What kind of stars are found here?

A star in this region of the Hertzsprung-Russell diagram has a temperature of roughly 9,000 kelvin (9,000 K), a luminosity 1400 times less than that of the Sun (0.0007 × LSolar), and a radius one hundred times smaller than the Sun (R = 0.01 × RSolar). This star lies along the narrow band in size, where white dwarf stars are found. The low temperature indicates that this star is the end-product of a nova of a low-mass star that took place quite some time in the past (a younger star would not have had time to cool, and to move down the white dwarf sequence to such extremely low luminosities and cool temperatures).

Try to read the values of L, T, and R for yourself from the diagram. Do you estimate values for the luminosity, temperature, and size of the star similar to those listed above?

Hertzsprung-Russell Diagram. The x-axis is labeled 'Surface Temperature' (in units of kelvins) with high temperatures around 60,000 on the left and low temperatures around 3,000 on the right. The points representing stars which appear furthest to the left are drawn in blue, those in the middle temperature range are drawn in yellow and orange, and those furthest to the right are drawn in red. The y-axis is labeled Luminosity (in units of solar luminosity), with low luminosities around 0.0001 at the bottom and high luminosities around 200,000 at the top. A third parameter, Radius (in units of solar radii), is also labeled. Lines of constant radius extend from the upper-left to the lower-right, covering the whole space with a set of parallel lines. In the lower-left corner we find the line labeled 'R is equal to 0.001 solar radii'; successive lines are labeled 0.01, 0.1, 1, 10, 100, and 1,000 solar radii, with the line for 'R is equal to 1,000 solar radii' being located in the upper-right corner. A series of blue, yellow, and orange points scattered along the 'R is equal to 0.01 solar radii' line is made up of white dwarf stars. A large set of red (and a few yellow and orange) points made up of giant stars appears between the 1 and 1,000 solar radii lines. The 1 solar radii line extends from the upper-left corner to the lower-right corner. The Main Sequence (a curved sequence of blue, yellow, orange, and red points) mainly follows the 0.1 to 10 solar radii lines; at the high luminosity end it curves up to slightly higher luminosities and at the low luminosity end it curves down to slightly lower luminosities. In addition, there are three green lines on the figure which intersect around the point near to 9,000 kelvins and 0.0007 solar luminosities. One points down to the x-axis, one points left to the y-axis, and one is parallel to the black lines of constant radius (being drawn at a radius of around 0.01 solar radii).

How much fainter has this white dwarf become since its formation?

We can use the Stefan-Boltzmann Law to relate the temperature (T), size (R), and luminosity (L) of a star to each other, and so determine how much this white has faded over time. Measuring L, R, and T in solar units, we say that:

Equation: L is equal to R-squared times T-raised to the fourth power

Solving for R squared, we see that

Equation: R-squared is equal to L, divided by T-raised to the fourth power

Examining the distribution of white dwarfs in the diagram, we observe that there is very little scatter in their sizes – they are uniformly one-hundredth the size of the Sun, no matter how hot or cold they are, no matter how bright or faint they are. We can use this fact to relate the luminosity and temperature of white dwarfs at each end of the temperature sequence.

Imagine one white dwarf, called A, has just entered the white dwarf phase, while another, B, has been cooling and fading for billions of years. As all white dwarfs share the same radius,

Equation: R-squared is equal to L_A divided by T_A-raised to the fourth power, which is equal to L_B divided by T_B-raised to the fourth power.

We want to find out how much fainter the cooled white dwarf is, so we solve for the ratio of the luminosities. By examining the white dwarf sequence on the Hertzsprung-Russell diagram, we can estimate the hottest and coolest temperatures as 29,000 K and 9,000 K.

Equation: L_A divided by L_B is equal to ( T_A divided by T_B )-raised to the fourth power, which is equal to ( 29,000 K divided by 9,000 K )-raised to the fourth power, which is equal to 3.22-raised to the fourth power, which is equal to 108.

The white dwarf has become one hundred times fainter as it cooled, ending up one-thousandth as bright as the Sun. Imagine how difficult it would be to find it in a telescope image!