Relationship between spectral temperature and luminosity

Stellar classification - Wikipedia

Note that the correlation between temperature and luminosity is a direct one including the fact that the broadband spectra of stars have the characteristic. Temp5. Stellar Spectra. Re-ordering the stellar spectra with the temperature Eclipsing Binary: periodic variation in brightness due to shadowing (the relation between the total energy radiated, radius and the surface. This spectral atlas contains a sample of the standard spectral type stars, peculiar in increasing sub-type (decreasing temperature) for each luminosity class.

Furthermore recall that the power, or equivalently, the luminosity emitted by a blackbody is: For a sphere all stars are spherical: Now, combining these three relations, we get: Could this relationship explain the direct correlation between temperature and luminosity seen in the H-R Diagram? It seems pretty plausible, since for a lot of reasons we think that stars emit mostly like blackbodies.

The way to do this is to create a model of how a star would emit if it behaved exactly like a blackbody. The simplest model is to assume that all stars are the size of the Sun, since the Sun is the one star whose size we know.

Astronomy - Ch. 17: The Nature of Stars (10 of 37) Relationship Between Intensity and Luminosity

Then our model gives us a direct relationship between the temperature and the luminosity as follows: This will give us a line on the H-R Diagram. If our model line and the Main Sequence were one and the same, we could conclude that our model "fits" the data, and that our simple blackbody model explains the correlation between temperature and luminosity in real stars. However, these two lines don't overlap, and so we can't claim to have explained the correlation.

In fact, our model does a pretty lousy job of predicting the luminosity of Main Sequence stars based on their temperature. For example, when we plug K for a temperature into the model, we get out a luminosity of about 14 times the luminosity of the Sun, or 14 Lo as indicated by the blue plus in the above figure.

However, real stars with surface temperatures of K have luminosities of nearly Lo, or about a factor of five or so higher.

Therefore, we have a lot more work to do before we can claim a fit. Even though the model doesn't fit very well, we would still like to keep some parts of it because they make sense. Astronomers do this with stars.

So far we have discussed the luminosity and colour or effective temperature of stars. These can be plotted to form what is one of the most useful plots for stellar astronomy, the Hertzsprung-Russell or H-R diagram. It is named after the Danish and American astronomers who independently developed versions of the diagram in the early Twentieth Century.

Classifying Stars - the Hertzsprung-Russell Diagram

In an H-R diagram the luminosity or energy output of a star is plotted on the vertical axis. Astronomers also use the historical concept of magnitude as a measure of a star's luminosity. Absolute magnitude is simply a measure of how bright a star would appear if 10 parsecs distant and thus allows stars to be simply compared.

Just to confuse things, the lower or more negative the magnitude, the brighter the star. Note how the temperature scale is reversed on the horizontal axis. Also take care if using magnitude to work upwards to negative values. The effective temperature of a star is plotted on the horizontal axis of an H-R diagram.

One quirk here is that the temperature is plotted in reverse order, with high temperature around 30, - 40, K on the left and the cooler temperature around 2, K on the right.

In practice astronomers actually measure a quantity called colour index that is simply the difference in the magnitude of a star when measured through two different coloured filters.

Stars with a negative colour index are bluish whilst cooler orange or red stars have a positive colour index. The third possible scale for the horizontal axis is a star's spectral class. The details of the H-R Diagram raise a number of questions. Why don't stars have just any Luminosity or Temperature?

Why is there such a distinct Main Sequence of stars?

What makes one Main Sequence star different from another? Were Giant, Supergiant, and White Dwarf stars born that way, or is something else going on? The answers to these questions forms the basis of the next unit of this course, namely the internal structure and evolution of the stars.

Astronomy Lecture 9

The H-R diagram will prove to be one of our most powerful tools for unravelling the mystery of the stars. These, combined with the measured apparent magnitudes, allow us to compute the Luminosities of the stars.

The Hipparcos satellite has made the most precise measurements of stellar parallaxes to date for nearby stars. Because the points for many stars will overlap each other in the plot, the Hipparcos team uses colors to show how many stars sit under a single point. Red means more than 10 stars at the place on the plot. This remarkable H-R diagram has the following notable features: Why this is true is an important clue to the nature of stellar evolution.

There are few if any Supergiants in the Solar Neighborhood.