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ASP2011 Measurement Techniques Lecture 1. SCHOOL OF PHYSICS Q: How do astronomers know anything about astronomical objects that are too far away to visit? A: We interpret the radiation (and sometimes particles) emitted by astronomical objects using the laws of physics that we know work well here on Earth. "Cosmological principle" Universe is isotropic and homogenous. ie. looks the same to all observers and obey same physical laws everywhere. Sources of information Visible light (since antiquity) Other “invisible” electromagnetic (EM) radiation: o Radio (1930s-) o X-rays & -rays (1960s-) Cosmic rays (1912-) Neutrinos (1980s-) Gravitational waves (201?-) Electromagnetic (EM) spectrum Observational windows The Earth's atmosphere is transparent to EM radiation in the visible and radio frequencies. Kutner M.L., Astronomy: Astrophysical Perspective. Harper & Row Various processes contribute to the opacity of the atmosphere in other bands: Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 2 1. Gamma rays and "hard" X-rays are stopped by collisions with gas molecules in the upper atmosphere. 2. X-Rays and UV C are absorbed in the ionosphere and the van-Allen radiation belts. 3. UV A and UV B are absorbed by ozone layer. 4. Infrared is absorbed by CO2 and H2O in atmosphere. Earth-based observational astronomy is thus restricted to these two "windows". We can push the limits of infrared (IR) astronomy by going to high altitude (Chile, Hawaii) or going to places that are very cold and dry (Antarctica) For UV through X-rays, we must get above the atmosphere, in rockets, balloons or (increasingly) satellites Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 3 The nature of light Case 1. Light as a wave Fig. 3.9 E. Hecht "Optics" 2nd Ed. Addison-Wesley; also Z&G ch 8 The figure shows that em waves are transverse waves, with field vectors E & B perpendicular to the direction of propagation. Frequency the number of wave crests passing a fixed point per second. In a vacuum, speed c c = = 2.99793x108 m/s Case 2. Light as a particle. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 4 The modern quantum-mechanical picture of em radiation: light is composed of individual elements (quanta) of energy, and behaves like particles "wave packets" called photons Energy E = h Both these explanations are equivalent! Measurable quantities Frequency (wavelength) Arrival time Polarisation Intensity (flux) Spectrum (flux vs. frequency) Polarisation Recall the wave picture for EM; the E-vector has two orthogonal components Ex and Ey, both perpendicular to the direction of transmission. For plane (linearly) polarised light, the direction of E does not change. Polarising films act as efficient filters, for example in sunglasses. Polaroid film consists of long chain molecules which readily absorb light with E field parallel to the molecule's long axis. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 5 PHOTOMETRY (measurement of light intensity) Photometer (a device that measures the intensity of an object in a part of the EM spectrum) Today for optical astronomy we use charge-coupled devices (CCDs, similar to those in digital still or video cameras) to precisely measure source fluxes. We sometimes quote the fluxes in units of photons or energy per unit time; HOWEVER astronomers customarily use a much older measure… …which requires some historical background… Astronomy is arguably the oldest science. Ancients named constellations - proper names in Latin. The eye is the oldest astronomical instrument (a highspeed but low efficiency photometer) About 200 BC Hipparchus ranked the brightness of stars by magnitudes. The brightest stars were described as being of first magnitude, next brightest stars 2nd magnitude, and so on until the faintest visible stars, ranked at 6th magnitude. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 6 Unit of brightness: magnitude (Apparent or "visual"- how bright is it seen from ) Because of the human eye's physiology (logarithmic), a change of 1 magnitude a doubling in brightness. With modern detectors we find that 5 magnitudes 100 fold change in flux (unit energy per unit area per unit time). In 1856, N. Pogson defined a difference of 5 magnitudes as equal to a 100 times change in brightness. i.e. A decrease of 1 magnitude = 5100 = 2.512 times brighter. With modern telescopes : a) we can measure brightness more accurately so we need divisions between magnitudes m = 2.7, 5.3 etc., b) we can see fainter stars so we need magnitudes greater than 6 and c) some stars are very bright so they should have negative magnitudes. e.g. Sirius m = -1.4 Note: A large magnitude means a faint star! This can get quite confusing… Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 7 Converting magnitudes to fluxes Take two stars m1, m2 : m2 > m1 Then the ratio of their brightness l1/l2 is... m1 m2 2.5 log 10 l1 l2 Very important everyday practical astronomer's equation since modern photometers give results in units of luminosity. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 8 How to add magnitudes Example: A certain binary is magnitude 4.1. It is believed the 2 component stars are equally bright. What is the magnitude of each? Let m1 = combined magnitude = 4.1 Let m2 = separate magnitudes, so m2 > m1 m2 = 4.85 What about the effect of distance? For two identical stars at different distances, how will the magnitudes differ? Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 9 The Inverse-Square law The apparent brightness of a star is inversely proportional to its distance. Apparent brightness 1/(distance)2 Knowing the distance to one star we can get a first estimate of the distances to other stars from their magnitudes. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 10 Sun's visual (apparent) magnitude m = -26.7 Take for example a 1st magnitude star mstar = 1 . m2 - m1 = 1-(-26.7) = 27.7 = 2.5 log10 (l / lstar) . l / lstar = 1.2 x 1011 Assuming the difference in brightness is due to the greater distance alone (that is we assume the other star is identical to our sun), . dstar = 3.47 x 105 x 150,000,000 km = 5.2 x 1013 km 5.5 ly Similarly a 6th magnitude star would be at 55 ly. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 11 ASP2011 Measurement Techniques Lecture 2. SCHOOL OF PHYSICS Units in Astronomy : Physicists use the SI or MKS (metre, kilogram, second) units system. Astronomers and astrophysicists more commonly use the cgs system (centimetre, gram, second), in addition to a variety of specific units Units of Distance: Astronomical Unit (AU) Mean to distance. 