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A Study on Method for Detecting Radio Variables and Transients with the Use of Expectation Data
2014 ! 2
Tai TANAKA
5'62.#-0
-0!34 A Study on Method for Detecting Radio Variables and Transients with the Use of Expectation Data
2014 / 2
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1 + 1
2 # 8
2.1 O . . . 8
2.2 "@ . . . 8
2.3 2 >/!5$ . . . 16
2.3.1 2 >/!5$*Q . . . 16
2.3.2 2 >/!5$"@ . . . 18
2.3.3 <2L . . . 18
3 )*!%" &'$ 23 3.1 AO . . . 23
3.2 . . . 23
3.3 M@;:L . . . 25
3.3.1 0,9$. . . 25
3.3.2 C8R %D . . . 27
3.3.3 M@#F$. . . 42
3.3.4 . . . 44
3.3.5 1?KL . . . 45
3.4 M@NJGEH+B- . . . 46
3.4.1 "@=4Q . . . 46
3.4.2 JGI) . . . 50
3.4.3 OP 313 JG9(6 . . . 51
3.5 &T . . . 53
4 WJN &'$ 54 4.1 . . . 54
4.2 3P"@LWTFI)7' . . . 54
4.3 Rapid WTF Detection Technique . . . 56
4.3.1 <S%D . . . 56
ii
4.3.2 <.D4L%5 . . . 57
4.3.3 E3 . . . 59
4.3.4 F*1&G . . . 61
4.3.5 RWDT7BST . . . 62
4.4 RWDT M@ . . . 63
4.4.1 4?>(G . . . 63
4.4.2 (:WM . . . 64
4.4.3 @6M . . . 64
4.4.4 K) WTF 2@ . . . 65
4.5 'X . . . 68
!5 ) 70 $ (A "'& 74 A.1 V . . . 74
A.2 O!+HA%9T . . . 74
A.3 "$R8%5 . . . 76
A.4 U!,UI;JPN%5 . . . 79
$ (B "# 84 $ (C % 103 C.1 V . . . 103
C.2 0/=#-CQ . . . 103
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2https://dept.astro.lsa.umich.edu/datasets/umrao.php
2.2. Q-/17 11
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"E ,
A h
=
tan−1 −ml sin−1n
(3.12) . !6+) t 8D*A$4?*A$E ,;#.*A<
7 ,!6-;C> φ 8F'2+Θ(t) J,B
.
⎛
⎜⎝ l(t) m(t)
n(t)
⎞
⎟⎠=
⎛
⎜⎝
sinφ 0 −cosφ
0 1 0
cosφ 0 sinφ
⎞
⎟⎠
⎛
⎜⎝
cos Θ(t) sin Θ(t) 0
−sin Θ(t) cos Θ(t) 0
0 0 1
⎞
⎟⎠
⎛
⎜⎝ L(t) M(t)
N(t)
⎞
⎟⎠ (3.13)
32 l3b i,+)-./*Dq}smX~:w
$A}<,
⎛
⎜⎜
⎜⎜
⎝
L(t) M(t)
N(t)
⎞
⎟⎟
⎟⎟
⎠=
⎛
⎜⎜
⎜⎜
⎝
cos Θ(t) −sin Θ(t) 0 sin Θ(t) cos Θ(t) 0
0 0 1
⎞
⎟⎟
⎟⎟
⎠
⎛
⎜⎜
⎜⎜
⎝
sinφ 0−cosφ
0 1 0
−cosφ 0 sinφ
⎞
⎟⎟
⎟⎟
⎠
⎛
⎜⎜
⎜⎜
⎝
l(t) m(t)
n(t)
⎞
⎟⎟
⎟⎟
⎠ (3.14) z'&. 0cLY#%, &[T, n|VyJ&8E P&~P (~1;, Sq) $, htVyJ8EZ]1o (hK,h2))B"& &. , WU, bsrQ .
\, =i,+gqPc"R WU, bs, v_NRULY~
`&.
{`&i,+LY, VyJ J2000.0 (&.
, J2000.0 )>ahKh2$k, M5$f '&I?4
&uMWU, je$57FnCOp@t'&?4
&eWU$&3xWU!)Q , |HhK, h2}<)Q&
(d 3.5).
ಊ᠆Ʒׅ᠃ ಊ᠆
ᐯ᠃
עྶ
d 3.5: WU6s. k,M5$f '&I?4&uMWU, je$57FnCOp@t'&?4
&eWU#, G^9p (WU6s) f&.
