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- Homework Statement
- Derive the abundance ratio for [O/Si] using the solar values from Anders and Grevesse (https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node117.html) and the 40A explosion model from Maeda+2003 (https://iopscience.iop.org/article/10.1086/378948/pdf - table 2).
How do we determine [O/Si]? Note, the answer should be 2.783.
- Relevant Equations
- [X/Si] = (X/Si) / (X/Si)_⊙
Where X and Si are number densities for some element X and silicon.
If we consider for Oxygen:
- Using the solar values from Anders and Grevesse, where O_⊙ = 8.51e-04 and Si_⊙ = 3.55e-05 (abundances number relative to H).
- Using the explosion model 40A from Maeda+2003 (Table 2), we know the ejecta mass (in solar units) for:
= 5.99 M_⊙ / 15.994 amu
=0.3745 M_⊙/amu
Si = (ejecta mass of Si-28 / atomic mass of Si-28) + (ejecta mass of Si-29atomic mass of Si-29) + (ejecta mass of Si-30 / atomic mass of Si-30)
= (1.87E−01 M_⊙/27.976 amu) + (3.57E−02 M_⊙ / 28.976 amu) + (2.73E−02 M_⊙ / 29.973 amu)
= 0.008827 M⊙/amu
[O/Si] = (X/Si)/(X/Si)_⊙
= (0.3745 / 0.008827) / (8.51E−04/3.55e−05)
=1.889
Which is not 2.783...
- Using the solar values from Anders and Grevesse, where O_⊙ = 8.51e-04 and Si_⊙ = 3.55e-05 (abundances number relative to H).
- Using the explosion model 40A from Maeda+2003 (Table 2), we know the ejecta mass (in solar units) for:
- oxygen-16 = 5.99
- oxygen-17 = 5.33e-08
- oxygen-18 = 5.48e-6
- silicon-28 = 1.87e-01
- silicon-29 = 3.57e-02
- silicon-30 = 2.73e-02
= 5.99 M_⊙ / 15.994 amu
=0.3745 M_⊙/amu
Si = (ejecta mass of Si-28 / atomic mass of Si-28) + (ejecta mass of Si-29atomic mass of Si-29) + (ejecta mass of Si-30 / atomic mass of Si-30)
= (1.87E−01 M_⊙/27.976 amu) + (3.57E−02 M_⊙ / 28.976 amu) + (2.73E−02 M_⊙ / 29.973 amu)
= 0.008827 M⊙/amu
[O/Si] = (X/Si)/(X/Si)_⊙
= (0.3745 / 0.008827) / (8.51E−04/3.55e−05)
=1.889
Which is not 2.783...