A.???? B.??????? C.??? D.??? E.????

1
????? I ?????
???????????????????? ????????????????????????????
?????? A.???? B.??????? C.??? D.??? E.????
F.????????? G.???? H.?? I.???? J.????? I
K.????? II L.??????? ?????????? ??????????????????
???????????????? ?????????? A??E??????????????????
?F?????????? ???????G??I?????????????????????J??L?
??????????????????????????????????? ?????????????
??
2
H ??
????? (H.1 ) ?????? ???????????????????????????
?????? ( H.2) ????? ??????????????????????????
????????? ( H.3) ???? ?????????????????????
???????????? ??????????????????? ( H.4) ????
??????????????????????????????????
?????????? ( H.5) UBV???? ??????????????????????
? ( H.6) ???????? ?????????????????????
????????HP???????? http//www.ioa.s.u-tokyo.ac.jp/
kisohp/STAFF/nakada/intro-j.html
3
H.1. ??????
???2??????????????????????????1???6????6??????????
?(?????????????????????????????)
????1830???????????1856??????????????
???????? ??Da????????A??????Db????????B?????? ????
?????????? ???? ADa2 BDb2 ?????? A / B
Db2 /Da2 ??????? ????????1??????????
(1/2.5)???????????????

4
?????????????????1?????????????????????
???(??????)???????? ???????????
??(M) -1 0 1 2 3 4 5
6 ?? 2 7 12 67 190 710
2000 5600 ??(NT) 2 9 21 88
278 988 2988 8588 log NT 0.30 0.95
1.32 1.94 2.44 2.99 3.48
3.93
???????????????? (1) ???????????? (2)
?????????? ???? (1)????????????? (2)??????????????
???????????? ????????
5
??????????? N0???????-1??0??? 9??
N4 4?????-1?0?1?2?3?4????? 988? ???N4?N0
??100? ????4?????????????100??????????????????????
???????? D0??????????? F0 ????????????????? V0
4pR3/3 ????????
(1) ??? XD0 ?????????? F ???????? (2) ?????? F
????????? ?? V ????????? (3) ?????? F ??????? N
?F, Fo, No ?????????

6
??????? m ?1???????? F ? 1/A ?????????
(1) 1?????????? F1(1/ A)F0 ???m?????????
???????? (2) 1?????? D1? D0 ???????????? (3) m
?????? Dm ? D0 ???????????? (4) m ???????? Nm ?
A?m?N0 ???? logNm ????????????

7
(1) ???????(m?logNm)??????????? (2)
?????????????????????????1?? (3) A????????
8
??????A?????????????????????????(1)? Fm (1/
A)mF0 ???????
????????? ??m??? m ??????????

?????????????? A2.5 ???????????????? ?A????????
????m??? m ??????????

9
H.2. ????? (apparent magnitude)
????????????? m ????? m(?)?2.5 log10 F(?) /
Fo (?) F(?) ??????????
Fo(?) ????(??)??????
?????????????????????????????????????????????
??????????????? ???????????1?????????1/A0.4?
????????????????????????????????????????????????
10
(1) ????????????m?????????F???????? (2)
????????1???????????1/A?????? A?????????

?????????????????1????????????
(1/2.5)???????????????? ?????????(????????)??????
???????????????????????????????????
11
??????????????????????????? ???m?m?m??????????? ?
?? m-2.5 log (Fm/Fo), m?m -2.5 log (
Fm?m/Fo) ?m-2.5 log ( Fm?m/Fm ) Fm?m/Fm
10-0.4 ?m exp-(ln 10)0.4 ?m ??
?mltlt1????????????? exp-(ln 10)0.4 ?m ? 1- (ln
10)0.4 ?m 1-2.3026 0.4
?m1-0.92 ?m ???? Fm?m/Fm ? 1-
?m ????0.1?????????1?????????? ??????????????

