The bulk of stars in the galaxy, including our Sun, Sirius and also Alpha Centauri A and B are all main sequence stars. The Sun"s family member longevity and also stability have detailed the problems necessary because that life to evolve right here on Earth. Our expertise of the procedures involved and also characteristics the this an essential group of stars has progressed in parallel through our understanding of atom physics.

Properties of main Sequence StarsNucleosynthesis and blend Reactions

Properties of key Sequence Stars

Main succession stars are characterised by the source of their energy. They space all undergoing fusion of hydrogen into helium within their cores. The price at i beg your pardon they carry out this and the quantity of fuel obtainable depends upon the fixed of the star. Massive is the crucial factor in identify the expectancy of a main sequence star, that size and also its luminosity. Stars on the key sequence likewise appear to it is in unchanging for lengthy periods of time. Any model of together stars must have the ability to account for their stability.

You are watching: What prevents a brown dwarf from undergoing nuclear fusion?

Hydrostatic Equilibrium

The simple model of any kind of main sequence star is the a thick gas/fluid in a state of hydrostatic equilibrium. The inward exhilaration force, gravity, is well balanced by outside acting forces of gas pressure and the radiation pressure. Except the very hot yet tenuous corona , the pressure and also temperature of stars basically rises as you method the core.

Main succession stars basically have a fixed dimension that is a function of your mass. The more massive the star, the better its gravitational pull inwards. This consequently compresses the gas more. As you shot and compress a gas the exerts a gas push back, it resists the compression. In stars this gas pressure alone is not enough to stand up to the gravitational collapse. When the main point temperature has reached around 10 million K, combination of hydrogen occurs, publication energy. This energy exerts an outwards radiation pressure due to the action of the photons ~ above the extremely thick matter in the core. The radiation pressure an unified with the gas press balances the inward pull of gravity avoiding further collapse.

Stellar Mass

As was noticeable from the evolutionary Hayashi monitor on the vault page, a star"s place on the key sequence its in reality a function of that mass. This is an incredibly useful relationship, called the mass-luminosity relation. If we recognize where ~ above the main sequence a star is we can infer its mass. In general the much more massive a star is, the additional up the main sequence the is found and also the an ext luminous the is. Mathematically this relationship is expressed by:

where n is about 4 because that Sun-like stars, 3 for the more massive stars and 2.5 for dim red key sequence stars. (*Note this formula is not required for HSC exams). A 0.1 solar massive star has actually only around one-thousandth the luminosity of the sunlight whereas a 10-solar massive star is has actually a luminosity 10,000 × the of our Sun.



Limits on the upper mass that stars is believed to it is in somewhere between 150 and also 200 solar masses based upon theoretical modeling. Such stars are incredibly rare and also short-lived.

The higher the fixed of a main sequence star, the higher its reliable temperature. This, linked with the larger radius of higher mass main sequence stars accounts for their much higher luminosity. Remember, LT4 and LR2 so also a little increase in reliable temperature will considerably increase luminosity.

Main-Sequence Lifespan

The key sequence is the phase where a star spends most of the existence. Loved one to other stages in a star"s "life" the is very long; our sunlight took about 20 million years to kind but will spend about 10 billion year (1 × 1010 years) as a key sequence star before evolving into a red giant. What determines the key sequence expectancy of a star?

Main succession stars differ in mass. You may imagine that a much more massive star has more fuel available so have the right to spend more time ~ above the key sequence fusing hydrogen come helium. You would certainly be not correct - the opposite is true. More massive stars have a stronger gravitational pressure acting inwards for this reason their main point gets hotter. The greater temperatures typical that the nuclear reactions take place at a much greater rate in substantial stars. They for this reason use up their fuel much faster than lower mass stars. This is analogous to the case with plenty of chemical reactions, the greater the temperature the much faster the reaction rate.

Lifespans for key sequence stars have actually a vast range. Whilst our sunlight will invest 10 billion years on the key sequence, a high-mass, ten solar-mass (10MSun) star will only last 20 million years (2.0× 107 years) top top the main sequence. A star through a only fifty percent the mass of Sun can spend 80 billion year on the key sequence. This is much much longer than the period of the world which means that all the low-mass stars the have developed are still on the main sequence - they have not had actually time come evolve turn off it.

Mass/MSunLuminosity/LSunEffective Temperature (K)Radius/RSunMain succession lifespan (yrs)


Although there room 92 naturally occurring elements and a couple of hundred isotopes, the composition of stars is remarkably similar and simple. Stars room composed almost entirely of hydrogen and helium. A star such as our sunlight is around 73% hydrogen through mass and also 25% helium. If figured out by variety of nuclei then it is 92% hydrogen and also 7.8% helium. The continuing to be 2% by mass or 0.2% through number is every the more heavier elements. In the history astronomers termed these aspects with atom numbers higher than two as metals. These include facets such together carbon and oxygen. The usage of "metals" is not to be perplexed with the more common chemical definition of the term.

