Lesson 4

The magnitude of a celestial object is a number denoting its brightness. The higher the magnitude value, the fainter the object. There are five scales of magnitude:

Absolute magnitude (M): a measure of a star's apparent magnitude it would show if it were located at a distance of 10 parsecs or 32.6 light years.

Apparent magnitude (m): a measure of an object's brightness as seen by an observer on Earth. It is adjusted to the value it would have in the absence of the atmosphere. The brighter the object, the lower is its apparent magnitude.

Bolometric magnitude (Mbol): a measure of the total light emitted by a celestial object across all electromagnetic spectrum wavelengths. The absolute bolometric magnitude is the bolometric magnitude that the star would have if it were located at a distance of 10 parsecs from Earth.

Limiting magnitude (LM): the apparent magnitude of the faintest objects visible given the local observing conditions.

Visual magnitude (Mv): a measure of only the visible light from an object. The brighter the object, the lower is its visual magnitude.

Apparent Magnitude

Amateur astronomers are most familiar with the apparent magnitudes of celestial objects as that scale is a measure of the relative brightnesses of astronomical objects. But how then do we assess the relative brightnesses of stars? Astronomers use a couple of reference stars whose brightnesses are set as standard to which other celestial objects' brightnesses are compared.

There was no standard reference star in times gone by, and ancient astronomers assumed that such-and-such a star shone at a particular brightness. The trouble was that they all had their own ideas of the magnitude scale.

2,000 or so years ago, the Greek astronomer Hipparchus classified stars apparent brightness, which he thought was linked to their size. He thought that the brightest star in the night sky, Sirius, in the constellation of Canis Major, was more extensive and, therefore, more prominent than all the others.

The 16th-century Danish astronomer, Tycho Brahe, measured the 'sizes' of stars in terms of their angular size. He reckoned that first magnitude stars measured 1/30th of a degree or two arcminutes across. He figured that magnitude 2 to 6 stars measured at 11⁄2, 11⁄12, 3⁄4, 1⁄2, and 1⁄3 arcseconds, respectively.

All seemed fine until the advent of the telescope, which then plainly showed that Tycho's star 'sizes' were utter nonsense. Through a telescope, stars continued to appear as mere points of light – even under the HIGHEST magnification.

By the 19th century, there was no working rule for classifying stellar brightnesses other than the observer's 'estimation,' so there was considerable disagreement between astronomers.

Today, the apparent magnitude scale is based on the relative brightness of stars compared with the bright stars Arcturus in the constellation of Boötes and Vega in the constellation of Lyra, both of which are stars of magnitude zero.

A celestial object's apparent magnitude will, in the end, depend on its intrinsic luminosity, its distance from the observer, any extinction of the object's light by interstellar matter, and the effect of the Earth's atmosphere along the line of sight to the observer.

Magnitude Mathematics

The modern magnitude scale is an inverse logarithmic relation in which a difference of 1.0 in magnitude corresponds to a brightness ratio of 5√100 (the fifth root of 100), which is 2.512 to three decimal points.

The magnitude scale works so that a celestial object of magnitude 6 is exactly 100 times fainter than a star of magnitude 1.

Between adjacent magnitudes, objects are 2.512 times brighter or fainter. For example, a star of magnitude 2 is 2.512 times brighter than a star of magnitude 3. A star of magnitude 5 is 2.512 times fainter than a star of magnitude 4. Get the idea?

A magnitude 1 star is, therefore, 2.512 squared or 6.3 times brighter than a magnitude 3 star. It is 2.512 cubed or 15.85 times brighter than a magnitude four star, and so on.

A star of magnitude 0 is 2.512 to the power of 7 or 631 times brighter than a magnitude 6 star.

The graph below helps visualize the relationship between an object's brightness and its apparent magnitude:

The apparent magnitude scale works in reverse, with objects brighter than magnitude zero having negative values. For instance, the full Moon is the brightest object in the night sky and shines at magnitude -12.7 on average. The more negative the magnitude value, the brighter the object:

Below is a visual representation of the apparent magnitude scale:

Celestial objects appearing farther to the left on this line are brighter, while objects appearing farther to the right are dimmer. So, zero apparent magnitude is in the middle, the standard, with the brighter objects to the left and the fainter ones to the right. 

