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Crystalline Diamond Maximum Mass

  1. Feb 2, 2008 #1

    The maximum mass of a 'naturally existing' cryogenic diamond crystal is equivalent to the Chandrasekhar limit of [itex]M_{t} = 1.43 \cdot M_{\odot}[/itex] and is called a Black Dwarf star, and can explode in a Type Ia supernova with energy: [itex]E_s = 1-2 \cdot 10^{44} \; \text{joules}[/itex].

    A Type Ia supernova emits equivalent to the amount of energy Sol emits by lifetime:
    [itex]L_{\odot} = 3.846 \cdot 10^{26} \; \text{joules} \cdot \text{s}^{-1}[/itex]
    [itex]t_{\odot} = 1.441 \cdot 10^{17} \; \text{s}[/itex]
    [itex]E_{\odot} = L_{\odot} \cdot t_{\odot} = \left(3.846 \cdot 10^{26} \; \text{joules} \cdot \text{s}^{-1} \right) \left( 1.441 \cdot 10^{17} \; \text{s} \right) = 5.543 \cdot 10^{43} \; \text{joules}[/itex]

    [itex]\boxed{E_{\odot} = 5.543 \cdot 10^{43} \; \text{joules}}[/itex]

    [itex]n_s = \frac{E_s}{E_{\odot}} = \frac{2 \cdot 10^{44} \; \text{joules}}{5.543 \cdot 10^{43} \; \text{joules}} = 3.608[/itex]

    [itex]\boxed{n_s = 3.608}[/itex]

    The estimated mass of star BPM 37093 is [itex]M_{s} = 1.1 \cdot M_{\odot} [/itex] and its temperature is [itex]T_s = 1.1 \cdot 10^4 \; K[/itex] and radius: [itex]r_s = 0.6 \cdot r_e = 3826.86 \; \text{km}[/itex].

    [itex]\boxed{r_s = 3826.86 \; \text{km}}[/itex]


    Reference:
    Wikipedia - Diamond
    Columbia Encyclopedia - White Dwarf
    Wikipedia - Chandrasekhar limit
    Wikipedia - White Dwarf
    Wikipedia - Black Dwarf
    Wikipedia - BPM 37093
    Wikipedia - Carbon detonation
    Wikipedia - Type Ia Supernova
     

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    Last edited: Feb 2, 2008
  2. jcsd
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