6 2016/5/ /6/19 z B (HDM) (CDM) CDM (Λ = 0) (k = +1) Friedmann ( ) dr 2 = Rmax R R 2 (4.1) dθ R(θ) = R max 2 t(θ) = R max 2c (1 cos θ), (4.2) (θ

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1 6 206/5/9 206/6/9 z B (HDM) (CDM) CDM (Λ = 0) (k = +) Friedmann ( ) dr 2 = Rmax R R 2 (4.) dθ R(θ) = R max 2 t(θ) = R max 2c ( cos θ), (4.2) (θ sin θ); (4.3) R(θ) θ = 0 θ = π (turn-around time) θ = 2π δ θ 0 δ 3 20 ( 2c R max ) 2/3 t 2/3 t 2/3 a (a RR0 ), (4.8) δ(z = 0; Ω m,0 ; Ω Λ,0 ) δ(z = 0; Ω m,0 = 0; Ω Λ,0 = 0) 5 [ ( 2 Ω m,0 Ω 4/7 m,0 Ω Λ,0 + + ) ( 2 Ω m, Λ,0)] Ω. (4.0) T (k) (k; z = 0) 2 = T (k) 2 f(a) 2 (k; z) 2. Press-Schechter Gauss ( ) [ α 2 ( ) ] 2α n(m) M exp M. (4.4) M (Initial Mass function: IMF) M

2 4 4.4 / O B 4.6 z / λ em λ obs λ em = + z λ obs 2 λ em,, λ em,2 z λ obs,, λ obs,2 λ obs, = λ em,( + z) λ obs,2 λ em,2 ( + z) = λ em, (4.7) λ em, Å Balmer 4000 Å * * 4000 Å Balmer Balmer 4000 Å A 2

3 S/N UBVRIJHK, ugriz Galactic Astronomy (James Binny & Merrifield Michael, 998, Princeton University Press) pp z / χ 2 z z phot = z spec (catastrophic failure) SDSS ugriz z ACES z COMBO-7 z 3

4 z z Lyman Lyα (26( + z) Å) Lyman (92( + z) Å) z B g U dropouts Lyman z dv/dz 0 (V Hubble.9 ) Hubble 4.0 Lyα Lyα 4000 Å [O II] λ z = 5.34 Lyα 4.5 ϕ(l) SDSS g g 4

5 ϕ(l) L ( ) α ) ϕ(l) = ϕ L exp ( LL. (4.8) L Schechter L ϕ, L, α *2 L dn/(dv dm) dn/(dv dl) M 0 pc F (d = 0 pc) M 2.5 log F (d = 0 pc) + const. L [ ] M = 2.5 log L 4π (0 pc) 2 + const. = 2.5 log L + const. dm = 2.5d(log L) = 2.5 ln 0 dl L dn dv dl = dn dv dm dm dl = 2.5 ln 0 L dn dv dm ρ V N ρ = N V = V N i= (4.9) V i V p i ( i N) (4.9) ρ = N V = V N i= p i (4.20) p i ( p i ) p i = p i p i ρ ϕ(l) ρ σ ρ = V N i= p i 2 (4.2) p i i *2 ϕ(l) 4.2 Press-Schechter ( ) [ α 2 ( ) ] 2α M M n(m) exp M M (4.4) M 2 L 5

6 d max,i V max,i V V max,i p i i p i = V max,i /V ρ = V N i= p i = V N i= V V max,i = N i= V max,i (4.22) ( ) ρ, L L + dl ϕ(l) = = L i in L L + dl V max,i (4.23) ϕ(l) /V max p i ϕ(l) p i 0 V V max V a p i = 0 p i *3 p i V p i *4 V /V max V/V max (percentile) p(x) (x x x 2 ) q : (00 q) x i ( i 00) p(x) i % x = x + i x 2 x 00 X ( 0) x F X (x) Pr(0 X x) = x 0 Pr(X = x )dx 4. x x c(x) c(x) = x x p(x )dx (x x x 2 ) 0 c V/V max d i i 0-d i 0-d i 0-d i V i /V max,i V i /V max,i 0 V i /V max,i V i /V max,i = /2 V i /V max,i *3 *4 z 6

