射电天文基础

1. 射电天文基础 姜碧沩 北京师范大学天文系 2009/08/24-28日，贵州大学

2. 大纲 • 射电天文基础 • 射电望远镜 • 连续谱辐射机制 • 谱线辐射机制 • 星际分子 参考书：《射电天文工具》 射电天文暑期学校

3. 射电天文 • Radio • 大气窗口 • 地面射电天文的频率上限和下限 • 空间 • Astronomy • Astro-: star • Radio astronomy • 与其它波段的区别 射电天文暑期学校

4. The waves used by optical astronomers • Electromagnetic Spectrum • 4000 to 8000 angstroms • 7.51014Hz to 3.751014Hz • The Sun • The solar system • Stars • Galaxies 射电天文暑期学校

5. The radio window • Atmospheric Transmission • From about 0.5mm to 20m • 600GHz to 15MHz • Troposphere（对流层） to ionosphere • FM radio (and TV) • AM radio • Mobile phone… • The solar system, stars, ISM, galaxies, cosmic microwave background…….. • The Sun 射电天文暑期学校

6. 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 射电天文暑期学校

7. 射电天文的辉煌 • 获得诺贝尔奖的发现 • 宇宙微波背景辐射的发现 • 脉冲星的发现：快速旋转的中子星 • 双星脉冲星的发现与引力波理论的验证 • 宇宙微波背景辐射的黑体形式以及非各向同性 • 其他重要贡献 • 星际分子 • 氢原子谱线 • 恒星形成区 • 磁场 •  射电天文暑期学校

8. The world’s 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 射电天文暑期学校

9. Fundamentals of Radio Astronomy • Some basic definitions • Radiative transfer • Blackbody radiation and brightness temperature • Nyquist theory and noise temperature 射电天文暑期学校

10. I: specific intensity • dW＝infinitesimal power, in watts， • dσ＝infinitesimal area surface, in cm2， • dν＝infinitesimal bandwidth，in Hz， • θ＝angle between the normal to dσand the direction to dΩ • Iν＝brightness or specific intensity, in Wm-2Hz-1sr-1。 射电天文暑期学校

11. The total flux of a source • Total flux of a source: integration over the total solid angle of the source Ωs • Unit • 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 射电天文暑期学校

12. Brightness is independent of the distance 射电天文暑期学校

13. The total flux density depends on distance as r-2 • Total flux received at an point P from an uniformly bright sphere 射电天文暑期学校

14. Radiation energy density • Energy density per solid angle: erg cm-3Hz-1 • Total energy density 射电天文暑期学校

15. Radiative transfer • For radiation in free space the specific intensity is independent of distance. But I changes if radiation is absorbed or emitted. 射电天文暑期学校

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17. Limiting cases • Emission only: • Absorption only: 射电天文暑期学校

18. Limiting cases (cont’d) • 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 射电天文暑期学校

19. Limiting cases (cont’d) • Local Thermodynamic Equilibrium (LTE) • Kirchhoff’s Law • Optical depth • Equation of transfer • Solution 射电天文暑期学校

20. LTE (cont’d) • 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 射电天文暑期学校

21. Blackbody radiation • Planck law • Total brightness of a blackbody 射电天文暑期学校

22. Wien’s displacement law • Maxima of B(T) and Bλ(T) • Bν/ν=0 and Bλ/λ＝0 • νmax • λmax 射电天文暑期学校

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24. Rayleigen-Jeans Law Radiation temperature Rayleigh-Jeans Law 射电天文暑期学校

25. Wien’s Law 射电天文暑期学校

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27. 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 射电天文暑期学校

28. Transfer equation of Tb • Transfer equation • General solution • Two limiting cases when Tb(0)=0 • Optically thin, τ<<1 • Optically thick, τ>>1 射电天文暑期学校

29. 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=kTN 射电天文暑期学校

30. Electromagnetic wave propagation fundamentals • Maxwell’s 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 射电天文暑期学校

31. Maxwell’s equations • Material equations • Maxwell’s equations • Continuity equation of charge density and current 射电天文暑期学校

32. Energy conservation and the Poynting vector • Energy density of an electromagnetic field • Poynting vector • Equation of continuity for S 射电天文暑期学校

33. Complex field vectors • Complex field vectors • The Poynting vector 射电天文暑期学校

34. The wave equation 射电天文暑期学校

35. Plane waves in nonconducting media • Nonconducting media • σ＝0 • The wave equation • Velocity of the wave 射电天文暑期学校

36. Plane waves (cont’d) • Harmonic wave solution of the wave equation • Wave number • Phase velocity • Index of refraction 射电天文暑期学校

37. Plane waves (cont’d) • A wave that propagates in the positive z direction is considered to be plane if the surfaces of constant phase forms planes z=const. 射电天文暑期学校

38. Group velocity • Dispersion equation • Group velocity • Energy and information are usually propagated with the group velocity 射电天文暑期学校

39. Plane waves in dissipative media • Dissipative media • Harmonic waves propagating in the direction of increasing x • Wave equations • Dispersion equation 射电天文暑期学校

40. Cont’d • Wave number • Field 射电天文暑期学校

41. Cont’d • Index of refraction and absorption coefficient 射电天文暑期学校

42. 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 射电天文暑期学校

43. Cont’d • Conductivity of the plasma • Wave number for a thin medium with ε≈1 andμ≈1 射电天文暑期学校

44. Cont’d • Phase velocity and group velocity • For ω>ωp, k is real, v>c, vg<c 射电天文暑期学校

45. 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 射电天文暑期学校

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47. Cont’d • Dispersion Measure 射电天文暑期学校

48. Dispersion Measure, DM, for pulsars at different Galactic latitudes 射电天文暑期学校

49. 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 RMλ2,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. 射电天文暑期学校

50. Equation of motion for an electron in the presence of a magnetic field If the magnetic field B is oriented in the z direction 射电天文暑期学校