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Simulations of the lunar-forming impact using a new equation of state

Wissing, Robert LU (2017) In Lund Observatory Examensarbeten ASTM31 20171
Department of Astronomy and Theoretical Physics
Lund Observatory
Abstract
In this thesis we add a temperature dependence to the newly developed variable polytrope equation of state (Varpoly EOS) from Weppner et al. (2015), making it more universal and more applicable for planetary simulations. In this process we develop a new model for the Gruneisen parameter, which is a parameter that describes how pressure changes with the internal energy. This new model conforms to theoretical infinite pressure values, which other models often fail to do. We also show that this new model fits well with high pressure melting data of hexagonal close packaged iron and to an experimental density model of the Earth (Dziewonski and Anderson, 1981). The giant-impact models are the closest to capturing all the properties of the... (More)
In this thesis we add a temperature dependence to the newly developed variable polytrope equation of state (Varpoly EOS) from Weppner et al. (2015), making it more universal and more applicable for planetary simulations. In this process we develop a new model for the Gruneisen parameter, which is a parameter that describes how pressure changes with the internal energy. This new model conforms to theoretical infinite pressure values, which other models often fail to do. We also show that this new model fits well with high pressure melting data of hexagonal close packaged iron and to an experimental density model of the Earth (Dziewonski and Anderson, 1981). The giant-impact models are the closest to capturing all the properties of the Earth-Moon system. However most of the models have a problem in recreating the isotopic and FeO deviation that we see between the Earth and the Moon. The similarity in isotopic compositions requires that the disk is composed of the same fraction of proto-Earth material as the Earth; while to explain the FeO deviation we require more material from the impactor in the resulting disk. Karato (2014) suggested that this is a problem with modeling planets with just one homogeneous silicate layer and that the compositional difference between the Earth and the Moon could be explained if Earth had a primordial magma ocean. During the collision the magma would have been asymmetrically heated and ended up enriching the orbiting debris, that eventually coalesced into the Moon. To verify the need of an additional enrichment source, we show from a compositional analysis that FeO/MgO ratio’s are inconsistent with a single homogeneous silicate layer and that additional enrichment of FeO in the disk is required. Using our new EOS we present simulations done on the lunar-forming impact, investigating the effect of a primordial magma ocean. This is investigated using the impact parameters of both the ’canonical’ case (Benz et al., 1989; Canup and Asphaug,2001) in which a Mars-sized impactor hit a non-rotating Earth at an oblate angle and the fast-rotating case (Cuk and Stewart, 2012), in which a half-sized Mars impactor hit a fast spinning Earth head on. We find that the magma ocean results in little to no different in the resulting Moon and we conclude that the ’canonical’ case best captures the dynamical aspect (final masses,spin and angular momentum) of the current Earth-Moon system. We find that the fast-spinning case is unable to form the Moon with our models. We also investigate the effect that an icy Theia would have on the lunar-forming collision, we find that this reduces the probability of a successful Moon forming collision. The simulations are done with the VINE smoothed particle hydrodynamics program (Wetzstein et al., 2009). Aside from this we also perform an analysis on the effect that the different artificial viscosity prescriptions in SPH have on the Moon-forming impacts. (Less)
Popular Abstract (Swedish)
Någon gång i våra liv har vi tittat upp på natthimlen och skådat vår allt lojala kompanjon. Månen har genom mycket av människans historia setts som ett oupn åligt objekt, men år 1969 så gick människan bortom sina gamla bergränsningar och tog sina första kliv på Månen. Från månstenar som samlats in genom detta uppdrag så upptäckte vi att Månen en gång i tiden måste ha haft ett magma hav. Men det underliga med detta är att Månen är för liten för att kunnat ha haft ett magma hav om den formats som de flesta andra himlakropparna. Detta sprakade iden om att Månen kan ha bildats från resterna av en kollision mellan Jorden och en Mars liknande himlakropp, kallad Theia. Från numeriska simuleringar så har man visat att man kan skapa en Måne från en... (More)
