# Spitzer Resistivity

I added spitzer resistivity to AstroBEAR and it does appear to make a significant difference to the formation of the stand-off/stagnation shocks.

For the spitzer resistivity, I am using

And then the magnetic diffusivity (with units of cm^{2}/s) as

# HEDP Simulations

Results

There were 4 sequences of runs to compare the effect of

- Cooling vs no cooling on fiducial data
- Effect of magnetic field with cooling
- Effect of changes in magnetic diffusion length (for cooling and 2X fiducial field)
- Effect of changing the cooling length from .1 to 10x for the 2X fiducial field with ½ the fiducial diffusion length

Reference Image |

First comparison is the fiducial setup but with and without cooling

With cooling |

Without cooling |

Next we just used cooling but adjusted the magnetic field from 1.75 T to 14 T in multiples of 2

1.75 T |

3.5 T |

7 T |

14 T |

We then looked at the 7T case and explored the effect of diffusion comparing the case with no diffusion, ½ the fiducial, the fiducial, and 10X the fiducial lengths

0 |

.366 mm (½ fiducial) |

.732 mm (fiducial) |

7.32 mm (10 * fiducial) |

And finally we looked at the effect of changing the cooling in the 7T half diffusion length case

.1 cooling |

½ cooling |

fiducial cooling |

2x cooling |

10x cooling |

# Dust in AstroBEAR - Update 2021/04/26

## Objectives

- Thesis stuff
- Debugging & Testing

## Progress:

- still mainly busy writing/correcting thesis chapters
- setting up new problem setup to reproduce Slavin+2020. Simulation is currently in the queue, no videos to show yet but I've plotted the initial density profile here. Velocity and temperature profile are still a work in progress, currently trying to find the best fits to reproduce observations.

## Next Steps:

- writing, writing, writing
- potentially further work with the setup, have to discuss with supervisor

# Fermi Project Update: March 2021

As a reminder, we had previously made the probe ranges and velocities normally distributed by introducing another variable called technology, making this normally distributed through random walks, then making the probe range and velocity relativistic functions of technology.

The current goal we have been working on is introducing a fixed probability of civilization destruction per timestep for the civilizations. We ended up accomplishing this by making the civilization lifetime exponentially distributed, analogous to how we had previously had the abiogenesis time exponentially distributed.

Click here for a summary of this and some parameter sweeps.

# Update March 2021

## Coupled EBM

I submitted the paper to AJ and arXiv.

Our Paper is on arXiv Here

ADS Link

## Fermi Project

# Magnetic Field Flux in 1D

Consider the induction equation for a MHD fluid:

For the x axis,

. Hence, only the y component of the above equation is important.This gives us 10 terms to plot on the RHS, but before doing that we take integral wrt x on both sides from x = -R to x (the asteroid surface is taken to be at 0). The resulting plot is shown below for the 3 cases. The plots are labelled in the order they appear in the above equation.

# Movies of 1D shocks that move with the shock

I've generated a new set of 1D movies. They are the same as the previous one except that the spatial coordinates are shifted so that 0.0 moves with the shock. This allows us to watch instabilities evolve as the shock moves. Values of Beta start at -1.0 in the top left, increasing by 0.5 moving to the right and 2.0 by moving down

# Update 03/01

### Current jet setup

Domian size | 8.000e+13 cm | 1.150e+03 Rsun | |

Base grid size | 1.562e+11 cm | 2.246e+00 Rsun | |

L4 cell size | 9.766e+09 cm | 1.404e-01 Rsun | |

ptcl rc | 1.676e+11 cm | 2.409e+00 Rsun | 1.716e+01 # of cells |

Primary radius | 3.350e+12 cm | 4.815e+01 Rsun | |

a0 | 3.409e+12 cm | 4.900e+01 Rsun | |

Jet radius | 1.562e+11 cm | 2.246e+00 Rsun | 1.600e+01 # of cells |

Jet Mdot | 1.261e+26 g/s | 2.000e+00 Msun/yr | |

Jet vrad | 4.375e+7 cm/s | 430.75 km/s |

- Problem: jets are launched inside the particle softening radius, and most of the material is bound relative to particle 2.