7 4.6 () X 0 x U X (2) N V = V max N N i= Vi V max,i () X p(x) = X σ 2 σ 2 = X 2 X 2 ( X ) [ ] 2 = x 2 p(x)dx xp(x)dx = 0 0 = 3 ( 2 [ x 2 dx 0 ) 2 = 2 0 xpdx ] 2 σ = / 2 (2) V i /V max,i ( i N) 0 V i /V max,i () σ 2 = /2 V/V max σ 2 /N V/V max σ/ N = / 2N 4.7 = V i /V max,i = /2 4.8 V i /V max,i = /2 = V/V max = /2 p i *5 4.9 α < Schechter L ϕ(l) ( ) α ) Lϕ(L) = L ϕ L exp ( LL L ( ) 4.2 L *5 7

8 [ 0 = d dl [Lϕ(L)] ( α)l α L α = [( α)l L] L α L L = ( α)l L L exp ] ) exp ( LL ) ( LL, L ( ) ϕ = L =, α = Euclid number counts Cygnus A C273 z = 0.58 *6 3C273 V ( 2. ) C273 (quasi-stellar object: QSO) 4.3, C273 m, m 2, S, S 2 ( ) S m m 2 = ( 2.5 log S + const.) ( 2.5 log S 2 + const.) = 2.5 log S 2 S S 2 = 0 0.4(m m2) = [( 26.3) ( 2.3)] = = 20 3C *6 z =

9 4.4 3C273 -UV Doppler 000 km/s -UV ( 000 au) > 0 8 M (Active Galactic Nuclei: AGN) * AGN AGN Seyfert Seyfert 2 Seyfert *7 (AGN) Seyfert (radio-loud) radio-quiet 9

10 radio-loud 0 % radio-loud radio-quiet Fanaroff-Riley (FR) I FR II FR I FR II FR II 4.6 Baldwin-Phillips-Terlevich BPT Seyfert (Low-Ionization Nuclear Emission-line Region: LINER) Schechter ϕ(l) = ϕ (L/L ) α + (L/L ) β (4.24) α > β L ϕ L β L ϕ L α L L L L 4.7 z = 2 ϕ (Pure Density Evolution: PDE) L (Pure Luminosity Evolution: PLE) PLE PLE radio-loud PLE z = 2 0 ( + z) 3 z = ( + z) 2.7±0.6 ( + z) 3 0

11 4.7 z ρ z 4.0 PDE (log ϕ)-(log L) ϕ(l) PLE PDE ϕ ϕ 2ϕ (4.24) ϕ [ ] log ϕ log ϕ 2ϕ = log (L/L ) α + (L/L ) β = log ϕ + log 2 (log ϕ)-(log L) log ϕ PLE L L 2L ϕ { } log ϕ log ϕ ϕ = log [L /(2L )] α + [L /(2L )] β log ϕ L = 2L log L log L = log L + log 2 (log ϕ)-(log L) log L 4. L Q ρ t r Q L 6/7 r 4/7 ρ /2 Tolman *8 L r 2 Q7/6 r 4/3 ρ 7/2 Q ρ r L/r 2 Tolman *8 ( + z) 4 Tolman 3.2

12 K (IR) K Hubble z 2 z 2 z 2 [O III] λ 5007 K z phot = z spec (catastrophic failure) ( ) α ) ϕ(l) = ϕ L exp ( LL. (4.8) L Schechter L /V max i V p i p i = V max,i /V ϕ(l) = L i in L L + dl V max,i. (4.23) V /V max /V max V i /V max,i = /2 (AGN) 4.5 AGN AGN Seyfert Seyfert 2 ϕ(l) = ϕ (L/L ) α + (L/L ) β. (4.24) z = 2 ϕ (PDE) L (PLE) 2

13 p.33 coarse p.23 incidentally p.34 outlier p.35 simplistic p.38 null hypothesis pejorative (n.) (adj.) overtone p.42 emanate cocoon p.42 burrow p.44 conspire 3

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