Caroline Chisholm College 4. Photometric measurements can be used for determining distance and comparing objects Caroline Chisholm College Physics Define absolute and apparent magnitude The apparent magnitude, m, is the measured brightness of the star as seen from the Earth. The more positive the magnitude is, the duller the star. Apparent magnitude is influenced by the actual brightness of the star, the distance and any matter in between. Hipparchus established a magnitude scale in the second century BC, with the brightest star at magnitude 1 and the dullest at magnitude 6. Since then, brighter (less than magnitude 1 and even negative values) and duller (more than magnitude 6) stars have been found. A difference in magnitude of 5 corresponds to a brightness ratio of 100. This means that a star of magnitude 1 is 100 times brighter than a star of magnitude 6. A star with a negative magnitude is even brighter. Mathematically, this means that so if the difference in apparent magnitudes is 5, the brightness ratio is 100.

Caroline Chisholm College Physics Define absolute and apparent magnitude The absolute magnitude, M, is the apparent magnitude that a star would have if it were at a distance of 10 parsecs (pc) (with no absorption by interstellar dust). Absolute magnitude indicates the actual (intrinsic) luminosity (or brightness) of the star. So if a star is further away than 10 pc, the apparent magnitde will be less than the absolute magnitude.

Caroline Chisholm College Physics Explain how the concept of magnitude can be used to determine the distance to a celestial object The relationship between the absolute magnitude, M, the apparent magnitude, m, and the distance to the star, d, can be expressed by the distance modulus formula: Therefore, if M and m are known, we can calculate d.

Caroline Chisholm College Physics Solve problems and analyse information using: and to calculate the absolute or apparent magnitude of stars using data and a reference star Proxima Centauri has magnitude 11, Algol has magnitude 2.1. Compare the brightness of these two stars. So Algol is 3600 times brighter than Proxima Centauri Achernar has apparent magnitude =0.45, absolute magnitude= -2.77 How far away is it?

Caroline Chisholm College Physics Outline spectroscopic parallax There are a number of steps to using spectroscopic parallax to determine distance. Firstly a spectroscope is used to determine the apparent magnitude of the star, m. Then the spectral class of the star is determined from the spectral lines The spectral class is used to find the range of absolute magnitudes on the Hertzsprung-Russell diagram This main sequence star has absolute magnitude between 2.5 and 4.5, so take the value as M=3.5 e.g Spectral class A2 Now we can use the distance modulus formula NB Spectroscopic parallax is not a precise technique because of the range of stars with the same spectral class. to determine the distance to the star.

Photometers use different filters to give different magnitudes. These Caroline Chisholm College Physics Explain how two-colour values (ie colour index, B-V) are obtained and why they are useful The colour of stars varies with the instrument used to observe them. Brightness, or apparent magnitude, also depends on the instrument used. INSTRUMENT MOST SENSITIVE TO MEASUREMENT NAME Eye Yellow-green (V) Visual Magnitude Camera/Film Blue (B) Photographic Magnitude Photometers Wide range - IR to UV (U) Ultraviolet Mag., (B) & (V) Photometers use different filters to give different magnitudes. These are U - ultraviolet filter, B - blue filter and V - yellow-green filter. A red star is brighter through a V filter, so has a lower value for V than B or U. A blue star is brighter through a B filter, so has a lower value for B than V or U. A yellow star is brighter through a V filter, so has a lower value for V than B or U.

Sample problem 15.8 on p.294 of text Explain how two-colour values (ie colour index, B-V) are obtained and why they are useful Caroline Chisholm College Physics Note that a low B magnitude does not necessarily mean that the star is blue - it may just be really bright and have an even lower V magnitude. It is the DIFFERENCE between them that is important. Colour Index = B - V C.I. gives an indication of the colour of the star. e.g. A red star is brighter through a V filter, so has a lower value for V than B or U. so Colour Index = B - V is positive. A blue star is brighter through a B filter, so has a lower value for B than V or U. so Colour Index = B - V is negative. A0 stars have colour index = 0, temp = 10000 K, colour=blue-white Add colour index to your table - try doing the whole table now N.B. The relationship between CI and temperature is not linear. CI from 0 to -0.6 gives a big temp.diff. compared to CI from 0 to +0.6. Sample problem 15.8 on p.294 of text NB could also discuss spectral features of each star

