a star depends on the fragment’s mass and mass accretion rate. Therefore, September 3-4 2003 Mini workshop @ Niigata filament

Mini workshop @ Niigata Mass Accretion Rate accretion disk stellar core mass accretion Envelope with angular momentum Formation of accretion disk Accretion rate depends on the rate of angular momentum transport. Mass of the first star depends on the mechanism of angular momentum transport. One of the possible mechanism is the turbulence by magnetorotational instability. (e.g. Sano, Inutsuka & Miyama 1998: Sano & Inutsuka 2001) But, we are neglecting the magnetic fields on the studies for first star, since one consider that magnetic flux in the early universe is very weak. Magnetic flux must be considered in primordial cloud too?! September 3-4 2003 Mini workshop @ Niigata

Thermal Evolution of Primordial Cloud Collapse of primordial gas cloud No heavy elements and grains Collapse at high temperature Much differential thermal history than present-day (Omukai 2000) Is dissipation history of the magnetic flux different ? September 3-4 2003 Mini workshop @ Niigata

Mini workshop @ Niigata Purpose In order to assess the seed magnetic flux in the accretion disk of first stars, we investigate the appearance of dissipation of the magnetic flux in the course of collapse of the primordial cloud. We will study the influence of seed magnetic flux for the transport of angular momentum in primordial clouds. We will derive the mass of first stars. September 3-4 2003 Mini workshop @ Niigata

Mini workshop @ Niigata Method : Contraction Free-fall core collapse One-zone approximation Equation of state with poritoropic index γ=1.1 (K : constant coefficient.) September 3-4 2003 Mini workshop @ Niigata

Method : Chemical Network Non-equilibrium of 24 species 114 chemical networks collision ionization, collision dissociation recombination, electron attachment 3 body reaction, etc. no photo-ionization, no photo-dissociation Rate equations September 3-4 2003 Mini workshop @ Niigata

Dissipation of Magnetic Flux Dissipation process Ohmic loss Magnetic energy loss as thermal energy, by charged particles colliding with neutral particles. Ambipolar diffusion Charged particles twine around the magnetic lines by Lorenz force. On the other hand, since neutrals are not influenced by the Lorenz force, neutral particles fall into the stellar core with the relative velocity for charged particles. So, magnetic flux seems to diffuse out the cloud at the point of neutrals. n n n p e e p e e p n p n n B B B p e p e p n n e n n September 3-4 2003 Mini workshop @ Niigata

Mini workshop @ Niigata Diffusion Velocity In this work, the relative velocity of dissipation for collapse gases is defined using the argument in Nakano & Umebayashi 1986. We investigate the degree of dissipation by looking a ratio of diffusion velocity for free-fall velocity. Ohmic loss Ambipolar diffusion : electrical conductivity : viscous damping time notation ν : charged particles notation n : neutral particles : reduced mass : momentum-transfer rate coefficient R : radius of cloud, c : speed of light q : charge, n : number density : free-fall velocity M : mass of cloud September 3-4 2003 Mini workshop @ Niigata

Results at Present-Day Evolution of ionized fraction at present-day diffusion velocity at present-day main charged particles : e, ions frozen dissipation main charged particles : charged grains (Nakano & Umebayashi 1986) September 3-4 2003 Mini workshop @ Niigata

Initial Conditions of Primordial Cloud Density : Temperature : Mass : Jeans mass : Chemical abundance : 　 values at 1+z =1 (Galli & Palla 1998) September 3-4 2003 Mini workshop @ Niigata

Mini workshop @ Niigata Initial Magnetic Flux rotation of protogalaxy Still too much uncertainty. generation of vorticity generation of seed magnetic flux (Biermann battery effect) We regard the initial magnetic flux as parameter. We take B = 10-25-105 G. dynamo by rotation of galaxy within galaxy formation time (Pudritz & Silk 1989) September 3-4 2003 Mini workshop @ Niigata

Results : Evolution Ionized Fraction Decreases by recombination September 3-4 2003 Mini workshop @ Niigata

Results : Diffusion Velocity Dissipation : Viscous dumping time Frozen 　：Cyclotron frequency Resign of ambipolar diffusion Resign of ohmic loss Br2=const. September 3-4 2003 Mini workshop @ Niigata

Inefficient Ohmic Loss diffusion velocity at present-day diffusion velocity at primordial Ohmic loss efficient main charged particles : grains (Nakano & Umebayashi 1986) September 3-4 2003 Mini workshop @ Niigata

Mini workshop @ Niigata Conclusions Magnetic fields are frozen, as far as the condition B<10-5(nH/1 cm-3) G is satisfied. If B=10-20 G at nH=1 cm-3, magnetic flux might be amplified to B～10-6 G at nH=1018 cm-3. future We next study the influence of seed magnetic flux for the transport of angular momentum in primordial clouds. September 3-4 2003 Mini workshop @ Niigata