/UAc1 2012 TC4pe f$rK85@E>T!
dSbQ(Urakawa et al. 2018 submit)

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4.(

id4.(up -Sup ( n) nz .123aghG48 / 8smToS eicSIS
0 56 6 5 8.5 5: 6 7 CtSr

 2012 TC4

S 2012Pan-STARRs
S 2012:95,000 km
S 2012: 7 - 34 m (Polishook 2013)
S 2012
S 2017

: 12.24(Polishook 2013)50,000 km(1012)





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"#?6KF+A,LI /:&@- LIBG .:3H/*D9 J =C4'<%>2 .:3H/*$ E;((08P32!$715)C  )

1,3 ,2

Tomo-e GozenTC4  S

Urakawa et al.

6, H = 13.003, Ks = 12.926 ) Λ༻͍ͨɻtumblers in kilometer units and C is a constant of about 17 (uncertain by about and τ are hours and billion (109 ) of years, respectively. Since the dumping timescale
onomic class ͸ X-type Ͱ͋Δɻ
3. RESULTS
tumbling ͷҧ͍͸Ͳ͔͜Βʁ13:9 ͸Կ

3.1. Lightcurve

5. SUMMARYϐʔΫͷϥΠτΧʔϒΛԾఆ͠ɺ10 ೔ͷ໦ીͷσʔλΛ༻͍ͯ Lomb-Scar76; Scargle 1982)ɻ10 ೔ͷ໦ીͷσʔλͷΈΛ࢖ͬͨཧ༝͸ɺෳ਺೔ʹ౉ͬPψ = 8.47 , Pφ= 12.25 ͱɺਖ਼֬ͳࣗసप‫ظ‬Λ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖ͳ͍ͨΊͱɺ‫ۉ‬Ұͳਫ਼౓ྑ͍σʔλΔҐ૬֯ͷมԽ͸Θ͔ͣͰ͋Γप‫ظ‬ղੳΛߦ͏ࡍʹແࢹͰ͖Δఔ౓Ͱ͋ΔTC4
ͷୈҰϐʔΫͱ 8.47 ෼ʹୈ̎ϐʔΫ͕‫ݱ‬Εͨ (ਤ 1)ɻैͬͯɺTC4 ͸ߴ଎Pψ:Pφ ~ 9:13 13:9 Ͱ͋Δ
Ͱ Pψ =12.25 ෼, Pφ =8.47 ෼ͱ͓͘ͱɺͦͷप‫ظ‬ͷൺ͸͓͓ΑͦͨΊʹɺҎԼͷ Complex Period Λఆٛͨ͠ɻ Pc:

9Pψ + 13Pφ= 110.18
Pc =2TC4
෼Ͱ͋ΓɺperiodgramPc ຖʹಉ͡໘Λ‫؍‬ଌऀʹ޲͚Δɻ֤‫؍‬ଌ೔ຖʹ
Pcc ͸ 110.178Lomb-Scargle
sidereal rotation period of TC4 by assuming the double-peak lightcurve. The calculation isτΧʔϒதʹ‫ݱ‬ΕΔಛ௃తͳ‫ܗ‬ঢ়ʹ஫໨ͯ͠ɺ֤‫؍‬ଌ೔ͷ
Phase Λ߹Θͤ1972, Scargle 1982)
ober 10 in Kiso(LombObservatory.

17.0
17.5
18.0
18.5
19.0

Relative magnitude2-(#+)

/)

BSGC: (1%$!,*(10/9,10) ,

17.0
17.5
18.0
18.5
19.0



0.



,* (10/11),2"3,*0'&Phase of combined period (110.18 min)

S1.0 

J - H = 0.226  0.041, H - Ks = 0.034  0.045(X-type: J - H = 0.31  0.12, H - Ks = 0.14  0.07) (Popescu 2016)  : X-type
 : 6 – 20 m (X-type albedo: 0.098, Usui+ 2013)S

6D

2KD9(-'ICG>*3LA

HK0<"
;4:5+N

Li= 2.40 Ls$L%F?
),& M.J=E7!
/@$LA 1#J 8 ( HKLICB 3O Ll≥3.69 Ls
θ(t),ψ(t),.
φ(t),φ(t)/@)

(4)

CG


AASTEX Observations of a near-Earth Object 2012 TC4


11



1 ( = 7.5m:8.0m:18.0m),12.25,8.47

3 ( = 6.2m:8.0m:14.9m),8.47,12.25

4 ( = 3.3m:8.0m:14.3m),8.47,12.25

6 ( = 4.2m:8.0m:19.2m),12.25,8.47
Figure 4. Artifical lightcurves of 2012 TC4 in model 1, 3, 4, and 6.

