????(Bolometric Correction)

1
?3? ???
2005?11?7?
????????HP???????? http//www.ioa.s.u-tokyo.ac.jp/
kisohp/STAFF/nakada/intro-j.html
????(Bolometric Correction)
??????????(Rayleigh Jeans Approximation)
2
3.1. ??????
??T???????????L3V???????????????????? B(??T)
?????????????????? n(?, O)?????????O????????????
n(?, O)d?dOdV??dV,???d????dO(???)
??????????????? B(?,T)ch?n(?, O) ????
???? n ?????????D????????????s(p)?????????
n(??O)d?dOdV D(??O)d?dOdVlts(p)gt??? ???????lts(p)
gt???D(p?O)?????
?P
?X
P
???????????p3?x 3 h3 ??2(??)????
X
3
lts(p)gt
??? ??????????????????ltsgt??????
cph? ???p??????????? Essh? ??s???????
Ps ??????????s???????
????ltsgt?sPs
???????????Ps? exp(-Es/kT)exp (?sh?/kT)
??????SPn1?????????
4
???????????xexp(-h?/kT) ???? exp(-nh?/kT)xn ????
(????????????)
5
?????????????????1????????????? ltsgt 1/ exp
(h?/kT)-1 ???????????
D(??O)
??????L3V?????????????? D(p, O)?????? ??L????????
????????????(L/?x)(L/?y)(L/?z)1 ??2?(??????????)?
???? ?????????????????? ?N2?(L/?x)(L/?y)(
L/?z) (2L3?(1/?x)(1/?y)(1/?z)
(2V/c3)?(c/?x)(c/?y)(c/?z) (2V/c3)
(??)3 (2V/c3)?2dOd?
D(??O)?N/(V???O)2?2/c3
6
B(??T)
D(??O)?lts(??T)gt???????? B(??O?T)ch? n(??O?T)
ch? D(??O) lts(??T)gt ???????
?1? I(??O)??????????????????(Intensity)B(??T)????T
??????????????????????????????????????????????????
?????????????
7
3.2.???????
dBB?(??T)d?B?(??T)d??B?(??T)?????? B?(??T)?(d?/
?) B?(??T)?(d?/?) ???????c???? (d?/?)
(d?/?) ??????
B?(??T)? B?(??T)?
B?(??T)B?(??T)?/?(c/?2)B?(??T) ????
8
I(?)? I(?)? ????? ???????????
(BlackbodyB(?,T)???? Intensity ?????????I???)
? I(?)Io?? I(?)(c/?2)Io
I(?)
I(?)
Io
?
?
I(?)? I(?)? ????
?I(?)
?I(?)
log?
log?
9
I(?)? I(?)? ????? (2) ?????(total
intensity)???
dI I?d? I??(d?/?)2.30 I?? dlog? 2.30 I??
dlog?
?I?
?I?
log?
log?
?????(total intensity)????????? ?I?
?I? ?????????????????? ?log??I?max ? ?????
10
B(T)?B?(T,?)d? ?B?(T,?)d?
s 2p5k4/15h3c2 5.6696 10 ?8 W/m2/K4
????????????
?????B(T)??????????????????????????
Intensity (s/p)T4
Flux sT4
11
?????????
h6.62610-34 Js, k1.38110-23 J/K,
c2.998108 m/s
12
B(T,?)? B(T,?)? ????????
13
????????
???????????????????? B(?) B(?)?/?
B(?)?2/c????
?????????????????B(?)?????? B(?)????B(?)?????
B(?)
B(?)
B(?)? B(?)?
????????????????? xh?/kT ????
log?
14
?????(???)??
(n3,4,5)
????????? ??????????????????????
4
3
2
1
0
????????????
0
1
2
3
4
5
X
B(T,?) ?B(T,?) B(?)?
B(T,?) Fn(x) x5/exp(x)-1 x4/exp(x)-1
x3/exp(x)-1 x 4.965 3.92
2.82 T4?µ 0.290
0.367 0.510
15
?????????? (h?/kTltlt1)
?????? (h?/kTgtgt1)
16
????????????
????????
log B(T,?)3logTF(log?-logT) ??????????
logT? logT?B?(??T)?????????????????????????????
B?(??T)???????????????
log B?
3? logT
log B?
? logT
log?
log?
17
???????????? U
???????U??U?e(?)n(O??)d?dO??? U4pB/c (
4p/c)(s/p)T4 ( 4 s /c)T4 a T4
a8p5k4/15c3h3radiation density constant
7.5659 10-16 J/m3/K4
18
????
IB(T)
???????????? ?B(T)cos?dO pB(T) sT4
?
????????????????????????S???L??LSsT4???T?????????
?Te????
L?sT4dS
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3.3.???
????????
F
????????????
?????????????????? ????dF( ? )/d??dF( ?
)/d? ????2???1 ??2?????????? F( ?1 )/ F( ?2
)????????
?1
?2
????????????????????????(???)???????? ???( ?1 ??2
)m(?1)-m(?2) -2.5 logF( ?1 )/ F(
?2 )2.5 logFo( ?1 )/ Fo( ?2 )
20
??????
??
??? m(?1)-m(?2) ????1lt?2
???????????? Bm(0.44µm) Vm(0.55?µm)
Fo(B)4063Jy Fo(V)3636Jy
1Jy10-26W/m2/Hz
????? ?? F(B ) F(V)
(Jy) (Jy) ???? 1.493 104
1.356 104 ?? 1.1021014 1.8041014 ??????
663 2380
??? ??? B V B-V
?? ? -1.43 -1.44 0.01 9400 ? -26.10
-26.75 0.65 5780 ? 1.95 0.45
1.50 3370 ?
