There is one very large difference between Astronomy and other disciplines like Physics, Chemistry, Biology, and others. In astronomy, we are, in almost all cases, prevented from directly experimenting on the objects we are studying. That is, we can never bring a star into a lab and dissect it or otherwise manipulate it to understand how it works. Therefore, astronomers spend their careers studying the light that reaches Earth from objects in space and using that light to learn about the nature of the Universe and the objects in it. So in this lesson we will devote a lot of time to describing light, how it is detected, and what it can tell us.

The majority of Astronomical (and astrophysical) observations are made using spots of Light. The Light is also known as electromagnetic radiation in Astrophysics, and the spots of light the Astronomers observe are nothing else then a few wavelength of the electromagnetic spectrum, including:

The Wave Properties of Light:

To begin our study of light, we’re actually going to first discuss waves in general. For example, what happens when a pebble is thrown into a pond?

As shown in the image above, where the pebble enters, the water starts to oscillate up and down. The "pieces" of water right next to where the pebble entered "feel" the water next to them going up and down, and they start to move up and down, too. The disturbance in the water moves outward as more pieces of water start to move up and down. The water in each place only moved up and down, but a wave moved outward from where the pebble entered the water. No water moved outward—what moved outward is the disturbance in the pond's surface. The outward motion of the disturbance transports energy from one place (the location where the pebble entered the water) to another (all points outward from the pebble entry point). So a wave is really a mechanism by which energy gets transported from one location to another.

Electric and magnetic fields can be disturbed in a similar way to the surface of a pond. When a stationary charged particle begins to vibrate (or more generally, if it is accelerated), the electric field that surrounds the particle becomes disturbed. Changing electric fields create magnetic fields, so a moving charge creates a disturbance in both the electric field and magnetic field near the charged particle. The outward moving disturbance in the electromagnetic field is an electromagnetic wave. The phenomenon that we refer to as “light” is simply an electromagnetic wave.

Light (or any other wave) is characterized by its wavelength or its frequency. For any wave, the wavelength is the distance between two consecutive peaks. If you stand at one particular point and count how many peaks pass by you per second, this number is the frequency.

Mathematically, the wavelength of light is usually referred to with the letter l or the Greek letter lambda (λ). The frequency is usually referred to with the letter f or the Greek letter nu (ν). Since frequency is the number of waves that pass by a point per second, and the wavelength is the distance between consecutive peaks of that wave, you can determine the speed of the wave by multiplying these two numbers, that is: c = λν. If we look at the units, wavelength is measured in some unit of distance, and frequency is measured as some number that is unitless (number of waves) per some unit of time, so by multiplying wavelength times frequency you get distance per time, which is the proper unit for a speed.

White light (for example, what comes out of a flashlight) is actually made up of many waves that each exhibit one of the different colors of light (red, orange, yellow, green, blue, and violet). The reason that different waves of light appear to be different colors of light is because the color of a light wave depends on its wavelength. For example, the wavelength of blue light is about 450 nanometers, while the wavelength of red light is about 700 nanometers. A light source that gives off white light is therefore emitting multiple waves of light with a wide range of wavelengths from 450 nanometers through 700 nanometers. All of these light waves move at the same speed (the speed of light), so you can determine their frequencies and see that red light has a lower frequency than blue light.

The wavelength of light can be extremely long (kilometers in length!) or smaller than the nucleus of an atom (one millionth of a nanometer!)—so, what do we call light that has a wavelength longer or shorter than the visible light that we are used to? Well, here is one example: light that has a wavelength just longer than red is called infrared light. The next example is light with a wavelength just shorter than violet light, which is called ultraviolet light. The entire range of possible types of light, from the longest wavelengths (radio waves) to the shortest wavelengths (gamma rays) is called the electromagnetic spectrum.

