# Presentation: 838155

## The Biermann Battery and First Structure Formation

- As a result of including a electron pressure gradient term in the generalized Ohm’s Law, a term (the Biermann battery) (1) appears in the fluid equations which generates a magnetic field.
- _x0018__x0013_
- Here ne and pe are the electron number density and pressure.  Currently we can measure ambient galactic magnetic fields of a few microGauss with Faraday rotation measurements.  The Biermann battery is one candidate for the source of a seed magnetic field (to be amplified via the traditional alpha-omega dynamo) that can generate the magnetic fields we see today.  Such cosmological magnetic fields can affect a variety of astrophysical mechanisms such as synchotron radiation and angular momentum transfer in star formation.
**Preliminary Results**
- We use ENZO to follow the evolution of three independent cosmological Gaussian initial conditions.  For each set of cosmological initial conditions, we follow with adaptive mesh simulations focusing on the five heaviest halos that form.  Our simulation box is 500 kpc/h, with two nested grids, initialized at z=99_x0018__x0013_ _x0013_from an Eisenstein and Hsu type power spectrum.  We use a top grid resolution of 1283 and an effective dark matter resolution of 5123.  We follow the evolution up to z=17.We follow the collapse up to 11 levels of refinement, doubling the resolution at each level based on over density in baryon and dark matter mass, and resolving the Jeans length.  This resolves the simulation to 21 pc.
- We approximate the amount of magnetic field generated by multiplying the magnitude of the Biermann term by the dynamical time
- This gives us an over-estimate but should be in the right order of magnitude.  We find that 10-22 Gauss fields are generated.  In Siegel and Fry (2006), cosmological perturbations at recombination are presented as a mechanism for generating seed fields of magnitude 10-28  at z=18.  This mechanism would strongly overpower that seed field, even at early times.
- Given the magnetic energy density, we can calculate the magnetic energy per particle, and therefore a temperature.  We find that the magnetic temperature is 10-31 eV, significantly less than the fluid temperature of 0.1eV.  Therefore the magnetic field should play no role in the fluid dynamics of the simulation up to redshift z=18._x0013_
**Further Directions**
- Finding the connection between vorticity and magnetic field generation (Davies & Widrow, 2000)
- Implementing MHD with advection.

**The Biermann Battery and First Structure Formation**
- Fen Zhao
- Advisor: Tom Abel
- Collaborators:  Marcelo Alvarez, Matthew Turk

- Abstract:  It is still unclear what the magnitude and effects of magnetic fields are in the early universe. Using the ENZO, a 3D adaptive mesh cosmological simulation code, we look at the statistics of magnetic fields generated in early structure formation by the Biermann battery process. Tracking six species (H, H+, He, He+, He++ and e-), we follow the formation of structure from multiple independent realizations of cosmological initial conditions to better understand how magnetic fields are generated by non aligned pressure and density gradients. These efforts are part of the larger framework of adding ideal MHD to the ENZO software.

*Biermann, L., 1950, Z. Naturforsch.** **5A, 65. *
*Davies, G., and L. M. Widrow, 2000, Astrophys. J.** **540, 755*
*Siegel, E. R. and J. N. Fry, arXiv:astro-ph/0604526*

**Density**

**Electron Fraction**

**n****e**

**Gradient of n****e**

**Gradient of p****e**

**p****e**

- Above we have the components of the Biermann battery along with density and electron fraction at z=18 for a 2.7 x 106 solar mass halo.  Side length is 40 kpc.  Note that the electron fraction is still very small.  Despite this we are still able to get significant B field generation.

- Above we see that most of the magnetic field generated can be found at the virial shock, though some is generated in the inner secondary shocks.  The second image is of the approximate magnetic field generated found from the dynamical time.

**Bierman Battery**

**Approximate Total Field Generated**

*Siegel and Fry 2006*

- This plot depicts the spectral energy density for the field generated by cosmological perturbations at recombination.  Even at the peak length scales, the field is six orders of magnitude smaller.  At the length scales of our simulation, the field generated is nine orders of magnitude smaller.