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culinary_services [2014/06/05 15:14]
warren
culinary_services [2014/06/06 15:52]
long
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 +==========Culinary Services==========
 +
 We are Culinary Services. \\ We are Culinary Services. \\
-\\ 
-Who ordered the extra side of <​sup>​44</​sup>​Ti?​ 
-  
  
 **GROUP MEMBERS**\\ **GROUP MEMBERS**\\
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 ==== TOPIC ==== ==== TOPIC ====
-Sensitivity ​studied ​of <​sup>​44</​sup>​Ti production in in core-collapse supernova environments.+Sensitivity ​studiy ​of <​sup>​44</​sup>​Ti ​and <​sup>​56</​sup>​Ni ​production in in core-collapse supernova environments.
  
 ===Scientific Background=== ===Scientific Background===
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 There are many uncertainties in our understanding of core-collapse supernovae, including the explosion mechanism and nucleosynthesis. ​ One way to gain insight into these phenomena is to study the nucleosynthesis of radioactive isotopes in the shock-heated material. ​ These isotopes, such as <​sup>​44</​sup>​Ti and <​sup>​56</​sup>​Ni,​ determine the features of the supernova light curve. ​ Observations of supernova remnants can be used to put bounds on the production of these isotopes. There are many uncertainties in our understanding of core-collapse supernovae, including the explosion mechanism and nucleosynthesis. ​ One way to gain insight into these phenomena is to study the nucleosynthesis of radioactive isotopes in the shock-heated material. ​ These isotopes, such as <​sup>​44</​sup>​Ti and <​sup>​56</​sup>​Ni,​ determine the features of the supernova light curve. ​ Observations of supernova remnants can be used to put bounds on the production of these isotopes.
  
- {{ ::​cassa.png?​nolink&​200 | Observation of Cassiopeia A.  Green shows <​sup>​44</​sup>​Ti distribution,​ blue is <​sup>​28</​sup>​Si,​ and the red shows the Fe distribution. ​ (From Grefenstette et al 2014)}}+ {{ ::​cassa.png?​nolink&​600 |Observation of Cassiopeia A.  Green shows 44Ti distribution,​ blue is 28Si, and the red shows the Fe distribution. ​ (From Grefenstette et al 2014)}} 
 +Figure: ​Observation of Cassiopeia A.  Green shows <​sup>​44</​sup>​Ti distribution,​ blue is <​sup>​28</​sup>​Si,​ and the red shows the Fe distribution. ​ (From Grefenstette et al 2014)
  
 Using simulations,​ we can use these observations to gain insight into the supernova environment. ​ By matching observed abundances, we can gain insight into the environment in which this nucleosynthesis must have taken place and in turn, the details of the explosion mechanism. ​ However, most core-collapse supernova simulations do not include sufficiently large reaction networks to simulate this nucleosynthesis. Using simulations,​ we can use these observations to gain insight into the supernova environment. ​ By matching observed abundances, we can gain insight into the environment in which this nucleosynthesis must have taken place and in turn, the details of the explosion mechanism. ​ However, most core-collapse supernova simulations do not include sufficiently large reaction networks to simulate this nucleosynthesis.
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 ===Simulations=== ===Simulations===
  
 +==Parameter Space==
 We have chosen to do a parameter space study in peak temperature,​ density, and electron fraction, tarting with a set parameter space of peak temperatures [T<​sub>​9</​sub>​ = 4 - 7] and densities [$\rho$ = 10<​sup>​5</​sup>​ - 10<​sup>​7</​sup>​ g/​cm<​sup>​3</​sup>​] for three values of the electron fraction [Y<​sub>​e</​sub>​ = 0.45, 0.50, 0.55]. ​ This parameter space roughly corresponds with the shock heated region in simulations of Cassiopeia A-like supernovae (Young & Fryer 2007). We have chosen to do a parameter space study in peak temperature,​ density, and electron fraction, tarting with a set parameter space of peak temperatures [T<​sub>​9</​sub>​ = 4 - 7] and densities [$\rho$ = 10<​sup>​5</​sup>​ - 10<​sup>​7</​sup>​ g/​cm<​sup>​3</​sup>​] for three values of the electron fraction [Y<​sub>​e</​sub>​ = 0.45, 0.50, 0.55]. ​ This parameter space roughly corresponds with the shock heated region in simulations of Cassiopeia A-like supernovae (Young & Fryer 2007).
  
