Stars of the First Magnitude

No, we aren’t talking about Tom Hanks or Meryl Streep. These are the stars you see in the sky at night. If you have ever been confused by statements like the following, then let’s see if we can help you out.

  • “On 29 November 2013, the coma dimmed to an apparent magnitude of 5. By the end of 30 November 2013, the coma had further faded to below naked-eye visibility at magnitude 7.” (from the Wikipedia article about Comet ISON)
  • “As it is configured now, the ISS has an apparent brightness, or “magnitude,” of around -3 (lower numbers denote brighter objects on this scale), said Joe Rao,’s nightsky columnist.”

As with so many conventions of math and science, it all goes back to the Greeks. Among the many achievements of Hipparchos, one of the greatest astronomers of antiquity, was the creation of the stellar magnitude scale. He assigned a value of 1 to the twenty brightest stars (stars of the first magnitude), all the way down to stars that were barely visible to the naked eye, to which he gave a value of magnitude 6. A modified version of this system is still in use.

Telescopes have extended our vision to encompass objects too dim for naked eye observation. For example, the star known as Kepler 62, with five known planets in orbit around it, has a magnitude of 13.75. What about objects brighter than the brightest star, such as Venus? The only other direction to go from 1 is to zero, and from there to negative numbers. The magnitude of Venus (it varies as its phase and distance from us changes) can be as bright as -4.6. The sun’s magnitude is -26.7.

That’s the quick and dirty. Now for the details—and the complications.

Do we still use Hipparchos’ magnitude scale?

Not really, although the modern scale follows the same general principles. Well into the nineteenth century, astronomers thought that magnitude measured actual size; brighter stars do, after all, look bigger. By mid-nineteenth century, however, enough was known about the nature of stars to realize that they are too far away to resolve as discs—they are point sources. Under magnification in a large telescope they will appear brighter (telescopes can gather more light than your eye alone) but no disc will ever appear. It was recognized that first magnitude stars are about 100 times brighter than sixth magnitude, and that was set as the standard. A five magnitude difference corresponds to a brightness difference of 100 times.

Since this is a logarithmic scale, a one magnitude difference will correspond to the fifth root of 100.Capture
A 3rd magnitude star is 2.512 times as bright as a 4th magnitude star, and 6.310 (2.512 squared) times as bright as a 5th magnitude star.

The second adjustment is to “anchor” the scale, in the same way that the boiling and freezing points of water anchor our temperature scales. Although there are more exact standards, the Vega system defines the apparent magnitude of Vega as zero.

And the last adjustment is to pretend there is no atmosphere absorbing the light. A star near the horizon appears dimmer because its light must pass through much more air than one that is overhead at the zenith. We ignore this effect in assigning magnitude values.

You slipped in that word “apparent”. I’ve seen both apparent magnitude and absolute magnitude in my reading. What’s the difference?

A star is bright because of one or both of the following:

  • It is inherently luminous; it puts out a lot of light.
  • It is nearby.

Apparent magnitude ignores the effect of distance on brightness. (Note that we are distinguishing between brightness [appearance] and luminosity [an inherent property].) To the ancients, all the stars were on an overhead dome that was not all that far away. With the modern age, though, we recognized that stars are distributed through three dimensional space. Let’s take two bright stars, Capella and Rigel, as examples.

Capella is the bright yellowish star in the constellation Auriga, easily visible at this time of year and at its highest point around midnight. Almost directly below it in the south at that time lies Rigel, the bluish lower right of the four prominent stars making up the body of Orion the hunter. These two stars have the same apparent magnitude, about 0.1.

Capella and Rigel

But Capella is 42 light years away, and Rigel is 860! Clearly Capella is less luminous, and only appears to be as bright as Rigel because it is closer. How can we quantify this?

We understand very well how brightness changes with distance. We can then determine how bright a star would appear to be if it were at a standard distance away from us. That standard distance is 10 parsecs, or 32.6 light years. A star’s  magnitude if it were at that distance is its absolute magnitude. Absolute magnitude removes the effect of distance on brightness, and lets us compare the inherent luminosities of stars. Capella’s absolute magnitude is -0.5 while Rigel’s is -7.8.

There are complications I have glided over. Both of these are variable stars whose luminosity changes periodically. And both of them are actually multiple star systems. Neither of these factors affect our basic points, however.

OK. I’ve also seen the term “apparent visual magnitude”. How is that different from any other kind?

Light comes in different wavelengths. The human eye is most sensitive to light that is centered around the green part of the visible spectrum, but light detectors usually have different sensitivities. A filter is used that restricts the light passed to a wavelength range centered around green, blocking both the red and blue ends of the spectrum. This closely matches the response of human vision, and gives values for the visual magnitude.

Take away points

  • A sixth-magnitude star is (just barely) visible in a dark sky.
  • Lower (or negative) magnitude numbers are brighter objects.
  • The higher the magnitude number, the dimmer the object.
  • Apparent magnitude tells us how bright a star appears to be from our vantage point on Earth.
  • Absolute magnitude tells us how inherently luminous a star actually is. It removes the effect of distance on brightness.
  • If it isn’t otherwise specified, a magnitude number is a visual magnitude. A star may be rather dim at visual wavelengths and quite bright in others such as ultraviolet or infrared.
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