Addendum to A1210 Lectures on Light and Telescopes

1. Addendum to A1210 Lectures on Light and Telescopes Bob Dickman

2. Correction: Temperature Scales • Temperature in Kelvins (Tk) and equivalent temperature in degrees Celsius (Tc) and Fahrenheit (TF): Tk= Tc+ 273 or Tk = (5/9)*[TF - 32]+ 273 • The absolute (Kelvin) scale is the only natural way to express the formulae on light and energy you’ve seen, e.g., the total energy – called the luminosity, L – emitted by a sphere of radius R and absolute temperature T is L = (4πR2)*(σT4) • If you use any other temperature scale, the formulae will be much more complicated and will give you a bad headache 

3. Telescopes • Telescopes are devices that collect electromagnetic (e.m.) radiationlike light or radio waves • The limitations of the human eye in doing this are: • Limited sensitivity (small area) • Limited resolving power • Limited detection range (the eye cannot detect ultraviolet light or radio waves) • How do we design devices to overcome these shortcomings?

4. Sensitivity • Sensitivity to light depends mainly on collecting area. The bigger the area of the energy-collecting surface of a telescope, the more light it gathers A = 4πR2 = (πD2)/4 • The fully-dilated pupil of a human eye is around 1 cm in diameter. The biggest optical telescope yet built is around 10m in diameter • Ratio of diameters is 10/0.01 = 1000 • Ratio of sensitivity goes as the square of this, i.e., 106 • The first telescopes coupled detected light to a human eyeball – this limits to what “colors” of light could be seen and there is no way to record the signal • Electronic detectors greatly expanded what e.m. radiation could be detected AND the ability to sum the collection of light over time (with long exposure photography and later with electronic detectors like the ones in digital cameras) enabling one to see far, far fainter objects than the simple ratio above would suggest – by over a factor of a billion (109)

5. Resolving Power • The fine detail made available by a telescope is called the resolving power (or resolution) of the telescope • Resolution is given in angular units (like seconds of arc or radians) – the smaller the resolution the better and the sharper the image: Examples of angular resolution: • 30 arc minutes (1/2 degree): diameter of the full moon. Early radio telescopes had resolutions in this range • 1 second of arc – best optical telescopes of the 1960s • 0.1 arc seconds: Hubble Space Telescope • 0.0001 arc seconds – NRAO VLBA • Magnification of an image reveals the telescope’s resolution – but if the resolution is limited (by optical quality or “seeing”), magnification won’t improve anything

6. What Governs Resolving Power? • Answer: The wavelength of the observations and the diameter of the collecting surface • The larger the diameter of the aperture, the better the resolution • The shorter the wavelength, the better the resolution • Resolution = Wavelength (λ)/Diameter(D)  smaller ratios better! • Also the precision of the reflecting surface can limit resolving power • Radio telescopes • Large antennas needed for resolution because λ is large for radio waves • Interferometers • Turns out if you use multiple antennas (or optical telescopes) and record their output simultaneously, andif you computer process the signals just right: • You can get an image with the resolution of a much larger telescope, whose diameter is equal to the largest separationof the individual telescopes (the “baseline” of the interferometer) • That’s why the VLBA’s resolution is so large – its baseline is the distance between St Croix, USVI, and Mauna Kea, HI! • No free lunch: Interferometers are like huge telescopes – but they are missing most of their collecting area. So their sensitivity is no better than the total collecting area of the individual telescopes. • Atmospheric blurring (“seeing”): • See your lecture summary for beautiful images of seeing • Removing the effects of atmospheric blurring: adaptive optic systems (cold war fallout) • Avoiding seeing limitations: • Fly the telescope on a very high-altitude aircraft • Put the telescope in space (but expensive, hard to fix if it breaks, and hard to upgrade) • Use radio waves (the atmosphere is basically not there)

7. Large Telescopes • The main surface of a large reflecting telescope is represents a critical balance between the precision curved surface necessary to bring the light together and the rigidity (and weight) needed to limit distortions of the surface due to gravitational deflection as the telescope is moved • The largest optical telescopes are multi-ton machines that cost well over $100M apiece (the new 42m EELT will cost at least ~$2B), all to support a precisely shaped metallic reflecting film that weighs a few ounces