RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS STUDENT NOTES (KS4)

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1 Resolution Astronomers need to be able to look at objects in the sky with high precision. Resolution, or resolving power, is a measure of how well an eye, or a telescope, can do this. It is measured by observing whether a telescope can see two very distant, very close together objects as separate from each other. For example: a car has two headlights. If the car is too far away then your eye will not be able to separate the two headlights and will see them as one lamp. This is an example from NASA. On the left is a photo taken at the Las Campanas observatory, and, on the right, one taken by the Hubble Space Telescope of the same object: Question 1: Which telescope has the highest resolution, the one at Las Campanas or the Hubble Space Telescope? One way of assigning a numerical value to resolution is to measure the smallest angle of separation between two objects that an observer can distinguish as separate: This angle, θ, is known as the angular resolution of a telescope. It has a particular value for a given telescope. The smaller the angle, the better the resolution.

2 Angular Resolution Two factors affect the angular separation of objects: i) How far apart are the objects? ii) How far away from the observer are the objects?

3 Angular Resolution A good example of angular resolution is whether you can distinguish car headlights as separate light sources over a large distance. Question 2: How far away do you think a car would need to be before you can only make out one, overall source of light, coming from both headlights? (Make a guess, then read on to find out the correct answer ) Question 3: Do you think the human eye has a better or worse angular resolution than an optical telescope? Why? Angular resolution depends on two factors: the size of the aperture of the telescope (in the case of an eye this is the size of the pupil) and the wavelength of the electromagnetic waves being detected. The formula is: θ = 70λ D Where λ is the wavelength of the electromagnetic waves in metres, D is the diameter of the aperture of the telescope, also in metres, and θ is the angular resolution of the telescope in degrees.

4 A Challenging Calculation For a human eye: the size of the pupil is about 2 mm (2 x 10-3 m) the average wavelength of visible light is about 5 x 10-7 m The resolution of the human eye, θ, can be calculated using the formula: θ = 70λ D θ = 70 x 5 x x 10-3 θ = For the human eye to resolve a pair of car headlights: the angular resolution of the human eye is the separation of the car headlights is about 1 m The distance of the car headlights away for the observer, d, is given by the formula: d = 1 sin θ d = 1 sin d = 3,274 m Therefore, the human eye can resolve a pair of car headlights when the car is about 3.3 km away from the observer. Question 4: Radio waves have a much longer wavelength than light (100,000 times longer). Do you think that the human eye has a better or worse angular resolution than a single radio dish? (HINT: think about the first formula you used above. Remember: the smaller the value of θ, the better the resolution). Question 5: Remember, the angular resolution of the human eye is about For a wavelength of 0.5 m, what approximate value of D would give a radio dish with the same resolution as the human eye? (HINT: use the formula!) Question 6: What does this tell you about the size of radio telescopes if they are to be any use for observing?

5 The Electromagnetic Spectrum and Astronomy Often we cannot see objects with visible light. It may be that an object, such as a star, is very dim because it is too small, less intense or very far away. Stars may emit electromagnetic radiation of other wavelengths however, and we can observe them using the correct wavelength telescope. Most of the telescopes at Lord s Bridge observe objects using radio-waves and microwaves which often allow us to see objects that would be invisible to us at optical wavelengths. The electromagnetic spectrum Radio Microwave >10-1 m 10-2 m Infra-red 10-4 m Visible Ultra-violet 10-6 m 10-8 m Wavelength X-ray m Gamma ray m <10-13 m Did you know? Microwaves are short wavelength radio waves. Microwave ovens work by producing intense microwaves with a wavelength of about 10 cm, which excite water molecules in food. The front grill on microwave cookers has regular holes a few millimetres across. These allow visible light waves to pass through so that you can see your cooking, but not the longer microwaves, which are dangerous to humans. The first artificial radio waves were produced in 1885, by Heinrich Hertz, although their existence had been predicted by James Clerk Maxwell in Hertz, who has the unit of frequency named after him, created the radio waves using a spark between two metal balls held close to one another with a large voltage across them. As an example of using different wavelengths of electromagnetic waves to study the universe, we can look at the binary star T Tauri, in the constellation of Taurus. Binary star systems consist of two stars (bi means two or double) very close together in the sky, so we need a high level of resolution to observe them separately. The two stars in the T Tauri binary system are known as T Tau N (the northern most star) and T Tau S (the southern most star). Question 7: T Tauri is too faint to see with the naked eye, so we need telescopes to view it. Can you think of the reason why telescopes can see dimmer objects than our eyes? (Hint: think about the size of the telescope apertures)