You may have learned in another course that light is peculiar in that it can be described (as we just did) as being a wave, but in some experiments it behaves, and can be described more accurately, as a particle. When we describe light as a particle, we'll refer to an individual "packet" of light as a photon. You can still refer to the wavelength and the frequency of that photon, even though you are considering it to be a particle rather than a wave. If you go back to the very first discussion at the beginning of this page, we talked about how waves transport energy. So each photon of light does carry energy, and the amount of energy depends on the wavelength or frequency of that photon. The equation is:

E = hν; or equivalently: E = hc/λ

In these equations, E is energy, h is Planck's constant, and c is the speed of light.

The Beginnings of Light in Astronomy:

Ole Rømer (1680's) was the first to measure the speed of light using Jupiter's moons => c=299,790 km/sec or about 185,000 mi/sec.

James Clerk Maxwell (1850's) showed that light is energy carried in the form of opposite but supporting electric and magnetic fields in the shape of waves, i.e. self-propagating electromagnetic waves.

The wavelength of the light determines its characteristics. For example, short wavelengths are high energy gamma-rays and x-rays, long wavelengths are radio waves. The whole range of wavelengths is called the electromagnetic spectrum.

Our eyes only see over the following range of wavelengths:

As we already know, Astronomy is a passive science, but observing phenomenon at different wavelengths has several advantages to overcome the lack of making experiments. There are different physics at different wavelengths, for example, high energy magnetic fields are seen in the x-ray, radiation from heat is seen in the infrared.

However, note that observing at different wavelengths requires vastly different technology and conditions. In particular, our atmosphere is opaque to certain wavelengths (good for us) meaning that they can only be observed from space (expensive for astronomers).

If you have ever seen a rainbow in the sky, or if you have ever seen light pass through a prism and appear to emerge as a rainbow, you have seen a spectrum. What you have witnessed in either of these two cases is white light being dispersed. The different colors of light bend by different amounts when they pass through a glass prism or water droplets. That is, when white light passes through water droplets in our atmosphere, the waves of red light get bent by a different amount than the waves of blue light, so the white light coming to you appears spread out into a rainbow.

light being dispersed by a prism

When astronomers refer to a spectrum of light, they usually mean one of two things. They either mean an image that has been taken of the dispersed light from a source, such as this example:

The spectrum of the sun

Or they mean a two dimensional graph of one of these images that plots the intensity (or brightness) of the light at a given color (which is represented usually by wavelength or frequency). See this example:

A Hubble Space Telescope spectrum of a peculiar type of star called a blue straggler.

In that plot, a wavelength (or color) where the intensity is near 1.0 means a lot of light was received from the source with this color. On the other hand, wavelengths where the intensity is near 0.0 received very little light from the source with this color.

We will use the word "spectrum" interchangeably to refer to these two different representations of the dispersed light from an object—either an image or a two dimensional plot—but in both cases what we can determine is how much light with a specific wavelength was received from an object.

As mentioned above, Earth's atmosphere (which we usually think of as transparent) is actually only transparent to certain wavelengths of light. This is illustrated in this cartoon below:

Cartoon of atmospheric windows for EM spectrum regions

All visible light penetrates the atmosphere, most radio light penetrates the atmosphere, and some IR light passes through the atmosphere. We refer to the ranges of wavelengths in the spectrum that can pass through the atmosphere as a "window". For example, there is an IR window for light with wavelengths from 3.0 to 4.0 microns (1 micron = 1 millionth of a meter).

In contrast, our atmosphere blocks most ultraviolet light (UV) and all X-rays and gamma-rays from reaching the surface of Earth. Because of this, astronomers can only study these kinds of light using detectors mounted on weather balloons, in rockets, or in Earth-orbiting satellites. If you study the plot from Infrared Windows (a NASA Web site), you will see that you can represent this idea of windows in a more rigorous way. You can plot how opaque the atmosphere is (or equivalently, what percentage of photons are blocked by the atmosphere) as a function of wavelength. So, for example, 0% of green photons are blocked by the Earth's atmosphere, but nearly 100% of all photons with wavelengths shorter than 100 nanometers are blocked from reaching the surface of the Earth.