Metallicity is a measure up of the abundance of elements heavier than helium in a star and is expressed together the portion of metals by mass. It have the right to be identified or at the very least inferred from spectroscopic and photometric observations. In basic stars with greater metallicities are inferred to be younger than those with an extremely low values. This is due to the reality that elements heavier than helium room made within stars through nucleosynthesis and also released right into interstellar room by mass-loss events such as supernova explosions in the late stages of mainly evolution. Early generations the stars

Stars discovered in the spiral eight of galaxies, consisting of our Sun, are usually younger and have high metallicities. Lock are referred to as populace I stars. Populace II stars are older, red stars with reduced metallicities and also are typically located in globular swarm in galactic halos, in elliptical galaxies and also near the galactic centre of spiral galaxies.

Nucleosynthesis and fusion Reactions

Nucleosynthesis merely refers come the production of nuclei heavier than hydrogen. This wake up in main sequence stars v two main processes, the proton-proton chain and the CNO bicycle (carbon, nitrogen, oxygen). Primordial nucleosynthesis occurred really early in the background of the Universe, resulting in some helium and little traces of lithium and also deuterium, the hefty isotope that hydrogen. Combination processes in post-main succession stars room responsible for many of the more heavier nuclei. Various other mechanisms such as neutron capture also occur in the critical stages of enormous stars. Both disputed in later pages.

Main succession stars fuse hydrogen into helium within their cores. This is sometimes dubbed "hydrogen burning" however you have to be careful with this term. "Burning" indicates a burning reaction through oxygen however the process within mainly cores is a atom reaction, not a chemical one.

The nuclear fusion in the cores of key sequence stars requires positive hydrogen nuclei, ionised hydrogen atoms or protons, come slam together, releasing power in the process. In ~ each phase of the reaction, the merged mass of the assets is less than the complete mass the the reactants. This mass difference is what accounts for the power released according to Einstein"s renowned equation: E = m c2 whereby E is the energy, m the mass and also c the speed of light in a vacuum. This is far better expressed as:

In conditions such together those top top Earth, if we shot to carry two proton (hydrogen nuclei) with each other the electrostatic communication tends to reason them come repel. This coulombic repulsion must be get rid of if the protons room to fuse. The actual process whereby two protons have the right to fuse entails a quantum mechanical impact known together tunneling and in exercise requires the protons to have very high kinetic energies. This way that they must be traveling an extremely fast, the is have very high temperatures. Nuclear fusion only start in the cores of stars once the thickness in the main point is an excellent and the temperature reaches around 10 million K.

There room two key processes by which hydrogen fusion takes place in key sequence stars - the proton-proton chain and the CNO (for carbon, nitrogen, oxygen) cycle.

Proton-Proton (pp) Chain

The main procedure responsible for the energy developed in most main sequence stars is the proton-proton (pp) chain. That is the dominant process in our Sun and all stars of less than 1.5 solar masses. The net result of the process is that four hydrogen nuclei, protons, undergo a sequence of combination reactions to develop a helium-4 nucleus. The succession shown listed below is the most common kind of this chain and is also called the ppI chain. The accounts for 85% of the blend energy released in the Sun.


The neutrinos are neutral and also have exceptionally low rest masses. They basically do not interact with regular matter and also so travel straight out indigenous the core and also escape indigenous the star at virtually the speed of light. Around 2% that the power released in the pp chain is brought by these neutrinos.

Positrons space the antiparticle of electrons. Back the pp chain involves the fusion of hydrogen nuclei, the cores that stars quiet contain electrons that have actually been ionised or ripped off from their hydrogen or helium nuclei. When a positron collides through an electron, an antimatter-matter event occurs in which each annihilates the other, publication yet more high-energy gamma photons.

Two other creates of the pp chain can happen in stars and contribute around 15% of the energy production in the Sun. In the ppII chain, a He-3 nucleus created via the an initial stages the the ppI chain undergoes blend with a He-4 nucleus, producing Be-7 and releasing a gamma photon. The Be-7 nucleus climate collides with a positron, publication a neutrino and forming Li-7. This subsequently fuses with a proton, separating to release 2 He-4 nuclei. A rarer occasion is the ppIII chain through which a Be-7 nucleus developed as above fuses through a proton to type B-8 and also release a gamma photon. B-8 is unstable, experience beta positive degeneration into Be-8, publication a positron and a neutrino. Be-8 is likewise unstable and also splits into two He-4 nuclei. This process only contributes 0.02% that the Sun"s energy. These develops are summarised as:

CNO Cycle

Stars with a mass of around 1.5 solar masses or an ext produce most of their power by a different form of hydrogen fusion, the CNO cycle. CNO represents carbon, nitrogen and oxygen together nuclei of these aspects are connected in the process. As its name implies, this process is cyclical. It calls for a proton come fuse through a C-12 nuclei to start the cycle. The result N-13 cell core is unstable and also undergoes beta positive degeneration to C-13. This then fuses with an additional proton come from N-14 which in turn fuses with a proton to offer O-15. Being stormy this experience beta positive degeneration to type N-15. Once this fuses with a proton, the resultant nucleus immediately splits to type a He-4 nucleus and also a C-12 nucleus. This carbon cell core is climate able to initiate one more cycle. Carbon-12 thus acts favor a nuclear catalyst, it is crucial for the procedure to proceed but ultimately is not supplied up by it.


