The effects of line-tying on resistive tearing instability in slab geometry is studied within the framework of reduced magnetohydrodynamics (RMHD).citep{KadomtsevP1974,Strauss1976} It is found that line-tying has a stabilizing effect. The tearing mod
e is stabilized when the system length $L$ is shorter than a critical length $L_{c}$, which is independent of the resistivity $eta$. When $L$ is not too much longer than $L_{c}$, the growthrate $gamma$ is proportional to $eta$ . When $L$ is sufficiently long, the tearing mode scaling $gammasimeta^{3/5}$ is recovered. The transition from $gammasimeta$ to $gammasimeta^{3/5}$ occurs at a transition length $L_{t}simeta^{-2/5}$.
The galaxies M82, NGC 253, NGC 1068, and NGC 4945 have been detected in gamma-rays by Fermi. Previously, we developed and tested a model for cosmic ray interactions in the starburst galaxy M82. Now, we aim to explore the differences between starburst
and active galactic nuclei (AGN) environments by applying our self-consistent model to the starburst galaxy NGC 253 and the Seyfert galaxy NGC 1068. Assuming constant cosmic-ray acceleration efficiency by supernova remnants with Milky-Way parameters, we calculate the cosmic-ray proton and primary and secondary electron/positron populations, predict the radio and gamma-ray spectra, and compare with published measurements. We find that our models easily fits the observed gamma-ray spectrum for NGC 253 while constraining the cosmic ray source spectral index and acceleration efficiency. However, we encountered difficultly modeling the observed radio data and constraining the speed of the galactic wind and the magnetic field strength, unless the gas mass is less than currently preferred values. Additionally, our starburst model consistently underestimates the observed gamma-ray flux and overestimates the radio flux for NGC 1068; these issues would be resolved if the AGN is the primary source of gamma-rays. We discuss the implications of these results and make predictions for the neutrino fluxes for both galaxies.
How cosmic rays sample the multi-phase interstellar medium (ISM) in starburst galaxies has important implications for many science goals, including evaluating the cosmic ray calorimeter model for these systems, predicting their neutrino fluxes, and m
odeling their winds. Here, we use Monte Carlo simulations to study cosmic ray sampling of a simple, two-phase ISM under conditions similar to those of the prototypical starburst galaxy M82. The assumption that cosmic rays sample the mean density of the ISM in the starburst region is assessed over a multi-dimensional parameter space where we vary the number of molecular clouds, the galactic wind speed, the extent to which the magnetic field is tangled, and the cosmic ray injection mechanism. We evaluate the ratio of the emissivity from pion production in molecular clouds to the emissivity that would be observed if the cosmic rays sampled the mean density, and seek areas of parameter space where this ratio differs significantly from unity. The assumption that cosmic rays sample the mean density holds over much of parameter space; however, this assumption begins to break down for high cloud density, injection close to the clouds, and a very tangled magnetic field. We conclude by evaluating the extent to which our simulated starburst region behaves as a proton calorimeter and constructing the time-dependent spectrum of a burst of cosmic rays.
Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number e
quations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial interest and may have strong implications for solar and stellar dynamo theories as the interface between the two, called the tachocline in the Sun, plays a crucial role in many solar dynamo theories. Here we study the properties of gravity waves in stably-stratified atmospheres. In particular, we explore how gravity waves are handled in various sound-proof equations. We find that some anelastic treatments fail to conserve energy in stably-stratified atmospheres, instead conserving pseudo-energies that depend on the stratification, and we demonstrate this numerically. One anelastic equation set does conserve energy in all atmospheres and we provide recommendations for converting low-Mach number anelastic codes to this set of equations.
We apply a wind model, driven by combined cosmic-ray and thermal-gas pressure, to the Milky Way, and show that the observed Galactic diffuse soft X-ray emission can be better explained by a wind than by previous static gas models. We find that cosmic
-ray pressure is essential to driving the observed wind. Having thus defined a best-fit model for a Galactic wind, we explore variations in the base parameters and show how the winds properties vary with changes in gas pressure, cosmic-ray pressure and density. We demonstrate the importance of cosmic rays in launching winds, and the effect cosmic rays have on wind dynamics. In addition, this model adds support to the hypothesis of Breitschwerdt and collaborators that such a wind may help explain the relatively small gradient observed in gamma-ray emission as a function of galactocentric radius.