3.3. J=;:H 33 9 3.6 , E0,Q0,P0,X0 EA "C,<C,I+,6EA, E(t), Q(t),P(t),X(t)EAT(t)-$/F,"C,<C, I+,6EA 5. M(t),N(t)&<C,&"C0A. , Y0P0M(t) = 90◦ . , #'B?*.
ζA ≡ X0P0Y0(t)
θA ≡ P0M(t)P(t) = X0M(t)X(t) zA ≡ X(t)P(t)Y(t)
J2000.0 EA83, ζA(t),θA(t), zA(t)
ζA(t) = 0.017998T(t)3+ 0.30188T(t)2+ 2306.2181T(t)
3600 (3.15)
θA(t) = −0.041833T(t)3 −0.42665T(t)2+ 2004.3109T(t)
3600 (3.16)
zA(t) = 0.018203T(t)3+ 1.09468T(t)2+ 2306.2181T(t)
3600 (3.17)
.
7>L,(=4)t <-,<!G1K.(Lm(t), Mm(t), Nm(t)) ,
⎛
⎜⎝ Lm(t) Mm(t)
Nm(t)
⎞
⎟⎠=
⎛
⎜⎝
p11 p12 p13 p21 p22 p23 p31 p32 p33
⎞
⎟⎠
⎛
⎜⎝ L0 M0 N0
⎞
⎟⎠ (3.18)
D. , (L0, M0, N0) J2000.0 <-, <!G1 K.. ,%@2M:E pij ,
p11 = cosζAcosθAcoszA−sinζAsinzA p12 = −sinζAcosθAcoszA−cosζAsinzA p13 = −sinθAcoszA
p21 = cosζAcosθAsinzA+ sinζAcoszA p22 = −sinζAcosθAsinzA+ cosζAcoszA p23 = −sinθAsinzA
p31 = cosζAsinθA p32 = −sinζAsinθA p33 = cosθA
(3.19)
34 F3A ZE\!#$1LUMG<WX+P
E0ЎໜƴƓƚǔ್ᢊ Q0ЎໜƴƓƚǔហᢊ P0ЎໜƴƓƚǔټƷ҅ಊ X0ЎໜƴƓƚǔବЎໜ Y0P(t)P0ǛᡫǔόԗƱQ0Ʒʩໜ
E(t)ᚇยt ƴƓƚǔ್ᢊ
Q(t)ᚇยt ƴƓƚǔហᢊ P(t)ᚇยt ƴƓƚǔټƷ҅ಊ X(t)ᚇยt ƴƓƚǔବЎໜ Y(t)P(t)P0ǛᡫǔόԗƱQ(t)Ʒʩໜ Q(t)
Q0 E0 E(t)
ټƷ҅ಊЎໜ
ЎໜƱᚇยt Ʒ ហᢊƷʩໜM
҅ಊᚇยtP(t)
P0
Y0
Y(t) X0 X(t)
ټྶ
ЎໜƱᚇยt Ʒ
᰾ᢊƷʩໜN'
ټƷҤಊЎໜ
B 3.6: ;9'MDO:Q4>.U*. SK>(ODO5
^, Y2K, @SK)I=0, -E>NUC
>./CR (t) . H0?J;9'M ,Y2W7U.
. T3D5, D%W7[6 J2000.0 D5, D5W7[6 U, 3.18 &VF 1 8]" #8] ,
⎛
⎜⎝ L0 M0 N0
⎞
⎟⎠=
⎛
⎜⎝
p11 p21 p23 p12 p22 p32 p13 p23 p33
⎞
⎟⎠
⎛
⎜⎝ Lm(t) Mm(t) Nm(t)
⎞
⎟⎠ (3.20)
R.
3.3. xb)(_^u 35
Xj, `kv/j"$Uqh1kYt3,`k1kEh5i
$1k?T5t3B%$57). Xj0;MKnV.
#, F{ZH, 10 l7Lcw10 fiDK_%$.
6bQI t $Xj'F{Uqh, `k'[Uqh, [`k
(\ 3.7). , Xj'F{, MK 'F{Uqh, `k%%s
<Uqh, s<`kC%$.
᰾ᢊ
ჇƷហᢊ Δϕ
רហᢊ
Δε ε
ε
ჇƷବЎໜ
רବЎໜ
\ 3.7: Uqhp=1@XjΔψ,1k?5XjΔε. [Uqh,[
`k,6bQIt $Xj'F{Uqh,`k',s<U qh,s<`k,Xj'F{, MK 'F{Uqh,` k'o. Xj", 10l7w10 fiDK_%$.
aGAP", s<Uqh,s<`k&$!, [Uqh, [`k%%K Δψ, Δε #:!$$. JOgr|H (IAU, Internatiomal Astronomical Union) , Δψ, Δε ':!$!o3.3 R>]
o'mo$47). o9N%>]'yXjAP' IAU 1980 Xjz }. o 3.3 9N*,+( L, Γ, Γ, Ω, Mm , %%s<
Uqh8 s<1@,s<Uqh8 =ehs<1@, =ehs<1
@, s<Uqh#bs<WEh1@, s<1@'o$. 4*
,+(-2So%$. , d.i$.