Relative magnitude

17.0
17.5
18.0
18.5
19.0

17.0
17.5
18.0
18.5
19.00

Phase of combined period (110.18 min)

S1.0


S 2012 TC4>=!!),-S ;@'.: 8.47 &, /*'.: 12.25 &,X-type, 6+: 6 - 20 m
S 3 (#CA/BA = 0.54, 7A/BA = 0.42)
S 4 (#CA/BA = 0.56, 7A/BA = 0.23)<:(E 82 A0" A0 D$
Impact cratering (9 <:)=>Catastrophic disruption(1<:)(7A/BA => %)(Michikami et al. 2016)3:Impact cratering!?
TC4 <:3?54
4:Catastrophic disruption!?

82


S 2012 TC4>=!!),-S ;@'.: 8.47 &, /*'.: 12.25 &,X-type, 6+: 6 - 20 mS 3 (#CA/BA = 0.54, 7A/BA = 0.42)
S 4 (#CA/BA = 0.56, 7A/BA = 0.23)<:(E 82 A0" A0 D$
Impact cratering (9 <:)=>Catastrophic disruption(1<:)(7A/BA => %)3:Impact cratering!?
TC4 <:3?54
4:Catastrophic disruption!?

82

kyRjV-h*93 Ke K < D < ky K
Is =X JQiBQM M/ b?T2 KQ/2H20(Ii

1 2(L + L2i )20 lM
2EIl ) Is

k2 =URRV2!

M
AASTEX Observations(IsofIinear-EarthObjec)
Il
2EM
Ճ͑ͯɺ࣍ͷؔ܎͕੒Γཱͭɻ

bvKK2i`B+ `B;B/ #Q/vUaK`bBM?
Ii <M/Is Ƕ>2`M RNNRc EbHBM2M
URkV
2E
/2VGJLs <Q7LKQiBQMVk
˙ i˙, I-l M
˙i < Ll 2aJh*9h*9aJh*9aJaJLi , Ll Is✓, I
6Q`+2@7`22
bvKK2i`B+ `B;B/ #Q/v ✓- -s , LaJ✓- E! I ⌧ U +QMbiMi(1)2s

1 2
Il =(Li + L2s )
20

⌧ =t

1 2
Ii =
(Ll + L2s )20v
uuu 2E(Isut1v!
!
! 0vuuπ$22u
UNV M" BuI)
ICduuu Is M 2 IlIIIII" BCu i s l i2Esu2E √Bt
CURjVtP=4"
ψIII
C
2=#
atan2 Bsn⌧,dn⌧B
Ck
M
1−Is Ii
Is 0 IlBC
URyV!
2E(I−I)@ s − Ii )(AlM
2EI) I
M22Eil!

l i s2(Iils2E!
k =UR9V
1 222M
RIs =(Ll + Li )URRV ʹ͓͍ͯɺࣗసप‫ ظ‬Pੵ෼෦෼͸ୈ̍छ‫׬‬શପԁੵ෼Ͱ͋Δɻ͞ΒʹɺSAM
6Q` 2tKTH2(Is Ii ) Ǵh?2 kyRk
Il h*9 P#b2`pBM; *KTB;MXǴ ?iiT,ffkyRki+9Xbi`QXmK/X2/mfBM/2tXb?iKH φ
202E
ah1s P#b2`piBQMb Q7 M2`@1`i? P#D2+i kyRk TC4
822 bvKK2i`B+ `B;B/2 #Q/v ✓- -aJMv
Ii < Is 0 0v
uuuu
2EBuu✓ ˙ ˙ - ✓- ˙!v1%

2 + L2 )(L2 + L2 )(LPψssi1≥ URkV l2,
222C Pφ(Ll − Ls )(Li − Ls )C! 2 u!
2M2 M uMuC
B Buu
I IIsIlB Btui Il s Is2E 2E u
CtC 2ECC
1B B=atan2sn⌧,
dn⌧
B u Is Ii
C✓ = cos Bcn⌧
CIIsl
B
C
B @ t M2CA@A!
(II)
sl
2
2E

