WWW.DISSERTATION.XLIBX.INFO
FREE ELECTRONIC LIBRARY - Dissertations, online materials
 
<< HOME
CONTACTS



Pages:   || 2 |

«5.1 Characteristics of the Signals 5.1.1 Electromagnetic Radiation: Rays, Waves, or Photons? Wavelength and frequency ranges; what’s λ, what’s ...»

-- [ Page 1 ] --

5. Some Basics of Radio Astronomy

This section contains some basic terms and concepts that are important in understanding radio

emission measurement techniques.

5.1 Characteristics of the Signals

5.1.1 Electromagnetic Radiation: Rays, Waves, or Photons?

Wavelength and frequency ranges; what’s λ, what’s ν?

The radio-frequency range is arbitrarily defined to be from frequencies (ν) beginning at the supersonic, meaning just above the range of sound waves that humans can hear, 20 kHz or so, up to about 600 GHz, where the far infrared begins. The corresponding wavelength (λ) range is from many kilometers down to about 0.5 mm or 500 microns. Frequency and wavelength are related,

as for any conventional wave phenomena, by:

ν = c/λ where c is the speed of light, 299792.5 km/s.

Over this frequency range and at moderate equivalent temperatures, we can usually ignore photons; that is, we need not quantize the electromagnetic field. In most cases, this results in both simplification and insight that is lacking if one thinks photons instead of waves.

Many formulas used in radio astronomy (and electrical engineering) are based on the RayleighJeans approximation to the Planck black-body law. If, furthermore, the antenna structures are large compared to a wavelength, as is usually the case at centimeter and millimeter wavelengths, then we can often ignore waves also and use just ray-trace optics.

5.1.2 Law of large distances Another helpful simplification involves the large distances and small angular sized of most astronomical objects. Angles in radians are, then, just the linear sizes divided by the distances.

5.1.3 Noise-like signals A. Law of large numbers Most astronomical sources are large in physical size, even though small in angular size, and radiation is emitted by a large number of statistically independent sources−atoms, molecules, or electrons. The resulting signals are noise-like, that is, the electric fields are Gaussian random variables with spectra that depend on the details of the emission mechanisms. Laboratory laser and maser oscillators are usually coherent because of the cavity in which they oscillate.

Astronomical masers have never been found to have non-Gaussian statistics.

For similar reasons, many radio-astronomical sources are unpolarized; that is, signals in one polarization are statistically independent of signals in the orthogonal polarization. But some sources, especially those involving magnetic fields that extend over a significant part of the spatial extent of the source, can be polarized, and studying such polarization sometimes leads to significant insights.

B. Law of large sizes As a rough rule with some exceptions, an incoherent source that is not resolved in angle can be seen to vary only on time scales long compared with the light travel time through the length of the emitting region. A black sphere with cyclic temperature variations, for example, will have these variations smoothed over as seen from a large distance if the cycle time is comparable to or less than the light travel time across a radius of the sphere. Some astronomical sources vary, and the time scales of the variations can sometimes be used to infer maximum sizes.

C. Significance for measurement techniques

Some of the techniques used in radio astronomy depend on these characteristics of the sources.

One-bit autocorrelation spectroscopy, for example, depends on the signal voltage being a Gaussian random variable. And many-hour-long interferometry depends on the source being stable over that time.

5.2 Spectra 5.2.1 Continuum sources, black body or ν n?

A black body at temperature T in the radio-frequency range has a specific intensity given by the

Raleigh-Jeans approximation to the Planck black-body law:

–  –  –

where I is the specific intensity in, for example, watts/(m2Hz ster), k is Boltzman’s constant,

1.380 x 10-23 watts/Hz/K and λ is wavelength.

The proportionality to temperature allows us to talk about intensities and powers in temperature units, K or Kelvins. If a source really were thermal emission from a black or gray body, then this radiation temperature would be independent of wavelength. More typically, however, sources are “colored”, that is, radiation temperatures vary with wavelength and are not necessarily related to physical temperatures of the sources. A synchrotron-emission source, for example, has a spectral index n, usually defined by I ∝ ν-n, that is related to the energy distribution of the emitting electrons. Regardless of the emission mechanism or spectrum, we can use the Rayleigh-Jeans equation above to define a brightness temperature, Tb, proportional to intensity, but then Tb will be, in general, a function of frequency. Even in the high-frequency low-temperature range where Rayleigh-Jeans is no longer useful, we can use this equation to define a convenient fake brightness temperature. Figure 1 is a cartoon example of such spectra.

Electrical engineers implicitly use the Rayleigh-Jeans approximation also. The noise power per unit bandwidth from a warm resistor into a matched load is just kT provided that the frequency and temperature are in the range for which Rayleigh-Jeans is precise. To see this, imagine a resistor coupled to a feed looking at a black body. Even in the range where Rayleigh-Jeans is no longer useful; in thermal equilibrium, equal power must flow each way.





− 5.2.2 Atoms and molecules−emission and absorption lines Emission and absorption lines in radio astronomy usually originate from atoms and small molecules or molecular ions in gaseous form, and molecular transitions at radio wavelengths are usually rotational. Emission lines result from warm gas overlying a cold background so that the intensity (or flux or radiation temperature) at the line frequency is sharply higher compared to nearby wavelengths. If such a gas cloud is optically thick (opaque), the specific intensity or "brightness" at the line frequency is given by the state temperature of the corresponding transition, which, at thermodynamic equilibrium, would be just the temperature. Thermodynamic equilibrium is, however, not very common in radio astronomy. Absorption lines result from cool gas overlying a hotter background source so that the intensity at the line frequency is sharply lower compared to nearby wavelengths. If such a gas cloud is optically thick, then the line center again gives the state temperature. Figure 2 is a cartoon of such spectra.

5.2.3 Doppler shifts and kinematics Doppler shifts are very important in spectral-line radio astronomy. The non-relativistic form is usually written as

–  –  –

where ∆ν is the change in frequency ν due to the Doppler velocity v, defined as the rate of change of distance from source to observer (hence the minus sign), and c is the speed of light.

Even when speeds are relativistic, this non-relativistic formula is sometimes still used to define a convenient fake velocity.

Line widths and line shapes are influenced by several line-broadening mechanisms including a) natural line widths related to the lifetimes of the states involved in the transition, b) kinematic temperatures characterizing the small-scale random motions of the atoms or molecules, c) turbulence or larger-scale random motions, and d) kinematics, by which we mean large-scale ordered motions such as expansions, contractions, or rotations. A useful exercise is to estimate the spectrum that would be seen from some simple kinematic models such as a circumstellar shell or sphere that is expanding, contracting (infalling), or rotating and is unresolved in angle. In some cases the central star ionizes nearby gas, which makes a central continuum source. Such an object can then show both emission and absorption lines.

5.3 Antennas at Radio Wavelengths 5.3.1 Parabolic-why?

Radio-astronomical sources are far away, so incoming signals often look like plane waves from a specific direction (point sources), and the first goal of a radio telescope is to catch as much energy as possible from such a wave and avoid as much as possible any other signals, especially local interference. The signal at the antenna in this case can be characterized by a flux density in Janskys (1 Jy = 10−26 w/m2/Hz), so the bigger the antenna, the more watts (well, pico-pico watts) we collect. A parabolic antenna (i.e., a parabola of revolution), which puts all this energy into a small spot where a feed can be placed, is usually an engineering optimum for centimeter and millimeter wavelengths.

5.3.2 Aperture efficiency and K/Jy

Consider a black sphere with diameter d and temperature T at a distance r from a circular receiving antenna with diameter D. Assume that r is much larger than either d or D. Figure 3 is a cartoon of this situation.

Then the power density (power per unit frequency interval) received by the antenna, P, can be calculated as its collecting area times the flux from the source at the antenna or as the specific intensity of the source times the solid angle of the antenna as seen from the source. Either way gives the same formula, namely,

–  –  –

The first three terms on the right are the source flux density, F, and A = πD2/4 is the antenna collecting area, which is usually smaller than its physical area due to various losses. If we characterize P in temperature units, P = 2kTR, as usual, then

–  –  –

is a figure of merit, sometimes called sensitivity, in Kelvins per Jansky for the antenna. That extra 2 is because the flux density refers to the total in both polarizations, but a single receiver can only receive one polarization. The ratio of the antenna collecting area from this formula to its physical area is called aperture efficiency usually expressed as a percentage and usually 60% or less.

5.3.3 Beam efficiency and beam dilution Another figure of merit, appropriate for sources extended in angle, is the beam efficiency, crudely defined as the ratio of TR to the brightness temperature of the source. (There are more precise but less useful definitions.) Beam efficiency by this definition is, however, a function of the source angular size and shape, alas. A more useful parameter is the beam dilution, defined in the same way but for an assumed circular source with a specified diameter in beamwidths and as a function of this diameter. Planets with known brightness temperatures and angular sizes are candidate calibration sources for measuring aperture efficiency when they are small in angle compared with a beamwidth or points on the beam-dilution curve when they are larger in angle. Figure 4 is a cartoon of this situation.

5.3.4 Cassegrain-why?

A Cassegrain antenna comprises a parabolical main reflector and a concave hyperbolical subreflector near the prime focus of the main reflector to reflect incoming signals back to a spot near the center of the main reflector, the secondary focus, where the feed is placed. This feed is usually mounted on the front of a receiver box that fits through a hole in the center of the main reflector. This arrangement trades a little additional aperture blockage (the subreflector is larger than a prime-focus feed would be), for the ability to place additional equipment, such as a cryogenic refrigerator, near the secondary focus.

5.3.5 Beamwidth: λD The beamwidth (full width to half power) of the radiation pattern of a circular antenna is approximately 1.2 λ/D in radians, where λ is the wavelength and D is the diameter of the antenna in, of course, the same units. The 1.2 factor depends somewhat on the feed illumination pattern, that is, on the pattern of the feed as seen from the main reflector. A circular antenna with circular illumination gives a circular beam.

When a finite antenna is used to map extended sources over a range of angles one can show the resulting maps are band limited in the sense that they contain no angular frequencies above a maximum (called the Nyquist limit) that depends only on the wavelength and the antenna diameter. Band-limited maps are, then, smooth continuous functions of two angles on the sky, but they can be specified or measured at a finite grid of evenly spaced points provided that these points are no farther apart than a Nyquist step, which is λ/(2D) in radians. A Nyquist is typically a little less than half a beamwidth. Smooth maps can be obtained from finite grids of points by convolution.

5.3.6 Requirements for surface precision

The effective area of an antenna is less than its physical area because of various losses, one of which is due to the departure of the surface from an ideal parabolic shape. An antenna with a surface that is rough on the scale of a wavelength will be almost useless because of low aperture efficiency and also susceptibility to interference scattered into the feed. An ideal antenna would have at least so-called 1/20-wave optics, meaning that the surface is within a 1/20 of a wavelength of perfect. We must sometimes make do with antennas less than ideal; all antennas have some short-wavelength limit based on this criterion.

5.4 Interferometers

5.4.1 Why? Resolution: λ /D



Pages:   || 2 |


Similar works:

«Astro2010 State of the Profession Position Paper (March 2009) Astroinformatics: A 21st Century Approach to Astronomy Primary Author: Kirk D. Borne, Dept. of Computational and Data Sciences, 4400 University Drive MS 6A2, George Mason University, Fairfax, VA 22030 USA (kborne@gmu.edu).Abstract: Data volumes from multiple sky surveys have grown from gigabytes into terabytes during the past decade, and will grow from terabytes into tens (or hundreds) of petabytes in the next decade. This...»

«Chapter 2 Historical Overview: The United States and Astronomy Until the 1860s Astronomy as an amateur recreation was entrenched in much of Western Europe by the eighteenth century, where there were the financial means, the knowledge base, the manufacture of tools and the genuine interest among those with the time to engage in such a recreation. It took most of the first half of the nineteenth century for this pastime to become popular in the relatively young United States. This new country...»

«Physical characterization of brown dwarfs Elena Manjavacas Max-Planck-Institut f¨ r Astronomie u Heidelberg 2014 Dissertation in Astronomy submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany, for the degree of Doctor of Natural Sciences Put forward by M.Sc. Elena Manjavacas ˜ born in Mota del Cuervo, Espana Oral examination: 03.02.2015 Physical characterization of brown dwarfs Elena Manjavacas Max-Planck-Institut...»

«ROBOTIC ASTRONOMY AND ITS APPLICATION TO THE STUDY OF GAMMA-RAY BURSTS ALBERTO J. CASTRO–TIRADO Instituto de Astrof´sica de Andaluc´a–Consejo Superior de Investigaciones ı ı Cient´ficas (IAA-CSIC), E-18008 Granada, SPAIN ı Abstract: An overview of Robotic Astronomical facilities (especially in Spain) is presented. The study focuses on two aspects: the control software (one of such example being the RTS2 system) and the network of BOOTES robotic telescopes, partly devoted to the study...»

«Hoja Informativa 2010-2011 Oficina de Intercambios y Programas Internacionales Introducción La Universidad Iberoamericana es una institución de educación superior privada confiada a la Compañía de Jesús, fundada en 1943. Tiene seis campus en el país y el más joven es el ubicado en Puebla. La UIA ofrece una amplia variedad de disciplinas – Humanidades, Negocios, Arte y más—con cursos enseñados en español y con énfasis en México y otros países de América Latina. Los estudiantes...»

«An Introduction to Astronomical Photometry Using CCDs W. Romanishin University of Oklahoma wjr@nhn.ou.edu The lastest version of this book (in pdf format) can be downloaded from http://observatory.ou.edu This is version wrccd4a.pdf built on: March 31, 2002 Foreword/ Thanks / Production Details This book began as a set of lecture notes for a junior/senior course entitled “Observatory Methods” that I teach each spring at the University of Oklahoma (OU). The book is intended as an introduction...»

«« All flat maps, and I am one » : Cartographic References in the Poems of John Donne Ladan NIAYESH Université de Paris 7 Jussieu As A. E. Nordenskiöld reminds us, the maps, connected with the oldest editions of the Geography of the second century Alexandrian astronomer, mathematician and geographer Claudius Ptolemaeus, known as Ptolemy, constitute the prototype of almost all geographical atlases, published since the discovery of the art of printing1. For a modern viewer, it is often hard to...»

«UNIVERSITY OF WISCONSIN MADISON Department of Astronomy Astronomy 113 Laboratory Manual Fall 2011 Professor: Snezana Stanimirovic 4514 Sterling Hall sstanimi@astro.wisc.edu TA: Natalie Gosnell 6283B Chamberlin Hall gosnell@astro.wisc.edu Contents Introduction 1 Celestial Rhythms: An Introduction to the Sky 2 The Moons of Jupiter 3 Telescopes 4 The Distances to the Stars 5 The Sun 6 Spectral Classification 7 The Universe circa 1900 8 The Expansion of the Universe ASTRONOMY 113 Laboratory...»

«Constellations, Fixed Stars and the Zodiac in Islamic Astronomy Author: Salim Ayduz IMPORTANT NOTICE: Chief Editor: Lamaan Ball All rights, including copyright, in the content of this document are owned or controlled for these purposes by FSTC Limited. In Production: Faaiza Bashir accessing these web pages, you agree that you may only download the content for your own personal non-commercial use. You are not permitted to copy, broadcast, download, store (in any medium), transmit, show or play...»

«A L I V E LY E L E C T R O N I C C O M P E N D I U M O F R E S E A R C H, N E W S, R E S O U R C E S, A N D O P I N I O N Astronomy Education Review 2011, AER, 10, 010101-1, 10.3847/AER2010040 Astrology Beliefs among Undergraduate Students Hannah Sugarman Department of Astronomy, University of Arizona, Tucson, Arizona 85721 Chris Impey Department of Astronomy, University of Arizona, Tucson, Arizona 85721 Sanlyn Buxner Department of Astronomy, University of Arizona, Tucson, Arizona 85721...»

«Research Giulio Magli The Megalithic Building of S. Erasmo di Dipartimento di Matematica Cesi: Architecture, Astronomy, and Politecnico di Milano Landscape Pzza. Leonardo da Vinci 32 20132 Milano, ITALY Giulio.Magli@polimi.it Abstract. One of the most enigmatic megalithic buildings of Italy is the structure which lies on the S. Erasmo hill near Cesi, in Umbria, a Nicola huge complex encompassing an area of around 8000 square meters and enclosed by refined cyclopean walls. Although its date is...»

«Emulation of a Quantum Spin with a Superconducting Phase Qudit Matthew Neeley,1 M. Ansmann,1 Radoslaw C. Bialczak,1 M. Hofheinz,1 Erik Lucero,1 A. D. O’Connell,1 D. Sank,1 H. Wang,1 J. Wenner,1 A. N. Cleland,1 Michael R. Geller,2 John M. Martinis1∗ Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106 Department of Physics and Astronomy, University of Georgia, Athens, GA 30602 ∗ To whom correspondence should be addressed; E-mail:...»





 
<<  HOME   |    CONTACTS
2016 www.dissertation.xlibx.info - Dissertations, online materials

Materials of this site are available for review, all rights belong to their respective owners.
If you do not agree with the fact that your material is placed on this site, please, email us, we will within 1-2 business days delete him.