Which main sequence star will live longest

A first order approximation for this value is surprisingly easy to derive. You will recall that the mass of a helium-4 nucleus is slightly less than the sum of the four separate protons needed to form it.

A proton has a mass of 1. A helium-4 nucleus has a mass of 4. From equation 6. The production of each helium nucleus releases only a small amount of energy, 10 J which does not seem a lot. We know though measurement that the Sun's luminosity is 3. To produce this amount of energy, vast numbers of helium, 3. Each second, million tons of hydrogen fuse to form million tons of helium. This means 4 million tons of matter is destroyed and converted into energy each second.

The high temperature needed for hydrogen fusion is only found in the core region of the Sun. The energy potentially available from this mass of hydrogen is roughly:. Given that the Sun's energy output is currently 3.

As it is currently about about 5 billion years old this means it is half way through its main sequence life. We have now seen how energy is produced in a star such as the Sun.

How, though, does this energy escape from the star? Two processes, radiation and convection, play a vital role. The Sun's interior comprises three main regions.

High-energy gamma photons produced in the core do not escape easily from it. The high temperature plasma in the core is about ten times denser than a dense metal on Earth. A photon can only travel a centimeter or so on average in the core before interacting with and scattering from an electron or positive ion.

Each of these interactions changes both the energy and travel direction of the photon. The direction a photon travels after an interaction is random so sometimes it is reflected back into the core. Nonetheless over many successive interactions the net effect is that the photon gradually makes its way out from the core. The path it takes is called a random walk. Photons lose energy to the electrons and ions with each interaction creating a range of photon energies.

This process is known as thermalisation and results in the characteristic blackbody spectrum that forms the continuum background spectrum of stars. Interactions between ions and electrons also produce many additional photons of various energies.

These also contribute to the blackbody spectrum. The electrons and nuclei formed in fusion reactions also carry kinetic energy that they can impart to other particles through interactions, raising the thermal energy of the plasma.

Neutrinos produced by the various fusion and decay reactions travel out from the core at almost the speed of light. They are effectively unimpeded by the dense matter in the core of main sequence stars. Here, convection currents are responsible for transporting energy to the surface. Deep cells, 30, km across are responsible for supergranulation. The cells just below the photosphere are only 1, km across and are responsible for the granulation seen on the surface of the Sun as in the image below.

What happens when a main sequence star runs out of hydrogen, the fuel in its core? This leads us to evolution off the main sequence which is discussed on the next page.

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Main Sequence Stars. Equation 6. Relative energy production for the pp chain and CNO cycle. Note that at the temperature range typically found in main sequence stars, the contribution due to the pp chain is dependent on T 4 whereas that from the CNO cycle is T Above 18 million K the CNO cycle contributes most of the energy and any further slight increase in core temperature leads to a greater increase in energy output.

Credit: Background image of the Sun at Inglis, Springer, A cross-section of the three main interior regions of the Sun. Radiation dominates in the dense core and surrounding radiative region. Convection currents are responsible for transporting energy out to top of the photosphere where it then escapes as radiation into space.

A random walk of a photon from the core of a star. The mean path length increases as it moves out from the core. The photon, initially a gamma-ray also loses some energy from each interaction so that by the time it reaches the convective region it is likely to be a visible light photon. On average a photon takes 23, years to make its way from the core of the Sun to the surface where it is radiated away into space. Credit: G. The Sun's surface in 3D. Note the sunspots neat top right.

At this point, it leaves the main sequence. Larger stars find their outer layers collapsing inward until temperatures are hot enough to fuse helium into carbon.

Stars die because they exhaust their nuclear fuel. Really massive stars use up their hydrogen fuel quickly, but are hot enough to fuse heavier elements such as helium and carbon.

When the helium fuel runs out, the core will expand and cool. The upper layers will expand and eject material that will collect around the dying star to form a planetary nebula. Finally, the core will cool into a white dwarf and then eventually into a black dwarf.

This entire process will take a few billion years. The inset chart plots the core composition of H, 3 He, and 4 He. We see that for the first trillion note trillion years hydrogen drops, while 4 He increases. It moves to the upper left on the diagram. The star has now been evolving for roughly 5. Before now, the energy created by fusion has been transported by convection , which heats up the stellar material, causing it to move and mix with other colder parts of the star, much in a same way how a conventional radiator heats your room.

This has kept the star well mixed, and maintained a homogeneous chemical composition throughout the star. Now, the physics behind the energy transport changes. The increasing amounts of helium lower the opacity of the star, a measure of radiation impenetrability.

Lowering the opacity makes it easier for photons to travel larger distances inside the star, making them more effective than convection at transporting energy. We say that the stellar core becomes radiative. This causes the entire star to contract and produces a sudden decline in luminosity see red arrow. Figure 3: The interior of a 0. Now the evolutionary timescale accelerates.

The core, now pure helium, continues to increase in mass as hydrogen is exhausted in a nuclear shell around it. Afterwards, the star turns a corner. The star starts to cool off, the shell source is slowly extinguished, and the luminosity decreases. The star is on the cooling curve, moving towards Florida on the Hertzsprung-Russel diagram, on its way to become a low-mass helium white dwarf. Incredible efficiency.

Additionally, the authors compare the lifespans of stars with masses similar to the 0. Their results are shown in Figure 4. The lightest object, a 0. Instead, it rapidly cools, and fades away as a brown dwarf. Stars with masses between 0. All of them travel increasingly to the left on the Hertzsprung-Russell diagram after developing a radiative core. The radiative cores appear at progressively earlier times in the evolution as the masses increase.

Stars in the mass range 0. These stars have a growing ability to swell, compared to the lighter stars.