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1 (Magnitude) 1
2 AB / = / / =
3 / λ logf(λ) λ (λ) log Fo(λ) α 3
4 α (A0 F F λ F F F λ F F λ (mag=,) λ U B V Rc Ic J H K L M N Q λ(µ) Fo(Jy) Bessell, Castelli,Plez 1998 Rieke,Lebofski,Low
5 α α ν IRAS B(10,000K,)=.09 10^3 [ 3 /(ep - 1) ] Jy = h/kt=hc/kλt =1.4388/ λ(µ)(t/10 4 K) U B V Rc Ic λ(µ) Fo(Jy) Vega
6 4 log F() (Jy) 3 B U V R I J H K Fo(Vega) F(IRAS) L log λ(µ)
7 7
8 8
9 π π log(d/10pc) Distance Modulus (mm)o 5 log(d/10pc) log(d/10pc) 9
10 Apparent Bolometric Magnitude BOL =.5 log [ F(λ)dλ / Fo BOL ].5 log ( / Fo BOL ) Fo BOL α V Absolute Bolometric Magnitude 10
11 F= F λ λ Fo VµF3V Bµ=0.38, Rµ=-0.36 αlyr F λ V λµ 11
12 Hipparcos catalogue (IAU19) Pg : photographic magnitude 0.43 µ Pv : photovisual magnitude 0.54 µ / / 1
13 H.L.Johnson and W.W.Morgan, 1953, Ap.J. 117, Corning 3384 Corrning 5030 Schott GG13 1P1 Corning 9863 UBV Response CurveA0 B V A0 3,000 4,000 5,000 6,000 λ(a)
14 ( V B-V Sp. V B-V Sp. αlyr A0V γuma A0V 109 Vir A0V α CrB A0V γ Oph A0V HR A0V -.5 log (B/ log (/ A0V UBV Primary Standard Stars ( V B-V Sp. V B-V Sp. α Ari KIII HR A1V β Cnc K4III η Hya B3V β Lib B8V α Ser KIII ε CrB K3III τ Her B5IV 10 Lac O9V HR K3V
15 UBV in Basic Astronomical Data 1963 V B8V KIII KIII B5IV B3V K3III K4III O9V A1V K5V B-V
16 λ λ λ 16
17 β λ λ λ αβ α
18 RIJKLMN Johnson/Mitchell 196 Comm.Lunar Plantary Lab.1,73 Johnson et al Comm.Lunar Plantary Lab.4,99 R I J K L M N Q λc Cousins 1976, Mem.RAS 81, 5 Rc Ic H λc Astron.J. JHK et al. AJ, 87, 109.
19 Stromgren 4-color system uvby B V A0 u: b y: λ(µ)
20 B V A λ(µ) 48
21 Thuan-Gunn PASP 88, 543 [OI] B V g=9.50 g-r=u-v=v-g=0 u v g λ(µ)0.7 A0 r
22 TL V BνT ν, ΩνΩ ν, ΩνΩVV,νΩ B(ν,T)νν, Ω D νωνωv DνΩνΩV<s(p)> <s(p)>dω p 3 3 = h 3
23 <s> ν Es=ν <>= P P ep(-es/kt)=ep (ν/kt) ΣPn=1 Ps = 1 ep hν kt hν hν K kt kt ep s = s Ps = hν hν 3hν 1ep ep 3ep kt kt kt hν hν 3hν 1 ep ep ep kt kt kt K K
24 ) (1...) (1...)...)( ( ) 3 (...) ( = = = = = ep(-hν/kt) ep(-hν/kt) 1 ep Pn 1 3 = = = = = kt h n ν ) ( = ν
25 DνΩ L/λL/λyL/λz /λ/λy/λz /λ/λy/λz V/ V/ D(νΩ) N/V ν Ων / 5
26 BνT D(νΩ)νT B(νΩT)ν (νωt) ν D(νΩ) νt B( ν, T ) = = c hν D( ν, Ω) ν = chν 3 c hν c 3 ep ep 1 hν 1 kt s ( ν, T ) 1 hν 1 kt IntensityBνTT 6
27 hν 3 1 hν ep kt hν c ( ν) = = kt = B T, c hc 1 ch ep λkt 1 3 hc kt hν ( λ) = = B T, λ 1 λ λkt ch ν c ckt λ kt λ hν hν kt ( ν) ep B T, c 3 ( λ) ep B T, hc λ 5 ch λkt
28 U ενωννω π π(σ/π)t 4 σ T 4 T 4 σ σ 8
29 B(T)cosθdΩ π(t σt 4 θ σt 4 σt 4 d 9
30 λ /λ ν /ν λ1 λ λ1 / λ λ λ λ λ1 λ λλ log[ λ1 / λ ] log[o λ1 / o λ ] 30
31 λλ λλ 0.44µ 0.55µ - W F(B ) F(V)
32 -.5 log[bt,b / BT,V ].5 log[ob /ov] BBB o ν oνb oν BT, ν= T(K) 3 [ 3 /(ep-1)] /λµ)/T4 T4, λ ). λ )..5 log[] /. T /. T4 [ ] BB = log{[ep(3.70/t4)- 1] / [ep(.616/t4)- 1]} 3
33 λ.6µ oν /.6 /T4 BB.5 log[]. =0.8.5 log{[ep(3.997/t4)- 1] / [ep(3.70/t4)- 1]} ν/ /λ BB BB ν (hν / )ep(-hν/t) [B-V] BB -.5log 10 (0.55/0.44).5log 10 [-0.654/T4].5log 10 (4063/3636) [U-B] BB -.5log 10 (0.44/0.36).5log 10 [-0.77/T4].5log 10 (1790/4063) [B-V] BB [U-B] BB 33
34 U-B B-V U-BK K B0V -1 U-B 0 1 A0V 30,000 [U-B][B-V] 10,000 G0V 6,000 4,000 M0V 0 B-V 1 3,000 34
35 t=10 7 yr Z=0.0 Bertelli K-M K-M 35
36 36
37 37
38 color magnitude diagram HR log(l/lo), logf log[fν /F(ν )] Te R,L,MV T,ρ 38
39 39
40 M=-1V-I=1 40
41 Baade s Window (Distance Modulus) Paczynski/Stanek 1998 ApJ 494, L19-
42 J-KTHICK DISK 4
43 logλf(λ) 1 (λ)λ V 0 V logλ(µ) 43
44 =-.5log[ F(λ)dλ/Fo BOL ]-.5log(/Fo BOL ) V Apparent V Magnitude () BOL 44
45 BOL BC = T T4 = T4 1 T4 B0 A0 F0 G0 K0 M0 M5 4,000 30,000 9,790 7,300 5,940 5,150 3,840 3,170 BC (star) M
46 46
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