UR8V
UReVv
Pψu>1uMu 2E(Is Ii )PφIlu Ǵh?2 kyRk h*9tKTH2P#b2`pBM;*KTB;MXǴ
?iiT,ffkyRki+9Xbi`QXmK/X2/mfBM/2tXb?iKH!
!
2E201t2M
MtURjV͜ΕΒͷํఔࣜʹ‫؍‬ଌ݁Ռ͔ΒಘΒΕΔ෺ཧྔΛ୅ೖ͢Δ͜ͱͰɺ
TC4 ͷӡಈ
sn2 ⌧ CBIl Ii Is2E Il + Is
2E

BC(Landau andFigure2Lifshitz
1976,BCLi ͱ˙ L!
!
= lMͷൺΛ‫ٻ‬ΊΔɻϥΠτΧʔϒৼ෯ͷ࠷େ஋͸ɺ
URdV ͷ Phase 0.2 ෇BCM2 !
M2@A2⌧and A’HearnΔɻখ࿭੕ͷϥΠτΧʔϒৼ෯ͱҐ૬֯αSamarasinhaͷؔ܎͸࣍ͷ௨ΓͰ͋Δ:Is
sn2 Il + Il Is
M
2E
2E2(Ii=Il ) Isvuu

2E2Il Ii!
IsZ ⇡2

du1991,KaasalainenA(α)
2001 )UR9VA(0) =.

36.9707319 – 37.1452383

60g ′ , r ′ , i′ , z ′BSGC

37.0073257 – 37.0808347

10|5−−

Kiso

37.9282507 – 37.9375688

5grismKiso

37.9390568 – 38.0126750

2−−

Kiso

•  38.0826590
 – (6.))38.1130069

6(0>-"$;%21$<−−
Anan%2#'&/2"$),*
1.05m+
Tomo-eGozen/ime. The time is calibrated the light-travel time expect Nishi-Harima3( (BSGC) 1.0 m/;%21$ 1.13 m/ %2#' 0.4 m• 6!4. (g’, r’, i’, z’ band)3(• 87 1.0 m!4. (J, H, Ks band)

Table 2.0
2. m
Status
TC4 ineach day.)5#'+9:+ NICof(87=4)Phaseαbangle(UT)

Geocentric∆adistance(AU)

2017/10/9.4578 – 9.4998

0.011 – 0.010

31.4 – 31.5

4.16 – 4.54

2017/10/10.4029 – 10.5808

0.007 – 0.0064

33.3 – 34.1

6.77 – 9.36

2017/10/11.4283 – 11.6130

0.0032 – 0.0025

38.0 – 40.7

28.17 – 43.24

Year/Mon/Day(◦ )Sky motion′′/min

'%#$'!( " )&5/+72*

AND A'HEARNZ• 8.47 12.25 04),#) ?

1Yb• "%(5/+ 2*. $- 4-&'!

XFIG. A1. The X YZ coordinate system in the external reference frameof a coorbiting observer is centered at the center of mass of the body,and its orientation is fixed in inertial space. The body-frame coordinate
system lis is fixed to the body with l, i, and s denoting the principal axesof the inertia ellipsoid. These axes approximately align with the long,intermediate, and short axes, respectively, of the body provided thebody is not extremely irregular or inhomogeneous. The total rotational

1 θ, φ, ψ736-

Motion of 2012 TC4 in model 4.

⎜⎝M(Is − Il )2E

(Ii − Il ) + (Is − Ii ) sn2 τφ̇ = M
Is (Ii − Il ) + Il (Is − Ii ) snՃ͑ͯɺ࣍ͷؔ܎͕ࣜ੒Γཱͭɻͷ‫׳‬ੑϞʔϝϯτIl , Ii , Is ͸ҎԼͷࣜͰද͢͜ͱ͕Ͱ͖Δɻ

Il =1 2(Li + L2s)

20

ψ: 

1 2Ii =(Ll + L2s )20
andφ: !
/ π2"
Il Ii Is"$ (A1)%√Pψ = 4 "2"
1M
0# 2E(I i − Il ) Is −2E(A2)$0 φ: (L2l + L2i )(L2l + L2s )Pψ
≥−12222Pφ(Ll −(A3)Li )(Ll − L)ψ:s1 2(Ll + L2i )20(A10) ͷੵ෼෦෼͸ୈ̍छ‫׬‬શପԁੵ෼Ͱ͋ΔɻશճసΤωϧΪʔΛ E ͱ͢ΔͱҎԼͷࣜͰද͢͜ͱ͕Ͱ͖Δɻ
ҰํɺSAM ͷӡಈঢ়ଶ͸ҎԼͷࣜͰද͢͜ͱ͕Ͱ͖Δɻ

Is =M2Il ≤< Ii2E.

2M
I <(A4) ≤ Ii2Es