Crystalline Diamond Maximum Mass

[Orion1]

white dwarf, in astronomy, a type of star that is abnormally faint for its white-hot temperature (see mass-luminosity relation). Typically, a white dwarf star has the mass of the sun and the radius of the Earth but does not emit enough light or other radiation to be easily detected. The existence of white dwarfs is intimately connected with stellar evolution. A white dwarf is the hot core of a star, left over after the star uses up its nuclear fuel and dies. It is made mostly of carbon and is coated by a thin layer of hydrogen and helium gases. The physical conditions inside the star are quite unusual; the central density is about 1 million times that of water.

Astronomers long believed this intense pressure could cause the carbon interiors of white dwarfs to crystallize. In 2004 the discovery of BPM-37093, a star that is located 50 light-years from the Earth in the constellation Centaurus and is both pulsating and has sufficient mass to have a crystalline interior. By measuring the pulsations it was possible to study this white dwarf's interior and determine that it had crystallized to form an enormous diamond, some 950 mi (1,500 km) wide. Were it a diamond as we commonly know it, it would weigh some 10 billion trillion trillion carats.

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: $r_s = 0.6 \cdot r_e = 3826.86 \; \text{km}$.

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

A carbon-oxygen white dwarf that approaches this mass limit ($M_{t} = 1.43 \cdot M_{\odot}$), typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as carbon detonation.[6][1]

A white dwarf undergoes carbon detonation only if it has a normal binary companion which is close enough to the dwarf star to dump sufficient amounts of matter onto the dwarf, expelled during the process of the companion's own late stage evolution.

If the companion supplies enough matter to the dead star, the white dwarf's internal pressure and temperature will rise high enough to fuse the previously unfuseable carbon in the white dwarf's core. Carbon detonation generally occurs when the accreted matter pushes the white dwarf's mass close to the Chandrasekhar limit of roughly 1.4 solar masses. $M_{t} = 1.43 \cdot M_{\odot}$

...which is seen as a type Ia supernova.

Beyond this limit ($M_{s} = 1.43 \cdot M_{\odot}$), the white dwarf would begin to collapse. If a white dwarf gradually accretes mass from a binary companion, its core is believed to reach the ignition temperature for carbon fusion as it approaches the limit.

Within a few seconds of initiation of nuclear fusion, a substantial fraction of the matter in the white dwarf undergoes a runaway reaction, releasing enough energy (1-2 × 10^44 joules)[3] to unbind the star in a supernova explosion.[4]

$E_s = 1-2 \cdot 10^{44} \; \text{joules}$

Reference:
http://en.wikipedia.org/wiki/Diamond"
http://www.answers.com/topic/white-dwarf?cat=technology"
http://en.wikipedia.org/wiki/Chandrasekhar_limit"
http://en.wikipedia.org/wiki/White_dwarf"
http://en.wikipedia.org/wiki/Black_dwarf"
http://en.wikipedia.org/wiki/BPM_37093"
http://en.wikipedia.org/wiki/Carbon_detonation"
http://en.wikipedia.org/wiki/Type_Ia_supernova"

 

[AndyW]

Hello,

Thank you for sharing this information about white dwarfs and their potential to form diamonds. I find this topic very intriguing and would like to add my thoughts to the discussion.

Firstly, I would like to clarify that while the Chandrasekhar limit is currently accepted as the maximum mass for a white dwarf, there are ongoing debates and studies about whether this limit can be exceeded under certain conditions. This is an active area of research in astrophysics and there is no definitive answer yet.

Secondly, the discovery of BPM-37093 is indeed a fascinating one, but it is worth noting that this is currently the only known white dwarf with a crystallized interior. This suggests that the conditions required for carbon crystallization may be quite specific and not all white dwarfs may undergo this process.

Lastly, I would like to mention that while the energy released in a Type Ia supernova is indeed enormous, it is not equivalent to the lifetime energy output of the sun. This is because the energy released in a supernova is released in a very short period of time, whereas the sun's energy output is spread out over billions of years. It is important to differentiate between these two types of energy outputs.

Thank you for bringing up this interesting topic and I look forward to further discussions on this subject.