Question

A main sequence star has the spectral classification of B5. Estimate its luminosity from the HR diagrams in your text. Explain in words how you can find its distance. What is this method of finding stellar distance called?

Answer 1

The total energy output per second of a star is called its luminosity, L, sometimes written as L_*. Our Sun's luminosity is about 3.84 × 10²⁶ W. Rather than use absolute values it is often convenient to compare the luminosity of a star, L_* to that of the Sun so that for instance it may be 1,000× L_Sun.

Stars vary enormously in luminosity, ranging from less than 10^-4 &times that of our Sun to 10⁶ × more luminous.

What is the relationship between distance to a star and its brightness (that is the intensity of light we receive from it)? As we can see in the diagram below as we move away from a star the radiation it emits has to cover a greater surface area. Imagine a sphere at a distance rfrom the star. Assuming a star is spherical and emits radiation equally in all directions the intensity of the energy at distance r over an area A will be I. If we double the distance from the star to 2r this same amount of energy is now distributed over four times the surface area, that is 4A. This means that the intensity per unit A is only ¼ the amount at r. At 3× the distance it will only be 1/9th the intensity per unit A and so forth.

Cr

This relationship for light (or any electromagnetic radiation) is called an inverse-square relationship.

I ∝ 1/r²

If we have two identical stars but one is 10× further away than the other the more distant star will appear 1/10² or only 1/100 times as bright as the closer one.

Distances to the Stars

“Space is big ... very big”
Distances in space are so vast they are hard for us to comprehend. Astronomers can measure the distance to the nearest stars using a method known as trigonometric parallax. This gives a distance to Alpha (α)Centauri, the nearest star system to us other than our Sun, of about 4.1 × 10¹⁶ m. The metre is not really a useful unit for such a large number. Astronomers actually use a unit of distance called the parsec (pc) to express distances to other stars and galaxies. One parsec is about 3.09 × 10¹⁶m so α Cen is about 1.3 parsecs distant. This is also equal to about 4.3 light years.

A light year is simply the distance that light travels in a vacuum in one Earth year (9.46 × 10¹⁵m). One parsec = 3.26 light years. All the stars visible to the unaided eye in the night sky are relatively bright stars in our local region of the Milky Way. Most stars are too far away to have their distance determined by trigonometric parallax so other methods have to be employed. ). The Milky Way itself is about 35,000 parsecs (or 35 kpc) across. The nearby satellite galaxy, the Large Magellanic Cloud is about 50 kiloparsecs distant. At the cosmological scale, the distance to most galaxies is measured in megaparsecs (millions of parsecs).

If we look at the region around the constellation Crux (the Southern Cross) in the night sky we see several bright stars. A long exposure photograph or CCD image reveals many more as shown below.

CCD image showing Crux and "The Pointers" (they are actually part of the constellation Centaurus). The dark patch to the left of Crux is the Coalsack Nebula and is a prominent example of a dark cloud of dust and gas obscuring light from more distant stars.

In the above image, α Cen (for Centaurus)appears slightly brighter than β Cen which in turn appears much brighter than ε Cru. Johannes Bayer in his 1603 catalogue introduced the idea of labelling the brightest apparent star in a constellation as α, the next brightest β and so on through the 24 letters of the Greek alphabet. When we determine the distance to each of the bright stars in Crux however we see that their distances vary greatly. α Cen is only 1.3 parsecs away whereas β Cen is 161 pc distant. Given that it appears only slightly dimmer than α Cen in the night sky this means that β Cen is intrinsically far more luminous.