1 AU = 1.496 1011 m Good measure within the solar system; Mercury’s distance from the sun is at most 0.39 AU Jupiter is 5.2 AU Pluto is at most 39.4 AU Light Year (ly) Distance light travels in a year 1 ly = 9.46 1015 m = 6.324 104 AU Parsec (pc) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 12 This unit illustrates the concept of (trigonometric) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 13 parallax As the Earth orbits the Sun, nearby stars appear to shift in position against the more distant background stars. The further away the star is, the smaller the parallax angle p. The star’s distance d (in parsecs) is found by taking the inverse of p (in arcsecs), d = 1/p. 1 pc = 3.086 1016 m = 3.26 ly (note the typo in Z&G 4th ed. P225!) This method is good to a few hundred parsecs; the Hipparcos satellite, launched by ESA in 1989, obtained milliarcsecond positions for 120,000 stars and thus determined their positions to high precision out to almost 1000 pc. The parsec is effectively the standard distance unit in astrophysics. For objects within our Galaxy, we typically use the kpc (the Galactic center is ~8.5 kpc away); for objects at cosmological distances, the Mpc Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 14 Unit of brightness: Absolute Magnitude We previously encountered the apparent magnitude of a star (as viewed from Earth) A star's absolute Magnitude is how bright the star would appear if it were moved to a standard viewing distance (defined at 10 pc). Parallax = p "arc (seconds of arc arcsec) Distance = d = 1/p parsec How much brighter (or fainter) would a star appear at 10 pc compared to it’s real distance away from us, d? Let l1 = luminosity (apparent brightness) of the star at distance d, and l2 = luminosity at 10 pc. Move the star from d to 10 pc then star becomes brighter using the inverse square law Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 15 Now since for most stars the parallax angle is too small to measure we will normally want to use this relationship the other way around using: d 10 m M 5 5 If we can determine a star's absolute magnitude M then we can compute its distance. Most stars are quite unlike the sun so before we can estimate absolute magnitudes we must consider differences in the distribution of stellar radiation. Blackbody Radiation As you heat up an iron bar you first notice "radiant heat" being given off by the bar. The bar is actually "glowing" in the infrared. After further heating the bar will begin to glow a deep cherry red, then bright red and finally a very bright white. If you could continue to heat the bar (without melting it!) would eventually glow with a blue colour. Stars and iron bars are good approximations of theoretical objects called blackbodies. A perfect blackbody is in thermal equilibrium (constant T) and it absorbs all EM radiation that strikes it. The absorbed radiation adds heat to the body. The thermal Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 16 motions of the charged particles in a body give rise to the emission of EM radiation. As the temperature is not increasing it follows that the blackbody must re-emit all the energy it has absorbed. The temperature of an object is a direct measure of the amount of motion of its constituent particles. The blackbody curve is also known as the Planck curve. Fig 4-2 N.F. Comins & W.J. Kaufmann III, Discovering the Universe 5th Ed. W.H. Freeman & Co. N.Y. OR Fig 8-14 Z&G Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 17 Blackbody radiation laws Wien's Law gives the relationship between wavelength of the colour peak and temperature. max 2.9 10 3 T (K ) Example: The Sun. The maximum intensity of sunlight is at max = 500 nm Stefan-Boltzmann law An object emits energy at a rate proportional to the 4th power of its temperature in Kelvins or Flux F = T4 Luminosity L = T44r2 Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 18 Colour indices The continuum spectra of stars approximate black body curves; astronomers can estimate the temperature (and hence spectral type) of a star by measuring its intensity at two or more wavelengths. Most photometers are equipped with a set of filters. These filters are used to block out all starlight except that which lies within a specific wavelength range. Johnson, Morgan UBV standard filter system Filter Central Wavelength U (ultra violet) 3600 Å B (blue) {photographic} 4200 Å V (visual) {human eye} 5300 Å R (red) 6400 Å Each filter has a band pass ~ 1000 Å wide. Using these filters we can measure "colour magnitudes" i.e. mU, mB, and mV or just U, B and V From any two of these we can make a colour index i.e. (U-B), (B-V) and (U-V) always "bluest" first. There is also an important colour index value that links the colour of stars to their spectral type ; e.g. for an A0 V Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 19 star (B-V) = 0 (see Z&G Table A4-3; more in stars, week 7 onwards) The Colour - Magnitude diagram In 1910, Hertzsprung and Russell independently devised a scheme to classify stars according to their colour and absolute Magnitude. Distance estimation using the colourmagnitude diagram is referred to as spectroscopic parallax. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 20 What can we discover from Photometry? Just to name a very few! Distance to stars Types of stars (via colour indices) Variable stars:Intrinsic variables, e.g. Cepheids Eclipsing binaries X-ray binaries Microlensing Temperatures of stars (Wien's Law) If we can estimate a star’s radius, then we can determine its absolute magnitude and distance. (Stefan-Boltzmann Law) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 21 ASP2011 Measurement Techniques SCHOOL OF PHYSICS Lecture 3. Spectral types O B Hot A F G K M (R N S) Cool or Oh Be A Fine Guy/Girl Kiss Me (Right Now Smack) Subdivisions 0 1 2 3 Hot 4 5 6 7 8 9 Cool Table 13-1. Z & G Luminosity Class I(a b) Supergiants II Bright giants III Giants IV Subgiants V Main sequence VI Dwarves sd sub dwarf, w white dwarf, p peculiar SPECTROSCOPY [Z&G sec. 9-4] Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 22 The measurement and interpretation of spectra (plural; singular is spectrum) Spectrograph 1. instrument by which spectra may be "photographed" (recorded) OR 2. a photograph of a spectrum (spectrogram) Spectrometer instrument to measure spectral intensity A spectrograph or spectrometer disperses the light collected by a telescope, using a prism or grating Z&G Fig. 9-14 Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 23 Spectrophotometer spectrometer with photoelectric detector Also there are task specific names used e.g. Spectrohelioscope, Infrared spectrometer, microspectrophotometer. "White" light, prisms, and simple spectroscopes Ordinary sunlight can be decomposed (using a prism) into a spectrum of colours; a lens and a second prism can recombine the dispersed spectrum back into white light. I. Newton Opticks (1704) The index of refraction of glass is a function of wavelength, thus so is the refracted angle, leading to dispersion. Bunsen 1856 noted that each element (compound), when placed in a flame, produces a distinctive fingerprint of bright lines. Bunsen & Kirchoff built first decent spectroscope. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 24 Grating Spectrographs Most modern spectrographs use a diffraction grating to disperse the incident light. Both reflection and transmission gratings are used Constructive interference at angles sin (n) /d where is the wavelength, d is the groove spacing and n is the order of the spectrum Z&G Fig. 9-13 Dispersion is approximately linear, at the expense of having multiple (overlapping) scattering orders Spectrograph capabilities Characterised by Bandpass Resolving power (E/E) Efficiency Resolution (for CCD detectors) Kirchoff's rules Fig 5.7 Chaisson McMillan Astronomy Today Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 25 Fig 4.11 Comins & Kaufmann 1. A hot and opaque (optically thick) solid, liquid or compressed gas emits a continuous (blackbody) spectrum. 2. A hot, transparent (optically thin) gas produces a spectrum of emission lines. Lines seen depend on the composition of the hot gas. 3. If light from a continuous source passes through a cooler gas then absorption lines appear. Lines seen depend on the composition of the cool gas. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 26 Emission spectra The “sample” is acting as the radiation source. The spectral lines will appear as a series of narrow peaks at the wavelengths characteristic of the elements present. The sample is emitting energy preferentially at those wavelengths; a continuum may also be present. The nearby (z=0.1028) cluster of galaxies PKS 0745-191 is bright in X-rays and contains a strong cooling flow. Such cooling plasmas are rich in X-ray line emission and make interesting targets for the Chandra HETGS. PKS 0745-191 is, however, an extended object making analysis of its spectrum more involved. http://space.mit.edu/ASC Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 27 Absorption spectra The sample is between a radiation source (ideally a source of continuous radiation) and the observer. The sample absorbs energy at particular wavelengths which are characteristic of the elements present in the sample. A series of dark lines are observed at those wavelengths. Example: The solar spectrum J. von Fraunhofer 1814 counted over 800 dark lines in the solar spectrum (mostly Fe). Now named Fraunhofer lines. Z&G sec. 10.2D Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 28 ASP2011 Measurement Techniques Lecture 4. SCHOOL OF PHYSICS Bohr Model of Hydrogen atom 1st postulate; "Only a discrete number of orbits (energy levels) are allowed to the electron ... " 2nd postulate; "a) radiation in the form of a single discrete quantum (photon) is emitted or absorbed as the electron jumps from one orbit to another b) the energy of this radiation equals the energy difference between the orbits" fig 40-18 Giancoli General Physics; see also Z&G 8-2B The energy levels for the Hydrogen atom can be found Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 29 from En 2.18 10 18 J n2 for transitions 1 1 Et En Em 2.18 10 18 2 2 J m n and since Et h hc the wavenumber (inverse wavelength) equals 2.18 10 18 1 1 2 2 m-1 hc m n 1 or 1 1 R 2 2 n m 1 where :R e 4 8 0 h 2 c 2 109677 .759 cm-1 is the Rydberg constant Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 30 Now calculate wavelengths Lyman series n=2 3 4 5 6 m=1 Lya Ly Ly Ly Ly 1216 Å Å Å Å Å Paschen series m = 3 ..... Balmer series m = 2 n= 3 4 5 6 . n= H H H H 6564.6 Å Å Å Å note: converging series in ; H = 3645.6 Å Paschen series m = 3 ..... Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 31 Spectral - line Analysis Line identification By matching observed spectral lines with those found in laboratory samples we obtain information regarding the chemical composition of astronomical objects. This analysis is complicated by the physical conditions at the emitting source such as temperature and pressure. Doppler Effect (non Relativistic version) Lines emitted by objects moving relative to us will be red- (blue) shifted. z v c where is the shift in wavelength relative to the “restframe” value , v is the speed of the emitter relative to the observer (us), and c is the speed of light. The Doppler effect is a key phenomenon for the modern study of cosmology, and objects at cosmological distances are often characterised by their redshift z, which is proportional to distance e.g. A Calcium line has rest wavelength 3933 Å. Measure this line in a star and find it shifted to 3972 Å. How fast is the object moving towards or away from us? Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 32 Doppler Effect (Special Relativity version) vr 1 c z 0 v r 1 c 1 2 1 Line intensity (depth) The intensity of a spectral line is proportional to the number of photons emitted (or absorbed). The intensity of the line depends only in part on the number (density) of atoms that give rise to the line. Line intensity is strongly dependent on the temperature of the emitter as this determines what fraction of atoms are in the right initial energy state to undergo any particular transition. In stellar atmospheres, the number of atoms in a particular state relative to the number in another state can be modelled using the Boltzmann and Saha equations. (See section 8-4 Zeilik & Gregory and 3rd yr ASP)! Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 33 The relative population of electrons in the first excited state N2 /N (Balmer lines) first increase with temperature, reach a maximum then decrease. This occurs for all elements. Fig. 8-13 Zeilik & Gregory, Introductory Astronomy & Astrophysics See also Fig. 10-3 Comins & Kaufmann, Discovering the Universe Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 34 Line Broadening (Z&G 8-5) Natural line broadening Heisenberg Uncertainty Principle. Energy of state may not be specified more accurately than, xp h h E t 2 or 2 where t is the lifetime of the state hence, 1 2t Thermal (Doppler) line broadening Fig. 4.17 Chaisson McMillan Astronomy Today Collisional (pressure) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 35 line broadening Atomic energy levels are shifted by neighbouring charged particles (Stark effect) Zeeman Effect Energy levels may split in a magnetic field. If the Zeeman components are not individually resolved then this looks like line broadening. Rotational line broadening Only detected for stars with very fast rotation Fig. 4.18 Chaisson McMillan Astronomy Today Spectral information from starlight Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 36 Observed characteristic Peak wavelength Lines present Line intensities Line width Doppler shift Information obtained Temperature (Wien's Law) Composition Relative abundance & Temperature Temperature, turbulence, rotation speed, density, pressure & magnetic field strength Radial (line of sight) velocity, Distance (Cosmological) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 37 ASP2011 Measurement Techniques Lecture 5. SCHOOL OF PHYSICS TELESCOPES I A telescope comprises a focusing (or collimating) system and a detector. The operating