# Lumosity mass relationship main sequence stars on diagram

### Lecture The Internal Structure of Stars

Since the Main Sequence is also a sequence in luminosity—that is, O stars are the If you plot the masses for stars on the x-axis and their luminosities on the. Feb 7, We can show the relationship of mass and luminosity more clearly by plotting a Mass-Luminosity Diagram for Main-Sequence stars. Jan 27, High-mass main sequence stars have shorter lifetimes than low-mass main diagram is a plot of the luminosity of stars versus their temperature. is that the physical relation among the pressure, temperature, and fusion rate.

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.

### Mass–luminosity relation - Wikipedia

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. 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. As a result, we can estimate the brightnesses of various stars by doubling or halving the mass, and multiplying or dividing the luminosity by The table below shows how this works: The Main-Sequence Lifetime of Stars The relationship between brightness and mass has serious implications for the lifetimes of the Main Sequence stars. The fuel that keeps stars shining is their mass or more specifically, the mass of hydrogen in the core of the starand stars that have more mass have more fuel to burn, so you might expect them to last longer than stars with less mass.

But the rate at which the fuel has to be burnt is proportional to luminosity, so brighter stars shouldn't last as long as fainter ones.

The ratio of a star's lifetime to the lifetime of the Sun would be given by how much more fuel it has, divided by how much faster it is burning that fuel. As a result, we can modify the table shown above to include the lifetimes of the stars.

In this table the lifetimes are rounded off, since the luminosities shown above are only approximately correct. Even the Sun's Main Sequence lifetime, which is around 12 billion years, is rounded off to 10 billion years, to keep the numbers simple.

## The Hertzsprung-Russell Diagram

Among the first brown dwarfs discovered is the companion orbiting the star Gliese Selecting the picture below of Gliese and its companion, Gliese B, will take you to the caption for the picture at the Space Telescope Institute.

With the discovery of several hundred brown dwarfs in recent infrared surveys, astronomers have now extended the spectral type sequence to include these non-planets.

Just beyond the M-stars are the L dwarfs with surface temperatures of about K to K with strong absorption lines of metal hydrides and alkali metals. Cooler than the L dwarfs are the T dwarfs. At their cooler temperatures, methane lines become prominent.

Stars with too much mass have so much radiation pressure inside pushing outward on the upper layers, that the star is unstable. It blows off the excess mass. The limit is roughly about to perhaps solar masses. The picture of Eta Carinae below shows two dumbbell-shaped lobes of ejected material from the star in an earlier episode of mass ejection.

Selecting the image will take you to more information about the image at the Space Telescope Institute will display in another window. The picture below from the Hubble Space Telescope shows the violet Pistol Star surrounded by hydrogen gas fluorescing from the copious ultraviolet light coming from the star.

Above this temperature, the fusion rate is strongly dependent on temperature: Because fusion is so temperature-sensitive, in a main-sequence star, fusion of hydrogen into helium occurs only in the hot, dense central core. All main sequence stars including the Sun are in hydrostatic equilibrium.

That is, the inward force of gravity, which tends to compress the star, is balanced by the outward force due to the pressure. For a review of hydrostatic equilibrium within the Sun, you can go to the lectures for Wednesday, January 8.

Introductory Astronomy: Luminosity, Temperature, and Surface Area

The observable properties of main sequence stars, such as their surface temperature, luminosity, and radius, are all dictated by the mass of the star. Thus, the main sequence is a MASS sequence. Consider taking a star and increasing its mass by pouring a little extra hydrogen gas onto it.