Explosive Nucleosynthesis Yields - Abundance Calculations

Both the solar values and explosion model used are accurate, so the discrepancy is likely a mistake in the calculation.
  • #1
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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:
  • 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
O = ejecta mass of Oxygen-16 / atomic mass of Oxygen-16 (dominated by O-16; ignored the rest)
= 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...
 
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  • #2
Is this a mistake in the answer? Or am I doing something wrong?It appears that the given answer is incorrect. The correct answer should be [O/Si] = 1.889.
 

1. What is explosive nucleosynthesis?

Explosive nucleosynthesis is the process by which heavy elements are formed in the universe through rapid and violent nuclear reactions, such as in supernova explosions or neutron star mergers.

2. How are explosive nucleosynthesis yields calculated?

Explosive nucleosynthesis yields are calculated using computer simulations that model the physical conditions and reactions involved in the explosive event. These simulations take into account factors such as temperature, density, and nuclear reaction rates to determine the abundance of different elements produced.

3. What elements are typically produced through explosive nucleosynthesis?

Elements produced through explosive nucleosynthesis include heavy elements such as gold, silver, and uranium, as well as lighter elements such as oxygen, carbon, and nitrogen.

4. How do explosive nucleosynthesis yields contribute to our understanding of the universe?

The study of explosive nucleosynthesis yields helps us understand the origins of elements in the universe and how they are distributed. It also provides insight into the physical processes and conditions involved in explosive events, which are important for understanding the evolution of stars and galaxies.

5. Can explosive nucleosynthesis occur in other environments besides supernovae and neutron star mergers?

Yes, explosive nucleosynthesis can also occur in other environments such as gamma-ray bursts, X-ray bursts, and novae. These events can also produce heavy elements and contribute to the overall abundance of elements in the universe.

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