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

2009/08/24-28 日射电天文暑期学校 2 Spectral Line Fundamentals The Einstein Coefficients Radiative Transfer with Einstein Coefficients Dipole Transition Probabilities Simple Solution of the Rate Equation

2009/08/24-28 日射电天文暑期学校 3 The Einstein Coefficients Line profile function

2009/08/24-28 日射电天文暑期学校 4 Transition between two states and the Einstein coefficients

2009/08/24-28 日射电天文暑期学校 5 Radiative Transfer with Einstein Coefficients

2009/08/24-28 日射电天文暑期学校 6 Stimulated Emission

2009/08/24-28 日射电天文暑期学校 7 Dipole Transition Probabilities --- Electric Dipole

2009/08/24-28 日射电天文暑期学校 8 Magnetic Dipole

2009/08/24-28 日射电天文暑期学校 9 Allowed Transition and Forbidden Transition Electric dipole transition probability –Mean electric dipole moment for hydrogen: μ mn =ea 0 /2=4.24× –Transition probability for atomic hydrogen close to the Lyman limit: A mn =10 9 /s Magnetic dipole transition probability –Mean magnetic dipole moment for hydrogen: μ mn =9.27× erg Gauss -1 –Transition probability for the lowest Bohr : A mn =10 4 /s Electric dipole transitions are referred to as “allowed” transition and magnetic dipole transitions are termed “forbidden”.

2009/08/24-28 日射电天文暑期学校 10 Simple Solutions of the Rate Equation The Rate Equation –Transition j→k –Process y Spontaneous emission Simulated absorption and emission Collisional absorption and emission

2009/08/24-28 日射电天文暑期学校 11 Radiative Processes Only

2009/08/24-28 日射电天文暑期学校 12 Collision Probability

2009/08/24-28 日射电天文暑期学校 13 Collisional Processes Involved

2009/08/24-28 日射电天文暑期学校 14 Excitation Temperature

2009/08/24-28 日射电天文暑期学校 15 Exercise We now investigate the variation of T ex with the collision rate C 21 and the spontaneous decay rate A 21 for a two-level system. From ‘Tools’ equation(11.41), the dependence on the kinetic temperature T K and the temperature of the radiation field is shown. Suppose that the collision rate C 21 is given by n where the value of n is When n =A 21 for the transition involved, this is referred to as the critical density, n*. For the 21cm line, A 21 =2.85× s -1. Find n* for this transition. For neutral hydrogen, in most cases, only two levels are involved in the formation and excitation of the 21cm line since the N=2 level is 9eV higher. Less secure is any result for a multi-level systems, However, to obtain an order of magnitude estimate, repeat this calculation for the J=1-0 transition for the HCO+, modelling the molecule as a two-level system in which the Einstein A coefficient is A 21 =3×10 -5 S -1. What is the value of n*? Compare this to the value for the 21cm line. For HCO+, take T K =100K, find the value of the local density for which T ex =3.5K. For the same density, calculate n* for the J=1-0 transition of the CO molecule, modelling this as a two-level system with A 21 =7.4×10 -8 s -1.

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2009/08/24-28 日射电天文暑期学校 17 Line Radiation of Neutral Hydrogen The 21cm Line of Neutral Hydrogen The Zeeman Effect Spin Temperature Emission and Absorption Lines The Physical State of the Diffuse Interstellar Gas Differential Velocity Fields and the Shape of Spectral Lines The Galactic Velocity Field in the Interstellar Gas Atomic Lines in External Galaxies

2009/08/24-28 日射电天文暑期学校 18 Radio Atomic Lines

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2009/08/24-28 日射电天文暑期学校 20 The 21cm Line of Neutral H Transition between the hyperfine structure levels 1 2 S 1/2, F=0 and F=1 –Magnetic dipole transition –Frequency:ν 10 = × 10 9 Hz –Spontaneous transition probability A 10 = × s -1 A factor of about smaller than that of an allowed optical transition Mean half-life time of the F=1 state t 1/2 =1.11×10 7 a –Collision changes the spin of electron in about 400 a

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2009/08/24-28 日射电天文暑期学校 22 Spin Temperature The relative population of the hyperfine structure levels is determined by collision in practically all astronomical situations –The excitation temperature in this case is usually called the spin temperature

2009/08/24-28 日射电天文暑期学校 23 Column Density

2009/08/24-28 日射电天文暑期学校 24 Optical Depth

2009/08/24-28 日射电天文暑期学校 25 The Zeeman Effect

2009/08/24-28 日射电天文暑期学校 26 Spin Temperatures

2009/08/24-28 日射电天文暑期学校 27

2009/08/24-28 日射电天文暑期学校 28 Emission and Absorption Lines Solution of the radiation transfer equation in terms of the brightness temperature –For positions without a background source T c =0 Pure emission profile In optically thin cases

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2009/08/24-28 日射电天文暑期学校 30 The Influence of Beam Filling Factors and Source Geometry

2009/08/24-28 日射电天文暑期学校 31 Optical Depth

2009/08/24-28 日射电天文暑期学校 32 Degree to Which the Continuum Source is Covered

2009/08/24-28 日射电天文暑期学校 33 Source Size

2009/08/24-28 日射电天文暑期学校 34 The Physical State of the Diffuse Interstellar Gas The value of the local kinetic gas temperature is determined by a balance between energy gain and loss Four classes medium –Cold neutral medium: T<50K –Warm neutral medium: T>200K –Warm ionized medium: T ～ 10 4 K –Hot ionized medium: T ～ 10 6 K

2009/08/24-28 日射电天文暑期学校 35 Differential Velocity Fields and the Shape of Spectral Lines

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2009/08/24-28 日射电天文暑期学校 37

2009/08/24-28 日射电天文暑期学校 38 The Galactic Velocity Field in the Interstellar Gas

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2009/08/24-28 日射电天文暑期学校 40 Terminal Velocity

2009/08/24-28 日射电天文暑期学校 41 Atomic Lines in External Galaxies

2009/08/24-28 日射电天文暑期学校 42 Virial Masses

2009/08/24-28 日射电天文暑期学校 43 The Tully-Fisher Relation