Caroline Chisholm College Physics Describe the advantages of photoelectric technologies over photographic methods for photometry Photographic photometry utilises visual comparisons between the images of stars on photographic film. The diameter of each star’s image on the film is related to its magnitude. It is possible to obtain photometry for thousands of stars from a single photograph using this technique. Lasers can be used to scan the plate to produce a digitised image which can then be analysed.  Photoelectric photometry uses a photomultiplier to convert weak light into a measurable electric current. Light from a single star falls through a pinhole onto a photocathode, causing electrons to be ejected in proportion to the intensity of the light. A photomultiplier produces a pulse of current for every electron ejected, and pulses are counted to produce an digital signal which can analysed by a computer. Several photomultipliers can be used simultaneously to measure the light from different stars. 

Caroline Chisholm College Physics Describe the advantages of photoelectric technologies over photographic methods for photometry Use p.295 to list these - not restricted to visible spectrum, much wider range of l - use a high resolution charge-coupled device (CCD) so pictures are good, although photographic can sometimes get even higher resolution. Modern CCD arrays are generally better than photographic it is an electronic signal, so it can be COLLECTED, MULTIPLIED, DIGITISED, ANALYSED AND STORED ELECTRONICALLY all much more quickly and from a remote location if necessary – e.g. Space telescope from Earth can be transmitted accurately over broad or narrow wavebands CCDs and photomultipliers are more sensitive to faint light sources than photographic film.

Caroline Chisholm College Physics Describe the advantages of photoelectric technologies over photographic methods for photometry CCDs have a more uniform response across the visible spectrum than photographic film does, and corrections must be made for this in photographic photometry. There is more scope for a greater level of analysis because of the increased quantity of data. Photoelectric photometry allows for a faster and more accurate measurement of magnitude than photographic photometry. Filters and CCDs  , Anglo-Australian Observatory. (This web site was last checked on 15 August 2006) (HSC ONLINE)

Caroline Chisholm College Physics Perform an investigation to demonstrate the use of filters for photometric measurements Sample procedure Produce simulated starlight from the incandescent lamp in a ray box kit, commonly available in school science laboratories. This has the advantage that coloured filters mounted in 35 mm slide frames can easily be inserted in the light path. If this is not available, filters can be held by hand in front of any incandescent lamp. Use a light intensity probe attached to a datalogger to measure the intensity of light at a set distance from the lamp. Set the datalogger to operate in manual or “snapshot” mode. A photographer’s hand-held light meter is a suitable alternative to measure light intensity. Place different coloured filters, one at a time, between the lamp and the light probe. For each filter, measure the intensity of light with the datalogger. You should note that the filters used in photometry, unlike those in a ray box kit, transmit a carefully calibrated range of frequencies. For each filter, also observe the light through a hand-held spectroscope to see qualitatively what effect the filter has on the spectrum of white light produced by the lamp. Use the in-built scale to measure the range of wavelengths transmitted. Record all your observations systematically in a suitable table. Compare your qualitative and quantitative observations for different filters. Use your observations to predict the effect of different filters on the measurement of apparent magnitude of stars of different spectral type. (HSC ONLINE)

Caroline Chisholm College Physics Identify data sources, gather, process and present information to assess the impact of improvements in measurement technologies on our understanding of celestial objects More accurate understanding of star temperature and characteristics More wavelengths give more knowledge of radiation emitted by objects Improvement in sensitivity and faster response times Digitised information can be quickly manipulated, shared, stored Faster analysis by computer Ability to quickly retrieve accurate images from anywhere in the world or space

Caroline Chisholm College Physics Identify data sources, gather, process and present information to assess the impact of improvements in measurement technologies on our understanding of celestial objects Sample topics One obvious new technology involving measurement is the use of electronic data collection and digital storage. Charge-coupled devices (CCDs) and computerised technology have enabled incredible leaps in the quantity and quality of data collected. Some other things to search for on the Internet that would admirably demonstrate the impact of new technology on our understanding of celestial objects are: the Cosmic Background Explorer the Wilkinson Microwave Anisotropy Probe the Hubble Space Telescope the Chandra X-ray Telescope and any of the NASA planetary probes History of Astronomy: Topics: Instruments   Dr Wolfgang R. Dick, Potsdam, Germany. Research Interests and History   Dr Michael Stanley Bessell, ANU Canberra and Siding Springs and Mt Stromlo Observatories. (These web sites were last checked on 15 August 2006) (HSC ONLINE)