principles of each of these components depends upon the waveband Optical & IR “Traditional” telescopes with lenses or mirrors X-ray & gamma-ray Grazing incidence optics, passive collimators, coded masks etc. VHE gamma ray & neutrinos Using the Earth’s atmosphere or the Earth itself as a detector Radio & Interferometry Combining signals from multiple detectors Lenses and mirrors – optics review Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 38 Light can be concentrated (focussed) either by a lens (refraction) or a curved mirror (reflection). See Z&G p154 & ch. 9 Law of reflection When light is reflected at a mirror, the angle of incidence (measured relative to the normal) equals the angle of reflection ir NOTE wavelength independent! Snell's Law For a plane wave passing from a medium with refractive index n1 into a medium with index n2, the angles between the incident and refracted rays and the normal to the interface obeys n1 sin i n2 sin r (the speed of light in a medium is different from that in a vacuum). Refractive indices also depend on the wavelength of the light Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 39 Thin lenses Simple lens - spherical surfaces, one piece of glass Positive lens - parallel rays converge Double convex Plano-convex Convex meniscus Negative lens - parallel rays diverge Double concave Plano-concave Concave meniscus Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 40 The telescope produces an image of the object of interest at the focus. The distance from lens to image for objects at large distances is the focal length f Note: incident rays are parallel for astronomical objects! Point source and Extended objects The figure depicts an extended object forming an image in the image plane; an extended image can be thought of as made up as an assemblage of point source images Diameter (Aperture) The primary lens typically forms the aperture; this determines the maximum cone angle for a bundle of rays to come to a focus in the image plane The larger the aperture, the greater the light-gathering power of the telescope (proportional to d2) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 41 f ratio (Focal ratio) {f value, f number} f = focal length / aperture diameter written f/#, where we replace # with the value of f. The “speed” of a lens or mirror system. A smaller f-ratio delivers more light per unit time to the image plane. There are other more practical advantages to building a fast telescope! Resolving power A telescope cannot separate arbitrarily close point sources. The resolving power is the inverse of the minimum angle between two points in order for them to be easily separated: RP=1/min This is a consequence of the diffraction pattern arising from the (circular) telescope aperture. Airy (Astronomer Royal mid 1800's) first to derive the solution 1.22min 206265 /d Where is the wavelength of the light and d the telescope’s aperture (206265 is the number of arcseconds in 1 rad). Such performance is rarely attained on the ground, due to the atmospheric effects which blur the image (seeing). Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 42 Rayleigh’s Resolution criterion Two star images are just resolved if the central maximum of one falls on the first minimum of the other. Dawes Resolution criterion Empirical “rule of thumb” min 11.6 D in arc seconds for D in cm. Plate scale & Magnification The size s of an image at the focus corresponding to 1 in the sky is s=0.01745f where f is the focal length of the lens (and 0.01745 is the number or radians in one degree). For small telescopes, an eyepiece is used to view the image at the focal point. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 43 Magnification is the apparent increase in size of the object compared to unaided visual observation. Magnifying power is the ratio of focal length of the objective (the lens or primary mirror) F to that of the eyepiece f: MP = F/f upright image +ve, inverted image –ve The shortest focal length eyepiece will not necessarily allow you to resolve smaller details, if you are already limited by the objective size. Furthermore, higher magnification makes extended objects dimmer. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 44 When optical systems go bad: aberrations We saw previously that the varying refractive index of glass to light of different wavelengths can be exploited to disperse the spectrum in a spectrograph. The same effect causes chromatic aberration in a telescope. Two types: Longitudinal colour (different wavelengths are focussed at different distances from the lens) Lateral or transverse colour (different wavelengths are focussed at different positions in the focal plane) Can use special glass or add an optical element (“achromatic doublet” or “achromat”). Most common type is Fraunhofer achromat, consisting of lenses made to bring red and blue to same focus Much worse for short focal ratios (“fast” lenses) Spherical aberration Rays striking spherical lenses or mirrors near the edge do not come to the same focus point as rays near the centre. Effect is worse for large and fast (again!) lenses. Can use a non-spherical lens, but these are harder to produce; alternatively add corrective optics. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 45 Large telescopes As telescope diameter d increases, chromatic and spherical aberration become more problematic, and the weight (and optical depth) of the lens increases. To avoid these problems most large modern telescopes are reflecting designs. Several types, each with advantages and disadvantages; Newton constructed the first practical example around 1670. Mirror equation - same as thin lens equation Magnification - same as lens Advantages: Mirrors do not suffer from chromatic aberrations+++ - "apochromatic" Only one surface of the mirror needs to be figured correctly Large lenses have to be supported at their edges, and can sag; a mirror can be supported evenly (also allows adaptive optics). Disadvantages: Spherical aberration (for non-parabolic primaries) Comatic aberration or coma (variation in magnification over the aperture) The secondary mirror blocks the primary Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 46 ASP2011 Measurement Techniques SCHOOL OF PHYSICS Lecture 6. Astronomical Telescopes 1608 Galilean Refractor 1611 Astronomical Refractor - Johannes Kepler Advantages: Disadvantages Good for planets, double stars and planetary nebulae. Long tube, large f ratio, limited max aperture (1733 Achromatic refractor; see also apochromatic Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 47 refractor) 1672 Newtonian Reflector - Isaac Newton Paraboloid primary (or spherical for smaller apertures/large f-ratio) and flat, angled secondary Advantages Disadvantages Cheap, simple, achromatic, low f ratio. Central obstruction. 