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Primer on Radio Astronomy and Resolution

When you look up in the night sky, you can see many pinpoints of light with the naked eye.  Add an optical telescope to your observation, and there seems to be no limit to the number of objects in the sky.  It might surprise you that even with an optical telescope, you are only seeing a small glimpse of the universe.  By limiting ourselves to visible light, we miss out on some of the most interesting and spectacular objects in the universe.  We also would be missing out on vital clues on the origins and status of the universe.

            When we think of light, we usually limit our discussion to visible light.  This is only a tiny portion of electromagnetic energy that is organized into the electromagnetic spectrum.  The energy of the electromagnetic spectrum has wave properties and particle properties.  In this discussion, we will focus on the wave characteristics.  If you examine a wave of water as it travels, you will notice crests (peaks) and troughs (valleys).  The distance between the crests of a wave is called the wavelength.  The number of wavelengths that pass through an area per second is the frequency, which is measured in a unit called the Hertz (Hz).  The various forms of electromagnetic energy are categorized according to their wavelength and/or frequency, which are inversely related to each other.  Wavelength or frequency can be found using the equation l (wavelength in km)=c/ν (frequency in Hz), where c= the speed of light (300,000km/sec).  All forms of electromagnetic energy travel at the speed of light.

The wave properties of light from a source can be affected by the motion of the emitting source.  This property is called Doppler motion.  The Doppler effect can be used to determine how fast an object is traveling and its distance.  The Doppler effect involves the lengthening of a wavelength of light (red-shifting) or shortening the wavelength of light (blue-shifting).  If an object is moving toward you, the light waves will start to bunch up.  This means the frequency will be greater (shorter wavelength).  If an object is moving away from you, the light will be stretched out, meaning that the frequency will be lower (longer wavelength).  It has been discovered that just about everything in the universe is running away from us, so most objects we observe have their light red-shifted. Every element and molecule has a unique pattern of emission (think of this as a bar code on a product), so it is possible to get information on an object by looking how the pattern for a specific atom or molecule has shifted.  An example of this would be if you wanted to view hydrogen in an object that was moving away from you.  You look for your spectral lines that only hydrogen can emit.  Although you see the same pattern of hydrogen lines, the pattern is shifted to an area of longer wavelength.  By seeing how much the pattern shifted, you could calculate how fast the object is moving away, and how far it is away from you.

So, how are radio waves emitted?  The two main classes for radio wave emissions are thermal and non thermal.  Thermal waves involve a change in the state of an atom or vibration and/or rotation of a molecule, with the result being the emission of a photon with a particular wavelength.  Most radio signals that are observed are of the non-thermal emission variety.  Non-thermal emission involves electrons that have been stripped off their atoms.  When electrons are stripped away from their parent nucleus (called ionization), a soup of electrons and ions called plasma is formed.  The lone electrons travel through space, but occasionally they are captured by magnetic field lines, which permeate the universe.  The electron spirals along these magnetic field lines and is accelerated to relativistic speeds (near the speed of light).  The accelerated electron then gives off energy in the form of radio waves called synchrotron radiation. 

We can use the emission of light from atoms and molecules to find the composition, density, structure, temperature, speed, and relative age of objects.  To get this information, astronomers rely on spectroscopy, which studies the different emission wavelength of light that comes from an object.  Radiation sources which spectra can be observed come in two forms: (1) Line emission/absorption – an electron absorbs energy and gives off a photon(s) that equals the absorbed wavelength (2) Continuous emission – this is emission from ionized gas (plasma) where the electron is free, and can absorb any wavelength and them emit in that wavelength.  This gives many different wavelength depending on what wavelength the electron absorbed

