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Low-mass star formation
Star forming regions are comprised of weakly ionised gas and are permeated by magnetic fields. Observational evidence suggests that, during the formation process of low-mass stars, outflows are launched and protostellar discs are formed. Thus, numerical simulations should reproduce these observed traits. Simulations that model ideal magnetic fields (i.e. those that assume that the gas is mostly ionised) launch well-defined first- and stellar-core outflows, however, they do not form discs.
Non-ideal magnetohydrodynamics (MHD) processes - Ohmic resistivity, ambipolar diffusion and the Hall effect - account for the neutral gas. Ohmic resistivity and ambipolar diffusion are dissipative terms; the Hall effect is dispersive, and is dependent on the orientation of the magnetic field with respect to the rotation vector of the gas. Simulations that include non-ideal MHD, include canonical ionisation rates, and are initialised with their magnetic field vector anti-aligned with the rotation vector form large protostellar discs, but launch weak first core outflows and no stellar core outflows. Read more
here, or here where we discuss the importance of each of the non-ideal MHD terms.
Below is a video of low-mass star formation using ideal magnetic fields, non-ideal magnetic fields with aligned magnetic field and rotation vectors, and non-ideal magnetic fields with anti-aligned vectors.
A collapsing, one solar mass gas cloud, modelled in the presence of a strong magnetic field. The left panel is modelled using ideal MHD, the centre panel models non-ideal MHD where the magnetic field and rotation vectors are aligned, and the right panel models non-ideal MHD where the magnetic field and rotation vectors are anti-aligned. The non-ideal MHD models use the canonical cosmic ray ionisation rate. The results are published in Wurster, Bate & Price (2018c).
In the non-ideal models, the maximum magnetic field strength is in a torus around the core rather than in the centre of it, as in the ideal models. The non-ideal processes allow for the formation of this 'magnetic wall', which prevents a strong magnetic field from building up in the centre of the core. The central magnetic field strength is much lower than expected if the magnetic field in young stars was formed by a so-called 'fossil field', thus the magnetic field must be generated by a dynamo process at a later time. Read more here.
By increasing the ionisation rate by even a factor of ten higher than the canonical rate yields results with no discs and weak outflows, as can be seen in the following videos, and discussed here.
A collapsing, one solar mass gas cloud, modelled in the presence of a strong magnetic field. The top video shows the evolution of the gas density in a slice through the code, and the bottom video shows the evolution of the magnetic field in a slice through the core; the left-hand model uses ideal MHD and the right-hand model uses non-ideal MHD with a cosmic ray ionisation rate ten times higher than the canonical value. The results are published in Wurster, Bate & Price (2018a).
Increasing the cosmic ray ionisation rate should make a non-ideal MHD model approach an ideal MHD model, while decreasing the ionisation rate should make a non-ideal MHD model approach a a purely hydrodynamical model. In Wurster, Bate & Price (2018b), we find that models with high ionisation rates can be equivalent to ideal MHD models; models with low ionisation rates are never equivalent to hydrodynamical models, but they do approach them.
The following images show a density cross-section for models with varying cosmic ray ionisation rates at three different maximum densities. The progression from ideal MHD through reasonable ionisation rates to purely hydrodynamical is clear. Click on the image for additional plots of magnetic field strength, rotational and radial velocities.
Density slices parallel to the axis of rotation through the core of the clouds at three different maximum densities. The cosmic ray ionisation rate decreases from left to right. Blank frames indicate missing data due to computational limitations. (Click image for additional plots of magnetic field and velocity slices.)
Nicil is a stand-alone Fortran90 module that calculates the ionisation values and the coefficients of the non-ideal magnetohydrodynamics terms of Ohmic resistivity, the Hall effect, and ambipolar diffusion. The module is fully parameterised such that the user can decide which processes to include and decide upon the values of the free parameters, making this a versatile and customisable code. The module includes both cosmic ray and thermal ionisation; the former includes two ion species and three species of dust grains (positively charged, negatively charged and neutral), and the latter includes five elements which can be doubly ionised.
The source code to the module is publicly available from BitBucket.org and the reference paper is Wurster (2016). The paper details both the algorithms, and how to implement it into an existing code. Nicil has been thoroughly tested in SPMHD codes, but is written to be platform independent, thus can also be implemented into grid codes. The following figures show the non-ideal MHD coefficients and their constituent components plotted against density and temperature. Both sets of plots use a barotropic equation of state, thus are drawn from the same data set.
The species number densities (first two columns), the conductivities (third column) and the non-ideal MHD coefficients (fourth column) as calculated by Nicil using a barotropic equation of state.
The library is under continual development, so please consult modifications.pdf in the home directory for details of how the code has evolved from that described in Wurster (2016).
In Wurster & Bate (2019), we performed 105 simulations to investigate disc formation and fragmentation. We investigated the effect of initial rotation rate, magnetic field strength, magnetic field orientation, and the inclusion of the non-ideal MHD processes. Most model form discs, although those with slow rotations and strong, ideal magnetic fields are susceptible to the magnetic braking catastrophe and do not form discs. Discs are more likely to fragment in the presence of fast rotations and weak magnetic fields. The image below shows the evolution of the gas column density of each model in our study.
The evolution of the gas column density of each model in Wurster & Bate (2019). Frames become black at the end of the simulation. The penultimate frame shows the final data we have for each simulation. The ultimate frame shows each simulation at its end time (either when the disc dissipates, fragments, or at approximately 16kyr after the formation of the disc).
When a galaxy's central region is very luminous (more luminous than expected, and often brighter than the rest of the galaxy), it is termed an active galactic nuclus (AGN). It is generally accepted that AGN are fuelled by gas flowing onto the supermassive black hole located at the at the centre of the galaxy. Some of the gas that is accreted onto the black hole is converted to energy and released to the surrounding environment. This feedback energy has the ability to shape both the large and small scale environment around the black hole.
There are many different numerical algorithms to describe AGN feedback. However, it is impossible to numerically compare them when they are modelled using different numerical codes and different initial conditions. Thus, to properly compare the algorithms, I model them under the same initial conditions using the same numerical code. My simulations start from two Milky Way-sized galaxies on parabolic orbits around one another, and after 1 Gyr, the two galaxies merge. Thus, I am able to track the affects the various AGN algorithms have on the evolution of the merging system. As expected, the various algorithms produce large and small scale differences, and I am able to quantify the differences since all simulations start from the same initial conditions and are all run using the numerical code, Hydra. Below are movies showing the evolution of the system, and comparing the evolution of six different models.
The evolution of Model WT.
The face-on evolution of gas density of six different models.
The edge-on evolution of gas density of six different models.
The evolution of gas density of Model WT. The simulation pauses to rotate at apoapsis, core merger and at the end of the simulation.