1672 Cassegrain Reflector - Guillaume Cassegrain Paraboloid primary and hyperbolic secondary reflecting the light through a hole in the primary to the focus Advantages Disadvantages Most compact Long F Ratio Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 48 Schmidt-Cassegrain Spherical primary and Schmidt corrector plate (an additional lens placed in the optical path) to avoid spherical aberration Advantages Disadvantages No spherical aberration; no coma. Long F Ratio. 1911 Ritchey-Chrétien Specialized Cassegrain with two hyperbolic mirrors Advantages Disadvantages free of 3rd order coma and spherical aberration at the focal plane 5th order coma, astigmatism, field curvature Most modern reflectors! Keck, Gemini, Hubble etc. Light Grasp (Gathering) and Magnification Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 49 Exit pupil d is an image of the objective seen in the eyepiece. Its size depends on magnification D 2 Light grasp d 2 Brightness of a point source, limiting magnitude or "What is the faintest star you can see with this telescope ?" Here we will assume d = 0.7 cm l1 l2 Use m2 m1 2.5 log 10 then D m2 2.5 log 10 6.0 d 2 Note: for point sources the telescopic brightness increase is not dependent on the magnification. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 50 Example. Limiting magnitude of a 20 cm telescope. m2 = Brightness of an extended object For extended objects their light is spread by the telescope over the viewed virtual image to cover an area M2 times larger than it covers on the celestial sphere. brightness of telescopic image D 2 So, brightness of naked eye image d 2 M 2 but magnification M = apparent field / true field or M f objective f occular D d therefore the point (on the sky) to point (in the image) relative intensity of an extended object is at best equal to unity Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 51 To obtain the maximum image brightness (richest field) we need an exit pupil that just matches the pupil diameter of the dark-adapted human eye = 7mm. Example. a) What magnification should be used to give so called “richest field” views with a 15 cm telescope? b) If this is an F7 instrument, what focal length eyepiece is required? Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 52 Telescope Mounts To make pointing of a telescope in any direction possible it must be movable in two planes, one perpendicular to the other. A useful mount must have a high degree of stability combined with smoothness and ease of movement about both axes. Altazimuth mounts Move "Up and down" in altitude and "round and round" in azimuth. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 53 A very popular sub type is the Dobsonian. Advantages: Compact, simple to construct and highly intuitive to point Disadvantages: Difficulty pointing at the zenith; balance Equatorial Mounts Two axes perpendicular to one another, however, not vertical and horizontal, but parallel to Earth's axis of rotation (Polar axis or RA axis) and perpendicular to it (Declination axis) Advantages: Even without a motor drive gives ease of following, ease of re-finding after a pause in observations. With a motor drive an equatorial mount will track the object making long and continuous observations or long photographic exposures possible. German equatorial (inventor: Fraunhofer) Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 54 Most common type English mounting Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 55 Horseshoe mounting Fork mounting Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 56 “Famous” Telescopes School of Physics, Monash University 90 mm Maksutov German equatorial mounting Camera 30 cm Monash Automated Observatory Schmidt Cassegrain F10 / F6.3 Fork mounting CCD camera 45 cm Mt Burnett Newtonian F4 / Cassegrain F16 German equatorial mounting Photoelectric (PMT) photometer & CCD Australian Observatories 1.3 m "The Great Melbourne Telescope" Mt Stromlo Newtonian, English equatorial mounting Destroyed in the fire of 2003 2.3 m Advanced Technology Telescope F7.85 Cassegrain Alt-Az mounting Visible & IR imaging & spectroscopy Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 57 3.9 m AAT Siding Spring F3.3 !!! 2 degree field "Newtonian" Deep sky survey Can record spectra from 200 stars at once! International Observatories 8 m Gemini north (Mauna Kea) and south (Chile) f/1.8 Altazimuth mount Visible, near- & mid-IR imaging and spectroscopywith AO 10 m Keck (I and II) Mauna Kea (Hawaii) f/1.75 Altazimuth mount 270 tonnes of moving telescope! Reading (browsing) list http://www.mso.anu.edu.au http://www.keckobervatory.org http://www.gemini.edu http://astro.uchicago.edu http://www.aao.gov.au http://www.eso.org http://en.wikipedia.org/wiki/List_of_largest_optical_re flecting_telescopes Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 58 ASP2011 Measurement Techniques SCHOOL OF PHYSICS Lecture 7. TELESCOPES II Beyond visible astronomy X-ray/Gamma-ray units E = h = 4.13 18 keV = 12.4/ keV where 18 = /1018 Hz where is in Angstroms Å Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 59 UV Methods of light gathering and detection for UV astronomy are similar to those of optical astronomy BUT The opacity of the atmosphere at these frequencies necessitates a largely space-based approach Example: The Extreme Ultraviolet Explorer (EUVE); NASA, 1992-2001. All-sky survey in 4 bandpasses with 6x6’ resolution & spectroscopy of white dwarfs etc. Energy range; 0.016-0.163 keV (760-70 Å) http://heasarc.gsfc.nasa.gov/docs/euve/euvegof.html Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 60 X-ray & gamma-ray Non-imaging Proportional counters A sealed volume with one or more anode/cathode pairs at high voltage, and filled to high pressure with a gas (usually xenon). When an incoming X-ray interacts with a xenon atom, it ionises the atom, ejecting an electron. The strong electric field within the detector accelerates the electron, causing it to knock the outer electron out of another xenon atom. This cascade results in an electron cloud which is registered in the detector electronics as a pulse with amplitude proportional to the incident X-ray energy. Advantages: sensitive to high-energy X-rays (typically up to a few hundred keV); large area, high timing resolution Disadvantages: low-resolution or no imaging; deadtime; high background Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 61 Examples: The ROSAT Position-Sensitive Proportional Counter (PSPC); Germany/US/UK, 1990-1999 Energy range; 0.1-2.5 keV, EUV 62-206 eV http://heasarc.nasa.gov/docs/rosat/rosat.html Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 62 The Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (PCA); NASA, 1995-present Energy range: 2-250 keV, area ~6500 cm2, timing down to 1s http://heasarc.nasa.gov/docs/xte/rxte.html ASTROSAT (India), proposed launch in 2008; very similar to RXTE, plus optical monitor http://www.rri.res.in/astrosat Solid-state detectors Scintillators are crystals (e.g. NaI) or organic liquids or plastics which measure the visible light