6 Optical Wavelengths T Tauri is more complicated than many other binary star systems, however, as one of the two stars is very bright at optical wavelengths and the other is very dim. Here is an optical image of the pair, viewed at optical wavelengths (i.e. 5 x 10-7 m): There is a cloud of dust on the right hand side of the binary star. This is known as a nebula. We can see it because it reflects light from T Tauri. Note how there appears to be only one star rather than two. Indeed, astronomers believed that there was only one star until it was viewed using radio waves in Radio Wavelengths Here is a radio picture of the binary star at wavelength 0.02 m: Here you can clearly see that there are two stars in the system. Declination (latitude) and Right Ascension (longitude) are astronomical measures of position in the sky, similar to latitude and longitude on the Earth.

7 The Electromagnetic Spectrum and Astronomy Question 8: Which of the two stars in the binary system, T Tau N or T Tau S, emits the most radio wavelength radiation? Question 9: Which telescope, the radio one or optical one, had the better resolution when these images were taken? Why? The telescope that took the radio image was the Very Large Array (VLA) in New Mexico, USA, shown here: Like the telescopes at Lord s Bridge, the VLA uses a technique known as interferometry to achieve the highest resolution possible. This technique involves combining the signals from an array of telescopes and adding them together to form a better image.

8 Using more of the electromagnetic spectrum We have now looked at images of T Tauri using radio waves and light waves. What other types of electromagnetic radiation could we use? We could use a smaller wavelength wave like Ultra-Violet waves or X-Ray waves. This would require using a satellite based telescope as these wavelengths of electromagnetic radiation do not penetrate our atmosphere. It turns out, however, that it is much more interesting to view the pair using Infra-red radiation, which has a wavelength that falls between radio waves and visible waves in the electromagnetic spectrum. Did you know? Infra-red radiation can be used to see in the dark. Everything, including you, emits Infra-red radiation. The wavelength of the radiation depends on the temperature of the object. Infra-red sensors can see humans and other warm objects against a background of colder objects. When we look at the T Tau binary star system using the Infra-red section of the electromagnetic spectrum this is what we see: This picture of T Tau was taken using an Infra-red camera called MIRLIN (Mid-Infra-red Large-well Imager) at the Hale telescope on Mt. Palomar in California, USA. Infra-red radiation cannot penetrate our atmosphere very well so observations have to be made from high up mountains or, ideally, in space. The wavelength of the Infra-red electromagnetic radiation used to make this image was 1x10-5m. Question 10: Which star, T Tau N or T Tau S emits the most Infra-red radiation?

9 Question 11: Consider your answers to Question 8 and Question 10. Now, which star do you think is the brightest in the visible region of the electromagnetic spectrum? You may be surprised to discover that it is actually T Tau N that is the brighter optical star, despite the fact that the radio plot and the Infra-red photo shows T Tau N as the lesser of the two sources. We can summarise all these results in a table: Radio Wavelength (λ = 0.02 m) Infra-red Wavelength (λ = 1 x 10-5 m) Optical Wavelength (λ = 5 x 10-7 m) T Tau N Dimmer Dimmer Brighter T Tau S Brighter Brighter Dimmer What is the explanation for this? Well, stars emit electromagnetic waves at all wavelengths. However, depending on the temperature of the star there will be a more intense section of the electromagnetic spectrum where the star radiates, usually in the Infra-red, Visible or Ultraviolet regions. The hotter the star, the shorter the dominant wavelength of radiation emitted. It is like the flame from a Bunsen burner: blue flames are hotter than yellow flames. The temperature governs the wavelength of light coming from the flame. Question 12: Our sun emits most of its light in the visible region of the spectrum. So too does T Tau N. T Tau S, on the other hand, emits most of its radiation in the Infra-red region of the spectrum. Therefore, which star is hotter, Tau N or Tau S? KEY WORDS: Resolution (resolving power): How well a telescope can distinguish two objects as separate Angular Resolution: The smallest angle of separation between two objects that can be resolved by a telescope. Binary Star: Two stars very close together in the sky. They can be close together in space, like T Tau, or they can be far apart in space, but along the same line of sight for the observer making them appear close in the sky. Declination: A measure of an object s elevation in the sky. The astronomical equivalent of latitude. Right Ascension: The astronomical equivalent of longitude. Along with declination, right ascension pinpoints an object s position in the sky.

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