Crystalline Diamond Maximum Mass

1. Feb 2, 2008

Orion1

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

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

$\boxed{E_{\odot} = 5.543 \cdot 10^{43} \; \text{joules}}$

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

$\boxed{n_s = 3.608}$

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

$\boxed{r_s = 3826.86 \; \text{km}}$

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