# What is the relationship between star mass temperature lifespan and brightness

The answer is yes, indirectly. The reason I say this is because stars do not have a dimmer switch - two stars with otherwise identical. 1. Luminosity. (from Brightness and Distance). 2. Mass. (from Doppler shifts in Binary Stars). 3. Temperature (from stellar spectrum – Blackbody curve). 4. Radius Of. Sun's radius. Main Sequence Mass Relationship. L = M As temperature. From our study of binary stars, we are able to calculate the mass of the stars in the the least luminous—there must be a relationship between mass and luminosity. At higher temperatures, the nuclear fusion reactions generate energy much.

The condition of hydrostatic equilibrium is that the pressure is balancing gravity.

### Main Sequence Lifetime | COSMOS

Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase.

So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars. At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star.

## Main sequence

If you actually look at the equations that govern stellar structure, you can derive from those equations that: L M n where the exponent varies a bit for stars of different masses, but, in general, is approximately equal to 3.

Below is a plot that obeys this relationship and gives the theoretical calculations of a star's luminosity given its initial mass on the Main Sequence. By contrast, in a convection zone the energy is transported by bulk movement of plasma, with hotter material rising and cooler material descending. Convection is a more efficient mode for carrying energy than radiation, but it will only occur under conditions that create a steep temperature gradient.

### The Mass-Luminosity Diagram and Main-Sequence Lifetimes

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. 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.

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. However, even perfect observation would show a fuzzy main sequence because mass is not the only parameter that affects a star's color and luminosity. Variations in chemical composition caused by the initial abundances, the star's evolutionary status[42] interaction with a close companion[43] rapid rotation[44] or a magnetic field can all slightly change a main-sequence star's HR diagram position, to name just a few factors.

As an example, there are metal-poor stars with a very low abundance of elements with higher atomic numbers than helium that lie just below the main sequence and are known as subdwarfs. The curve represents the actual relationship between mass and luminosity; the straight line represents a simple approximation to the actual relationship.

For those who are mathematically inclined, the curve may look pretty simple too. But keep in mind that the range of luminosity shown here is over 10 billion times, and the range of mass is about times. To show the results of such a huge range of numbers in such a compact graph requires the use of log-log coordinate paper.

On such a graph even a straight line represents an exponential equation, and curved lines represent very complex relationships.

The relationship between mass and luminosity shown on the above graph is so important to our understanding of the characteristics of Main-Sequence stars that it is given a special name.

• Mass–luminosity relation
• Explain the relationship between the size of a star, its luminosity, and its life span?
• The Mass-Luminosity Relationship

If we represent it by a graph we call it the Mass-Luminosity Diagram. If we represent it by an equation we call it the Mass-Luminosity Relationship shown in the above diagram as a straight-line approximation, with Luminosity approximately proportional to an exponential power of the Mass.

The Mass-Luminosity Relationship As shown in the graph above, the brightness of Main-Sequence stars varies proportional to some power of their masses. For most of the range of stellar masses the proportionality is as the 3.