Spectra

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light as an electromagnetic wave

Wavelength and Frequency

In astronomy light is mostly frequently interpreted as a wave of electromagnetic energy. The wavelength (λ) of light is the length of a full oscillation of the wave, such as shown in figure to the right. Wavelength has the dimensions of length. The frequency (ƒ) of light is the number of wavelengths that pass a certain point in period of time. Frequency has the dimensions of inverse time.

Light travels very quickly (exactly 299,792,458 m/s in a vacuum and that speed is denoted by the letter c). Wavelength and frequency are related by the speed of light.

c = λƒ

Electromagnetic Spectrum

Different kinds of light are distinguished by wavelength or frequency (being able to convert from on the other other very easily). A range of frequencies is referred to as a spectra. For example the spectrum of light some people can see is from about 380 nm to 780 nm and is called the visible or optical spectrum.

But the full spectrum of light is much larger than the visible spectrum. It includes the very long wavelengths of radio waves to the very short wavelengths of gamma rays. The figure below shows more of the full spectrum of light and where the visible spectrum fits into the full spectrum.

The full spectrum of light

Spectral Plot of a white dwarf star

Image Source: SDSS Collaboration

Intensity

Light coming from a source will not be equal in strength at all wavelengths. Specific intensity (I_ƒ) refers to the light power coming from a direction for a particular frequency. The total intensity is the sum of the intensities of all frequencies.

How much light from a star or other source that is coming from which frequency is extremely useful to astronomers. A plot of intensity (or some equivalent measure) of wavelength vs. frequency (or wavelength) is a spectral plot (or even just a spectrum). The plot to the right shows a spectral plot for a white dwarf star from the Sloan Digital Sky Survey. From it all manner of information such as temperature and chemical composition were obtained.

Blackbody

Part of the reason a lot of information can be obtained is because chemicals compounds don't emit a full or continuous spectrum of light. Depending on how the light from the chemical compound is observed, an emission or absorption spectrum will be observed (this is discussed more in detail in another NAAP module). Below is the emission spectrum of hydrogen. Note how only certain frequencies emit any intensity of light.

Blackbody radiation is the light that an object emits based purely on its temperature. While all objects in the universe emit radiation thermally, no true blackbody exists in nature as other factors play into how a body radiates energy. But many objects come close. The remnant thermal radiation from the beginnings of the universe is very close to a blackbody. The light emitted from a dense, solid object is somewhat close. Stars emit something close to a blackbody.

Though a blackbody emits radiation at all frequencies, the intensity at each frequency is different. The intensity vs. frequency relationship in a blackbody is well defined (I_ƒ = 2hƒ³/c² × (e^(hƒ/kT)-1)^-1). But two relationships are particular important/useful, the Stefan-Boltzmann law and Weins's law.

The Stefan-Boltzmann law states that the total power per area emitted by a blackbody is proportional to the fourth power of the the temperature. That is:

where F is energy per area (flux density) and σ = 5.67 × 10^-8 W m^-2 K^-4 is the Stefan-Boltsmann constant and T is temperature given in Kelvins. Wein's law gives the location of the peak of the blackbody curve – the most intense frequency of light. It is

The graph below shows the blackbody curves for three different temperatures. Not how the flux density (i.e. energy per area) emitted by higher temperature is much greater as it scales with temperature to the fourth power. The vertical scale slider will need to be used to see the lower temperature curves.