What are the observables

Astronomy is truly an observational science. Unlike in a laboratory experiment, the conditions cannot be changed. That is, we on Earth are passive observers (so far) in almost all astronomical experiments, and we can do nothing other than intercept (observe) the various forms of energy which reach the Earth from the depths of space. Of course, there have been a few notable exceptions for solar system studies involving manned and unmanned spacecraft that have returned samples to Earth, and from time to time we can retrieve rocks from space which have survived passage through the Earth's atmosphere in the form of meteorites. Otherwise, the energy forms that we can intercept passively can be summarized as

electromagnetic radiation (gamma rays through radio waves)

— cosmic rays (extremely energetic sub-atomic charged particles)

— neutrinos (tiny neutral particles with almost immeasurably small mass)

— gravitational waves (disturbances in a gravitational field).

Of these, the study of electromagnetic radiation which, as shown by the great Scottish mathematical physicist James Clerk Maxwell (1831-1879) in 1865, incorporates visible light, is still the most dominant. Gravitational waves, ripples in spacetime predicted by Einstein (1879-1955), have not yet been detected directly, but in the U.S.A. the Laser Interferometer Gravitational-Wave Observatory (LIGO), with sites in the states of Washington and Louisiana, went into operation in 2002; similar facilities exist in Germany, Italy, and Japan. Neutrino detectors and cosmic ray experiments have been developed successfully. Among the most well-known of the neutrino observatories are the Homestake Gold Mine in South Dakota (U.S.A.) where Ray Davis (1914-2006; Nobel Prize in Physics 2002) first uncovered the "solar neutrino problem'' in which the Sun seemed to be emitting only one-third of the expected number of neutrinos based on the well-understood theory of nuclear hydrogen-helium fusion, and the Sudbury Neutrino Observatory in Ontario (Canada) which resolved the problem by detecting all three neutrino types when it was eventually realized that three kinds of neutrinos existed. The Kamiokande neutrino observatory in Japan was sufficiently sensitive that it detected neutrinos from the supernova explosion (SN1987A) of a star in the Large Magellanic Cloud about 170,000 lightyears away; a lightyear is about 9.5 trillion kilometers (about 5.9 trillion miles) and is the distance light travels in one year. The vast majority of cosmic ray particles are protons, the positively charged nucleus of the hydrogen atom, although heavier nuclei are also observed. Low-energy cosmic rays must be detected from spacecraft, but higher energy rays generate an "air shower'' when they impact the Earth's atmosphere resulting in faint flashes of blue light known as Cherenkov radiation which can be detected by a suitably designed large telescope on the ground. One of the first telescopes built to detect Cherenkov radiation was the Whipple telescope on Mt. Hopkins in Arizona (1968) but many newer facilities now exist.

Maxwell's equations are a set of four fundamental relationships that quantify experimental findings about electric and magnetic phenomena, especially those involving the magnetic field due to an electric current (Ampere's Law modified by Maxwell) and the electric field caused by a changing magnetic flux (Faraday's Law of electromagnetic induction). These two equations can be combined to show that both the electric and magnetic fields satisfy the known form for a wave equation. Maxwell's analysis revealed that light is essentially characterized by oscillations of electric and magnetic fields which give the radiant energy the property of a wave motion. Different regions of the electromagnetic "spectrum" correspond to different "wavelengths" (denoted by the Greek letter lambda, A; see Appendix A for Greek alphabet), and the energy in the wave moves through empty space at a speed of 299,792,458 meters per second (m/s), which is of course the speed of light (usually denoted by the letter c); actually, Maxwell derived this number from two electrical constants. Useful approximate values for the speed of light are 300,000 km/s, 186,000 miles per second, and 670 million miles per hour. The frequency of the oscillations (denoted by the Greek letter nu, v) is related to the wavelength by the very simple equation vA = c (1.1)