When most people think of radio, they think of sound waves.  Contrary to what many people think, radio astronomers do not listen to the sky.  Radio waves are light, not sound waves.  Sound is much slower than the speed light, and sound waves are unable to travel through the vacuum of space (its true, in space, no one can here you scream).  Radio waves have the longest wavelength, and therefore the lowest frequency of all the light spectra.  The radio waves are followed by (in order of increasing frequency) the infrared spectrum, visible light, ultraviolet light, X-rays, and finally the shortest wavelength (and highest frequency) gamma rays.  All of these groups in the electromagnetic spectrum exhibit the same behavior as the visible light we see everyday.  Although we are not capable of observing these wavelengths with our eyes, we have many tools that can.  Earth’s atmosphere effects what type of light we may observe on the ground.  Fortunately for us, ultraviolet and X-rays are absorbed by the upper atmosphere.  The Earth’s atmosphere is transparent to visible light, radio, and a small set of infrared waves.  Radio waves have the added advantage over visible light of being able to be observed during the daytime and during inclement weather.  Another advantage of radio waves over visible light is that radio waves penetrate interstellar dust better than visible light waves.  This is evident if you try to observe the center of our galaxy.  Radio images provide us with a better understanding on what is occurring there than visible light due to the dense nature of this region of the galaxy.

            What can radio waves tell us?  Radio waves are a great source of information, and can give us many clues on where the universe came from, how it works, and what will happen.  One of the most significant results in astronomy was observed using radio astronomy.  In 1963, Arno Penzias and Robert Wilson observed a signal that had a temperature of about 3 Kelvin.  This turned out to be the cosmic background radiation that had been theorized to be left over from the big bang.  This observation is considered one of the strongest pieces of evidence for the big bang theory.

So what can we “see” with radio waves?  Some of the most interesting and distant objects and phenomena are observable by radio waves.  Radio galaxies are among the most massive and active objects in the universe.  They are thought to have a supermassive black hole in the middle, which heats gas and ejects it into two jets of highly energized plasma, which can range in length from tens of thousands to 100,000 light years in length.  At the ends of these jets are large radio lobes where the jets slam into interstellar medium and emit in the radio range.  The emission we see is non-thermal emission (called synchrotron emission).  Quasars are radio galaxies that are the most distant objects in the universe.  They are also considered to be the oldest objects in the universe.  Remember that the further things are away from us, the longer we are looking back in time.  Some quasars have been observed at 15 billion light years (this was found using red-shift).  This is close to the age of the entire universe!  Think about the energy that must be radiated from such a distant object in order to see it.  In fact, a quasar can emit the energy of ten thousand billion (1013) stars like the sun (Verschuur)!  Neutron stars are remnants of a massive explosion called a supernova.  Neutrons are commonly called pulsars.  They rotate at very high speeds and send out signals at various wavelengths.  Among these are radio signals.  Pulsars are known to be the most accurate clocks in the universe with an accuracy of 10-12 seconds (Verschuur)!  Another group of objects are the massive interstellar hydrogen clouds.  These gas clouds are the seeds of the universe.  Neutral hydrogen does not emit in the visible range, so what seems to be black and empty space to an optical telescope is teeming with massive hydrogen clouds.  These clouds can range from a couple to a few hundred light years across.  A typical hydrogen cloud a couple of light years across with a density of about 100 atoms per cubic centimeter would contain 1058 atoms (Verschuur).  This would be approximately 10 times the mass of the sun.  Another exciting aspect of radio astronomy is the study of the spectra of interstellar dust clouds.  Many of these clouds contain organic molecules, which can be observed by the radio emission they give off due to rotation of the molecule.  This is a very important topic of study as it brings in other important field such as biology and chemistry into studying the universe.  Another interesting project using radio astronomy is the Search for Extra-Terrestrial Life (SETI) program.    