produced when the X-rays interact with and are absorbed by the atoms comprising the detector. The amount of light provides a measure of how energetic the incoming X-ray was. Another kind of detector, called a calorimeter, directly measures the heat produced in the material when an incoming X-ray is absorbed. Imaging Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 63 Coded-masks Spatial (or temporal) “coding” allows simultaneous measurement of multiple pixels in a field. The detector records the shadow of a specially-designed mask produced by the sources in the field of view. A compromise between a scanning instrument (e.g. a proportional counter) and a focussing instrument. Advantages: low cost, moderate spatial resolution Disadvantages: inefficient, requires large detector, thus high background Examples: Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 64 INTEGRAL (ESA) IBIS & JEM-X; 2002-present Energy range: IBIS 15 keV – 10 MeV: JEM-X 3-35 keV Angular resolution: IBIS 12’, JEM-X 1’ http://isdc.unige.ch IBIS uses an array of scintillation (cadmium telluride or CdTe) detectors, while JEM-X uses a position-sensitive proportional counter detector Grazing-incidence optics Focussing of X-rays by mirrors or lenses is clearly impossible; but focussing can be achieved by exploiting narrow (grazing) incident angle interactions with suitably-shaped mirror shells. Advantages: can achieve high resolution (~1”) for low-energy (<10 keV) X-rays Disadvantages: small effective area, requires very precisely figured optics! Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 65 Examples: The Chandra X-ray Observatory; NASA, 1999-present Energy range; 0.5-10 keV http://chandra.harvard.edu XMM-Newton; ESA; 1999-present Energy range: 0.5-10 keV (RGS 0.5-2 keV) http://xmm.vilspa.esa.es XMM = X-ray Multi-Mirror; three mirror assemblies for large surface area; sacrificing precision of the mirrors, and hence resolution (only about 1’) VHE Gamma-ray Gamma-ray observatories use proportional counters and solid state detectors, with coded-mask imaging, to reach Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 66 up to GeV energies (e.g. INTEGRAL, GLAST etc.). But ground-based observatories are also exploring the TeV (1012 eV = 1027 Hz!!) band. Emission mechanisms in this range are highly uncertain, but are thought to be related to the production of highenergy cosmic rays, which can reach energies of 1021 eV (see e.g. Z&G p407). Emitting sources are active galactic nuclei, pulsars, X—ray binaries, and supernova remnants. TeV gamma rays do not reach ground level, but are sufficiently energetic to produce a cascade of highenergy subatomic particles. These particles are travelling very close to c, which is faster than the speed of light in the medium (air). A “shock wave” of visible light, called Cerenkov radiation, is emitted; this very short-lived burst of light can be detected by ground-based optical telescopes, and the direction and energy of the incoming gamma-ray can be reconstructed. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 67 Example: High Energy Stereoscopic System (HESS), Germany/France/UK etc., array of four ~12m telescopes in Namibia, f/1.2 Energy range: 0.1-10 TeV http://www.mpi-hd.mpg.de/hfm/HESS Neutrino The number of neutrinos detected from nuclear reactions within the sun are deficient by a factor of 2-3; the solar neutrino problem. Solar neutrinos are abundant at the Earth (1015/s/m2!) but interact very weakly with matter, so detection is an enormous challenge. Observatories (beginning with the Homestake mine in South Dakota; 390 m2 of drycleaning fluid) have sought to resolve this problem, and today observations seem consistent with the deficiency arising from neutrino oscillations. These efforts also led to the detection of a handful of neutrinos approximately 3 hr before the visible light of SN 1987A (in the LMC, closest since SN 1604!) reached the Earth. The largest detection was 11 events by Kamiokande II (Japan, water Cerenkov detector). Current goals include detection of neutrinos from gamma-ray bursts. Example: Antarctic muon and neutrino detector array Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 68 (AMANDA) 1996-; now part of IceCube (under construction). Water ice Cerenkov detector http://amanda.uci.edu http://icecube.wisc.edu Gravitational wave Gravitational waves (GW) are a consequence of Einstein’s general theory of relativity, and are thought to travel through space at the speed of light (much like EM radiation). Unlike EM they comprise periodic stretching and compressing of spacetime itself, and arise from motions of massive objects. GW have never been detected, but have been indirectly confirmed by observations of the Hulse-Taylor pulsar. Currently several observatories around the world are attempting to be the first to directly detect GW, primarily via large laser interferometers Example: Laser Interferometer Gravitational Wave Observatory (LIGO), Caltech/MIT, 2x 4km interferometers in the US http://www.ligo.caltech.edu Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 69 Detectors Quantum Efficiency Zeilik & Gregory Fig. 9-10 Photographic Photographic film (or plates) consists of a thin layer of light sensitive emulsion on a celluloid or glass base. The emulsion contains film grains that will become "exposed" after receiving a sufficient number of photons. After developing, the exposed grains become black and the areas of the film containing the highest concentrations of exposed grains become the darkest. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 70 Films are made with different ISO or ASA ratings Fast for low light levels > ASA 1000 Slow for daylight < ASA 100 Usually a film is made fast by increasing the surface area of the film grains. This increases the likelihood that a film grain will capture enough photons to become exposed but it lowers the spatial resolution (and information storage capacity) of the film. Advantages of film - High storage capacity, cheap. Disadvantages - Non-linear intensity response, Low QE Photomultipier Tubes A vacuum valve device that multiplies (amplifier) the charge generated when the photons leaving the telescope are directed onto a photocathode surface where electrons are released via the photoelectric effect. The invention of the photomultiplier tube allowed astronomers to detect the arrival of individual photons at the detector (photon counting) for the first time. CCD’s have made photomultiplier tubes mostly obsolete . Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 71 Advantages - Better QE than film and a linear intensity response. Disadvantages - Can't form image, expensive. Charge coupled devices (CCD) CCD’s are solid-state electronics devices (Silicon chip manufactured using integrated circuit technology). Consist of a large number of small light sensitive regions called “pixels”. When a photon is absorbed by a pixel a small charge is generated and stored just below the pixel surface. The charge is proportional to the number of photons that have struck the pixel. The CCD is "read out" digitally and this can be done very rapidly and accurately. CCD cameras have revitalised the small telescope in astronomical research as they have a very high QE approaching 100%. The 30 cm MAO telescope has demonstrated an ability to detect stars of 15th magnitude in CCD images recorded in as little as 60 seconds in Melbourne’s light-polluted skies. Advantages - Highest available QE, Images are digital and hence ready for computer post-processing, a very linear response. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 72 ASP2011 Measurement Techniques Lecture 8. SCHOOL OF PHYSICS Statistics and signal-to-noise Observations almost always include some contribution from background (aka noise) Optical/IR: sky brightness, dark/bias current in CCDs, light pollution etc. X-ray: charged particles, diffuse X-ray Background Spectroscopy: Continuum photons As part of our data reduction process, we must account for the background in our measurement, as well as treating the resulting uncertainty appropriately. If the number of expected counts from our source (emission line) in a given time interval ∆t is S, and the number of expected background counts in the same time interval is B, our detector will measure in ∆t ON AVERAGE S+B counts Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 73 We want to know i) what is the most probable value of S ii) in what range are we likely to find the “true” value of S (i.e. what is the uncertainty) Counting statistics The Poisson distribution gives the probability Px of detecting a particular number of events x within a time interval, given an expected rate m: m x em Px x! where x! = x(x-1)(x-2)…2*1 Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 74 Note that this distribution is NOT symmetric about m (except for very large values). The probability of detecting precisely the mean rate m (even if it is an integer) is rather low! The standard deviation of multiple measurements xi is (for large m) just m1/2. For large m, the Poisson distribution approaches the normal (Gaussian) distribution (x m) 2 1 Px exp 2 2 2 the conventional “bell curve” of probability Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 75 Thus if we expect S+B counts in a measurement, the standard deviation (uncertainty) is just (S+B)1/2. Similarly, the uncertainty in the background counts is B1/2. Given these uncertainties, what is the uncertainty on S? It can be shown that in adding and subtracting variables x and y, each distributed normally with standard deviations x & y, the variance (square of the standard deviation) of the sum or difference of x is just the sum of the variances x2y x2 y2 So that the uncertainty on S is just B (S B) S 2B We refer to the ratio of the source counts to uncertainty S / S S / S 2B as the significance or the signal-to-noise (S/N) ratio Example: the estimated count rate for an X-ray source observed with Chandra is 0.1 count/s; the equivalent background rate is 0.05 count/s. What is the signal-tonoise in a 1000 s observation? How long would you need to observe to achieve a S/N ratio of 10? Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 76 Reddening Light from distant stars is affected by scattering within clouds of dust between the star and Earth. Bluer photons are scattered preferentially, so the residual light that reaches us is redder than when it was emitted by the star. This effect is referred to as interstellar reddening or interstellar extinction Bradt, “Astronomy Methods” Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 77 This effect is an important consideration for optical (and even low-energy X-ray) observations, and (e.g.) limits the range of visibility within the plane of the Milky Way galaxy to only about 5000 ly (the Galaxy is ~105 ly in diameter). Much less extinction is experienced for directions out of the plane. The extinction AV is the number of magnitudes by which the light in the visible (V) band is dimmed by the intervening dust: AV = mV – mV,0 Where mV is the apparent magnitude of the star at Earth, and mV,0 is the apparent magnitude that would be measured IF there were no reddening. (Recall how this is related to the absolute magnitude). Example: In the Galactic plane the extinction is about 0.6 mag for every 1000 ly of distance (although this is quite variable, depending upon the precise direction). What fraction of intensity is lost in V-band for every 1000 ly of distance? AV = mV – mV,0 = 2.5 log10 (l0/l) = 0.6 Since the scattering depends upon the wavelength of light, it follows that AV AB AR … Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 78 Bradt, “Astronomy Methods” A consequence of this is that for a star of known (intrinsic) colour (e.g. an A0 star, with B-V = 0) we measure a colour excess because the reddening in B is larger than the reddening in V. E.g. AB = 1.324 AV (Rieke & Lebofsky, ApJ 288: 618, 1985) So that for the above example, for an A0 star at 1000 pc, the colour will not be B-V = 0 but… Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 79 Adaptive optics A system to improve the resolution of Earth based telescopes by mathematical removal of the atmospheric blurring. A laser beam is used to generate a fluorescent spot in the mesosphere and thus create an artificial star, which is then observed with the telescope and analysed by computer to determine how the telescope’s “figure” should be altered (in real time) to correct for the turbulence in the atmosphere. The correction to the telescope’s figure is achieved with a thin, flexible mirror in the telescope’s optical path that changes shape about 1000 per second. Computer driven piezoelectric actuators located on the back of the adaptive mirror alter the mirror’s figure. Typically the mirror surface moves by only a few tens of nanometers. Reading list http://cfao.ucolick.org/ http://www.ucsc.edu/news_events/press/photos/imag es/distant_galaxies/Fig1.jpg http://www.ifa.hawaii.edu/ao/ http://www.eso.org/outreach/press-rel/pr2005/images/phot-03-05-normal.jpg Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 80 Bradt, “Astronomy methods” Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 81 Timing Many phenomena in astronomy are periodic, that is they repeat on a regular timescale. Frequently we are in the position of trying to determine, is a particular phenomenon actually periodic? If so, what is the period? This can be difficult to answer if the phenomenon is low amplitude, the sampling is uneven, or the period varies significantly. For evenly-sampled data, the Fourier Transform allows us to test for an excess of power at particular periods (frequencies) Example: the first detection of millisecond oscillations in an accreting neutron star, 4U 1728-34 (Strohmayer et al. ApJ 469, L9 1996) This neutron star is spinning 363 times every second! Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 82 For noisy astrophysical signals, the Fourier power spectrum has some characteristic variation in the absence of a signal. The usual approach is to identify a significance (power) threshold such that it is exceedingly unlikely that the Fourier power could exceed this value from noise alone. An important factor here is the number of trials. By measuring the power spectrum within a range of frequencies, we effectively make n trials, where n is the number of (independent) frequency bins. Even though a particular power threshold may be unlikely to be exceeded by noise alone, it may be reached if we make sufficiently large number of trials! The situation for unevenly-spaced data (e.g. photometric observations spanning more than one night, or in which some portion of the night was clouded out) is more difficult. We can use the Lomb-Scargle Periodogram, a generalisation of the Fourier Transform, and set our significance thresholds accordingly. There are a number of other techniques commonly used. Once the signal is detected, we need to precisely determine the period (and its uncertainty). Typically the statistics are too complex to treat analytically and we must do simulations. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 83 In-situ Measurement Techniques in Space Cassini-Huygens http://saturn.jpl.nasa.gov/home http://www.esa.int/SPECIALS/Cassini-Huygens Full range of optical, IR and UV imagers and spectrographs; plasma spectrometer; cosmic dust analyser; mass spectrometer; magnetometer and magnetospheric imaging instrument; and radar Huygens “lander”: atmospheric structure instrument, measuring the electrical properties of Titan’s atmosphere; Doppler winde experiment to measure wind speed; imager/spectrometer; GCMS; aerosol collector and pyrolyser; and surface science probe to measure the physical properties of the surface. Mars Exploration Rovers http://marsrovers.nasa.gov/technology/si_in_situ_instr umentation.html Miniature Thermal Emission Spectrometer (Mini-TES) Remote investigation of mineralogy of rocks and soils. Near infrared region of the spectrum. Mineralogical information that Mini-TES returns is used to select from a distance the rocks and soils that will be investigated in more detail. Can also provide temperature profiles through the Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 84 Martian atmosphere. Mössbauer Spectrometer Placed directly on the target sample the spectrometer illuminates rock surfaces with gamma particles emitted by cobalt-57. Detailed mineralogy of different kinds of iron-bearing rocks and soils. Microscopic Imager Voyager I & II http://voyager.jpl.nasa.gov Launched in 1977, these RTG-powered instruments are still operating and still returning useful science data! Voyager 1 is now at the outer edge of our solar system, at 100 AU (as of August 2006), in an area called the heliosheath, the zone where the sun's influence wanes. This region is the outer layer of the 'bubble' surrounding the sun, and no one knows how big this bubble actually is. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 85 Redundant material Spitzer Space Telescope http://www.spitzer.caltech.edu/technology/index.shtml Infrared Array Camera (IRAC) Imaging near- and mid-infrared wavelengths. (3.6, 4.5, 5.8, and 8 m). Infrared Spectrograph (IRS) Spectroscopy at mid-infrared (5.3-40 microns) - the fingerprint region of atoms and molecules. Multiband Imaging Photometer for Spitzer (MIPS) Imaging and limited spectroscopic data at far-infrared wavelengths. Chandra X-Ray Observatory http://chandra.harvard.edu/about/science_instruments.html Chandra Advanced CCD Imaging Spectrometer (ACIS) X-ray images and measure the energy of each incoming Xray. Makes pictures of objects using only X-rays produced by a single chemical element such as a supernova remnant in light emitted by oxygen ions, neon ions or iron ions. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 86 E=E0 cos Law of Malus I E2 I=I0 cos2 Light emitted by "normal" stars is unpolarised. Starlight may become polarised by interacting with interstellar matter and magnetic fields. Example 1. A photon may be absorbed by an interstellar dust particle (molecule) and then re-emitted with a polarisation characteristic of the particle's alignment and elongation. Hence, the degree and direction of polarisation can reveal information about :a) the size and density of the dust grains. b) the orientation of the galactic magnetic field responsible for the alignment of the grains. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 87 Example 2. In the Crab Nebula, high energy electrons emit em radiation as a consequence of their acceleration in a strong magnetic field. The direction of the electric field vector E is perpendicular to the direction of the nebular's magnetic field. Fig. 3.20 E. Hecht "Optics" 2nd Ed. Addison-Wesley True and Apparent field Lens maker's equation Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 88 f= n= R1 and R2 = Some common approximations (exact for n = 1.5) Double convex if R1 = R2 then f = R Plano convex f = 2R Sign convention for lenses Thin lens equation Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 89 Graphical Ray Tracing Required modifications for negative optical elements are given in brackets Lens A ray passing through the centre of the lens is not deviated Mirror Rule 1 A ray passing through the centre of curvature is reflected back over the same path Rule 2 An on axis ray will (appear An on axis ray will (appear to) pass through the to have) pass(ed) through far/(near) focal point the focal point Rule 3 A ray through the A ray through the focal near/(far) focal point will point will be reflected on be refracted on axis axis The intersection of any 2 of the 3 rays will locate the image Photographic image brightness (extended source) Most astronomical photography is performed with the film (or CCD) located at the real image at the prime focus. Here the size of the image is directly proportional to the focal length. D 1 or Prime focus image intensity f 2 F 2 since F = f / D. Example. What is the ratio of the intensities of an image of an extended object on the film of a) a SLR camera Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 90 with 50 mm lens at F stop F2 to b) the Mt Palomar 5 m telescope with a focal length of 1650 cm ? Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 91 Resolution of telescopes The ability of a telescope to separate objects. Ideally, resolution is “diffraction limited”. Airy (Astronomer Royal mid 1800's) first to derive the solution for diffraction pattern produced by a circular aperture. min = 1.22 / D in Radians Rayleigh’s Resolution criterion Two star images are just resolved if the central maximum of one falls on the first minimum of the other. Dawes Resolution criterion min 11.6 D in arc seconds for D in cm. Monash University Physics ASP2011 ‘Measurement Techniques’ ASP2011_2007 92