- Increasing jet radial speed by a factor of 2 (the green lines below):

Energy relative to P2, with smoothed gravity

# Fermi Project Update 02/18/21

**Goal:** Figure out how to make the probe velocity and range normally distributed within our FORTRAN model.

**Method:** First added a local variable called 'technology' to the program.
Then used random walks to have it be normally distributed around the technological capabilities of the abiogenesis seed (first habited system). Finally, I made the probe range and velocity relativistic functions of this new technology variable. The table below shows the initial values inputted into the model.

Inputs | ||
---|---|---|

v0 | 0.0001c=30 km/s | Initial Probe Velocity |

r0 | 10 lyr | Initial Probe Range |

t0=r0/v0 | 100,000 years | Initial Probe Lifetime |

**Click here to see the PDF which summarizes calculation/implementation of the normally distributed probe ranges/distances**

**Click here for more information about the input variables for the models shown below.**

**Notes**

- The pink boxes surround systems that are uninhabited.
- All simulations begin with 10 systems originally habited.
- Galaxy Model shows time with unit Myr. Total runtime being 1000 Myr.
- In contrast, the periodic box model has a total runtime of 1 Myr. Thus I show frames instead of time, where each frame is approximately 1/1000 Myr.
- x=(number of habited systems)/(total number of systems)

## Galaxy Model

## Periodic Box Model

## Analytic Model

# Update 02/15

Notes about the Federrath+14 jet/outflow model:

http://www.pas.rochester.edu/~yzou5/CE/notes_Federrath+14_jet_model.pdf

Jet parameters in our model:

Jet Data | ||

jet_radius | 16 | size of outflow region in finest level cells |

jet_collimation | .2618 | pi/12 !collimation of outflow |

jet_temp | 30000. | jet temp in Kelvin |

jet_index | 1. | exponent of collimation |

jet_masslossrate | 2e0 | solar masses / yr |

lcorrect | T | Apply conservative correction |

jet_vrad | 430.75 | km/s radial velocity of jet, use Keplerian velocity for m2 and 1 solar radius |

jet_vphi | .5 | km/s approximate rotation speed of jet |

spin_axis | 0d0,0d0,1d0 | outflow axis |

to-do's

- understand the feedback module. what are the initial profiles of density and velocity inside the spherical cones launching the jets?

- compute how much of the jet material is unbound, using the spline potential, velocity profile and density profile.

- plot the jet tracer density

# Updates 2/15/21

### Early Asteroid Magnetization

Adding lineouts of the day side to illustrate the issues of theoretical estimates of amplification.

### Moon Impact Magnetization

Settled on a spherical field distribution of the form:

Will add another blog post about the equations and plot for current, and magnetic potential.

### Hot Neptunes

I have forgotten how to compile code it seems. Should be an easy fix.

# Fermi Project Update (02/13/2021)

**Goal:** Figure out how to make the probe velocity and range normally distributed within our FORTRAN model.

**Method:** First added a local variable called 'technology' to the program.
Then used random walks to have it be normally distributed around the technological capabilities of the abiogenesis seed (first habited system). Finally, I made the probe range and velocity relativistic functions of this new technology variable. See the pdf below for more details about calculation/implementation.

**Click here to see the PDF which summarizes my progress so far and potential steps.**

### Current Model Output (Colored by Technology, Pink=Unsettled)

Inputs | ||
---|---|---|

v0 | 0.0001c=30 km/s | Initial Probe Velocity |

r0 | 10 lyr | Initial Probe Range |

t0=r0/v0 | 100,000 years | Initial Probe Lifetime |

**Figure:** The above gif shows the temporal evolution of a model galaxy. Beginning with 10 habited solar systems (ie: abiogensis seeds), these systems send probes out to nearby systems, thus making those systems inhabited and repeating the process until the entire galaxy is filled with life. The uninhabited systems are shown as the pink boxes. Note that a selection effect results in the systems on the outer edge of the galaxy gaining high technological abilities before systems near the center.

# Initial Conditions for Lunar Impact Magnetization

Based on the impactor conditions from Oran et al. (2020) https://advances.sciencemag.org/content/6/40/eabb1475 and its supplementary material https://advances.sciencemag.org/content/suppl/2020/09/28/6.40.eabb1475.DC1/abb1475_SM.pdf we have most impact plasma conditions apart from the magnetic field (which they do not seem to inject by any mechanism).

