Magnitudes and Luminosity (Brightness)

The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth. Credit: Cora Skywalkers Blog
The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth. Credit: Cora Skywalkers Blog

What is Apparent Magnitude?

Apparent Magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere. The brighter the object appears, the lower the value of its magnitude. Generally the visible spectrum (vmag) is used as a basis for the apparent magnitude, but other regions of the spectrum, such as the near-infrared J-band, are also used.

Example Table of Apparent Magnitudes. Source: ESA
Example Table of Apparent Magnitudes. Source: ESA

What is Luminosity?

In astronomy, luminosity is the amount of electromagnetic energy a body radiates per unit of time. It is most frequently measured in two forms: visual (visible light only) and bolometric (total radiant energy), although luminosities at other wavelengths are increasingly being used as instruments become available to measure them.

A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. When not qualified, the term “luminosity” means bolometric luminosity, which is measured either in the SI units, watts, or in terms of solar luminosities. A star also radiates neutrinos, which carry off some energy, about 2% in case of our Sun, producing a stellar wind and contributing to the star’s total luminosity.

While bolometers do exist, they cannot be used to measure even the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum that is most likely to match those measurements. In some cases, the process of estimation is extreme with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red.

A star’s luminosity can be determined from two stellar characteristics: size and effective temperature. The former is typically represented in terms of solar radii, while the latter is represented in kelvins, but in most cases neither can be measured directly. To determine a star’s radius, two other metrics are needed: the star’s angular diameter and its distance from Earth, often calculated using parallax. Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is merely a number that represents the temperature of a black body that would reproduce the luminosity, it obviously cannot be measured directly, but it can be estimated from the spectrum.

An alternate way to measure stellar luminosity is to measure the star’s apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction that is present, a condition that usually arises because of gas and dust present in the interstellar medium (ISM), the Earth’s atmosphere, and circumstellar matter. Consequently, one of astronomy’s central challenges in determining a star’s luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium.

In the current system of stellar classification, stars are grouped according to temperature, with the massive, very young and energetic Class O stars boasting temperatures in excess of 30,000K while the less massive, typically older Class M stars exhibit temperatures less than 3,500K. Because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an even vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes. The most luminous stars are always young stars, no more than a few million years for the most extreme. In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class 0 stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are found above and to the right of the main sequence, more luminous or cooler than their equivalents on the main sequence. Increased luminosity at the same temperature, or alternatively cooler temperature at the same luminosity, indicates that these stars are larger than those on the main sequence and they are called giants or supergiants.

Hertzsprung–Russell diagram identifying stellar luminosity as a function of temperature for many stars in our solar neighborhood. Credit: Wikipedia
Hertzsprung–Russell diagram identifying stellar luminosity as a function of temperature for many stars in our solar neighborhood. Credit: Wikipedia