A black dwarf is a white dwarf that has cooled down to the temperature of the cosmic microwave background, and so is invisible. Unlike red dwarfs, brown dwarfs, and white dwarfs, black dwarfs are entirely hypothetical.
Once a star has evolved to become a white dwarf, it no longer has an internal source of heat, and is shining only because it is still hot. Like something taken from the oven, left alone a white dwarf will cool down until it is the same temperature as its surroundings. Unlike tonight’s dinner, which cools by convection, conduction, and radiation, a white dwarf cools only by radiation.
Because it’s electron degeneracy pressure that stops it from collapsing to become a black hole, a white dwarf is a fantastic conductor of heat (in fact, the physics of Fermi gasses explains the conductivity of both white dwarfs and metals!). How fast a white dwarf cools is thus easy to work out … it depends on only its initial temperature, mass, and composition (most are carbon plus oxygen; some maybe predominantly oxygen, neon and magnesium; others helium). Oh, and as at least part of the core of a white dwarf may crystallize, the cooling curve will have a bit of a bump around then.
The universe is only 13.7 billion years old, so even a white dwarf formed 13 billion years ago (unlikely; the stars which become white dwarfs take a billion years, or so, to do so) it would still have a temperature of a few thousand degrees. The coolest white dwarf observed to date has a temperature of a little less than 3,000 K. A long way to go before it becomes a black dwarf.
Working out how long it would take for a white dwarf to cool to the temperature of the CMB is actually quite tricky. Why? Because there are lots of interesting effects that may be important, effects we cannot model yet. For example, a white dwarf will contain some dark matter, and at least some of that may decay, over timespans of quadrillions of years, generating heat. Perhaps diamonds are not forever (protons too may decay); more heat. And the CMB is getting cooler all the time too, as the universe continues to expand.
Anyway, if we say, arbitrarily, that at 5 K a white dwarf becomes a black dwarf, then it’ll take at least 10^15 years for one to form.
One more thing: no white dwarf is totally alone; some have binary companions, others may wander through a dust cloud … the infalling mass generates heat too, and if enough hydrogen builds up on the surface, it may go off like a hydrogen bomb (that’s what novae are!), warming the white dwarf quite a bit.
Stars can be big or small, hot or cool, young or old. In order to properly organize all of the stars out there, astronomers have developed an organizational system called the Hertzsprung-Russell Diagram. This diagram is a scatter chart of stars that shows their absolute magnitude (or luminosity) versus their various spectral types and temperatures. The Hertzsprung-Russell diagram was developed by astronomers Ejnar Hertzsprung and Henry Norris Russell back in 1910.
The first Hertzsprung-Russell diagram showed the spectral type of stars on the horizontal axis and then the absolute magnitude on the vertical axis. Another version of the diagram plots the effective surface temperature of the star on one axis and the luminosity of the star on the other.
By using this diagram, astronomers are able to trace out the life cycle of stars, from young hot protostars, through the main sequence phase and into the dying red giant phases. It also shows how temperature and color relate to the stars at various stages in their lives.
If you look at an image of a Hertzsprung-Russell diagram, you can see there’s a diagonal line from the upper left to the lower right. Almost all stars fall along this line, and it’s known as the main sequence. In general, as luminosity goes down, temperature goes down as well. But there’s a branch that goes off horizontally at the 100 solar luminosity mark. These are the red giant stars nearing the end of their lives. They can be bright and cool, because they’re so large. But this stage usually only lasts a few million years.
Astronomers can also use the Hertzsprung-Russell diagram to estimate how far away stellar clusters are from Earth. By mapping out all the stars in the cluster and grouping them together and comparing them to groups of stars with known distances.
We have written many articles for Universe Today about the star life cycle. Here’s an article about the cluster M13, and how astronomers use the Hertzsprung-Russell diagram to study it.
Here are some good resources on the Internet for Hertzsprung-Russell diagram. Here’s a very simple version of the diagram from the University of Oregon, and here’s more information.