Någon gång i våra liv har vi tittat upp på natthimlen och skådat vår allt lojala kompanjon. Månen har genom mycket av människans historia setts som ett oupn åligt objekt, men år 1969 så gick människan bortom sina gamla bergränsningar och tog sina första kliv på Månen. Från månstenar som samlats in genom detta uppdrag så upptäckte vi att Månen en gång i tiden måste ha haft ett magma hav. Men det underliga med detta är att Månen är för liten för att kunnat ha haft ett magma hav om den formats som de flesta andra himlakropparna. Detta sprakade iden om att Månen kan ha bildats från resterna av en kollision mellan Jorden och en Mars liknande himlakropp, kallad Theia. Från numeriska simuleringar så har man visat att man kan skapa en Måne från en sådann kollision, men problemet har varit att de mesta av materialet som formade Månen kom från rester av Theia. Detta är osannolikt pågrund av data uppsamlat från en analys av månstenar, som visat att Jorden och Månen har en nästan identisk syreisotops sammansättning. Detta betyder att mer av resterna som formade Månen måste ha kommit från Jorden. Detta har lett till nya teorier om formationen av Månen men ingen har ännu kunnat återskapa alla dess egenskaper. 2014 så föreslåg Shun-Ichiro Karato att den missade pusselbiten kan komma från Jordens ursprungliga magma hav. Han föreslåg att det skulle kunnat ha skett en större uppvärmning på Jordens yta pågrund av magma havet, vilket skulle i teorin leda till att mer material som formade Månen skulle komma från Jorden. Denna effekt har än så länge inte tagits hand om i någon av de förgående mån formations simuleringarna. Detta mycket på grund av att det saknas en material formulering som kan beskriva magma havet. I denna uppsats så har vi utvecklat en formulering som till en större grad kan beskriva magma havet och vilket i allmänhet förbättrar beskrivningen av planetära material. (Less)
Please use this url to cite or link to this publication:
author
Wissing, Robert LU
supervisor
organization
course
ASTM31 20171
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Lund Observatory Examensarbeten
report number
2017-EXA116
language
English
id
8921891
date added to LUP
2017-07-27 09:58:19
date last changed
2017-07-27 09:58:19
@misc{8921891,
  abstract     = {In this thesis we add a temperature dependence to the newly developed variable polytrope equation of state (Varpoly EOS) from Weppner et al. (2015), making it more universal and more applicable for planetary simulations. In this process we develop a new model for the Gruneisen parameter, which is a parameter that describes how pressure changes with the internal energy. This new model conforms to theoretical infinite pressure values, which other models often fail to do. We also show that this new model fits well with high pressure melting data of hexagonal close packaged iron and to an experimental density model of the Earth (Dziewonski and Anderson, 1981). The giant-impact models are the closest to capturing all the properties of the Earth-Moon system. However most of the models have a problem in recreating the isotopic and FeO deviation that we see between the Earth and the Moon. The similarity in isotopic compositions requires that the disk is composed of the same fraction of proto-Earth material as the Earth; while to explain the FeO deviation we require more material from the impactor in the resulting disk. Karato (2014) suggested that this is a problem with modeling planets with just one homogeneous silicate layer and that the compositional difference between the Earth and the Moon could be explained if Earth had a primordial magma ocean. During the collision the magma would have been asymmetrically heated and ended up enriching the orbiting debris, that eventually coalesced into the Moon. To verify the need of an additional enrichment source, we show from a compositional analysis that FeO/MgO ratio’s are inconsistent with a single homogeneous silicate layer and that additional enrichment of FeO in the disk is required. Using our new EOS we present simulations done on the lunar-forming impact, investigating the effect of a primordial magma ocean. This is investigated using the impact parameters of both the ’canonical’ case (Benz et al., 1989; Canup and Asphaug,2001) in which a Mars-sized impactor hit a non-rotating Earth at an oblate angle and the fast-rotating case (Cuk and Stewart, 2012), in which a half-sized Mars impactor hit a fast spinning Earth head on. We find that the magma ocean results in little to no different in the resulting Moon and we conclude that the ’canonical’ case best captures the dynamical aspect (final masses,spin and angular momentum) of the current Earth-Moon system. We find that the fast-spinning case is unable to form the Moon with our models. We also investigate the effect that an icy Theia would have on the lunar-forming collision, we find that this reduces the probability of a successful Moon forming collision. The simulations are done with the VINE smoothed particle hydrodynamics program (Wetzstein et al., 2009). Aside from this we also perform an analysis on the effect that the different artificial viscosity prescriptions in SPH have on the Moon-forming impacts.},
  author       = {Wissing, Robert},
  language     = {eng},
  note         = {Student Paper},
  series       = {Lund Observatory Examensarbeten},
  title        = {Simulations of the lunar-forming impact using a new equation of state},
  year         = {2017},
}