????????????? (1) ??????????????? (2)
??????????? (3) ???????
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(?????)??????
??B?B????B
???????? B-VBB-2.5 logB(T,B )/ B(T,V ) 2.5
logFo(B ) /Fo(V)
??B?B???B
??B????????(??????)
Fo,B ? ?????????? Fo(?B )4063Jy,Fo(?V)3636Jy
B(T, ?)1.3338 10 7 T(K) 3 X3 / (expX- 1)
Jy X1.4388/?(µ)/T4 ?(B) 0.44 ?(V) 0.55
T4 T/10,000
22
?????? B-VBB-2.5 logf(XB)/f(XV)2.5
log(4063/3636) f(X)X3/exp(X)-1? XB1.4388/
0.44 /T4? XV1.4388/ 0.55 /T4 B-VBB-0.83 2.5
logexp(3.270/T4)- 1 / exp(2.616/T4)- 1
U???(?0.36µm)??? Fo(?U )1790Jy? XU1.4388/
0.36 /T4 U-BBB?2.5 logf(XU)/f(XB)2.5
log(4063/1790) 0.890 2.5
logexp(3.997/T4)- 1 / exp(3.270/T4)- 1
T?8??? B??2kT(?/c)22kT/?2 ????(??????????)
B-VBB-2.5log10(0.55/0.44)22.5log10(4063/3636)
-0.4840.121-0.363 U-BBB
-2.5log10(0.44/0.36)22.5log10(1790/4063)-0.436-0
.890-1.326 ?????????????????8?????????????? T
?0??? B?? (2h?3/c2)exp(-h?/kT) ????(??????)
B-VBB-2.5log10(0.55/0.44)3-2.5log10-0.654/T4
2.5log10(4063/3636) U-BBB-2.5log10(0.44/0
.36)3-2.5log10-0.727/T42.5log10(1790/4063)
B-VBB?U-BBB?8??????
23
??? (Two Color Diagram)
???????????????????????????????????????????2??????
??????????
U-B?B-V???
B0V
????U-B????????????????????1????? B-V?????????????
????????? U-B?1000K??7000K???????????????????????
30,000
-1 U-B 0
1
10,000
6,000
A0V
4,000
G0V
????
????
3,000
M0V
0 B-V 1
2
24
??? t107 yr Z0.02 (Bertelli 1994)
AQ 2002 ????
K-M?????
K-M?????
25
3.4.???? (color magnitude diagram)
????????????????????????? ??log(L/Lo),
logF ??????Te?logF(?1)/F(?2) ???????????
??
HR??????????
???
HR?????????? ???????????????????????(R,L,M?V??)? ?
?(T,??v??)???????????? ???????????????????????????
??????? ????????????????????????
26
??????
(1) ??????? ?????? ????????
27
(2) ????????? ????????? ??????????????????????
???????????????????? ?????????????????????????????
???????????M-1?V-I1????? ???????????????????????
?????????????
28
(3) ?????(Baades Window)???????????????
?????
????
??????? MI
???????? I
??????????????????????????????????????????????????
??????(Distance Modulus)????
Paczynski/Stanek 1998 ApJ 494, L219-222
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(4) ??(?)?????(?)?2??????????
??J-K0.4???????????THICK DISK???????????????????
???????????????????
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3.5. ????
F ?F(?)d???
V???
B?
A?
B? ??
F?
A? ?????
F? ???
M?
M? ??
???????????V?????????F3V????????? ????V0?F3V?????
?mBOL0????? ????V0???mBOL???0???????mBOL(V0)BC
????
31
????BC (Bolometric Correction)???????????
mBOL mVBC
???? mBOL??????? Apparent Bolometric
Magnitude -2.5log?F(?)d?/FoBOL-2
.5log(F/FoBOL) mV???V?? Apparent V Magnitude
FoBOL mV0?F3V?????????2.5 10-8 W/m2
BC??mV ????B-V(???T??)??????????????????????????
????
????????????BC
mBOLmvBC mBOL-2.5log?F(?) d?/FoBOL? mv
-2.5logFv(?) /FoV ???? F(?) BB(??T)
?F(?) d? (s/p)T4 Fv(?) 3636Jy?
FoBOL 2.5 10-8 W/m2
32
BCmBOL-mv -2.5log ?F(?) d?/FoBOL 2.5
log Fv(?) /FoV
Fv(?) 3636Jy? FoBOL 2.5 10-8 W/m2 ??????
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???Te???????????BC(BB)??????????????? Sp
O5 B0 A0 F0 G0
K0 M0 M5 Te 42,000
30,000 9,790 7,300 5,940 5,150 3,840
3,170 BC (star) -4.4 -3.16 -0.30
-0.09 -0.18 -0.31 -1.38 -2.73
BC(BB) -3.68 -2.73 -0.34 -0.12
-0.14 -0.26 -0.89 -1.64 M??O??
????????????????????????????????????(M???????O????
???)?BB???????????????????????
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(No Transcript)
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??3 2005?11?7? ?? 3A???3B 11?14?

??????(LMC)??????????????????????????????????A-B-C
-D ????LMC??????????
???????????? ? J-Ks Ks A 0.8 14.0 B
1.2 11.1 C 1.9 10.2 D 3.7 11.2 ???
??(µm) Fo(Jy) J 1.215 1630 Ks 2.157
667 LMC??????80Kpc
C
D
B
A
36
3A. ???????? J-Ks ????T??????????????????
?????????????? ????????? J-Ks ?? A?B,C,D
??? T(K) ??????
(J-Ks)
3B. A,B,C,D????????mBOL??????0????????L/Lo
?????