Apparent Magnitude Examples 

Absolute Magnitude

Absolute magnitude (symbol M) is a measure of the luminosity of a celestial object if it were located at 10 parsecs, and its light is not affected by any extinction (dimming) due to its absorption by interstellar matter, or the Earth's atmosphere.

A parsec (symbol pc) is an astronomical distance unit used to measure vast distances across space. It is the distance at which one Astronomical Unit (1 AU, which is 93 million miles – the distance to the Sun from the Earth) subtends an angle of 1 arcsecond. A parsec spans 3.26 light years. So, 10 parsecs add up to 32.6 light years.

Suppose we hypothetically place stars and other celestial objects at the standard reference distance from the Earth of 10 parsecs. In that case, their luminosities can be directly compared on the absolute magnitude scale.

When using that scale, astroscientists can easily work out the actual light output of celestial objects.

The table below shows the true brightnesses of some interesting celestial bodies. Keep in mind that the absolute magnitude values are for particular objects if placed 32.6 light-years away.

The data in the table indicates that some bodies out there in the Galaxy emit copious amounts of light and that some stars that appear to be 'bright' in the night sky are only bright because they are nearby neighbors to the Solar System.

Solar System Body Magnitudes

Solar System bodies apart from the Sun are only visible due to reflected sunlight. Astronomers, therefore, use a slightly different definition of 'absolute' magnitude for reflecting celestial objects. The base unit H is the amount of reflected sunlight from a planet or other body if it is located at the standard distance of 1 AU.

For meteors, the standard distance for measuring their apparent magnitudes as they burn up in the Earth's atmosphere is at an altitude of 62 miles (100 km) at the observer's zenith.

Visual Magnitude

Astronomers measure the apparent magnitudes of celestial by photometric methods. They do this at various wavelengths of light, such as ultraviolet, visible, and infrared.

The astronomical notation for apparent magnitude is Mv, as in Mv = 6, which describes a magnitude six object. The subscript "v" indicates the value is for the visible spectrum.

Amateur astronomers use the visual magnitude (v), which is just the brightness of a celestial object as seen with the unaided eye.

Limiting Magnitude

In astronomy, limiting magnitude is the faintest apparent magnitude of a celestial body detectable. In areas affected by artificial lighting, the limiting magnitude is elevated due to the night sky's brightness. You are already familiar with this from Lessons 1 and 2.

At dark sky sites, the limiting magnitude is that of the faintest stars visible on moonless nights with the unaided eye around the zenith.

Places of low humidity away from urban lights such as deserts and high mountains have the best visibility – hence why professional observatories are situated there.

The limiting magnitude of the unaided eye is close to 8 for observers with perfect eyesight and is the extreme naked-eye limit, or Class 1 on the Bortle scale – the darkest skies available on Earth. The Bortle scale is a nine-level measuring the night sky's brightness at a particular location. It quantifies numeric scale the observability of celestial objects taking into account the interference caused by light pollution.

The limiting magnitude varies from one to four in urban areas, depending on the local levels of artificial lighting. In the suburbs, it is usually around magnitude five.

Big telescopes at professional observatories increase the limiting magnitude by using long CCD integration times, followed by image-processing techniques that increase signal-to-noise ratios. With adaptive optics technology, these techniques allow stars as faint as magnitude 26 to be captured.

Space-based telescopes do even better due to the absence of the Earth's atmosphere. The Hubble Space Telescope, for instance, can detect objects as faint as magnitude 31.

When the long-awaited HST replacement, the James Webb Space Telescope, becomes operational, its bigger mirror is expected to have a limiting magnitude of 34.

Bolometric Magnitude

An object's absolute bolometric magnitude (Mbol) is its total luminosity over ALL light wavelengths, including instrumental passband additions, atmospheric absorption, and extinction by interstellar dust.

Is that of concern to amateur astronomers? Not a tiny bit. We need not be concerned about the bolometric magnitude scale.



DISTINCTION: 90-100%   GRADE 2: 75-89%   GRADE 3: 60-74%   GRADE 4: 40-59%

FAIL: 0-39%