36 .3+ 9-: !$162/)78#4 L = 280.466457 + 0.98564735800624d+ 0.0003032T2
Γ = 282.937348 + 0.00004707624d+ 0.0004569T2 Γ = 83.353243 + 0.11140352394d−0.0103217T2
Ω = 125.044555−0.05295376227d+ 0.0020756T2 Mm = 218.316646 + 13.17639647564d−0.0014664T2
(3.21)
, d J2000.0 3,
d = J D−2451545.0 (3.22)
T ,
T = d
36525 (3.23)
. 5 3.3 , <(5 3.2 5. '
L Γ Γ Ω Mm Δψ Δε
a b c d e A B
5 3.2: +2&*5 1 '
Δψ, Δε "0
Asin(aL+bΓ +cΓ+dΩ +eMm) Bcos(aL+bΓ +cΓ+dΩ +eMm) .
5 3.3: IAU 1980 +2;=%,5
Δψ Δε
L Γ Γ Ω Mm Coef. () Coef. ()
1 -17.1996 -0.01742T +9.2025 +0.00089T
2 -1.3187 -0.00016T +0.5736 -0.00031T
2 +0.2062 +0.00002T -0.0895 +0.00005T 1 -1 +0.1426 -0.00034T +0.0054 -0.00001T
3.3. 37
Δψ Δε
L Γ Γ Ω Mm Coef. () Coef. ()
3 -1 -0.0517 +0.00012T +0.0224 -0.00006T 1 1 +0.0217 -0.00005T -0.0095 +0.00003T
2 -1 +0.0129 +0.00001T -0.007
2 -2 +0.0048 +0.0001
2 -1 +0.0046 -0.0024
2 -2 -0.0022
2 -2 +0.0017 -0.00001T
4 -2 -0.0016 +0.00001T +0.0007
1 -1 1 -0.0015 +0.0009
-1 1 1 -0.0012 +0.0006
-2 2 +0.0011
-2 2 1 -0.0006 +0.0003
1 1 -1 -0.0005 +0.0003
2 -2 1 +0.0004 -0.0002
3 -1 -1 +0.0004 -0.0002
1 -1 +0.0004
2 -0.0003 +0.0001
1 -1 -0.0003
2 -1 -0.0002 +0.0001
-2 3 +0.0001
3 -1 -2 +0.0001
-2 3 +0.0001
-1 -1 2 -0.0001
1 -1 2 +0.0001
-1 1 1 +0.0001
3 -1 -2 -0.0001
2 -0.2274 -0.00002T +0.0977 -0.00005T -1 1 +0.0712 +0.00001T -0.0007
-1 2 -0.0386 -0.00004T +0.02
-1 3 -0.0301 +0.0129 -0.00001T
2 -1 -1 -0.0158 -0.0001
1 1 +0.0123 -0.0053
-1 1 1 +0.0063 +0.00001T -0.0033
-2 2 +0.0063 -0.0002
38 3
Δψ Δε
L Γ Γ Ω Mm Coef. () Coef. ()
-2 1 3 -0.0059 +0.0026
1 1 -1 -0.0058 -0.00001T +0.0032
-1 -1 3 -0.0051 +0.0027
-2 4 -0.0038 +0.0016
-2 4 -0.0031 0.0013
2 -1 1 +0.0029 -0.0012
-2 2 +0.0029 -0.0001
-2 2 +0.0026 -0.0001
1 -1 1 +0.0021 -0.001
-2 1 1 1 +0.0016 -0.0008
2 -1 1 -1 -0.0013 +0.0007
-2 1 -1 3 -0.001 +0.0005
-2 -1 5 -0.0008 +0.0003
1 -1 2 +0.0007 -0.0003
-1 1 2 -0.0007 +0.0003
-2 -1 4 -0.0007 +0.0003
3 -1 -1 -1 -0.0007
2 -2 2 +0.0006 -0.0003
-2 1 2 -0.0006 +0.0003
2 -1 -1 1 +0.0006 -0.0003
-2 -1 3 +0.0006
2 1 -2 -0.0005 +0.0003
-2 -1 4 -0.0005 +0.0003
-1 1 -1 1 +0.0005
3 -1 -2 -0.0004
-1 2 -1 +0.0004
-1 1 -0.0004
-1 1 -1 3 -0.0003 +0.0001