Why does the CNO cycle conquer in higher-mass stars? The answer has to do v temperature. The very first stage the the pp chain involves two proton fusing together whereas in the CNO cycle, a proton has to fuse through a carbon-12 nucleus. Together carbon has actually six protons the coulombic repulsion is greater for the an initial step the the CNO cycle 보다 in the pp chain. The nuclei therefore require higher kinetic energy to overcome the more powerful repulsion. This method they need to have a greater temperature come initiate a CNO fusion. Higher-mass stars have actually a more powerful gravitational traction in their cores which leads to greater core temperatures.

The CNO cycle becomes the chief source of power in stars the 1.5 solar masses or higher. Core temperatures in these stars are 18 million K or greater. Together the Sun"s main point temperature is around 16 million K, the CNO cycle accounts for just a minute fraction of the full energy released. The family member energy developed by each process is presented on the plot below.


Calculating the Sun"s key Sequence Lifespan

As we have already seen, the Sun has a main sequence expectancy of about 10 billion (1 × 1010) years. Exactly how do astronomers calculate such a value? A first order approximation because that this value is surprisingly simple to derive.

You will recall that the massive of a helium-4 cell nucleus is slightly less than the amount of the four separate protons required to form it. In atom physics, the masses dealt with are so tiny that the atomic mass unit or amu is used instead of the kilogram where 1 amu = 1.66 × 10-27 kg. A proton has actually a fixed of 1.0078 amu so 4 protons add up come 4.0312 amu. A helium-4 nucleus has a massive of 4.0026 which way that the mass defect, the difference between the two total masses, is 0.0286 amu or just 0.7%. From equation 6.2:

E = Δm c2 so substituting in values givesE = 0.0286(1.66 × 10-27)(3 × 108)2 ∴ E = 4.3 × 10-12 J

The production of each helium cell core releases only a little amount of energy, 10-12 J i m sorry does no seem a lot. We recognize though measurement that the Sun"s luminosity is 3.90 × 1026 J.s-1. To develop this amount of energy, vast numbers that helium, (3.90 × 1026)/(4.3 × 10-12) = 9 × 1037, should be formed every second. Each second, 600 million lots of hydrogen fuse to kind 596 million tons of helium. This method 4 million lots of issue is destroyed and converted into power each second.

The high temperature needed for hydrogen blend is only uncovered in the core region of the Sun. This comprises only around 10% that its complete mass. The power potentially obtainable from this fixed of hydrogen is roughly:

Etotal = (mass defect per He cell core produced) × c2 × (mass the H in core) ∴ Etotal = 0.0071(9 × 1016)(0.1 × 2.0 × 1030) = 1.28 × 1044 J

Given that the Sun"s power output is currently 3.90 × 1026 J. S-1 and assuming the it will certainly be roughly constant for its key sequence lifespan, then the sun has enough core hydrogen for around 10 exchange rate years. As it is currently about about 5 billion year old this method it is half way through its main sequence life.

Energy move in a Star

We have now seen how energy is created in a star such together the Sun. How, though, go this power escape from the star? 2 processes, radiation and convection, pat a an essential role.

The Sun"s internal comprises three main regions. The core, just 25% the the Sun"s diameter, a radiative zone expanding from the main point to 70% the the diameter and the outer an ar where convection procedures dominate.

High-energy gamma photons produced in the core execute not escape easily from it. The high temperature plasma in the main point is about ten times denser than a thick metal top top Earth. A photon deserve to only travel a centimeter or so on median in the core before interacting with and also scattering native an electron or hopeful ion. Each of this interactions alters both the energy and travel direction that the photon. The direction a photon travel after an communication is arbitrarily so sometimes it is reflected earlier into the core. Nonetheless over plenty of successive interaction the net result is the the photon slowly makes its way out native the core. The route it take away is referred to as a random walk. Photons lose power to the electrons and ions through each interaction creating a variety of photon energies. This procedure is known as thermalisation and results in the characteristic blackbody spectrum that develops the continually background spectrum the stars.

Interactions in between ions and also electrons additionally produce many additional photons of various energies. These additionally contribute come the blackbody spectrum.

The electrons and also nuclei formed in fusion reactions also carry kinetic energy that they have the right to impart to various other particles v interactions, increasing the thermal power of the plasma. Neutrinos developed by the various blend and degeneration reactions take trip out from the core at nearly the speed of light. Lock are successfully unimpeded by the thick matter in the core of main sequence stars. They lug away about 2% that the total energy.

See more: What Does W/C Stand For

The outer 30% the the sun is at lower temperature and also density than the within parts. Here, convection currents are responsible for transporting energy to the surface. Deep cells, 30,000 km across are responsible for supergranulation. The cells just below the photosphere are only 1,000 km across and space responsible for the granulation checked out on the surface of the sun as in the picture below.