輻射の量子論、選択則、禁制線、許容線

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Radiative Processes in Astrophysics 005/8/1 http://wwwxray.ess.sci.osaka- u.ac.jp/~hayasida

Semi-Classical Theory of Radiative Transitions r r 1/ 4 H = ( cp ea) m c + + eφ nonrelativistic limit, Coulomb gauge r p e r r e A H = A p+ m mc mc 3 epa/ mc 3 η ( n pha0 ) >> 1 ( ea/mc 0 1 0 1 H = H + H H H H 0 φ = E φ k k k ψ () t = a () t φ exp( ie t/ h) k k k

Transition Probability w 4π = H h T ( ω ) 1 fi fi fi T 1 1 1 iωt' fi ωfi π 0 fi H ( ) ( ) H ( t') e dt' E 1 * 1 3 f Ei H fi () t φf H φid x, ωfi h ikr Art (, ) = Ate ( )... ( ) 4 e j ω r π rr fi ik wfi = f e l j i mc ω fi r r r l l r r r r = c( φ + E) = ce ω r j( ω) = ( ω) ct

Dipole Approximation r φ e I d x r r * ik 3 f jφi r r r ik r 1 r r e = 1 + ik + ( ik ) +... r d e j j 4π r r wfi = ( l d) ( ) fi j ω fi h c 4π wfi = d ( ) fi j ω fi h c

Einstein Coefficients and Oscillator Strength w lu = B J lu ν 4 3π B = d j( ω ), B B 3ch lu ul ul ul= lu 4 3 64πνul dul Aul = 3 3ch Oscillator Strength f ul 4π e classical B = f = B f hν mc lu lu lu lu ul lu

Selection Rules Dipole 0 (forbidden) (permitted) (selection rule) l= 1, m=0, 1 S=0, L=0, 1, J=0, 1 (except J=0 to J=0) Laporte's rule ( li ) 3 φ φ parity r Qd e r d x r r fi f j i j j j One-electron jump rule 1 orbital orbital

Density dependence of transition in ionized gas radiative de-excitation + collisional de-excitation = collisional excitation NA + NNσ = NNσ N N N N N 1 e 1 1 e 1 ( N N, N e 1 1 1 1 e 1 1 1 1 1 1 1 1 1 σ A = + 1 σ N σ A / σ ( e crit σ N e crit = + 1 σ Ne j = N A E = N A E σ N + 1 = XN A ( N =XNe 1 e crit 1 1 1 1 1 1 e 1 1 σ 1 Ne 1 N << N j = XN E e e crit 1 e 1 1 N >> N j = XN A E / σ e e crit 1 e 1 1 1 1 σ σ 1 E σ σ 1 1 N N e crit e + 1 1 1

Forbidden Transition N e crit A / σ 1 1 ( N << N j N e e crit 1 e N >> N j N e e crit 1 e j 1 N e N e-crit N e-crit

1cm Radio Wave

[OIII] Interpreting Astronomical Spectra by Emerson

Broad Line ( 1000-10000km/s Permitted only Density High N>10^8 /cc Narrow Line(1000km/s Permitted Forbidden Low Density N~10^3-10^6/cc Active Galactic Nuclei, by Blandford, Netzer, &Woltjer, Springer-Verlag

Emission from Thin Thermal Plasma neniv(=emission Measure) V Recombination (radiative, dielectric)

Ionization Equilibrium 1 n q i e i = q n ( q + α ) n + α n i 1 i 1 i i i i+ 1 i+ 1 : ionization rate coefficient α : recombination rate coefficient i dn dt Radiative Recombination + i + i 1 A + e A + h Dielectic Recombination + i + i 1 A + e A e ( =excited states) ( =excited states) + ν ' + i 1 + i 1 A e A h ν

The Saha Equation 0 + 0 ( χi + ( 1/) mv e ) + dn0 () v g = exp N0 g0 kt χ :ionization potential I dn N ( v) : number of ions in the ground level with free electrons (v~v+dv) : number of atoms int he ground level 3 dxdydzdp + xdpydpz 8π mvdv e g=g 0 ge, ge = = 3 3 h Nh Integrate over all v, + 3/ 3 3/ 0 e 8π + e 0 / I kt kt χ x π + e 0 χi / kt = e e x ds e 3 0 N0 h g0 m = e h g0 N N m g m kt g e The number of atoms or (1st ionization stage) ions in any state, using the Boltzmann laws + N0 g N 0 g 0 0 =, =, UT ( ) = partition_function = giexp( Ei / kt) + + N U( T) N U ( T) Saha's equation For j,j+1th ionization stages + + 3/ N Ne U ( T) π mekt = N U( T) h χ / kt N N U ( T) π mkt = j+ 1 e j+ 1 e N j U j( T) h e I 3/ j, j 1/ kt e χ +

W49B ASCA SIS Fujimoto et al.,1995

Einstein FPCS Cyg- Loop Vedder et al., 1986, ApJ307,p.69

Line profiles FeXXVI (H-like) 1s - p S 1/ - P 3/ 5a 6.977 kev Resonance line S 1/ - P 1/ 5b 6.956 kev Resonance line FeXXV (He-like) 1s - 1sp 1 S - 1 P w 6.70 kev Resonance line 1 S - 3 P x 6.683 kev Intercombination line 1 S - 3 P 1 y 6.669 kev Intercombination line 1s - 1ss 1 S - 3 S z 6.638 kev Forbidden line FeXXIV (Li-like) 1s p - 1sp P 3/ - D 5/ j 6.645 kev Satellite line Highly Ionized Iron P 1/ - D 3/ k 6.655 kev Satellite line P - S 1/ m 6.679 kev Satellite line 1s s - 1sps S 1/ - 1 P 3/ q 6.664 kev Inner-shell excitation S 1/ - 1 P 1/ r 6.653 kev Inner-shell excitation S 1/ - 3 P 1/ t 6.677 kev Inner-shell excitation http://www-x.phys.metro-u.ac.jp/~furusho/emissionline/line.html

Energy level diagram of H-like, He-like, and Li-like ions. http://wwwx.phys.metrou.ac.jp/~furusho/ emissionline/line. html

MEKA model

X-ray Spectrum from Plasma High resolution spectrum Stellar Coronae Capella observed with Chandra LETG Mewe et al., 001, A&A,368,p.888

Photo-Ionized Plasma ( ξ L/nR ) AGN Broad Line Region X

Ionization Structure Kallman & Mcray,198, ApJ,,50,p.63

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