Other parallax methods involve the motion of the sun among nearby stars. The sun moves relative to the fixed stars at a velocity of 20 km s-1 or about 4.1 AU per year in the direction of the constellation Hercules. However, the stars do not remain stationary and are all moving with their angular displacements or proper motions across the sky just like the sun, so we have to look at a group of stars and calculate the mean parallax of the group. The way this is done is quite elaborate and involves intricate statistical calculations, but the result is that we can reliably measure distances to a few 100 pc using this statistical parallax method. The Hubble Space Telescope can make parallax measurements to a precision of 0.001" and the recently launched Hipparchus satellite to 0.002".

The Period Luminosity (P-L) Relation

When we observe stars we find that there are some which vary in luminosity with time. These stars are called variables. The star Delta Cephei is one such star and its variation in luminosity with time has been extensively studied. There are many other stars like Delta Cephei and they go under the collective name of Cepheid Variables or cepheids. It turns out that the longer the period the more luminous the cepheid star. The P-L relation was calibrated from apparent to absolute magnitudes by measuring the distance to a single Cepheid by statistical parallax methods. We can use the P-L relation to find the distance to the cepheid using the following steps: Step 1: Locate a cepheid. Step 2: Measure its period by observing it nightly. Step 3: Find the star's absolute magnitude using the P-L relationship. Step 4: Measure the star's received light flux to determine its apparent magnitude Step 5: Calculate the star's distance using the distance-magnitude relation. Variable stars that are used in this way to estimate distances are an example of what are called standard candles; objects that can be used as 'yardsticks' to determine astronomical distance scales.

PERIOD-LUMINOSITY RELATION
The mass-luminosity relation with diagram
http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html

Mass-luminosity relationship for main sequence stars with diagram
http://zebu.uoregon.edu/~imamura/208/jan23/ml.html

Since in most cases, the radiation received from celestial objects is weak, collectors of radiation are needed so that enough energy can be gathered for measurements to be made. Most visual and radio astronomy can be done from the ground, and once the energy is collected it must be analysed and detected so that information can be extracted from it.

Optical Telescopes

The invention of the optical telescope revolutionised our knowledge of astronomy by making distant objects appear closer and therefore larger. There are many different designs of telescope but all use an objective either in the form of a lens or a reflecting mirror, to concentrate starlight. Three important features of a telescope are its... (i) magnification (ii) light gathering power (iii) image resolution. A telescope is rather like a bucket for collecting photons. Astronomers like big telescopes because of their ability to gather light, and a measure of how much light one can collect is called the Light Gathering Power (LGP). The LGP of a telescope is directly proportional to the square of the diameter of its objective and is a relative measure for comparing the ability of different telescopes to 'grasp' light.

Although the atmosphere readily admits electromagnetic radiation at optical wavelengths, in practice the 'seeing' is limited by atmospheric conditions particularly by convection currents and air turbulence as well as minute changes in the primary mirror shape due to structural flexing. Two techniques, active optics and adaptive optics has been devised to overcome these. In active optics, alterations in the mirror shape due to mechanical stresses are made in a few minutes by mechanical actuators to ensure that the image is kept in the sharpest focus.

Adaptive optics is concerned with compensating for the effects of atmospheric turbulence. The optical wavefronts from a reference star are distorted as they travel through the atmosphere. These distortions are measured and the information sent by a computer to piezoelectric transducers that distort the mirror of the telescope so that it matches that of the turbulent atmosphere. The effect is to cancel out the effect of the turbulence resulting in better image resolution.

Radio Telescopes

Radio astronomy was born when a telephone engineer Karl Jansky (1905-1950) was looking for sources of static noise affecting radiotelephone communications. Using a radio aerial, Jansky found that some of this noise was coming from the Milky Way. Later, other workers found numerous celestial radio sources including the sun and radio telescopes were developed to study them.

The simplest radio telescope consists of a 'flux bucket' in which radio energy is concentrated in a parabolic dish aerial and brought to a focus at a receiver. A radio telescope has a low resolving power because of the long wavelengths of radio waves. Remember that the resolving power is proportional to the wavelength, so that for an optical telescope and a radio dish of the same aperture, the radio telescope will have at least 100,000 times less resolution. However there is a way to increase the resolving power without having to build huge dishes. Radio astronomers use interferometry to improve the image resolution. If a celestial source is directly overhead then the signals from it arrive at the aerials in phase and constructively interfere giving a strong signal. Conversely, when the signals are 1800 out of phase the signals destructively interfere. As the source moves across the sky an interference pattern of maxima and minima are recorded exactly like that for light passing through a double slit. In order to build up a complete image of the source we need to have interferometers at different orientations. The Very Large Array in New Mexico is able to map the sky at radio wavelengths. This technique of mapping a complete object is called aperture synthesis and involves sophisticated signal processing.

