Estimation of Magnetic Fields from Synchrotron Emission: Numerical Tests

Abstract

We use models of spectrally resolved cosmic ray (CR) transport in TIGRESS MHD simulations of the local ISM to produce synthetic synchrotron emission and to test, on scales from a few kpc down to ~10 pc, the traditional estimate of magnetic field strength based on the assumption of equipartition between the magnetic and total CR energy densities. Our analysis shows that the traditional equipartition estimate works well at the kpc scale of the simulation box, but breaks down at smaller scales. We find that the predicted magnetic field strength can be improved at small scales by assuming a constant CR energy density across each mock radio observation. The large-scale mean CR energy density can be estimated by assuming equipartition with the large-scale mean magnetic energy density, or as a function of additional observable quantities such as the star formation rate surface density or gas weight. In addition to estimating the magnetic field strength, we use synthetic polarized emission to create maps of the magnetic field direction. We find that the true magnetic field direction can be recovered well from the mock observations.

Figures (11)

• Figure 1: Comparison of the CR and magnetic energy densities. Each point represents the mass-weighted average value for $z < 300$ pc in one time snapshot. This includes both the R8 and R8 Arm models shown in red and blue respectively. The black diagonal line shows $e_c = e_{\rm mag}$.
• Figure 2: Vertically integrated and mass-averaged quantities from one snapshot of the R8 simulation. From left to right, the four panels show synchrotron intensity ($I_\nu$) at 1.5 GHz (\ref{['eq:Iv_synch']}), the vertical mass-weighted average of total CR energy density ($e_\textrm{c,avg}$), the vertical mass-weighted average magnetic field strength ($B_{\rm avg}$), and the traditional equipartition estimate of the magnetic field strength ($B_{\rm eq}$) as determined by \ref{['eq:equipartition']} from the synchrotron intensity. We can see that $e_\textrm{c,avg}$ is nearly constant spatially while $B_{\rm avg}$ has much greater variation. Therefore, the spatial distribution of $I_\nu$ primarily traces $B_{\rm avg}$, and the traditional equipartition estimate fails at small scales.
• Figure 3: The blue distribution represents a two-dimensional histogram of the traditional equipartition magnetic field strength, $B_{\rm eq}$ (\ref{['eq:equipartition']}), compared to the measured (mass-weighted) average magnetic field strength, $B_{\rm avg}$. The distribution includes each pixel in projected maps across all R8 model snapshots. The best fit power law to this distribution is included as a purple line with $B_{\rm eq} \propto B_{\rm avg}^{0.36}$. The black, dashed line represents $B_{\rm eq} = B_{\rm avg}$. The red points represent the values of $B_{\rm eq}$ and $B_{\rm avg}$ averaged over each kpc-scale simulation snapshot individually. While the large-scale snapshot-averaged value of $B_{\rm eq}$ estimates the large-scale average of $B_{\rm avg}$ well, the pixel-by-pixel comparison shows that $B_{\rm eq}$ fails to recover the true $B_{\rm avg}$ at smaller scales.
• Figure 4: The same as in \ref{['fig:snapshot']} for a snapshot of the R8 Arm simulation. As in \ref{['fig:snapshot']}, we see that $e_{c, \rm avg}$ is approximately constant while $B_{\rm avg}$ has greater variation. The spatial variation of $I_\nu$ is again determined by $B_{\rm avg}$, and $B_{\rm eq}$ does not estimate the small-scale magnetic field well.
• Figure 5: As in \ref{['fig:eq_dist']}, now considering the R8 Arm model. The blue distribution represents a two-dimensional histogram of the equipartition magnetic field strength, $B_{\rm eq}$, compared to the simulated, mass-averaged magnetic field strength, $B_{\rm avg}$. The best fit power law to this distribution is included as a purple line with $B_{\rm eq} \propto B_{\rm avg}^{0.45}$. The black, dashed line represents $B_{\rm eq} = B_{\rm avg}$. The red points represent the values of $B_{\rm eq}$ and $B_{\rm avg}$ averaged over the full simulation snapshots. The green points represent the averages over non-overlapping, 1 kpc-scale patches of each snapshot.