12
0?????? Fo (1)
??????????????????????????????????????????????????
??????????????????????????????????????????????????
(1) IAU(International Astronomical Union)1922???
????(photographic magnitude)?
??????(photovisual magnitude) ?????
(north pola r sequence) ?96?????
aUMi(????Polaris)2???????????????????
(2) Johnson(1953)?????????????????? aLyr
(A0?) 0? (3) CCD?????????????????????????????? (
4) ???????AB???????????????????????
13
0??????(2)
?????????????????????m???????????????????????
m? -2.5log10F(?)/Fo(?) -2.5log10?F(?)/?Fo(
?) -2.5log10?F(?)/?Fo(?)
-2.5log10F(?)/Fo(?)m? ??????
?????????????Fo??????????????????????????????????
?????V(??)0.03?A0V?????0 ?????????????????????Fo
(?)?????????????????1Jy10-26W/m2/Hz ???
F(mag0,?)
? ?? U B V
Rc Ic J H K L
M N Q ?(µ) 0.366 0.438
0.545 0.641 0.798 1.22 1.63 2.19 3.45
4.8 10.6 21 Fo(Jy) 1790 4063 3636
3064 2416 1590 1020 640 285 170 36
9.4

Bessell, Castelli,Plez 1998

Rieke,Lebofski,Low 1985
14
0??????(3) aLyr
aLyr(Vega) ???????10000K???????????????????????IRA
S(InfraRed Astronomical Satellite
1983)?????T10,000K, ???O1.5710-16??????????????
0???????????
A0V????R????2.5?1.74109m aLyr???D?7.7pc2.37101
7m ??????????R/D7.3410-9
aLyr????p?21.6910-16 ??1.57?????(8)??A0V????
??Teff9800K??2? ?????????????(8)??????????
15
aLyr?????????????????????? 1) UBV?????????????????
??? 2) ???????????????????????????????????? ???(2)
???????????? ??aLyr ????????????????????????????
??????? aLyr ?????????????????????????????????Fo?
??IRAS ???????????????????????????????????????????
???????????? UBV ???????12-100
µ??????????????????????????????
? ?? U B V Rc Ic
?(µ) 0.366 0.438 0.545 0.641 0.798
12 25 60 100 Fo(Jy) 1790
4063 3636 3064 2416 Vega
1736 3941 3527 2972 2343 41.5
11.0 9.5 7.7 FIRAS 2420 2887 2951
2764 2397 28.3 6.73 1.19
0.43
16
4 log F(?) (Jy)
3
2
B
B
V
aLyr(Vega)???????????
R
I
J
Fo(Vega)
U
H
F(IRAS)
K
L
?????? ????????
?????
1
0
-0.5 0
0.5 1
1.5 log ?(µ)
17
H.3. ???? (absolute magnitude)
??????????????????????????????????????????????????
??? ??????????????????????????????????????????????
???????????????????????????????????10pc???????????
??????? ???? ?????10pc???????????
a Lyrae (??) ?????????????(???)???0??? a Lyr
????? 8pc ??? a Lyr ?????????????

