Synthetic Observations of Radio Jets in Cluster Environments

Introduction
We have performed several different calculations of jets in galaxy cluster environments^[1]. In these simulations a pair of bi-directed jets are launched from the center of a model cluster. The galaxy cluster is initialized with a NFW dark matter density distribution. This distribution defines the gravitational potential for the jets and cluster plasma. A two component density β-profile is used for the ICM plasma. The ICM magnetic field is tangled with a magnitude that keeps the gas pressure a factor 100 higher than the magnetic pressure. The jet plasma is introduced onto the grid at Mach 30 in pressure equilibrium with the local ICM but is a factor of 100 less dense. A toroidal magnetic field is used for the jets.

Observations
In a post processing step we calculate the X-ray and Radio emission from the simulations. These observations allow us to make direct comparisons between the simulation and real observations. We are particularly interested in the X-ray morphology of the X-ray cavities produced by the low density jet plasma, the high energy X-ray emission from inverse Compton up-scattering of CMB photons by cosmic rays and the spectral properties from the radio synchrotron emission. We test observational techniques for determining physical parameters by comparing their results with known values directly from the simulation^[2].

Simulations
Each simulation is calculated on a 600x480x480 Cartesian grid. Each zone is 1 kpc³.

Observational Tests
Many physical parameters can be calculated from real observations of galaxy clusters and AGN. We seek to test the reliability of those measurements made from the radio lobes/X-ray cavities.

X-ray Observational Tests

1. X-ray Cavity Enthalpy: These cavities provide a geometrical means to measuring the power from the AGN. A lower estimate the the total energy from the AGN can be derived by the sum of the thermal content of a cavity and the work required to inflate it against the pressure of the surrounding ICM, H = U_therm + pV, where H is the enthalpy of the cavity. Assuming pressure balance between the ICM and cavity, a common assumption, the enthalpy is given by H = γpV/(γ - 1), where γ is the ratio of specific heats. By simply measuring the cavity volume and surrounding pressure from observation an estimate of the cavity enthalpy can be derived.
2. X-ray Cavity Age: Three different timescales are commonly used to estimate cavity age; buoyant rise time, refill time and sound crossing time. The former two depend on knowing the geometry of the cavity and the gravitational acceleration in the region the cavity is rising through. The latter requires knowing the sound speed. All of these quantities can be measured from observation from assumptions such as hydrostatic equilibrium and an isothermal ICM. This age can be directly compared with the known age of the cavity from the simulation.
3. Cavity Power: By simply taking the ratio between cavity enthalpy and cavity age you have an estimate of the mechanical power of the AGN. If none of the energy from the AGN went into any other form such as kinetic, thermal or gravitational energy in the ICM this measure should give the total power. Since this is not the case in our simulations, mechanical luminosity gives you a lower limit to the total power. Exactly how the energy gets partitioned between these various forms depends on the history of the jet.

Radio Observational Tests

1. Equipartition: A commonly used method for estimating magnetic field strength is the equipartition or minimum energy calculation. This begins by considering the total energy in the radio lobes as the sum of the energy in particles and the energy in the magnetic field, E_tot = (1+k)E_particles + VfB²/8π, where Vf is the volume filled with magnetic field and k is a correction to account for heavy particles. Equipartition is when both terms on the right hand side are equal and one solves for B. Minimum energy is done by taking a derivative of this formula, setting it equal to zero and solving for B. The quantity E_particles can be measured from the total radio luminosity. The radio emission is synchrotron emission from relativistic charged particles. The power radiated by a single particle is dependent on its energy. The total luminosity is an integral over the particle distribution function. Minimum energy and equipartition differ only by a small factor. We can test this measure of the magnetic field with the known line of sight values from the simulation.
2. Spectral Index: Radio synchrotron emission from a power law distribution of particles has a power law spectrum ∝ ν^-α, where α is related to the particle spectrum. High values of alpha are called steep spectrum while low values are flat. Radio spectra will be steep at high frequencies because the density of particles with sufficient energy to radiate at those frequencies is low. This happens because these particles will quickly lose kinetic energy and move to lower energies in the particle distribution. The rate at which particles move from high to low energy is related to the strength of the magnetic field. If one has a measure of the magnetic field, say from equipartition measures, one can measure the age of the particle population. We can compare this age with the time since jet termination.

High Energy X-ray Observational Tests

1. Spectral Index: Just as in synchrotron emission, energetic particles will also lose energy when the collide with photons from the Cosmic Microwave Background (CMB) in a way that is dependent on their kinetic energy. High energy particles will on average lose more energy in a collision and quickly move to lower energies in the distribution. Here, however, the rate that this occurs at is related to the very well known energy density of the CMB photon field. Measuring the spectrum of the inverse Compton emission at high energies should give a good measurement of the particle population. We can test this by comparing with the particle populations known in our simulations.

Presentations
This work was initially presented at the Radio Galaxies in the Chandra Era meeting in July, 2008 in Boston, MA. You can view the poster from that meeting from the attachment listed at the bottom of this page.

References
^[1]O'Neill, S. M. & Jones, T. W. 2008, The Astrophysical Journal, in preparation
^[2]Mendygral, P. J., O'Neill, S. M. & Jones, T. W. 2009, The Astrophysical Journal, in preparation