In order to understand how telescopes are able to observe far away objects, the topic of resolution must be explored.  Resolution is the ability to distinctly make out two point objects.  The closer two objects get, the more resolution you will need to make each one out rather them forming into a blob.  Resolution can be measured in degrees that are divided into arc minutes that are in turn divided into arc seconds.  There are 3600 arc seconds in one degree.  To conceptualize what an arc second is, imagine placing a dime two kilometers away.  The fraction of sky filled by the dime is one arc second (Verschuur)!  The full moon represents about a half a degree of arc (1800 arc seconds).  The two major factors that affect resolution are wavelength and the diameter of the collecting dish.  This relationship can be shown with the equation:

(q) = 1.22 (l/d)

Where θ = resolution in radians

            d = diameter of dish                               

            As you can infer, the longer the wavelength of light, the bigger your value in degrees of arc becomes.  The value of θ places a limit on the ability to resolve distinct features of an object.  Why doesn’t distance fit into the equation?  Well, it does indirectly.  An object that is farther away than the same object at a closer distance will take up less space in the sky, so the object has a smaller degree of arc value.  An important point to remember is that although an object’s size never changes, its angular size can vary depending on the distance.  This explains why the sun and moon take up the same angular space in the sky (~ 0.5 degrees) even though the sun is many orders of magnitude bigger.  The above equation tells you the limit a telescope can observe.  If your telescope’s numerical resolution is greater than the object area in space (also measured in degrees of arc), you might see the object, but only as a blob of light with no discernable features.  A small number is equated with better resolution.

Example: The human eye has a resolution of about 20 arc seconds across. If a donut with sprinkles fills a space of about 10 arc seconds. You may be able to see a fuzzy shape of a donut, but you would not be able to make out the sprinkles.

            Optical telescopes view visible light, which has a small wavelength (about 400-700nm).  Using these wavelengths, a one-meter optical telescope can achieve a resolution of 0.1 arc seconds.  Radio waves have the longest wavelength, so resolution becomes a problem.  To illustrate, let us compare the same one-meter telescope, but have it observe radio waves at 21 cm.  The resolution becomes 14.8 degrees, or almost 30 times the size of the sun in the sky!  You can see the problem this presents radio astronomers.  Why should different wavelength make a difference?  Imagine looking at a brick wall, and you send out a radio wave.  Radio waves are as big as individual bricks, and when they return, you will only be able to make out an area as big as the wave, so you would be able to see the individual bricks but nothing more in detail.  However, if you use visible light, which has wavelength in the nanometers, those tiny waves can fit into all the nooks and crannies, and when the waves bounce off the brick back to you, you’ll be able to see all the details of the brick.  The difference between these two forms of light helps determine its resolution.

Another factor in resolution is the diameter of the telescope.  Looking at two objects that are close together causes two beams (one for each object) of a specific width (beamwidth) to form on the telescope.  Light is bent around the edge of a surface; this causes a blurring of the light.  This creates interference patterns and also relates to the beamwidth of light.  If the beams overlap, you will only see one object.  The narrower the beamwidth, the more likely they will be distinct and not overlap.  Looking at the equation, you can see that as d gets bigger, the numerical value for resolution gets smaller, which means we can look at smaller objects with a higher degree of detail.  Therefore, the larger a dish is, the narrower the beamwidth.  So in radio astronomy, bigger is better with respect to antennas. 

Telescope design is driven by the need for better resolution.  The best resolution radio telescopes are the ones with the biggest diameter.  Huge moveable radio telescopes can be made by using mesh wire for the dish.  Since radio waves have such a long wavelength, the dishes do not have to be solid.  Mesh wire dishes are used to catch radio waves, whereas visible light passes right through.  Using mesh wiring allows for lighter dishes, therefore we can increase our diameter limit.  Naturally, there is a limit in size for a moveable radio telescope.  Currently the largest moveable telescope is in Effelsberg Germany at a size of 100 meters.

            Radio astronomers have found an interesting way around the resolution problem.  Since dishes cannot get much bigger and still move, radio astronomers have borrowed a system to increase the observing diameter.  By using a number of different telescopes in different locations and time coding the observations, they can create a virtual telescope with a huge diameter.  This field of radio astronomy is called interferometry.  The distance between telescopes is called the baseline.  The very long baseline interferometer (VLBI) is a collection of telescopes around the world that results in a virtual telescope that has the diameter of the longest baseline.  As you may guess, this system gives remarkable resolution capabilities.  Why would we use single dishes as opposed to interferometers then?  Single dishes are cheaper and much easier to use than VLBI. 

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