Mass radius relationship for main sequence stars definition

Main Sequence Stars

mass radius relationship for main sequence stars definition

Main sequence stars are stars that are fusing hydrogen atoms to form helium atoms The mass and luminosity of a star also relate to its color. the stellar mass-luminosity relationship (Figure ), or the Main Sequence Consider two stars with masses M1 and M2 and radii R1 and R2. We define: x = r1. In contrast, mass-radius relations (MRR) for main-sequence stars began to appear in .. diagram is still discouraging to define a unique MRR, even though it is.

Holberg University of Arizona Main sequence stars fuse hydrogen atoms to form helium atoms in their cores. About 90 percent of the stars in the universe, including the sun, are main sequence stars. These stars can range from about a tenth of the mass of the sun to up to times as massive.

Stars start their lives as clouds of dust and gas. Gravity draws these clouds together. A small protostar forms, powered by the collapsing material. Protostars often form in densely packed clouds of gas and can be challenging to detect. Instead, they become brown dwarfsstars that never ignite. But if the body has sufficient mass, the collapsing gas and dust burns hotter, eventually reaching temperatures sufficient to fuse hydrogen into helium.

The star turns on and becomes a main sequence star, powered by hydrogen fusion. Fusion produces an outward pressure that balances with the inward pressure caused by gravity, stabilizing the star. How long a main sequence star lives depends on how massive it is.

mass radius relationship for main sequence stars definition

A higher-mass star may have more material, but it burns through it faster due to higher core temperatures caused by greater gravitational forces.

While the sun will spend about 10 billion years on the main sequence, a star 10 times as massive will stick around for only 20 million years.

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A red dwarfwhich is half as massive as the sun, can last 80 to billion years, which is far longer than the universe's age of This long lifetime is one reason red dwarfs are considered to be good sources for planets hosting lifebecause they are stable for such a long time.

When this fuses with a proton, the resultant nucleus immediately splits to form a He-4 nucleus and a C nucleus. This carbon nucleus is then able to initiate another cycle. Carbon thus acts like a nuclear catalyst, it is essential for the process to proceed but ultimately is not used up by it. As with the various forms of the pp chain, gamma photons and positrons are released in the cycle along with the final helium and carbon nuclei.

All these possess energy. The answer has to do with temperature. The first stage of the pp chain involves two protons fusing together whereas in the CNO cycle, a proton has to fuse with a carbon nucleus.

As carbon has six protons the coulombic repulsion is greater for the first step of the CNO cycle than in the pp chain. The nuclei thus require greater kinetic energy to overcome the stronger repulsion. This means they have to have a higher temperature to initiate a CNO fusion. Higher-mass stars have a stronger gravitational pull in their cores which leads to higher core temperatures.

The CNO cycle becomes the chief source of energy in stars of 1. Core temperatures in these stars are 18 million K or greater. As the Sun's core temperature is about 16 million K, the CNO cycle accounts for only a minute fraction of the total energy released. The relative energy produced by each process is shown on the plot below. Adapted from an image by Mike Guidry, University of Tennessee. 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 T4 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.

How do astronomers calculate such a value? 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.

Main Sequence Stars: Definition & Life Cycle

A proton has a mass of 1. A helium-4 nucleus has a mass of 4. 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: As it is currently about about 5 billion years old this means it is half way through its main sequence life.

Energy Transport in a Star We have now seen how energy is produced in a star such as the Sun. How, though, does this energy escape from the star?

Lecture The Main Sequence

Two processes, radiation and convection, play a vital role. The Sun's interior comprises three main regions. Background image of the Sun at 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. Because there is a temperature difference between the core and the surface, or photosphereenergy is transported outward.

The two modes for transporting this energy are radiation and convection. A radiation zonewhere energy is transported by radiation, is stable against convection and there is very little mixing of the plasma.

By contrast, in a convection zone the energy is transported by bulk movement of plasma, with hotter material rising and cooler material descending.

Main sequence

Convection is a more efficient mode for carrying energy than radiation, but it will only occur under conditions that create a steep temperature gradient. Consequently, there is a high temperature gradient in the core region, which results in a convection zone for more efficient energy transport.

The outer regions of a massive star transport energy by radiation, with little or no convection.

mass radius relationship for main sequence stars definition

This results in a steady buildup of a helium-rich core, surrounded by a hydrogen-rich outer region. By contrast, cool, very low-mass stars below 0. Since it is the outflow of fusion-supplied energy that supports the higher layers of the star, the core is compressed, producing higher temperatures and pressures.

Nuclear Fusion and the Main Sequence Star

Both factors increase the rate of fusion thus moving the equilibrium towards a smaller, denser, hotter core producing more energy whose increased outflow pushes the higher layers further out. Thus there is a steady increase in the luminosity and radius of the star over time. This effect results in a broadening of the main sequence band because stars are observed at random stages in their lifetime. That is, the main sequence band develops a thickness on the HR diagram; it is not simply a narrow line.