18
??????????????????????????? ?????????10pc?????????
?????????????????
????
?????
???????? ?????aLyr???? 8pc
?????10pc????? ?????aLyr???? 8pc
aLyr ??
aLyr ??
7.7pc
7.7pc
10pc
19
????(Distance Modulus)
?? L ?????????????????????????????????????????????
???? L???????????? L??????????????????? L ???????
?????L???10pc????????????????????M???????????D
???????????m????????? m??? M?m?????????????
m-2.5 log (FD/Fo)? M -2.5 log (F10pc/Fo)
???? FDL/(4pD2)? F10pcL/(4p10pc2)
????? mM-2.5 log (FD/F10pc) M-2.5 log (
10pc2 /D2 ) M5 log (D/10pc)
???????D10pc?? mM? Dgt10pc?? mgtM
??????????????
20
????????? m-M5 log(D/10pc) ??? ??????????????????
???M?????????????????m?????????( m-M
)?????????? ?????????????????D?????? ( m-M
)??????? ( m-M )???????????????????( distance
modulus ) ???????
?????? ?? ??
???? aCen 1.4 pc
-4.3 aLyr
7.7 pc -0.57 ??????
50 kpc 18.5 M31(????????)
0.71 Mpc 24.3 Virgo???
18 Mpc
31.3
21
H.4.???? (Bolometric Magnitude)
???? mBOL ??????????????? ?F(?)d? ?????????
mBOL-2.5 log ?F(?)d? / FoBOL-2.5
log (F / FoBOL)
???????A0??????????? (a Lyr) ?????????????????????
?????????????????????????????????? ????????????
mV0 ??? F3????????? ???????? FoBOL 2.5
10-8 W/m2 ???A0 ????? F3 ???????????V???????????
??????A0????F3??????????
???????????????????????????????? ???????
Apparent Bolometric Magnitude
mBOL-2.5 log ?F(?)d? / FoBOL-2.5 log (F /
FoBOL)
?????? Absolute Bolometric Magnitude
MBOL?10pc?????????
22
F ?F(?)d???
V???
B?
????? V
A?
B? ??
F?
A? ?????
F? ???
M?
M? ??
???????????V?????????F3V????????? ????V0?F3V?????
? mBOL0??????? ????V0??? mBOL
???0????????? mBOL(V0)????(BC)??????
23
???? Bolometric Correction????????????
mBOL mVBC
??????????? Apparent Bolometric Magnitude
mBOL-2.5log?F(?)d?/FoBOL-2.5log(F/FoBOL)
FoBOL mV0?F3V?????????2.5 10-8 W/m2
BC??mV ???????B-V???T???????????????? ??????????
???????
24
H. 5. UBV????
???? ???????? (?2??) 1????????
6???????????? Pogson 1856
ma-mb-2.5log(Ea/Eb)
m?? E???????
?? D m ??????????????????? ??????????7mm ?
mb6? D m ? Eb( 7mm)2 Ea
(D m)2 ma mb-2.5log(7mm/D m)2
62.5log(D2106/49)
16.8 5logD
?????? ???????96?(???)????????? (IAU1922)
Pg photographic magnitude 0.43 µm
Pv photovisual magnitude 0.54 µm
25
UBV???????????????????? H.L.Johnson and
W.W.Morgan, 1953, Ap.J. 117, 313-352
U Corning 3384 350 nm B
Corrning 5030 Schott GG13 1P21 ?????
430 nm V Corning 9863 (RCA) 550 nm
UBV Response Curve ? A0???????? ( )
???
A0?
U
B
V
3,000 4,000 5,000 6,000
?(A)
26
UBV????????
?????? (????? )
V B-V Sp.
V B-V Sp. aLyr
0.03 0.00 A0V ?UMa 2.45 0.00
A0V 109 Vir 3.75 -0.01 A0V
a CrB 2.23 -0.02 A0V
? Oph 3.72 0.04 A0V HR
3314 3.89 -0.01 A0V
B-V-2.5 log (B??/V??)1.040? U-B-2.5 log
(U??/B??)- 1.120 A0V 6?????????U-BB-V0
UBV Primary Standard Stars (????? )
V B-V Sp.
V B-V Sp.
a Ari 2.00 1.151 K2III
HR 875 5.17 0.084 A1V
ß Cnc 3.52 1.480 K4III ? Hya
4.30 -0.185 B3V ß Lib
2.62 -0.111 B8V a Ser 2.66
1.165 K2III e CrB 4.15
1.227 K3III t Her 3.89 -0.155
B5IV 10 Lac 4.88 -0.203
O9V HR8832 5.57 1.010 K3V
27
UBV ??? H.Johnson in Basic Astronomical Data 1963
0
V
??????????????? B-V (???????????????)
1
2
K2III
K2III
B8V
3
B5IV
K4III
4
K3III
B3V
O9V
5
A1V
K5V
6
1
0
B-V
1.6
-0.4
28
???????(1) (???????????????????)
?????? A????? B???????????????????????????????B???