Infrared Astronomy

Observing in the infrared is limited to only a few wavelength ranges due to absorption by CO2 and water vapour in the Earth's atmosphere. An optical telescope is used with a special detector called a Bolometer placed at its focus. The telescope concentrates the infrared object onto the bolometer from which its temperature can be determined. Since the infrared observations are restricted from the ground, much infrared astronomy is done using space astronomy, the IRAS satellite being a notable example.

OPTICAL TELESCOPES
Site on the Nordic Optical Telescope (NOT) including much information on its structure, size, resolution etc.
http://www.not.iac.es/

Diagrams of how Microwave and Optical Telescopes work
http://www.coseti.org/9008-014.htm

RADIO TELESCOPES
Information on radio telescopes
http://csep10.phys.utk.edu/astr162/lect/light/radio.html

Images of major radio telescopes around the world
http://astrosun.tn.cornell.edu/faculty/haynes/asat/radiotel.html

INFRARED ASTRONOMY
Excellent source of information on IRAS
http://irsa.ipac.caltech.edu/IRASdocs/iras.html

The use of high altitude balloons, rockets, satellites and spacecraft enables us to observe space at wavelengths that would not normally be absorbed by the Earth's atmosphere. This method of observation usually goes under the name of Space Astronomy.

X-Ray Astronomy

A rocket borne experiment launched in 1962, provided the first direct evidence that some celestial objects are strong X-ray emitters. Detectors aboard the rocket revealed a sharp increase in X-ray photon flux as they were pointed in the direction of Scorpius and also in the constellations of Sagittarius and Cygnus. In addition the photon flux never dropped to zero indicating that the sky was immersed in a background of interstellar origin. Subsequent experiments flown on spacecraft have revealed more information about the number and disposition of X-ray sources in the universe and located many more X-ray sources. X-ray sources are of great interest to astrophysicists as they are associated with highly energetic processes involving very high temperatures. Nearly all types of astronomical objects from planets to stars and galaxies are found to emit X-rays.

Gamma Ray Astronomy

During the cold war, the US military launched a series of satellites called Vela that were designed to ensure compliance with the 1963 nuclear test ban treaty. Vela were able to detect the flash of gamma rays given off by the detonation of a nuclear weapon. The Vela satellites did indeed detect gamma ray flashes but they were not coming from Earth but from space! These gamma ray bursters (GBRs) last from about 0.01 to 1000 s with energies ranging between 1 KeV to 100 MeV. In 1991 the space shuttle Atlantis released the Compton Gamma Ray Observatory (CGRO). This satellite is equipped with sensitive gamma ray detectors that can assign position information in order to correlate the bursts with known objects. The CGRO has found that the sources are spread evenly across space but their distribution is not uniform. The origin of GRB's is currently a mystery and it is not known whether they originate within the galaxy or outside it.

Gamma-ray Astronomy
Basic encyclopaedic information and further links
http://www.encyclopedia.com/html/g1/gammaray.asp


NASA's "World of Gamma-ray Astronomy"
http://imagine.gsfc.nasa.gov/docs/introduction/gamma_information.html

X-ray Astronomy
Superb Harvard site about X-ray Astronomy
http://chandra.harvard.edu/xray_astro/index.html


X-ray Astronomy and the Sun
http://imagine.gsfc.nasa.gov/docs/science/know_l1/xray_sun.html

Detecting and recording electromagnetic radiation from space has far advanced from the time when drawings were made by astronomers looking through the eyepiece of a telescope. Modern technology has extended the range of wavelengths and intensities normally accessible to the human eye and the processing of images by computers can reveal information and structure not immediately discernible to the brain.

Photographic Emulsion

Photography is extensively employed to record astronomical images. A photographic emulsion is made up of lots of tiny grains a few microns across. The chemical development of these grains after being activated by incident photons is what forms the image and the grain size determines the image resolution. The emulsion is coated onto a glass plate which does not flex or expand easily and from which positions and intensities of stars can be accurately measured. Photographic plates have long storage lifetimes and emulsions can also be optimised for certain wavelengths, with the resulting image digitised for input into a computer. An important measure of a detectors sensitivity to electromagnetic radiation is its Quantum Efficiency QE. This is defined as: QE =        Number of photons detected     x 100% Number of photons incident An ideal detector would have a QE of 100% and the QE of photographic emulsion is quite low being only a few percent. However it is relatively cheap, simple to use and it can compensate for its low Q if exposures are made over long time periods or integrating the light received. It also presents a large sensitive surface area to the image.

