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33
bibliographie.bib
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@ -74,23 +74,22 @@
}
@InProceedings{CollisionParameters,
author = {{Maindl}, Thomas I. and {Dvorak}, Rudolf},
title = {{Collision parameters governing water delivery and water loss in early planetary systems}},
booktitle = {Exploring the Formation and Evolution of Planetary Systems},
year = {2014},
editor = {{Booth}, Mark and {Matthews}, Brenda C. and {Graham}, James R.},
volume = {299},
series = {IAU Symposium},
month = {Jan},
pages = {370-373},
doi = {10.1017/s1743921313008971},
eprint = {1307.1643},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
adsurl = {https://ui.adsabs.harvard.edu/abs/2014IAUS..299..370M},
archiveprefix = {arXiv},
file = {:/home/lukas/Bachelorarbeit/papers/collision parameters.pdf:PDF},
keywords = {solar system: formation, celestial mechanics, methods: n-body simulations, Astrophysics - Earth and Planetary Astrophysics},
primaryclass = {astro-ph.EP},
author = {{Maindl}, Thomas I. and {Dvorak}, Rudolf},
title = {{Collision parameters governing water delivery and water loss in early planetary systems}},
booktitle = {Exploring the Formation and Evolution of Planetary Systems},
date = {2014-01},
editor = {{Booth}, Mark and {Matthews}, Brenda C. and {Graham}, James R.},
volume = {299},
series = {IAU Symposium},
pages = {370-373},
doi = {10.1017/s1743921313008971},
eprint = {1307.1643},
eprintclass = {astro-ph.EP},
eprinttype = {arXiv},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
adsurl = {https://ui.adsabs.harvard.edu/abs/2014IAUS..299..370M},
file = {:/home/lukas/Bachelorarbeit/papers/collision parameters.pdf:PDF},
keywords = {solar system: formation, celestial mechanics, methods: n-body simulations, Astrophysics - Earth and Planetary Astrophysics},
}
@Article{CollisionTypes,

59
main.tex
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@ -26,26 +26,61 @@ Here comes some short science explanation about how planets form and water is tr
\section{The perfect merging assumption}
To better understand how this process works, large n-body simulations over the lifetime of the solar systems have been conducted.\todo{give an example} Most of these neglect the physical details of collisions when two bodies collide for simplicity and instead assume that a perfect merging occurs. So all of the mass of the two progenitor bodies and especially all of their water is retained in the newly created body. Obviously this is a simplification as in real collisions perfect merging is very rare and most of the time either partial accretion or a hit-and-run encounter occurs. (\cite{CollisionTypes}) Therefore the amount of water retained after collisions is consistently overestimated in these simulations.
To better understand how this process works, large n-body simulations over the lifetime of the solar systems have been conducted.\todo{give an example} Most of these neglect the physical details of collisions when two bodies collide for simplicity and instead assume that a perfect merging occurs. So all the mass of the two progenitor bodies and especially all of their water (ice) is retained in the newly created body. Obviously this is a simplification as in real collisions perfect merging is very rare and most of the time either partial accretion or a hit-and-run encounter occurs. (\cite{CollisionTypes}) Therefore the amount of water retained after collisions is consistently overestimated in these simulations. Depending on the parameters like impact angle and velocity a large fraction of mass and water can be lost during collisions.
\section{Some other heading}
To understand how the water transport works exactly one has to find an estimation of the mass and water fractions that are retained during two-body simulations depending on the parameters of the impact.
\todo{And here the explanation of the chapters}
\begin{figure}
\centering
% \includegraphics[width=.5\linewidth]{thefile.png}
\caption{\blabla}
\label{fig:bla}
\end{figure}
\chapter{Simulations}
\lipsum[1-2]
\section{Model}
Even more \enquote{Text} with \SI{20.4e5}{\kilo\meter\per\hour}!
For a realistic model of two gravitationally colliding bodies the SPH (smooth particle hydrodynamics) code \texttt{miluphCUDA} as explained in \cite{Schaefer2016} is used. It is able to simulate brittle failure and the interaction between multiple materials.
\begin{align}
\dv{a}
\end{align}
In the simulation two celestrial bodies are placed far enough apart so that tidal forces can affect the collision. Both objects consist of a core with the physical properties of basalt rocks and a outer mantle made of water ice.
To keep the simulation time short and make it possible to do many simulations with varying parameters 20k SPH particles are used\todo{Why 20k?} and each simulation is ran for 300 timesteps of each \SI{144}{\second} so that a whole day of collision is simulated.
%These will be split into two bodies according to the parameters of the simulations and placed far enough away that
\section{Parameters}
Six parameters have been identified that have an influence on how the result of the simulation
\subsection{impact velocity}
The collision velocity $v_0$ is defined in units of the mutual escape velocity of the projectile and the target. Simulations have been made from $v_0=1$ to $v_0=5$. As one expects a higher velocity results in a stronger collision and more and smaller fragments.
\subsection{impact angle}
The impact angle is defined in a way that $\alpha=\ang{0}$ corresponds to a head-on collision and higher angles increase the chance of a hit-and-run encounter. The simulation ranges from $\alpha=\ang{0}$ to $\alpha=\ang{60}$
\subsection{target and projectile mass}
\todo{make sure I am not mixing up target and projectile here}
The masses in this simulation range from about two Ceres masses (\SI{1.88e+21}{\kilogram}) to about two earth masses (\SI{1.19e+25}{\kilogram}). In addition to the target mass $m$, the mass fraction between target and projectile $\gamma$ is defined. As the whole simulation setup is symmetrical between the two bodies only mass fractions below and equal to one have been considered.
\subsection{water fraction of target and projectile}
Both bodies
\begin{table}
\centering
\begin{tabular}{r|rrrrr}
$v_0$ & 1 & 1.5 & 2&3 & 5 \\
$\alpha$ & \ang{0} & \ang{20} & \ang{40} & \ang{60} &\\
$m$ &\SI{e21}{\kilogram} & \SI{e23}{\kilogram} & \SI{e24}{\kilogram} & \SI{e25}{\kilogram} &\\
$\gamma$ & 0.1 & 0.5 & 1 &&\\
water fraction target & \SI{10}{\percent} & \SI{20}{\percent} &&&\\
water fraction projectile & \SI{10}{\percent} & \SI{20}{\percent} &&&\\
\end{tabular}
\label{tab:first_simulation_parameters}
\caption{parameter set of the first simulation run}
\end{table}
\section{More text}

5
template.tex
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@ -38,11 +38,12 @@ british, % language of the document
% properly format
\usepackage{siunitx}
\DeclareSIUnit{\nothing}{\relax}
\sisetup{
per-mode=fraction, % create a fraction instead of km h^-1
% locale=DE,
locale=US,
output-decimal-marker = {.}, % usefull even for German
output-decimal-marker = {.}, % useful even for German
separate-uncertainty = true,
quotient-mode=fraction
}
@ -78,7 +79,7 @@ british, % language of the document
\PassOptionsToPackage{hyphens}{url}\usepackage[
backend=biber,
style=authoryear, % choose a style from https://de.overleaf.com/learn/latex/Biblatex_citation_styles
style=authoryear-comp, % choose a style from https://de.overleaf.com/learn/latex/Biblatex_citation_styles
%sortlocale=de_AT,
sortlocale=en_GB,
backref=true % use if you like it -- puts a link to the page where it is cited into the bibliography