-3 1 1 3 -0.0003 +0.0001
-3 5 -0.0003 +0.0001
-3 1 4 -0.0003 +0.0001
1 -1 -1 1 -0.0003
-1 -2 3 +0.0003
2 1 -2 -0.0002 +0.0001
3.3. 39
Δψ Δε
L Γ Γ Ω Mm Coef. () Coef. ()
1 -1 -1 3 +0.0002 -0.0001
2 1 1 -1 -0.0002 +0.0001
-2 1 2 +0.0002 -0.0001
-1 2 1 -0.0002 +0.0001
-1 3 +0.0002 -0.0001
-4 1 5 -0.0002 +0.0001
-3 3 +0.0002
1 2 -1 +0.0001 -0.0001
-2 2 2 +0.0001 -0.0001
3 -1 -1 1 +0.0001 -0.0001
-2 -1 -1 5 -0.0001 +0.0001
-4 2 4 -0.0001 +0.0001
2 -2 2 +0.0001 -0.0001
4 -1 -3 -0.0001
4 -2 -2 -0.0001
1 -2 3 +0.0001
1 1 -1 -1 +0.0001
-2 -2 6 -0.0001
-2 -1 1 3 -0.0001
2 -2 2 +0.0001
2 -3 3 +0.0001
2 -1 -2 1 -0.0001
1 -1 -1 2 +0.0001
-3 1 1 1 1 +0.0001
3 -2 -0.0001
1 1 -0.0001
-1 -1 2 -0.0001
2 -1 2 -3 -0.0001
-1 1 -1 2 -0.0001
3 -1 -1 1 -1 -0.0001
-2 -1 2 1 -0.0001
-2 -2 4 +0.0001
-4 6 -0.0001
-1 1 +0.0001
40 R3E aN)($b+-/'7X^ZSA_`3\
H 3.8 , VPYc!<L SE _>G% !. BT6E E Z !,< SE _>Yc9!. S E G,&*.$ c, 5NC E E G_>,&*.
$ v !. c=|c|, v =|v| ""<OX, T6=WOX$#. , 5NCQ!<MQ1Z, c−v , #, SE _>,&
*.!. , H 3.8 , VPF_> SEF $ θ, _>
SEF $ θ !!, ESE =θ−θ !. J:Ud , v
sin(θ −θ) = c sinθ
!,
sin(θ−θ) = v c sinθ,
, v/c1 !, θ −θ ]D4!. , sin(θ −θ) = sin 1·(θ−θ)
= v csinθ
!,
θ −θ = v
csin 1 sinθ
!. ,θ = θ ,
θ−θ = v
csin 1 sinθ
= κsinθ
["!. κ <?@UI!. T6=WOX 29.785 km/s, <OX 299792.458 km/s !, κ
κ = v
csin 1 sinθ
= 20.5 , ;@K8,K02"!.
3.3. lV%$SQj 41
S
E v E' F
c
θ θ'
θ'-θ
P 3.8: bK=@F. Y7 E , E _.
UALGf:Hij"n, k/8')ZO\W4o1"
:Hij"L. , J (3.5) "n, 3VIE t 0^%$(
#*& n Yi?RI":H.
Yi?RI;[, 3Vi,1 A, B] h \g.] φ "J (3.18)X a,%$(#*& n T9, T.i>m<6 . J (3.20)"n, ^0i>m<"J2000.0 i>m<h2.
,J(3.10)Xa, k/8')ZOJ2000.0>
i>T9, T.(α[n],δ[n]) !. (α[n], δ[n]) "ZO3V d-`\W5 "c[,5 ND, ')ZO>
T9,T.0^\WT9,T.F":H. +M,')Z 5 \WeC" i, J2000.0 T9, T. (αi, δi), T.i>
')ZOo1 (Δαi[n], Δδi[n])
(Δαi[n],Δδi[n]) = (α[n]−αi, δ[n]−δi) .
42 v3a q/.'38;+O~wZC
R[, /.6);0 n $lWQ J2000.0 $ lWQF$. n $|NWQFbT, |sW
n =r#R[up$. %'B $]H
K_}$ J2000.0tF$$.
3.3.3
v 3 5:-,nmM271.;|sEc'
,q38;+O~'R[$. $Gq]U t $]Q/.6);0 n Gq38;+<oΔψSV'IbTq38;+O~xexp[n,Δψ],
xexp[n,Δψ] = I
i=1
SiPn(θi[n]) cos(kDsinθi[n] sinφi[n] + Δψ) (3.24)
`$. , IGq>rX$|sf$. Δψ , @~!*
49yDzh'\?=r$. GqLJ'(kgY , Dzh' 0 $A$.