Photomultiplier Tubes (PMTs)

These make use of the photoelectric effect. An incident photon striking the surface of certain metals will eject electrons from it if it has a certain minimum energy given by the Planck relation... E = hf - W where E and f are the respective energy and frequency of the incident photon, and W is the work function which is the energy needed to remove the electron from the surface of the metal. A photomultiplier consists of a series of dynodes arranged in an evacuated glass tube. Light falling on the first dynode ejects electrons by the photoelectric effect which are then accelerated through a potential difference to the next dynode where more electrons are released by secondary emission. As a result an electron amplification process occurs at each diode stage right through to the final electrode where a useful current is produced. Photomultipliers do not produce images but measure intensities with a QE value as high as 20%.

Gamma Ray Detection

PMTs are used in conjunction with sodium iodide crystals to detect gamma rays. when struck by a gamma ray the sodium iodide crystal emits a flash of light which is detected by the PMT and amplified. The gamma ray detectors on CGRO incorporate sodium iodide crystals and PMT's as a means of detecting gamma ray bursts.

Charge-Coupled Devices

A charge-coupled device (CCD) is a type of microchip in which incident light is converted directly into digital information. CCDs are made out of a silicon wafer divided into small regions called pixels. A typical CCD may have as many as a million pixels extending over an area of a few cm2 arranged in rows and columns. When light strikes the CCD, electric charge is accumulated in pixels which is proportional to the brightness of the image at a particular pixel location. Unlike photographic film, this makes the response of a CCD linear. The QE of a CCD is close to 100% making it a near ideal radiation detector. This means that the light gathering power of a smaller telescope equipped with a CCD as a detector, gives comparable performance with a much larger one using photographic film. The fact, the CCDs output their information digitally makes them ideally suited to computer processing and data transmission. The images you see taken by the HST are recorded using CCDs. The WFPC and FOC employ 800 x 800 pixel CCD cameras, and the readouts are transmitted to Earth in digital form for image processing.

Bolometers

A Bolometer is a device which measures increases in temperature due to the radiant energy it receives at all wavelengths. There are two types; thermistors which operate at room temperature, and semiconductor bolometers made of germanium, which need to be cooled to low temperatures ~2K. In both kinds, as the device heats up, its electrical resistivity is altered and its resistance to an electric current also changes. The variation of current with temperature indicates how much energy the bolometer is absorbing. Bolometers are extensively used in infrared astronomy. The IRAS telescope uses infrared bolometric detectors cooled by liquid helium to 2K which operated for 9 months before the helium ran out

Charge-Coupled Devices
Contains a section on Charge-Coupled Devices
http://www.aao.gov.au/local/www/sl/filters.html

Bolometers
Good NASA site about the COBE Bolometers
http://cryowwwebber.gsfc.nasa.gov/COBE/Bolometers.html

ANALYSING RADIATION FROM SPACE

In general there are four types of analysers used for astrophysical measurements: i) Spectrometers for measuring the spectra of starlight ii) Photometers for measuring the brightness of stars iii) Polarimeters for measuring the degree of polarisation of starlight iv) Interferometers for high precision angular measurements of the separation of double stars and the diameter of single ones. Spectrometers Spectrometers are instruments that split light into its component wavelengths. This is accomplished by using prisms or diffraction gratings to disperse light into a spectrum. For light of a particular wavelength h, the performance of a spectrometer are governed by two criteria: The dispersion = the change in wavelength the change in distance along the spectrum and the spectral resolution R=the wavelength smallest wavelength interval that can be measured on the film Higher dispersions increase the amount of detail we can see in the spectrum but also dilute the light and we can only obtain high dispersion spectra for the brighter stars using telescopes with large apertures. Typical dispersions for astronomical work range from 200 nm mm-1 and spectral resolutions of 10 to 10 000. For prism spectrometers, relatively low levels of starlight must travel through a thick prism causing much light to be absorbed. In addition, the spectrum of light is not dispersed evenly- the red end compressed while the blue and violet is spread out. The spectrometer more commonly used for astronomical work is the grating spectrometer. This uses a diffraction grating as the dispersion element. A disadvantage of grating spectrometers is that the light energy is spread over several spectra corresponding to different orders rather than concentrated into a single spectra by a prism spectrometer. However, the resolving power of gratings are generally better than for a prism and by using reflection gratings it is possible to analyse wavelengths that would normally be absorbed by a glass prism.