Wave Properties:

Due to its wave-like nature, light has three properties when encountering a medium:

  1. reflection
  2. refraction
  3. diffraction

When a light ray strikes a medium, such as oil or water, the ray is both refracted and reflected as shown below:

The amount of refraction increases (meaning the angle of refraction decreases) for a denser medium and is also a function of wavelength (i.e. blue light is more refracted compared to red and this is the origin to rainbows from drops of water)

Diffraction is the constructive and destructive interference of two beams of light that results in a wave-like pattern


Inverse Square Law:

The brightness of an object varies inversely as the square of the distance. This is a geometric consequence of the fact that light moves outward in a spherical fashion.



Doppler effect:

The Doppler effect occurs when on object that is emitting light is in motion with respect to the observer. The speed of light does not change, only the wavelength. If the object is moving towards the observer the light is "compressed" or blueshifted. If the object is moving away from the observer the light is "expanded" or redshifted.

We can use the Doppler effect to measure the orbital velocity of planets and the rotation of the planets.


Planck's curve:

One of the primary results from the field of spectroscopy was the discovery of how the energy outputed by an object (its spectrum) changes with temperature. In particular, was the formulation of the laws of radiation commonly expressed as two laws:

The energy outputed by an object (a star, a piece of metal, a human body) takes on a particular shape called Planck's curve, shown in the following plot of energy versus wavelength.

Notice that all objects emit all kinds of electromagnetic radiation. Except, cool objects (like humans) emit very little at short wavelengths (x-rays) and long wavelengths (radio). Most of our energy comes out in the infrared (our peak emission is at 10 microns).


Blackbody Radiation:

First, let's do a quick review of temperature scales and the meaning of temperature. The temperature of an object is a direct measurement of the energy of motion of the atoms and/or molecules. The faster the average motion of those particles (which can be rotational motion, vibrational motion, or translational motion), the higher the temperature of the object.

For this course, to keep with astronomical convention, we'll refer to temperatures using the Kelvin scale. Below is a table that compares Kelvin to the more familiar temperature scales:

The magnitude of one degree Celsius is the same as one Kelvin. The only difference between those two scales is the zero point.

Part of the reason for the quick review of temperature is because we are now going to begin studying the emission of light by different bodies, and all objects with a temperature above absolute zero give off light.

Our strategy will be to begin by studying the properties of the simplest type of object that emits light, which is called a blackbody. A blackbody is an object that absorbs all of the radiation that it receives (that is, it does not reflect any light, nor does it allow any light to pass through it and out the other side). The energy that the blackbody absorbs heats it up, and then it will emit its own radiation. The only parameter that determines how much light it gives off and at what wavelengths is its temperature. There is no object that is an ideal blackbody, but many objects (stars included) behave approximately like blackbodies. Other common examples are the filament in an incandescent light bulb or the burner element on an electric stove. As you increase the setting on the stove from low to high, you can observe it produce blackbody radiation; the element will go from nearly black to glowing red hot.

The temperature of an object is a measurement of the amount of random motion (the average speed) exhibited by the particles that make up the object; the faster the particles move, the higher the temperature we will measure. If you recall from the very beginning of this lesson, we learned that when charged particles are accelerated, they create electromagnetic radiation (light). Since some of the particles within an object are charged, any object with a temperature above absolute zero (0 Kelvin or –273 degrees Celsius) will contain moving charged particles, so it will emit light.

