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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 7.51014Hz to 3.751014Hz 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 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

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 temper ature Nyquist theory and noise temperature 2009/08/24-28 I: specific intensity

dW I cosddd dW infinitesimal power, in wat ts d infinitesimal area surface, i n cm2 d infinitesimal bandwidth i n Hz angle between the normal t o dand the direction to d I brightness or specific inten sity, in Wm-2Hz-1sr-1 2009/08/24-28 The total flux of a source Total flux of a source: integration over the total s olid angle of the source s

S I ( , ) cos d Unit s W m-2Hz-1 Jy 1Jy=10-26 W m-2Hz-1= 10-23 erg s-1 cm-2Hz-1 A 1Jy source induces an signal of only 10 -15W. Few sources are as bright as 1Jy 2009/08/24-28 Brightness is independent of the distance I 1 (r1) I 2 (r 2)

2009/08/24-28 The total flux density depends on distance as r-2 Total flux received at an poin t P from an uniformly bright s phere 2 c S I ( , )cos d I sin cos d d s 0 c

2 R R sin c S I 2 I r r 2009/08/24-28 Radiation energy density Energy density per solid angle: erg cm-3Hz-1 1 u () I c

Total energy density 1 u u ( )d I d c ( 4 ) ( 4 ) 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. dI I ds,

dI ds, 2009/08/24-28 I (s ds) I (s) dsd d d I dsd d d dI I ds 2009/08/24-28 Limiting cases Emission only: 0 dI , ds

s I ( s ) I ( s0 ) ( s )ds s0 Absorption only: 0 s dI I , I ( s ) I ( s 0 ) exp ( s)ds ds s0 2009/08/24-28

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 dI 0, I B (T ) ds 2h 3 1 B (T ) 2 c e h / kT 1 2009/08/24-28

( s ) Limiting cases (contd) I ( s ) I (0)e B (T ( ))e d (s)

0 Local Thermodynamic Equilibrium (LTE) Kirchhoffs Law B (T ) s ds Optical depth d ds 0 Equation of transfer 1 dI dI I B (T ) ds Solution 2009/08/24-28

d LTE (contd) The medium is isothermal T()) T(s) T=const. I ( s ) I (0)e ( s ) B (T )(1 e ( s ) ) Optical depth is very large )(0) I B (T ) Difference with the intensity in the absence of an intervening medium

I ( s ) I ( s ) I (0) ( B (T ) I (0))(1 e ) 2009/08/24-28 Blackbody radiation Planck law 2h 3 1 B (T ) 2 c e h / kT 1 2hc 2 1 B (T ) 5 hc / kT e 1 Total brightness of a blackbody

4 4 2 k B(T ) T , 2 3 1.8047 10 5 erg cm 2 s 1 K 4 15c h 4 2009/08/24-28 Wiens displacement law Maxima of B (T) and B(T) B/=0 and B/ 0 max max T

58.789 GHz K max max cm 2009/08/24-28 T 0.28978 K

2009/08/24-28 Rayleigh-Jeans Law Rayleigen-Jeans Law h kT 2 T 20.84 GHz K e h / kT

Radiation temperature c h 1 J (T ) I 2 h / kT k 2k e 1 h 1

kT 2 2 BRJ ( , T ) 2 kT c 2009/08/24-28 Wiens Law h kT e h kT 1

3 2h h / kT BW ( , T ) 2 e c 2009/08/24-28 2009/08/24-28 Brightness temperature Tb 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 2 2 c 1 Tb B B 2 2k 2k 2009/08/24-28

Transfer equation of Tb Transfer equation dTb ( s ) Tb ( s ) T ( s ) d General solution Tb ( s ) Tb (0)e ( s ) ( s ) T ( s ) e d

0 Two limiting cases when Tb(0)=0 Optically thin, )<<1 Tb T Optically thick, )>>1 Tb T 2009/08/24-28 The Nyquist Theorem Johnson noise The thermal motion of the electrons in a resistor will p

roduce a noise power which is the noise determined b y the temperature of the resistor The average noise power per unit bandwidth pro duced by a resistor R is proportional to the its te mperature, i.e. the noise temperature, and indep endent of its resistance P=kTN 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

J E D E B H Maxwells equations D 4 B 0 1 E B c 4 1 H J D c c Continuity equation of charge density and current

J 0 2009/08/24-28 Energy conservation and the Poy nting vector Energy density of an electromagnetic field 1 1 u E D B H E2 H 2 8 8 Poynting vector c

S E H 4 Equation of continuity for S u S E J t 2009/08/24-28 Complex field vectors Complex field vectors E E 1 i E 2 e i t H H 1 iH 2 e it