Impact Plasma conditions from iSALE-2D :

**Initial Vapour temperature:**2000 K (varies down to 500 K for some models)

**Wind Speed:**400 km/s to 1000 km/s

**Wind Density:**Plots in S4, but no analytical form. Looks proportional to y.

**Magnetic field:**Probably several equations work.

Assuming the field distribution is similar to that of a very thick (radius

), finite length ( ), current carrying wire, the field and vector potential in cylindrical coordinates are:**Resistivity Profile**: Same as used for the NSF proposal.

We can start

# Runs with larger Jets

From left to right: slice of density, slice of temperature, projection of density along the axis, projection of density along the side,

Beta = -1.0, Alpha increased x10:

(projections will be done when the run completes)

Beta = +1.0, Alpha increased x10:

Beta = +3.0, Alpha increased x10:

Courtesy of Visit, two additional movies of the last run sliced in a different location than usual:

Update 8 February: Added two additional values of Beta. Original post only had Beta=+1.0

Update 16 February: Added additional run at Beta=3.0 with a larger Alpha
Update 2 March: Added runs at Beta= ± 1.0 with larger Alpha

# Thoughts on time stepping and MHD

## Thoughts on Energy Tracking in AstroBEAR

AstroBEAR does not track the thermal, magnetic, and kinetic energy separately (because it is trying to conserve total energy via conservative fluxing). It does however separately track density, momentum, and magnetic fields - which can be used to derive magnetic and kinetic energy - using thermal energy as a reservoir for discretization errors.

When you have flows that are dominated by non-thermal forms of energy (

or ), discretization errors in total energy (while dynamically unimportant) can still lead to significant relative errors in thermal energy - which can be problematic if there are significant temperature-dependent microphysical processes. In those cases it might be better to solve the thermal energy equation independently and not worry about conserving total energy.## Thoughts on time-stepping

Simulations typically run for a few dynamical times - and for flows that are kinetic energy dominated (

and ) the computational time is independent of the flow speed (only a function of resolution ). However, for flows that are magnetic or thermally energy dominated - the time stepping is limited by the Alfven or sound speeds respectively - and the computational time goes as (ignoring the extra factor of due to changes in the number of zones with resolution)This can be combined as

This makes simulating the RT instability

relatively computational expensive. Alfven waves can also restrict the time stepping when.

So simulations with modest

but very small will also be relatively computational expensive.High Alfven speeds are also somewhat easier to generate - since the magnetic fields/energy and density are not as tightly coupled as the thermal energy and density - due to material being free to leave along field lines - and the lack of flux freezing when magnetic resistivity is used.

## Explicit Magnetic Resistivity

Astrobear currently implements magnetic resistivity explicitly - without subcycling - so time steps are limited by the smaller of the cell diffusion time

and the cell crossing time . The cell diffusion time will be smaller than the cell crossing time when

So the computational time to simulate a crossing time will go as

So - you pay a penalty with explicit time stepping when

that could be avoided with implicit time stepping.## Simulations involving advection around and diffusion through an obstacle

Simulations involving advection around and diffusion through an obstacle will need to run for the longer of the crossing time around - and the diffusion time within (which is longer than the crossing time by a factor of

) - so in the explicit case we have

Making the resistive solve implicit would reduce this to

# Dust in AstroBEAR - Update 2021/01/10

## Objectives

- Debugging
- Production runs for some setups
- Thesis writing

## Main progress over break:

**Writing**: I've mainly been writing over the break and will probably be quite heavily focused on that for the next few weeks as well

**Time-stepping issue with the Gas Drag**: I'm pretty sure the time-stepping issue for the gas drag is NOT due to the equations being too stiff (not yet certain about the grain-grain collisions, still working on other stuff there). It looks like one cell eventually has a temperature that messes stuff up and leads to a runaway increase of number density (see screenshots: 1 2 3 4). Need to go back to the equation next week to see if there are any caveats for certain temperature regimes that might cause this.

**Next steps**:

- Continue with above