????????A????????????????????
A
B
??
??? (???????)
??? (???????)
?
?A
?B
???????????????A?????????????B????????????????? B?
????????A(??)????????????????????
29
???????(2)
VA?VB???????????????????????????????????????????VA
?VB??????????????????????
A
B
??
VA-VB
?1
?1
?1
?2
ß
?2
?
0
1
???(B-V)B
?A
?B
VA?VBa(B-V)Bß ????1????????? a?????????
(B-V)A??(?0)??(?1.5)??????? ??gt
????O,B,A?(??)?K?(??)??????????
30
H.6.UBV???????
RIJKLMN Johnson/Mitchell 1962 Comm.Lunar
Plantary Lab.1,73 Johnson
et al. 1966 Comm.Lunar Plantary Lab.4,99
??? R I J K L
M N Q ?c
0.7 0.9 1.25 2.2 3.4 4.9
10.2 20.0 Cousins 1976,
Mem.RAS 81, 25 ? R, I ???????? ???
Rc Ic ?c 0.638
0.797 H (1.63µ) Glass 1974
MNAS SA,33, 53 ???? ?? ?(R)??(Rc)
??(?)??(?c)?????????????
??????????????????????? UBVRcIc Landolt
1992?Astron.J. 104,340 JHK Elias
et al. 1982?AJ, 87, 1029.
31
????????(1)
Stromgren 4-color system uvby
U
B
V
???????????????????????A-F????
???
A0?
u ??????????? ??????? b ?????????B
???????? y ?????V????? ?????
u
b
v
y
0.3 0.4 0.5
0.6 ?(µ)
m1(v-b)-(b-y) ??? c1(u-v)-(v-y)
??????? b?y ??
32
????????(2) DDO system
McClure 1976 AJ 81?182 G,K?????????????
35????? 4-color?u ??? 38?????
v????????? 41????? CN????? 42,45,48 ???
U
B
V
???
A0?
48
45
38
41
35
42
0.3 0.4 0.5
0.6 ?(µ)
(35-38)??? ???????? (38-42)???
??? (42-45)????(45-48)??? ?????
33
????????(3) Thuan-Gunn ????
Thuan/Gunn1976 PASP 88, 543
???????????OI? ?????
????? CD174708 (G???) ?????? g9.50 g-ru-vv-g0
???????
U
B
V
???
A0?
u
v
g
r
0.3 0.4 0.5
0.6 ?(µ)0.7
34
????????(4) AB??
F?(0?)3631Jy SDSS??? AB-2.5 log
f?/3631Jy 8.900-2.5 log f?(Jy)
???????AB???????? F(mag0,?)
? ?? U
B V Rc Ic J H
K L M N Q ?(µ)
0.366 0.438 0.545 0.641 0.798 1.22 1.63
2.19 3.45 4.8 10.6 21 Fo(Jy) 1790
4063 3636 3064 2416 1590 1020 640
290 170 36 9.4 AB 0.768 -0.122
0.002 0.184 0.442 0.897 1.378 1.885
2.744 3.324 5.009 6.467
35
(No Transcript)
36
???????????? D0??????????? F0 ?????????????????
V0 4pR3/3 ????????
(1) ??? XD0 ?????????? F ???????? (2) ?????? F
????????? ?? V ????????? (3) ?????? F ??????? N
?F, Fo, No ?????????
(1). FFo/X2 (2). VX3Vo (3).(2)?? NX3No???(1)??
X(Fo / F)1/2 ???? N(Fo / F)3 / 2 No
37
??????? m ?1???????? F ? 1/A ?????????
(1) 1?????????? F1(1/ A)F0 ???m????????? Fm
???????? (2) 1?????? D1? D0 ???????????? (3) m
?????? Dm ? D0 ???????????? (4) m ???????? Nm ?
A?m?N0 ???? logNm ????????????
(1).Fm (1/ A)mF0 (2).?????(1)?????F1 Fo/X2
(1/ A)F0 ???? D1XDoA1/2Do (3).Fm Fo/X2
(1/ A)mF0 ???? XAm/2? Dm Am/2 D0
(4).(3)?????m????????Vm?Vm A3m/2 V0
??????Nm A3m/2 N0 logNm (3 logA/2)m
logN0
38
(1) ???????(m?logNm)??????????? (2)
?????????????????????????1?? (3) A????????
(2) log Nm0.90.5m
(3) ???????? (4)?????? log A 1/30.33
log 20.30, log2.5 0.4 ???? A2.2
39
??????A?????????????????????????(1)? Fm (1/
A)mF0 ???????
????????? ??m??? m ??????????
?????????? log Fm -m log A log F0
m-(1/ log A )log(Fm/F0)?log A1/3 ????
m-3 log(Fm/F0)
?????????????? A2.5 ???????????????? ?A????????
????m??? m ??????????
???????A2.5??????? (1/log 2.5)2.5129 ????
m-2.5129 log(Fm/F0)
40
(1) ????????????m?????????F???????? (2)
????????1???????????1/A?????? A?????????
(1) m?2.5 log10(F / Fo )??? F10-0.4m Fo
(2) ????1?????F?10-0.41/ 100.4 ????
??????A100.4 2.512 ????