Diamonds in the Sky

by Nicholas Mee on November 1, 2014

Alvan Clark, an American telescope manufacturer,  was testing a new 18.5″ telescope in 1862 when he discovered that Sirius, the brightest star in the night sky, has a very faint companion. Sirius is known as the Dog Star, so its companion Sirius B is sometimes referred to as the Pup.

Sirius A and its white dwarf companion Sirius B or the Pup. (copyright NASA, HST)

In 1914, Walter Adams described the first member of a new class of stars later named white dwarfs and the following year, the Pup was identified as a second such star. At a mere 8.6 light years, it is the closest white dwarf to us. These stars are remarkable because they are extremely faint compared to other similar stars. As the Pup is orbiting Sirius A, it is possible to estimate its mass, and it turns out to be comparable to the mass of the Sun. Sirius A is about twice the mass of the Sun. The bright star in the Hubble Space Telescope image on the right is Sirius A, the small dot at the bottom left is the white dwarf Sirius B – the Pup. (The spikes and rings are artefacts of the optics.)

 

Logic is the Beginning, Not the End of Wisdom!

Sirius B is notoriously difficult to see, because it is drowned out by the brilliance of Sirius A. The easiest white dwarf to see is a member of a triple star system known to astronomers as omicron 2 Eridani. This star system is a close stellar neighbour at about 16 light years distance. It is also known by the name Keid, which is derived from the Arabic for broken eggshell. The main star, which is visible to the naked eye, is orbited by a binary that requires a telescope to be seen. The binary consists of a white dwarf and an even fainter red dwarf. (Red dwarfs are ordinary stars, but lower in mass than the Sun, they are like very feeble versions of the Sun that are generating energy by converting hydrogen into helium.) According to Gene Roddenberry, the creator of Star Trek, Spock’s home planet Vulcan orbits the star Keid A.

The large star is Keid A. It is orbited by a binary system composed of a white dwarf and a fainter red dwarf. These stars are point-like when viewed from Earth, but they have been intentionally imaged slightly out of focus. (copyright Euan Mason)

 

The Puppy Dog’s Tale

The great astrophysicist Sir Arthur Eddington argued in 1924 that the only reasonable explanation for the remarkable faintness of white dwarfs was that they must be very small compared to normal stars. He estimated that the Pup must be similar in size to the Earth and therefore incredibly compact with a density of around million times the density of water or 50,000 times the density of gold. Eddington realised that the Pup offered a great opportunity to test general relativity, Einstein’s new theory of gravity. According to general relativity the intense gravity of the Pup would produce a shift in the wavelength of the light that it emits.Einstein had shown in 1905 that light consists of particles known as photons. Short wavelength, high frequency light is carried by high-energy photons and long wavelength, low frequency light is carried by low-energy photons. So blue light corresponds to high-energy photons and red light corresponds to low-energy photons. According to general relativity, just as a ball thrown upwards loses energy as it travels away from the surface of the Earth and gains energy as it travels back downwards, so a photon will lose energy as it travels away from a gravitating body and gain energy as it travels towards a gravitating body. And due to the correspondence between energy and wavelength, this will appear as a shift in the wavelength of the light.

Eddington’s calculations suggested that the gravitational redshift of light emitted from Sirius B would be the equivalent of a 20 kilometres per second Dopper shift. The following year Adams made precise spectrographic observations of Sirius B and measured the shift in the lines in its spectrum. After accounting for the shift due to the orbital motion of the white dwarf, there remained a redshift equivalent to a Doppler shift of 19 kilometres per second, just as Eddington had predicted. This was acclaimed by Eddington as a great triumph for Einstein’s theory of general relativity.

35 years later in 1959 a more accurate measurement of gravitational redshift was undertaken in a classic experiment at Harvard University by Robert Pound and Glen Rebka. Pound and Rebka fired gamma ray photons down the 22.5 metre Jefferson Tower at the university and measured the blueshift in the frequency of the photons at the bottom of the tower due to the fall in the Earth’s gravitational field. This effect is tiny. In the Earth’s rather weak gravitational field, the shift in frequency is just one part in a thousand trillion, but the results were again in line with the predictions of general relativity.

X Marks the Spot!

The difference between the predictions of Newtonian gravity and general relativity are minute in the vicinity of the Earth. They are so small that we might expect to be able to ignore them completely and never take account of the relativistic corrections to Newton’s theory. It is rather surprising therefore that we rely on an every day technology that is dependent on general relativity for its accuracy. The effects of gravitational time distortion are now routinely taken into account by the GPS (Global Positioning System) network, which is used daily by millions of people around the world. The GPS system could not function for more than a few minutes, if the predictions of general relativity were not incorporated into the system.

A Golden Ring

We now know how a white dwarf star forms. It is the dying embers of a star that has come to the end of its nuclear fusion generation. When the fuel runs out, the core contracts and the temperature rises. The outer layers of the star’s envelope may disperse into space to form a planetary nebula leaving the naked shrunken core radiating into space at a temperature of around 100,000 degrees. The image below from the Hubble Space Telescope shows a white dwarf at the centre of a famous planetary nebula known as the Ring nebula. (The white dwarf is the relatively bright star that is just to the bottom left of the centre of the ring.)

Within about 10,000 years the planetary nebula will have dispersed into the background interstellar gas leaving the white dwarf shining without its halo.

The Diamond in the Ring

There are thought to be two main types of white dwarf depending on whether fusion stops after the hydrogen burning stage or after the helium burning stage. The first type of white dwarf is composed mainly of helium, the second type, which includes Sirius B, is composed of a mixture of carbon and oxygen. As the white dwarf radiates its heat into space, it cools and begins to crystallise from the centre outwards, as shown in the illustration below. These stars are sometimes likened to giant diamonds.

Carbon-Oxygen White Dwarf (Credit: Travis Metcalfe and Ruth Bazinet, Harvard-Smithsonian Center for Astrophysics.)

The greater the mass of a white dwarf, the more it is crushed by its own gravity. Unlike ordinary stars whose size increases with mass, the size of a white dwarf decreases with mass. An accurate new measurement of the size of Sirius B was published recently. We now know that its radius is just 5,800 kilometres. By comparison the radius of the Earth is 6,371 kilometres, so just as Eddington deduced almost 90 years ago, Sirius B has almost the same mass as the Sun, but is packed into a volume smaller than the Earth.

The Dog Star

Although the Pup is very difficult to spot, even with a telescope, Sirius is a magnificent sight on a winter night in the northern hemisphere. Sirius is one of the dogs of Orion the Hunter and can be found by following the line of Orion’s belt, as shown in the illustration below.

It takes 50 years for Sirius A and B to complete one orbit. Their average separation is comparable to the distance between the Sun and Uranus. At the moment they are approaching their widest separation, which will occur in 2019, so if you do fancy trying to spot the Pup through a telescope the next few years will offer the best chance.

An Alternative Star Trek

If the Pup proves too tricky, you could try Keid which is on the other side of Orion, as shown in the following illustration.


Live Long and Prosper!


Further Information

There is a lot more information about compact stars and general relativity in my book Gravity: Cracking the Cosmic Code. www.virtualimage.co.uk/html/gravity.html

The following website gives detailed instructions about how to go about seeing Sirius B: http://florin.myip.org/blog/how-see-sirius-b

 

{ 5 comments… read them below or add one }

Fazal e Khaliq November 6, 2014 at 5:16 am

Thank you Nicholas Mee for the very interesting article

Reply

mercy joseph November 6, 2014 at 6:21 am

This is a very interesting book. Thank you for giving this information

Reply

Bob Sullivan November 8, 2014 at 4:32 am

Nicholas,

I have an autographed copy of “Higgs Force” 24 August 2012. I bought ” Gravity” last month from Amazon. I enjoyed both books. My hobby is reading about particle and physics and about the cosmos.
I have a comment to make about “Gravity – Cracking the Cosmic Code”. It is a minute detail. On page 336, under the line “The Lie of the Land” you have written “What if the hokey cokey really is what it is all about?”
Please see below:

The Hokey Pokey

You put your right hand in,
You put your right hand out,
You put your right hand in,
And you shake it all about,
You do the hokey pokey
and you turn yourself around
That what it’s all about.

I am intrigued with the thought of a hollow planet and how gravity would work on the inside.

I apologize for being critical about such a small thing.

Bob Sullivan
Freeport, FL
US

Reply

Nicholas Mee November 10, 2014 at 9:55 am

Dear Bob

I’m glad to hear that you like the books.

The hokey cokey is quite familiar in the UK. It is a strange custom that people perform at social gatherings on occasions such as New Year’s Eve, or at least they used to. It is usually considered to be just a bit of nonsense. I used the epigram because I like the idea that this bit of nonsense might really be what it’s all about rather than something much more profound like string theory.

In my experience, it is always known as the hokey cokey rather than ‘hokey pokey’. However, if the lyrics were originally ‘hokey pokey’, they may have been changed to hide any sexual connotations. Perhaps there is some connection with hocus pocus. I’m sure it is all very deep and mysterious.

Reply

Lopamudra Pal November 16, 2014 at 10:22 am

Thank you Nicholas Mee for enlightening me with more information.
I will appreciate to get more like these articles. It is real pleasure to read it.
Thanks once again.

Reply

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