The Poynting vector c S Re E Re H 4 c * S Re E H 4 2009/08/24-28

The wave equation 4 H 2 H 2 H c c 2 4 E 2 E 2 E c c 2 2009/08/24-28 Plane waves in nonconducting media Nonconducting media

0 The wave equation 1 u 2 u 0 v 2 Velocity of the wave v 2009/08/24-28 c Plane waves (contd)

Harmonic wave solution of the wave equation u u 0 e i kx t Wave number 2 k 2 c Phase velocity c v k

2 Index of refraction 2009/08/24-28 c c n k v 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. E z 0, H z 0

E H 0 E H 2009/08/24-28 c S 4 2 E

Group velocity Dispersion equation (k ) d (k ) 0 (k k 0 ) dk Group velocity d vg 0 dk Energy and information are usually propagated with the group velocity

2009/08/24-28 Plane waves in dissipative media Dissipative media 0 Harmonic waves propagating in the direction of increasing x E( x, t ) E 0 e i ( kx t ) Wave equations 2 2 4 E k c 2 i c 2 H 0 Dispersion equation

2 4 2 k 2 1 i c 2009/08/24-28 Contd Wave number k a ib 2 1

4 a 1 1 c 2 2

1 4 b 1 1 c 2 Field

E ( x , t ) E 0 e bx e i ( ax t ) n E( x, t ) E 0 exp nx exp i x c c 2009/08/24-28

t Contd Index of refraction and absorption coefficient 2 1 4 n 1 1

2 2 1 4 n 1 1 2

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

me v mer -eE 0 e it Solution 2009/08/24-28 e e it v E0e i E ime me Contd Conductivity of the plasma Ne 2

i me Wave number for a thin medium with 1 a nd1 2 p 2 k 2 1 2 c 2 2009/08/24-28 2

4 Ne p2 me Contd Phase velocity and group velocity For >p, k is real, v>c, vg

2009/08/24-28 2 2 p vg c 1 2 n 1 2 p

2 2 p 2 Dispersion measure of pulsars A pulse emitted by a pulsar at a distance L will be received after a delay 2 dl 1 1 p D 1 2

v c 2 0 g 0 L L L 2 1 e 1

dl 1 N (l ) dl 2 c 0 2me The difference between the pulse arrival time measured at two frequencies 2 e D 2cme 2009/08/24-28

L 1 1 2 2 N (l )dl 1 2 0 2009/08/24-28 Contd Dispersion Measure N l DM

d 3 pc 0 cm DM 4 D 2.410 10 3 cm pc ss 2009/08/24-28

1 1 2 2 1 2 MHz MHz 1 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 a nd a magnetic field, also known as Faraday effect. The amount of rotation, in radians, is given by RM2, where RM is the rotation measure of the source and is the w avelength. Observation of the Faraday rotation in pulsar s is the most important means of determining the magne tic field of the Galaxy. It is named after the English physi cist Michael Faraday. 2009/08/24-28

Equation of motion for an electron in the presence of a magnetic field mv mr -e E r B If the magnetic field B is oriented in the z direction rx ry e e Bry E x m m e e Brx E y

m m 2009/08/24-28 e e r i Br E m m r rx iry E E x iE y Solution Linearly polarized wave can be regarded as the superposition of circularly polarized waves 1

1 E x ( E E ), E y ( E E ) 2 2i Solution in the form of harmonic waves E Ae i ( k x t ) r r0 e 2009/08/24-28 i ( k x t ) Parameters of the material 2 Ne Conductivity: purely imaginary i

e m B m e c B Cyclotron frequency which is in resonance m with the gyration frequency of the electrons e in the magnetic field c B 2m 2 2

p 2 k 1 Wave number c 2 ( c ) 2009/08/24-28 Phase propagation velocity Index of refraction 2

n 1 Phase propagation velocity 2009/08/24-28 p2 ( c ) v c / n Relative phase difference Two circularly polarized waves will have a relative phase difference after a propagation distance due to the slightly different phase velocity

2 (k k )z 3 2 p c 2 Ne3 B z 2 2 z 2 2c m c L e 1

B N (z )dz 2 2 // 2 m c 0 5 8.1 10 rad m 2009/08/24-28 2 L / pc B// N z d

3 Gauss cm pc 0 Rotation Measure RM 5 8.110 -2 rad m L / pc 1 rad

2 1 m B// N z d 3 Gauss cm pc 0 2 rad

2 2 m B// 6 RM 1.23 10 Gauss DM 2009/08/24-28 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 foll owing parameters: an ionospheric depth of 20k m, an average electron density of 105cm-3 and a magnetic field strength (assumed to be parall el to the direction of wave propagation) of 1G. Find RM Carry out the calculation for the Faraday rotation, for frequencies of 100MHz, 1GHz and 10GHz, if the rotation is /rad=(/m)2RM What is the effect if the magnetic field direction is p erpendicular to the direction of propagation? What i s the effect on circularly polarized EM waves? 2009/08/24-28