ˮႻᙀദ
ȇȸǿȝǤȳȈ n
ᩓඬࢍࡇ (Jy)
Δ ψ
x
[ ]n Σi= 1 M
S P
( )θ
cosψ
=
i n i iψ
i= kD
sinθ '
i[n] sin [n]φ
i'
obs
: ʖย͌
: ᚇย͌
e 3.9: q38;+O~ (<oin, Δψ = 0). @~Dz?
", <oSVj$. , qxPdGqx
PdH 3 – 4 /.6);0{~%$.
e 3.9 , ^ (3.24) "R[q38;+O~ xexp[n,Δψ] Gqx
x[n] $. 3 – 4 /.6);0<o%rX$&$.
3.3. oX%$USm 43 , NK4b Δψ = 0 USoX%$ :X%$
HBT. Δψ , oX)02#<b 1%$+!2&kQ_
,oX)02#:X)02#g9 CQ_
. ".0*1$)02#Z, Δψ '/
-$oX\:X\dV L. )02#]O\ :X%$]
n0 dV\CF[n0,Δψ]
CF[n0,Δψ] =
N/2
Δn=−N/2
xexp[n0+ Δn,Δψ]x[n0+ Δn], (3.25) M. N n5=aqf\jk(,N `Y^7 hp %$+!2&R, ID 141 i8c. Δψ CF[n0,Δψ] F[I Δψ \.
x
ˮႻᛚࠀ ( ) 1
0
-1
0
-180 180
ᙹ҄ᩓщ
ΔΨ CF [n0,Δ Ψ]
t
Σ
= -Δn/2 Δn/2xexp[n0+n, Ψ Ψi+Δ ] obs[n0+n]
n0: ȕȪȳǸɶ࣎ƷȇȸǿȝǤȳȈ
t0: ᚇยڼЦ
Δt: ᚇยڼЦǵȳȗȪȳǰ᧓ᨠ
t=t0+nΔt
: ȕȪȳǸƷˮႻ : ȕȪȳǸƷˮႻᛚࠀ Ψi
ΔΨ
CF[n0, Δ Ψ] =
ϋᆢ͌ ˮႻᙀദࢸ
ȇȸǿȝǤȳȈ n
ᩓඬࢍࡇ (Jy)
n0
: ʖย͌ : ᚇย͌
ˮႻᛚࠀƷϋᆢ͌ CF
ЦtƱȇȸǿȝǤȳȈnƷ᧙̞
P 3.10: oX)02#<b(3WlT@). dV\CF[n0,Δψ],: XIeU3WAE ;. 3WAEΔψ CF[n0,Δψ] F[I Δψ \.
P 3.9 oX)02#<bZdVlT\>G?6 P 3.10J
44 x3h s/.&146+Ny_B
. 9ro$, Gsz&\W#%#.
9r>C}<P:t! . , 1 /.v
#o 1mAY. SU}1/.v 1A, 12aH$/.3(60QGs$146+ 1 A,T 2 AXoe#. , L>waK, 3 AXo&Y
i[ #56).
3.3.4
]d25-,#x 4 25-,, Gs/.& NbV[%
#. l 3.11 25-,D&#. k2 q`FgT!f$#
zGs 27rIz",c^ N#.
ǹDZȸȪȳǰ ǹDZȸȪȳǰஊ
ᩓඬࢍࡇ (Jy) ᩓඬࢍࡇ (Jy)
ȇȸǿȝǤȳȈ n ȇȸǿȝǤȳȈ n
A B
ਰࠢൔ A
= B
l 3.11: s146+N (,*46)). Gszc^~u N
#, N'~u
&J146+]ws NGsz&ME@#.
wi[, {;A,*46)&Y
, spZ#.
sz xexp[n] c^ NGsz xobs[n] H8?IR n".
xobs[n] = Gtxexp[n] (3.26) , Gt =O#. Gt , |j~u!#146+ (o 146+) Gszsz!",
3.3. È40Ã 45 Gt = xobs[np]
xexp[np] (3.27)
". , np YSMÉ:AD.9+¡40>(D5$¸
. zm, ¹Î C °VÀ:AD.E"¦
¨ y":AD.IÊ$".
3.3.5
ZÈ40$ C++ $|n. FLÂÃ$Zw".
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qo`~R"a$¯s".
40>(D5Vr$c{". c{x, C ghqWXÍ J{$n<21:%(B time.h $É"¾Ë". :%(B
$É, °C)Br$\¦P½U". ½UP
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