Terminology: Apparent MagnitudeColor IndexSpectral Type

Demonstrations: HR FittingHR diagram explorer

## Temperature of a Star

Stars are classified by their temperatures and luminosities. The spectral class of a star denotes its temperature, and we use the Morgan-Keenan scale, “O”, “B”, “A”, “F”, “G”, “K”, “M”, for spectral types, where O stars are the hottest and largest, and M stars are the coolest. The spectral types of stars are then further subdivided using a scale from 0-9, where 0 is hotter than 9. For example, a O8 star is hotter than a O9 star, and both are much hotter than a G0 star.

## Luminosity

We generally report luminosities of stars in units of solar luminosity. So, the Sun has a luminosity of 1 solar luminosity.

From observations, astronomers classify the luminosities of stars using the Luminosity Class. The luminosity classes are listed below:

• main sequence stars: luminosity class V (roman numeral 5)
• sub giant stars: IV (4)
• giants: III (3)
• bright giants: II (2)
• super giants: I (1)
• white dwarfs: D or VII (7)

So, the Sun is a G2V star, meaning that it is a main sequence star with a temperature of 5800 K.

Examine the HR-Diagram to the right. You will notice that a range of stars of different luminosities can occupy the same temperature. It’s important to specify the luminosity class and the spectral class for a star, as a K5 star could be a main sequence, giant, or super giant.

## Magnitude

When you observe a star with a telescope, you are actually measuring its brightness, not its luminosity. The luminosity (L) and brightness (B) are related by the Inverse Square Law

where d is the distance to the star. Ancient astronomers measured the brightness of stars by ranking them by visual appearance. In the magnitude scale, which is logarithmic, the brightest stars have the smallest numbers, while the dimmest stars have the largest numbers. For example, a star with a magnitude of -1 is brighter than a star with a magnitude of 2.

We use two magnitude scales to describe the brightness of stars. The first is apparent magnitude, which is what is generally measured with a telescope. The second is absolute magnitude, which is how bright the star would be if it were at a distance of 10 parsec. The two scales are related by

M = m - 5 log10 (d/10)

where M is the absolute magnitude, m is the apparent magnitude, and d is the distance in parsecs.

## Color Index

The color index is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature. To measure the index, one observes the magnitude of an object successively through two different filters, such as U and B, or B and V, where U is sensitive to ultraviolet rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: UBV system). The difference in magnitudes found with these filters is called the U-B or B–V color index, respectively. The smaller the color index, the more blue (or hotter) the object is. Conversely, the larger the color index, the more red (or cooler) the object is.

Learning Goals: Students will learn how astronomers accurately measure the brightness of stars, as well as how the flux of a star through different colored filters can reveal its temperature. They will then use the brightness and temperature of stars to make inferences about their properties.

Suggested Observations: B, V image of an evolved open cluster such as M67

Challenge: Your team will take images of an open cluster - a group of stars that formed together at roughly the same time. You will measure the apparent magnitude of several stars and calculate their surface temperature.