Repeat previous problem for the condition s which hold in the solar system: the aver age charged particle density in the solar s ystem is 5 cm-3, the magnetic field 5G, a nd the average path 10AU. What is the m aximum 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 1.2102, 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 approac hes a surface with conductivity. The wave penetrates to a depth of . Apply equation (2.25), taking >>/4, so to this equation i 2 E (4The solution / c 2 ) E s an exponentially decaying wave. Use this to estimate the 1/e penetration depth . Estimate the value of c / 4 for copper, which has (in CGS units) =1017s-1 and 1 f or =1010Hz.

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 10-6s) will traverse the radio spectrum at a rate, in MHz s-1, of 4 v 1.2 10 ( DM ) 1[ / MHz ]3 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 3 3

t 8.3 10 DM [ / MHz ] B s 2009/08/24-28 Examples In the near future there may be an anti-collisio n radar installed on automobiles. This will oper ate at ~70GHz. The bandwidth is proposed to be 100MHz, and at a distance of 3m, the powe r per area is 10-9Wm-2. Assume the power level is uniform over the entire bandwidth of 100MH z. What is the flux density of this radar at 1km distance? A typical radio telescope can measu re to the mJy level. At what distance will such r adars disturb such radio astronomy measurem ents?

2009/08/24-28 Examples A signal passes through two cables with the same optical depth ). They have te mperatures T1 and T2, with T1>T2. Which should be connected first to obtain the l owest output power from this arrangem ent? 2009/08/24-28 Examples The 2.73K microwave background is one of the most important pieces of evidence in support of t

he big bang theory. The expansion of the univer se is characterized by the redshift z. The ratio of the observed wavelength o to the (laboratory) re st wavelength r is related to z by z=(o / r)-1. T he dependence of the temperature of the 2.73K microwave background on z is T=2.73(1+z). Wh at 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 dispersio n measure DM=57 cm-3pc, and a period of 0.0 333s. Staelin and Reifenstein (1969 Science 162, 1481) discovered this pulsar at =110M Hz, using a 1MHz-wide receiver bandwidth. S

omeone tells you that this pulsar would not h ave been found at 110MHz if the pulses all ha d the same amplitude. Do you believe this? Use the following relation to support your deci sion: the smearing t of a short pulse is (202/ MHz)3DM ms per MHz of receiver bandwidth. 2009/08/24-28 Homework A cable has an optical depth )of 0.1 and a tempe rature of 300K. A signal of peak temperature 1K is connected to the input of this cable. Use equat ion (1.34) in the textbook with T being the tempe rature of the cable and T (0) the temperature of t he input signal. What is the temperature of the o utput 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 pl

anets to estimate the surface temperature if each planet i s assumed to absorb all of the radiation it receives (this i s an albedo of zero this is the upper limit the planet ca n absorb since in reality some radiation is reflected). As a first approximation, assume that the planets have no at mosphere and no internal heating sources and that the r apid rotation equalizes the surface temperatures. The dis tances 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 fo und to have a brightness temperature of more than 500K . Could the temperature of Jupiter be caused by solar he ating? 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 membrane 15-m, sub-mm(surface accuracy 14-18 m), Mauna K ea 2009/08/24-28 Telescopes Interferometers

VLBA: 10 radio telescopes across USA VLA: 27 25-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 separ ation 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 Teles cope 30 elements, Guizhou

Large radio telescope: 50-m MSRT FAST DLH Urumqi Sheshan 2009/08/24-28 The future of radio astronomy Bigger telescopes Atacama Large Millimeter Array(ALMA) ESO,IRAM,OSO,NFRA,NRAO,NAOJ 64 12-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 frequenc y of electromagnetic radiation which one can rece ive due to the plasma cutoff? Compare this to the ionospheric cutoff frequency if the electron densit y, Ne, in the ionosphere is ~105cm-3. Use p Ne 8.97 3 kHz cm

Where p is the plasma cutoff frequency. 2009/08/24-28 2009/08/24-28 2009/08/24-28 2009/08/24-28 2009/08/24-28

2009/08/24-28 2009/08/24-28 JCMT 2009/08/24-28 JCMT without membrane 2009/08/24-28

Parkes 2009/08/24-28 2009/08/24-28 2009/08/24-28 2009/08/24-28

VLA 2009/08/24-28 2009/08/24-28 2009/08/24-28 FAST 2009/08/24-28

2009/08/24-28 Nobeyama 2009/08/24-28 White light, radio and X-ray Sun 2009/08/24-28 2009/08/24-28

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