A blackbody, which is an "ideal" or "perfect" emitter (that means its emission properties do not vary based on location or the composition of the object), emits a spectrum of light with the following properties:

  1. The hotter the blackbody, the more light it gives off at all wavelengths. That is, if you were to compare two blackbodies, regardless of what wavelength of light you observe, the hotter blackbody will give off more light than the cooler one.
  2. The spectrum of a blackbody is continuous (it gives off some light at all wavelengths), and it has a peak at a specific wavelength. The peak of the blackbody curve in a spectrum moves to shorter wavelengths for hotter objects. If you think in terms of visible light, the hotter the blackbody, the bluer the wavelength of its peak emission. For example, the sun has a temperature of approximately 5800 Kelvin. A blackbody with this temperature has its peak at approximately 500 nanometers, which is the wavelength of the color yellow. A blackbody that is twice as hot as the sun (about 12000 K) would have the peak of its spectrum occur at about 250 nanometers, which is in the UV part of the spectrum.

Here is a two-dimensional plot of the spectrum of a blackbody with different temperatures:

The first of the two properties listed above (and seen in the image above) is usually referred to as the Stefan-Boltzmann Law, and is stated mathematically as:

E = σ T4

where:

E is the energy emitted per unit area, or intensity
σ is a constant
T is the temperature (measured in Kelvins)

What this equation tells you is that each time you double the temperature of a blackbody, the energy it emits per square centimeter goes up by 24 = 2x2x2x2 = 16. So, for example, a blackbody that is 5000 K emits 16 times more energy per unit area than one that is 2500 K.

The total luminosity of a blackbody, that is, how much energy the entire object gives off is the energy per unit area (E) multiplied by the surface area. For a sphere, this is:

L = 4 π R2σ T4

Here, L is the luminosity (energy per unit time) and R is the radius of the sphere.

The second of the two properties listed above is referred to as Wien's Law. To determine the peak wavelength of the spectrum of a blackbody, the equation is:

λ max = (0.29 cm K) / T

For example, for the sun, λ max = (0.29 cm K) / 5800 K = 5 x 10-5 cm = 500 nm


Kirchoff's Law and Spectroscopy:

Studying blackbody radiation is a useful exercise. However, blackbody radiation is only emitted by an "ideal" or "perfect" radiator. In reality, few objects emit exactly a blackbody spectrum. For example, consider this two spectra: the sun and a blue straggler star. Recall that blackbody radiation is continuous with no breaks. If you look at the two spectra of stars, you see there are black bands in the image of the sun’s spectrum and areas in the plot where the intensity goes to zero or nearly zero in the spectrum of the blue straggler. These gaps in the spectrum where there is no light emitted are called absorption lines. Other astronomical sources (and also light sources you can test in a lab) are found to create spectra that show little intensity at most wavelengths, but a few precise wavelengths where a lot of intensity is seen. These are referred to as emission lines.

In the early days of spectroscopy, experiments revealed that there were three main types of spectra. The differences in these spectra and a description of how to create them were summarized in Kirchhoff’s three laws of spectroscopy:

  1. Continuous spectrum - a solid or liquid body radiates an uninterrupted, smooth spectrum (Planck curve).
  2. Emission spectrum - a radiating gas produces a spectrum of discrete spectral lines.
  3. Absorption spectrum - a continuous spectrum that passes through a cool gas has specific spectral lines removed (inverse of an emission spectrum).

You can also summarize Kirchoff's laws in a diagram, like this one:

Like Kepler's laws of planetary motion, these are empirical laws. That is, they were formulated on the basis of experiments. In order to understand the origin of absorption and emission lines and the spectra that contain these lines, we need to first spend some time on atomic physics. Specifically, we will consider the Bohr model of the atom.

Whenever you are studying the light from an astronomical object, recall that there are three things you need to consider:

  1. the emission of the light by the source,
  2. processes that affect the light during its travel from the source to the observer, and
  3. the process of detection of the light by the observer.

We observe absorption lines when the light from a background source passes through a cool gas. Somehow, it is the gas that causes the absorption lines to appear in what would otherwise appear to be a continuous spectrum. So, what is going on inside the gas?