Much like any living being, stars go through a natural cycle. This begins with birth, extends through a lifespan characterized by change and growth, and ends in death. Of course, we’re talking about stars here, and the way they’re born, live and die is completely different from any life form we are familiar with.
For one, the timescales are entirely different, lasting on the order of billions of years. Also, the changes they go through during their lifespan are entirely different too. And when they die, the consequences are, shall we say, much more visible? Let’s take a look at the life cycle of stars.
Stars start out as vast clouds of cold molecular gas. The gas cloud could be floating in a galaxy for millions of years, but then some event causes it to begin collapsing down under its own gravity. For example when galaxies collide, regions of cold gas are given the kick they need to start collapsing. It can also happen when the shockwave of a nearby supernova passes through a region.
As it collapses, the interstellar cloud breaks up into smaller and smaller pieces, and each one of these collapses inward on itself. Each of these pieces will become a star. As the cloud collapses, the gravitational energy causes it to heat up, and the conservation of momentum from all the individual particles causes it to spin.
As the stellar material pulls tighter and tighter together, it heats up pushing against further gravitational collapse. At this point, the object is known as a protostar. Surrounding the protostar is a circumstellar disk of additional material. Some of this continues to spiral inward, layering additional mass onto the star. The rest will remain in place and eventually form a planetary system.
Depending on the stars mass, the protostar phase of stellar evolution will be short compared to its overall life span. For those that have one Solar Mass (i.e the same mass as our Sun), it lasts about 1000,000 years.
T Tauri Star:
A T Tauri star begins when material stops falling onto the protostar, and it’s releasing a tremendous amount of energy. They are so-named because of the prototype star used to research this phase of solar evolution – T Tauri, a variable star located in the direction of the Hyades cluster, about 600 light years from Earth.
A T Tauri star may be bright, but this all comes its gravitational energy from the collapsing material. The central temperature of a T Tauri star isn’t enough to support fusion at its core. Even so, T Tauri stars can appear as bright as main sequence stars. The T Tauri phase lasts for about 100 million years, after which the star will enter the longest phase of its development – the Main Sequence phase.
Eventually, the core temperature of a star will reach the point that fusion its core can begin. This is the process that all stars go through as they convert protons of hydrogen, through several stages, into atoms of helium. This reaction is exothermic; it gives off more heat than it requires, and so the core of a main sequence star releases a tremendous amount of energy.
This energy starts out as gamma rays in the core of the star, but as it takes a long slow journey out of the star, it drops down in wavelength. All of this light pushes outward on the star, and counteracts the gravitational force pulling it inward. A star at this stage of life is held in balance – as long as its supplies of hydrogen fuel lasts.
And how long does it last? It depends on the mass of the star. The least massive stars, like red dwarfs with half the mass of the Sun, can sip away at their fuel for hundreds of billions and even trillions of years. Larger stars, like our Sun will typically sit in the main sequence phase for 10-15 billion years. The largest stars have the shortest lives, and can last a few billion, and even just a few million years.
Over the course of its life, a star is converting hydrogen into helium at its core. This helium builds up and the hydrogen fuel runs out. When a star exhausts its fuel of hydrogen at its core, its internal nuclear reactions stop. Without this light pressure, the star begins to contract inward through gravity.
This process heats up a shell of hydrogen around the core which then ignites in fusion and causes the star to brighten up again, by a factor of 1,000-10,000. This causes the outer layers of the star to expand outward, increasing the size of the star many times. Our own Sun is expected to bloat out to a sphere that reaches all the way out to the orbit of the Earth.
The temperature and pressure at the core of the star will eventually reach the point that helium can be fused into carbon. Once a star reaches this point, it contracts down and is no longer a red giant. Stars much more massive than our Sun can continue on in this process, moving up the table of elements creating heavier and heavier atoms.
A star with the mass of our Sun doesn’t have the gravitational pressure to fuse carbon, so once it runs out of helium at its core, it’s effectively dead. The star will eject its outer layers into space, and then contract down, eventually becoming a white dwarf. This stellar remnant might start out hot, but it has no fusion reactions taking place inside it any more. It will cool down over hundreds of billions of years, eventually becoming the background temperature of the Universe.