In the simplest case of a monochromatic (single wavelength) wave traveling in the x-direction and vibrating in a fixed (x, y) plane, the oscillation can be described by a simple sinusoid (e.g., y = a sin(u — kx + 4>) with u = 2kv and k = 2k/A) and the average intensity of light is proportional to the square of the amplitude (or swing) a2 of the wave. The term ^ is the phase, and can be set to zero by an appropriate choice of origin. A cosine works too because cos(9) = sin(0 + k/2), which is just a sine wave with a phase shift of -k/2. The importance of Equation (1.1) is that it implies no restrictions on the frequencies or wavelengths themselves, only that their product must be the speed of light. Optical measurements show that normal visible light corresponds to wavelengths around 0.5 millionths of a meter and frequencies of 600 trillion cycles per second, but waves of much lower frequency (300 million cycles per second) with huge wavelengths of 1 meter or more should be possible. This result led to the prediction and subsequent discovery of radio waves. The unit of frequency (1 cycle per second) is now called the hertz (Hz) after Heinrich Hertz (1857-1894) who validated Maxwell's predictions by experiments with early radio antennas. Electromagnetic waves can bounce off certain surfaces (reflection), be transmitted through certain materials with a change of direction (refraction), curl around obstacles or through openings by diffraction, and "interfere" with one another to cause cancellation or amplification of the wave. Of these, the phenomenon of diffraction sets a wavelength m—Range of CCDs wavelength

Visible !

Visible !

1 Sub-mm

X-rays

Gamma rays

Radio waves

Radio waves m1'- ÏÏF" iii:: HI1" 10 ni" iir WAVELENGTH(m)

Figure 1.3. The electromagnetic spectrum: X-rays, light, and radio waves are all different forms of electromagnetic radiation. In the vacuum of empty space, each of these forms of radiant energy travel in straight lines with the same speed, the speed of light.

fundamental limit on measurements, and we will mention this limit many times in the quest for ultimate perfection in imaging. For now, we note only that the "angular resolution" or ability to separate two closely spaced stars a small angle apart on the sky, for a telescope of diameter D collecting light of wavelength A, is given approximately by 57.296°A/D in the diffraction limit. Maxwell's equations, electromagnetic waves, and their interactions through interference, reflection, refraction, and scattering are described in any good college physics text. More details will be presented as needed in subsequent chapters. Because electromagnetic oscillations are transverse to the direction of propagation of the energy, these waves can be "polarized", which means they have an associated "plane of vibration''.

As shown in Figure 1.3, all the well-known forms of radiant energy are part of this electromagnetic spectrum. The range in wavelengths is incredibly large. Radio waves are characterized by wavelengths of meters (m) to kilometers (km), whereas X-rays have wavelengths around 1 nanometer (nm) or one-billionth (10~9) of a meter, comparable with the size of atoms. Other length units such as the micron (^m, 10~6 m) and the angstrom (A, 10~10 m) are commonly used; scientific notation (powers of ten) and prefixes to standard units (such as nano- and micro-) are summarized in Appendix A. Visible light, with wavelengths from about 390 nm to 780 nm (or 0.39 ^m-0.78 ^m), occupies only a very small portion of this enormous radiant energy spectrum.

The rate at which the energy flows from a source is called the "radiance" or power, and the power emitted by the Sun, for example, is about 3.8 x 1026 watts (1 watt is equivalent to 1 joule per second). The power that is received by one square meter is the "irradiance" (measured in watts/m2) and irradiance drops off inversely as the square of the distance from the source. Thus, at the average distance of the Earth from the Sun the solar irradiance is about 1366 watts per square meter above the Earth's atmosphere. Measurements that can be made on electromagnetic radiation are limited. Basically, we can determine

— the direction and time of arrival of the radiation

— the intensity at each wavelength or spectral energy distribution

Intensi polaris versus

IMAGE

Intensi polaris versus

IMAGE

Position a SO

Wavelength or frequency

5Â. Spectral resolution

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