 +==Thermodynamic Trajectories==
 We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations: We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations:
  
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 \end{equation} ​ \end{equation} ​
  
-Where $\tau$ is the free-fall ​timescale.  ​+where $\tau$ is the hydrodynamic ​timescale.  ​
 This leads to temperature and density trajectories:​ This leads to temperature and density trajectories:​
  
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 where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova. ​ where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova. ​
  
 +==Reaction Network ==
 We used the [[https://​wikihost.nscl.msu.edu/​talent/​lib/​exe/​fetch.php?​media=xnet_public.zip|XNet]] reaction network code.  Our code included 447 isotopes ranging from hydrogen through germanium. ​ We took the reaction rates from the [[https://​groups.nscl.msu.edu/​jina/​reaclib/​db/​library.php?​action=viewsnapshots|JINA Reaclib database]]. ​ We set the threshold temperature for NSE to be 5 GK. We used the [[https://​wikihost.nscl.msu.edu/​talent/​lib/​exe/​fetch.php?​media=xnet_public.zip|XNet]] reaction network code.  Our code included 447 isotopes ranging from hydrogen through germanium. ​ We took the reaction rates from the [[https://​groups.nscl.msu.edu/​jina/​reaclib/​db/​library.php?​action=viewsnapshots|JINA Reaclib database]]. ​ We set the threshold temperature for NSE to be 5 GK.
 +
 +==Initial Abundances and Y$_{e}$==
 +For any given peak temperature and density, our initial composition was pure $^{28}$Si (therefore Y$_{e}$ = .5) In order to change the initial Y$_{e}$, we just added protons or neutrons to the initial composition according to the following equations: ​
 +
 +\begin{equation}
 +X(^{28}Si) = 1 - \left | 2Y_{e} - 1 \right | \\
 +X(p) = \left | 2Y_{e} - 1 \right |  \hspace{1cm} ​ X(n) = \left | 2Y_{e} - 1 \right | \\
 +proton-rich \hspace{1cm} neutron-rich
 +\end{equation}
 +
 +Finally we looked at the mass fraction of several isotopes. In particular, $^{4}$He, $^{28}$Si, $^{44}$Ti, and $^{56}$Ni. We then compare our results to that of Magkotsios //et al// with in our parameter space. ​
  
 ===Results=== ===Results===
 +
 +==$^{44}$Ti Production==
 +{{ :​44ti.png?​nolink&​900| 44Ti production for a given peak temperature and peak density.}}
 +$\hspace{2cm}$ $^{44}$Ti production for a given peak temperature and peak density for three different Y$_{e}$'​s
 +
 +==$^{56}$Ni Production==
 +{{:​56ni.png?​nolink&​900| 56Ni production for a given peak temperature and peak density}}
 +$\hspace{2cm}$ $^{56}$Ni production for a given peak temperature and peak density for three different Y$_{e}$'​s
  
 **REFERENCES** \\ **REFERENCES** \\
 [[http://​adsabs.harvard.edu/​abs/​2010ApJS..191...66M|Trends in 44Ti and 56Ni from Core-Collapse Supernovae (Magkotsios et al 2010)]]\\ [[http://​adsabs.harvard.edu/​abs/​2010ApJS..191...66M|Trends in 44Ti and 56Ni from Core-Collapse Supernovae (Magkotsios et al 2010)]]\\
 [[http://​adsabs.harvard.edu/​abs/​1998ApJ...504..500T|Nuclear Reactions Governing the Nucleosynthesis of 44Ti (The et al 1998)]]\\ [[http://​adsabs.harvard.edu/​abs/​1998ApJ...504..500T|Nuclear Reactions Governing the Nucleosynthesis of 44Ti (The et al 1998)]]\\
-[[http://​adsabs.harvard.edu/​abs/​2004NewAR..48...61V|X-ray and gamma-ray studies of Cas A (Vink 2004)]] +[[http://​adsabs.harvard.edu/​abs/​2004NewAR..48...61V|X-ray and gamma-ray studies of Cas A (Vink 2004)]]\\ 
-[[http://​adsabs.harvard.edu/​abs/​2007ApJ...664.1033Y|Uncertainties in Supernova Yields I One-dimensional Explosions (Young & Fryer 2007)]] +[[http://​adsabs.harvard.edu/​abs/​2007ApJ...664.1033Y|Uncertainties in Supernova Yields I One-dimensional Explosions (Young & Fryer 2007)]]\\ 
-[[http://​adsabs.harvard.edu/​abs/​2014Natur.506..339G|Asymmetries in core-collapse supernovae from maps of radioactive ​<​sup>​44</​sup>​Ti ​in Cassiopeia A (Grefenstette et al 2014)]]+[[http://​adsabs.harvard.edu/​abs/​2014Natur.506..339G|Asymmetries in core-collapse supernovae from maps of radioactive ​44Ti in Cassiopeia A (Grefenstette et al 2014)]]
culinary_services.txt · Last modified: 2014/06/06 15:52 by long