# Understanding Spectral Index: A Plain Explanation

• Sanjay87
In summary, spectral index is a measure of the dependence of a quantity on the frequency or wavelength of a wave. It is calculated by comparing the intensity of radiation at different frequencies or wavelengths and is typically shown on a logarithmic scale. A higher spectral index indicates a slower increase in intensity as frequency or wavelength increases, while a lower spectral index indicates a faster increase. In astronomy, spectral index is used to study the emission, composition, and physical properties of objects such as stars, galaxies, and interstellar gas. It can also be negative, indicating a decrease in intensity at higher frequencies, which is seen in objects that absorb radiation.

#### Sanjay87

Hi,

Can anybody please explain to me (in everyday language) what spectral index is? The wikipedia entry doesn't shed much light, and a lot of the textbooks give very convoluted explanations for its derivation.

Thanks.

In radio terms (in my experience), spectral index applies to synchrotron sources which have brightness, S, which changes with for different frequencies, $$\nu$$, such that $$S \propto \nu^{\alpha}$$. For a negative $$\alpha$$ this means that when a synchrotron source is observed at higher frequencies, it will be fainter. The opposite is true for positive $$\alpha$$.

Last edited:

## 1. What is spectral index?

Spectral index is a measure of the dependence of a quantity on the frequency or wavelength of a wave. It is often used in the fields of astronomy and physics to describe the behavior of electromagnetic radiation.

## 2. How is spectral index calculated?

Spectral index is calculated by comparing the intensity of radiation at different frequencies or wavelengths. It is typically calculated using a logarithmic scale, with a steeper slope indicating a higher spectral index.

## 3. What does a high or low spectral index indicate?

A high spectral index indicates that the intensity of radiation increases at a slower rate as frequency or wavelength increases. This can be seen in objects that emit radiation at a constant rate, such as a blackbody. A low spectral index, on the other hand, indicates that the intensity of radiation increases at a faster rate as frequency or wavelength increases.

## 4. How is spectral index used in astronomy?

In astronomy, spectral index is used to characterize the emission of various objects, such as stars, galaxies, and interstellar gas. It can also be used to study the composition and physical properties of these objects, as different materials have distinct spectral indices.

## 5. Can spectral index be negative?

Yes, spectral index can be negative. This indicates that the intensity of radiation decreases as frequency or wavelength increases. This can be seen in objects that absorb radiation, such as dust, where the intensity decreases at higher frequencies.