Photometers

Measuring the light intensity or magnitude of stars with detectors is called photometry and an instrument which does this is called a photometer. The eye, photographic film, CCDs and bolometers can all be used for photometric measurements. Photomultiplier tubes are commonly employed as photometers in conjunction with an arrangement of filters called the UBV filter system. The bolometric magnitude is the apparent magnitude of a star measured above the Earth's atmosphere at all wavelengths. However in practice, astronomers measure the radiant energy of a star through three filters U, B and V transparent to a specific wavelength. These are defined as i) U, being a filter transparent to a star's Ultraviolet apparent magnitude centred at a wavelength of 356 nm with a bandwidth either side of 68 nm. ii) B, being the star's Blue apparent magnitude as seen through a filter centred on 440 nm with a bandwidth of 98 nm. iii) V, being the star's apparent Visual magnitude as seen through a filter centred on 550 nm with a bandwidth of 89 nm. The V filter approximates the sensitivity of the human eye. Astronomers use photometry to determine the colour of a star so that they can estimate its temperature and find out how hot it is. The temperature of a star is determined by aiming a telescope at it and measuring the intensity of the light as it passes through each of the filters in turn. The relative intensities in neighbouring wavelengths are compared by subtracting the ultraviolet and blue magnitudes (U-B) and the blue and visual magnitudes (B-V. These are called the stars colour indices. We can therefore write B-V=MB-MV and U-V=MU-MV Note that because a colour index is the difference of two magnitudes, we vdo not need to know the star's distance. The colour index of a star tells you how brighter or dimmer a star is in one wavelength band than in another. Assuming that stars are near ideal blackbodies, we know from Wien's law that the hotter a star is, the more its peak wavelength is skewed towards the ultraviolet, so that the magnitude is greater through the U filter than through the B and V filters. If the star is relatively cool then its magnitude will be greater in the V than in the B and U filters. From the laws of blackbody radiation, it can be shown that a mathematical relationship exists between the temperature of a star and its colour index.

Photographic methods

The images of stars on a photographic plate can be measured photometrically using an instrument called a microdensitometer. This consists of a device which shines a beam of light through the image and measures the transmitted intensity as a variation in voltage. Since the light response of photographic emulsion is non-linear the response curve must be known beforehand so that the conversion of the stellar image into intensity is properly calibrated. If we have a microdensitometer which transmits light of intensity Iin through an image in which transmitted intensity is Iout then these are related to the to the photographic intensity D by D=log Iin - log Iout and using the characteristic curve we can relate D to the original image brightness.

Polarimeters

Light from distant stars is polarised as it passes through clouds of interstellar gas and dust in the Milky Way. Dust grains are aligned by the presence of magnetic fields which causes the polarisation of starlight as it passes through. The degree of polarisation is measured with a polarimeter and from this we can deduce the magnetic field strength existing inside the clouds.

Interferometers

A Michelson Stellar Interferometer is capable of measuring the angular separations of stars and even the angular size of the nearest stars. The stellar interferometer works in the same way as the Young's double slit experiment. In Young's experiment, light passes through two slits separated by a distance d. In a stellar interferometer, the light sources can be two stars, or light from opposite ends of a star along its diameter. Unlike the Young's slit experiment however, the light from the two sources is not coherent. The two independent fringe sets simply cancel out due to the bright and dark fringes overlapping.

Image Processing

In the last 20 years, there has been a revolution in computing power with computers increasing in processing ability while at the same time decreasing in cost. This, together with technological advances in acquiring astronomical data in digital form using detectors such as CCDs, has meant that the manipulation of images inside a computer has become routine tool in extracting the maximum amount of information from an astronomical object. Some common image processing techniques are: i)Noise removal. Noise may be digitally removed and replaced with the average intensity of their adjacent areas. ii) Background subtraction. If the extent of the background signal is known, then this is a systematic error that can be subtracted out in the final image. iii) Contrast Stretch. A typical computer can display 16 levels of grey while a CCD can resolve more than 256 changes in intensity. In order to make use of the CCD's greater range of levels, a contrast search is applied. This involves mapping the dominant grey levels in the image to the maximum range of the computer display. iv) False colour. Sometimes it is helpful to assign colours from the computers colour palette to particular intensities on the image. This is particularly useful when we want to find for example, the temperature distribution of an object or the intensity variation of radiation across the sky.

Interferometers
Interferometry - rather technical but some useful links
http://www.geocities.com/CapeCanaveral/2309/page1.html

Young's slits experiment
Theory of the Young's double slit experiment
http://www.astro.virginia.edu/~eww6n/physics/YoungsDoubleSlitExperiment.html