A cloud of gas is made up of atoms, which are the smallest components of an element that retain all the properties of that element. A typical cloud of gas in space is likely to contain a lot of hydrogen and helium and trace amounts of heavier elements, like oxygen, nitrogen, carbon, and perhaps iron. The atoms inside the cloud of gas are made up of a nucleus of positively charged protons and neutrons, which have no charge. Surrounding the nucleus are one or more negatively charged electrons. Here is a cartoon image I put together of a helium atom:


The particles labeled n are neutrons, p are protons, and e are electrons.

Returning to atomic physics and spectroscopy, it is the electrons that are the primary cause of the absorption lines we see in stellar spectra. Bohr proposed a simple model for atoms that required the electrons to occupy "orbits" around the nucleus. The crucial part of his model is to understand that the electrons can only exist in these specific orbits, and not in between. Each orbit has a specific energy associated with it—that is, when the electron is in a specific orbit, it has a specific amount of energy. Thus, the orbits can also be referred to as energy levels. If an electron absorbs exactly the energy difference between the level it is in and any higher level, it can move up to a higher level. Once an electron is in a higher level, it will eventually fall back down to a lower level (either all at once back down to level 1, or by a series of steps down to level 1), and each time it falls from one level to a lower one, it emits a photon that carries exactly the amount of energy equal to the difference in energy between the starting energy level and the ending energy level of the electron. This is shown below. In the top panel, the electrons are falling from higher levels to lower levels, and emitting photons. In the lower panel, the electrons are absorbing photons, causing them to jump to higher levels from their lower levels.


Recall that the energy carried by a photon is given by E = hν. So if the energy of an electron in level 2 is given by E2 and the energy that corresponds to level 1 is given by E1, then the difference in energy between those levels, ΔE = E2 - E1. So if an electron is in the E2 energy level and falls to the E1 energy level, it will emit a photon with a frequency given by:

E = hν,

so, ν= E/h,

and in this case E = ΔE = E2 - E1

giving us ν = (E2 - E1)/h

In the top panel above, there is an electron dropping from level 2 to level 1, emitting a photon with an energy equal to the energy difference between those two levels. So an astronomer studying the light from that cloud of gas will see an emission line in the spectrum of that cloud with a yellow color, the one labeled "2 - 1" in the spectrum on the right.

Let's tie this idea of electrons moving between energy levels back to the observed spectra of astronomical objects.

Absorption spectrum:

A continuous source of light emits photons with all different energies. When these photons pass through a foreground cloud (or clouds) of gas, they can encounter the atoms in that gas, each of which has a set of electrons with specific energy levels. Those photons that have precisely the correct energy to kick an electron in an atom of the gas up to a higher level can be absorbed. All those photons that do not have the exact amount of energy to excite an electron pass through the cloud without being absorbed. Thus, what we see after light from a blackbody (that is, the continuous source) passes through a cloud of gas, is that most of the photons in a narrow range of frequency (or color) don't make it, leading to breaks, or absorption lines in the otherwise continuous spectrum of the light source. The absorption lines all correspond precisely to wavelengths or frequencies that are determined by the energy difference between the energy levels of electrons in the atoms that make up the cloud. So, again referring to the energy level diagram above, when an electron goes from level 1 to level 2 by absorbing a photon, an astronomer will observe an absorption line at the frequency that corresponds to that 1 - 2 energy level difference.

Emission spectrum:

If you have a low density cloud of gas that is being warmed by some process, the electrons in the atoms in that cloud of gas will not be in the lowest level—they will be in higher levels. So, as they cascade down to the ground level, they will emit photons with precise frequencies, giving rise to emission lines. Neon lights you see in store windows contain low density gas, and the electrons get excited when you run current through the bulb. As the electrons cascade down to the ground level (level 1), they emit emission lines in the red part of the spectrum. Here is an image of a neon containing bulb, and the spectrum it creates when you pass its light through a prism:

Light from a neon bulb.

Spectrum from a neon bulb.

A few consequences:

Finally, let's end this discussion of spectrum with a few consequences of the above physics: