2009/08/24-28 Radio – Astronomy –Astro-: star Radio astronomy –
2009/08/24-28 The waves used by optical astronomers Electromagnetic Spectrum 4000 to 8000 angstroms Hz to Hz The Sun The solar system Stars Galaxies
2009/08/24-28 The radio window Atmospheric Transmission From about 0.5mm to 20m 600GHz to 15MHz –Troposphere to ionosphere –FM radio (and TV) –AM radio –Mobile phone… The solar system, stars, ISM, galaxies, cosmic microwave background…….. –The SunThe Sun
2009/08/24-28 Some advantages of radio astronomy Transparent to terrestrial clouds: visible in cloudy time The Sun is quiet: visible in day time Transparent to the vast clouds of interstellar dust: able to see distant objects Different origin of radiation
2009/08/24-28 The worlds largest radio telescopes The Arecibo Telescope Type: Fixed reflector, movable feeds Diameter of reflector: 1000 ft (304.8 m) Surface accuracy: 2.2 mm rms Working wavelength: from cm to dm The Effelsberg Telescope Type: Fully steerable Diameter: 100-m Working wavelength: up to 3mm, mainly cm
2009/08/24-28 Fundamentals of Radio Astronomy Some basic definitions Radiative transfer Blackbody radiation and brightness temperature Nyquist theory and noise temperature
2009/08/24-28 I : specific intensity dW infinitesimal power, in watts dσ infinitesimal area surface, in cm 2 dν infinitesimal bandwidth in Hz θ angle between the normal to dσand the direction to dΩ Iν brightness or specific intensity, in Wm -2 Hz -1 sr -1
2009/08/24-28 The total flux of a source Total flux of a source: integration over the total solid angle of the source Ω s Unit –W m -2 Hz -1 –Jy 1Jy= W m -2 Hz -1 = erg s -1 cm -2 Hz -1 A 1Jy source induces an signal of only W. Few sources are as bright as 1Jy
2009/08/24-28 Brightness is independent of the distance
2009/08/24-28 The total flux density depends on distance as r -2 Total flux received at an point P from an uniformly bright sphere
2009/08/24-28 Radiation energy density Energy density per solid angle: erg cm -3 Hz -1 Total energy density
2009/08/24-28 Radiative transfer For radiation in free space the specific intensity is independent of distance. But I changes if radiation is absorbed or emitted.
2009/08/24-28 Limiting cases (contd) Limiting cases (contd) Thermodynamic Equilibrium (TE): radiation is in complete equilibrium with its surroundings, the brightness distribution is described by the Planck function, which depends only on the thermodynamic temperature T of the surroundings
2009/08/24-28 Limiting cases (contd) Local Thermodynamic Equilibrium (LTE) –Kirchhoffs Law –Optical depth –Equation of transfer –Solution
2009/08/24-28 LTE (contd) The medium is isothermal –T(τ) T(s) T=const. Optical depth is very large –τ (0) –Difference with the intensity in the absence of an intervening medium
2009/08/24-28 Blackbody radiation Planck law Total brightness of a blackbody
2009/08/24-28 Wiens displacement law Maxima of B (T) and B λ (T) – B ν / ν=0 and B λ / λ 0 –ν max –λ max
2009/08/24-28 Rayleigh-Jeans Law Rayleigen-Jeans Law Radiation temperature
2009/08/24-28 Wiens Law
2009/08/24-28 Brightness temperature T b One of the important features of the Rayleigh-Jeans law is the implication that the brightness and the thermodynamic temperature of the blackbody that emits the radiation is strictly proportional. In radio astronomy, the brightness of the extended source is measured by its brightness temperature which would result in the given brightness if inserted into the Rayleigh-Jeans law
2009/08/24-28 Transfer equation of T b Transfer equation General solution Two limiting cases when T b (0)=0 –Optically thin, τ<<1 –Optically thick, τ>>1
2009/08/24-28 The Nyquist Theorem Johnson noise –The thermal motion of the electrons in a resistor will produce a noise power which is the noise determined by the temperature of the resistor The average noise power per unit bandwidth produced by a resistor R is proportional to the its temperature, i.e. the noise temperature, and independent of its resistance P=kT N
2009/08/24-28 Electromagnetic wave propagation fundamentals Maxwells equations Energy conservation and the Poynting vector Complex field vectors The wave equation Plane waves in nonconducting media Wave packets and the group velocity Plane waves in dissipative media The dispersion measure of a tenuous plasma
2009/08/24-28 Maxwells equations Material equations Maxwells equations Continuity equation of charge density and current
2009/08/24-28 Energy conservation and the Poynting vector Energy density of an electromagnetic field Poynting vector Equation of continuity for S
2009/08/24-28 Complex field vectors The Poynting vector
2009/08/24-28 The wave equation
2009/08/24-28 Plane waves in nonconducting media Nonconducting media –σ 0 –The wave equation –Velocity of the wave
2009/08/24-28 Plane waves (contd) Harmonic wave solution of the wave equation Wave number Phase velocity Index of refraction
2009/08/24-28 Plane waves (contd) A wave that propagates in the positive z direction is considered to be plane if the surfaces of constant phase forms planes z=const.
2009/08/24-28 Group velocity Dispersion equation Group velocity Energy and information are usually propagated with the group velocity
2009/08/24-28 Plane waves in dissipative media Dissipative media Harmonic waves propagating in the direction of increasing x Wave equations Dispersion equation
2009/08/24-28 Contd Wave number Field
2009/08/24-28 Contd Index of refraction and absorption coefficient
2009/08/24-28 Dispersion measure of a tenuous plasma Plasma: free electrons and ions are uniformly distributed so that the total space charge density is zero Tenuous plasma –Interstellar medium –dissipative medium Equation of motion of free electrons –Solution
2009/08/24-28 Contd Conductivity of the plasma Wave number for a thin medium with ε1 andμ1
2009/08/24-28 Contd Phase velocity and group velocity –For ω>ω p, k is real, v>c, v g
2009/08/24-28 Dispersion measure of pulsars A pulse emitted by a pulsar at a distance L will be received after a delay The difference between the pulse arrival time measured at two frequencies
2009/08/24-28 Contd Dispersion Measure
2009/08/24-28 Dispersion Measure, DM, for pulsars at different Galactic latitudes
2009/08/24-28 Faraday rotation In 1845, Faraday detected that the polarization angle of dielectric material will rotate if a magnetic field is applied to the material in the direction of the light propagation The rotation of the plane of polarization of an EM wave as it passes through a region containing free electrons and a magnetic field, also known as Faraday effect. The amount of rotation, in radians, is given by RMλ 2, where RM is the rotation measure of the source and λ is the wavelength. Observation of the Faraday rotation in pulsars is the most important means of determining the magnetic field of the Galaxy. It is named after the English physicist Michael Faraday.
2009/08/24-28 Equation of motion for an electron in the presence of a magnetic field If the magnetic field B is oriented in the z direction
2009/08/24-28 Solution Linearly polarized wave can be regarded as the superposition of circularly polarized waves Solution in the form of harmonic waves
2009/08/24-28 Parameters of the material Conductivity: purely imaginary Cyclotron frequency which is in resonance with the gyration frequency of the electrons in the magnetic field Wave number
2009/08/24-28 Phase propagation velocity Index of refraction Phase propagation velocity
2009/08/24-28 Relative phase difference Two circularly polarized waves will have a relative phase difference after a propagation distance due to the slightly different phase velocity
2009/08/24-28 Rotation Measure Magnetic field parallel to the line of sight
2009/08/24-28 Example Determine the upper limit of the angle through which a linearly polarized EM wave is rotated when it traverses the ionosphere. Take the following parameters: an ionospheric depth of 20km, an average electron density of 10 5 cm -3 and a magnetic field strength (assumed to be parallel to the direction of wave propagation) of 1G. –Find RM –Carry out the calculation for the Faraday rotation, Δψ for frequencies of 100MHz, 1GHz and 10GHz, if the rotation is Δψ/rad=(λ/m )2 RM –What is the effect if the magnetic field direction is perpendicular to the direction of propagation? What is the effect on circularly polarized EM waves?
2009/08/24-28 Repeat previous problem for the conditions which hold in the solar system: the average charged particle density in the solar system is 5 cm -3, the magnetic field 5μG, and the average path 10AU. What is the maximum amount of Faraday rotation of an EM wave of frequency 100MHz, 1GHz? Must radio astronomical results correct for this?
2009/08/24-28 Example A source is 100% linearly polarized in the north-south direction. Express this in terms of Stokes parameters. Intense spectral line emission at 18cm wavelength is caused by maser action of the OH molecule. At certain frequencies, such emission shows nearly 100% circular polarization, but little or no linear polarization. Express this in terms of Stokes parameters.
2009/08/24-28 examples If the DM for a given pulsar is 50, and the value of RM is 1.2×10 2, what is the value of the line-of-sight magnetic field? If the magnetic field perpendicular to the line of sight has the same strength, what is the total magnetic field?
2009/08/24-28 Homework A plane electromagnetic wave perpendicularly approaches a surface with conductivityσ. The wave penetrates to a depth of δ. Apply equation (2.25), taking σ>>ε/4π, so The solution to this equation is an exponentially decaying wave. Use this to estimate the 1/e penetration depth δ. Estimate the value of for copper, which has (in CGS units) σ=10 17 s -1 and μ1 for =10 10 Hz.
2009/08/24-28 Contd Assume that pulsars emit narrow periodic pulses at all frequencies simultaneously. Use eq. (2.83) to show that a narrow pulse (width of order s) will traverse the radio spectrum at a rate, in MHz s -1, of Show that a receiver bandwidth will lead to the smearing of a very narrow pulse which passes through the ISM with dispersion measure DM, to a width
2009/08/24-28 Examples In the near future there may be an anti- collision radar installed on automobiles. This will operate at ~70GHz. The bandwidth is proposed to be 100MHz, and at a distance of 3m, the power per area is Wm -2. Assume the power level is uniform over the entire bandwidth of 100MHz. What is the flux density of this radar at 1km distance? A typical radio telescope can measure to the mJy level. At what distance will such radars disturb such radio astronomy measurements?
2009/08/24-28 Examples A signal passes through two cables with the same optical depth τ. They have temperatures T 1 and T 2, with T 1 >T 2. Which should be connected first to obtain the lowest output power from this arrangement?
2009/08/24-28 Examples The 2.73K microwave background is one of the most important pieces of evidence in support of the big bang theory. The expansion of the universe is characterized by the redshift z. The ratio of the observed wavelength λ o to the (laboratory) rest wavelength λ r is related to z by z=(λ o / λ r )-1. The dependence of the temperature of the 2.73K microwave background on z is T=2.73(1+z). What is the value of T at z=2.28? What is the value at z=5 and z=1000?
2009/08/24-28 Examples The pulsar in the Crab nebula has a dispersion measure DM=57 cm -3 pc, and a period of s. Staelin and Reifenstein (1969 Science 162, 1481) discovered this pulsar at ν=110MHz, using a 1MHz-wide receiver bandwidth. Someone tells you that this pulsar would not have been found at 110MHz if the pulses all had the same amplitude. Do you believe this? Use the following relation to support your decision: the smearing Δt of a short pulse is (202/ν MHz ) 3 DM ms per MHz of receiver bandwidth.
2009/08/24-28 Homework A cable has an optical depth τof 0.1 and a temperature of 300K. A signal of peak temperature 1K is connected to the input of this cable. Use equation (1.34) in the textbook with T being the temperature of the cable and T (0) the temperature of the input signal. What is the temperature of the output of the signal? Would cooling the cable help to improve the detectability of the input signal?
2009/08/24-28 Homework (contd) A signal passes through two cables with the same optical depth, t. These have temperatures T1 and T2, with T1>T2. Which cable should be connected first to obtain the lowest output power from this arrangement?
2009/08/24-28 Homework (contd) Apply the Stefan-Boltzman relation to the Sun and the planets to estimate the surface temperature if each planet is assumed to absorb all of the radiation it receives (this is an albedo of zero – this is the upper limit the planet can absorb since in reality some radiation is reflected). As a first approximation, assume that the planets have no atmosphere and no internal heating sources and that the rapid rotation equalizes the surface temperatures. The distances for assumed circular orbits (in AU) are: Mercury (0.39AU), Venus (0.72AU), Earth (1 AU), Mars (1.5AU), Jupiter (5.2AU). At a wavelength of 68cm, Jupiter was found to have a brightness temperature of more than 500K. Could the temperature of Jupiter be caused by solar heating?
2009/08/24-28 Telescopes The Green Bank Telescope Type: off-axis, fully steerable Diameter: 100 by 110 meters Surface accuracy: 1.2mm--0.3mm Working wavelengths: cm to mm The Parkes Telescope Diameter: 64-m, in the southern sky Working wavelength: cm The Nobeyama 45-m JCMT JCMT with no membraneJCMTJCMT with no membrane 15-m, sub-mm(surface accuracy m), Mauna Kea
2009/08/24-28 Telescopes Interferometers VLBA: 10 radio telescopes across USA VLA: m antennas, Y-shape, largest separation of antenna 36km (0.04 arcsecond at 43GHz) The VLA looking south MERLIN: an array of radio telescopes in UK, with separation up to 217km (0.05 arcsecond at 5GHz) List of radio telescopes
2009/08/24-28 Radio astronomy in China Telescopes Miyun Synthesis Radio Telescope: linear array of 28 9-m antennas working at 232MHz Shanghai: 25-m Urumuqi: 25-m Qinghai Delingha: 13.7-m Projects FAST: Five hundred meter Aperture Spherical Telescope 30 elements, Guizhou Large radio telescope: 50-m MSRT FAST DLH Urumqi SheshanMSRTFAST DLHUrumqiSheshan
2009/08/24-28 The future of radio astronomy Bigger telescopes –Atacama Large Millimeter Array(ALMA)Atacama Large Millimeter Array(ALMA) ESO,IRAM,OSO,NFRA,NRAO,NAOJ…… m antennas, 10mm-0.35mm, 150m-10km Year 2012 –VSOP-2 Research Fainter objects, finer structure
2009/08/24-28 Homework If the average electron density in the interstellar medium is 0.03 cm -3, what is the lowest frequency of electromagnetic radiation which one can receive due to the plasma cutoff? Compare this to the ionospheric cutoff frequency if the electron density, N e, in the ionosphere is ~10 5 cm - 3. Use Where p is the plasma cutoff frequency.