White dwarfs
7.5 White dwarfs
At the centre of a planetary nebula lies a white or blue-white star. They are not very bright so that relatively large telescopes are required to see them visually. (The author has once, using a 16 in. telescope under perfect conditions, observed the star at the centre of the Ring Nebula.) This star is approaching the fi nal stage of its life when it will become a ‘white dwarf ’. Once nuclear reactions have ceased, what is left at the centre of the star will contract under gravity. It is composed mainly of carbon and oxygen, and devoid of its outer layers through a combina- tion of the intense stellar winds and the ejection of a planetary nebula. The fact that contraction fi nally ceases is due to a quantum-mechanical effect known as degeneracy pressure . In 1926, R.H. Fowler realised that, as a result of the Pauli exclusion principle, no more than two electrons could occupy a given energy state. As the allowed energy levels fi ll up, the electrons begin to provide a pressure – the electron degeneracy pressure – which fi nally halts the contraction. This pressure only depends on density, not temperature, and this has the interesting result that the greater the mass of the white dwarf, the less its radius!
A further consequence of being supported by electron degeneracy pressure is that there is a limiting mass which cannot be exceeded. This depends on the composition of the star; for a mix of carbon and oxygen, it turns out to be ∼ .4 solar masses. This result was published in 1931 by Subramanyan Chandrasekhar when he was only 19 years old! (To be totally accurate, Chandrasekhar had assumed that there would be a greater percentage of heavier elements within the white dwarf so resulting in a limit of 0.91 solar masses.) In 1983, Chandrasekhar rightly received the Nobel Prize for this and other work. We will see later what hap- pens when the mass of the collapsing stellar remnant exceeds the Chandrasekhar Limit.
White dwarfs range in size from 0.008 up to 0.02 times the radius of the Sun. The largest (and thus least massive) being comparable with the size of our Earth whose radius is 0.009 times that of the Sun. The masses of observed white dwarfs lie in the range 0.17 up to 1.33 solar masses so it is thus obvious that they must have a very high density. As a mass comparable with our Sun is packed into a volume 1 million times less, its density must be of order 1 million time greater – about 1 million grams per cubic centimetre. (A ton of white dwarf material could fi t into a matchbox!)
7.5.1 The discovery of white dwarfs
The fi rst known white dwarf was discovered by William Herschel in 1783; it was part of the triple star system 40 Eridani. What appeared surprising was that
Stellar Evolution – The Life and Death of Stars
a very low luminosity. This is, of course, due to its small size so, although each square metre is highly luminous, there are far fewer square metres! The second white dwarf to be discovered is called Sirius B, the companion to Sirius, the brightest star in the northern hemisphere. Friedrich Bessel made very accurate measurements of the position of Sirius as its proper motion carried it across the sky. The motion was not linear and Bessel was able to deduce that Sirius had a companion. Their combined centre of mass would have a straight path across the sky but both Sirius and its companion would orbit the centre of mass thus giving Sirius its wiggly path. Due to its close proximity with Sirius, Sirius B is exceedingly diffi cult to observe as it is usually obscured by light scattered from Sirius within the telescope optics. A very clean refractor has the least light scatter, and it was when Alvin Clark was testing a new 18 in. refracting telescope in 1862 that Sirius B was fi rst observed visually.
7.5.2 The future of white dwarfs
The observed surface temperatures of white dwarf stars range from 4000 up to 150 000 K so they can range from orange to blue-white in colour. Their radiation can only come from stored heat unless matter is accreting onto it from a com- panion star. As their surface area is so small it takes a very long time for them to cool; the surface temperature reduces, the colour reddens and their luminosity decreases. The less the surface temperature the less the rate of energy loss, so a white dwarf will take a similar time to cool from 20 000 down to 5000 K as it will from 5000 to 4000 K. In fact, the universe is not old enough for any white dwarfs to have cooled much below 4000 K; the coolest observed so far, WD 0346⫹246, has a surface temperature of 3900 K.
7.5.3 Black dwarfs
Eventually the white dwarf will cool suffi ciently so that there is no visible radia- tion and will then become a black dwarf . They could still, however, be detected in the infrared, though will be very faint, and the presence of those in orbit around normal stars could still be deduced by the effect they have on the motion of a com- panion star.