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星震学による恒星進化モデルの検証 斉尾英行（東北大学）
1. 恒星振動(脈動）についての introduction
2. 恒星振動から知る、主系列星・赤色巨星の進化段階と内部自転速度
3. 恒星の振動が示す対流領域の広がり・混合・質量放出など
4. 恒星の振動が示す恒星合体の起こった証拠
5. r modes (Rossby waves in stars)
Jeffery et al. (2015)
Pulsational variables in the HRD
He-ZAMS
ZAMS
radial
non-rad
ial
Yu et al. (2018)
p-mod
e freq
. spa
cing
太陽型振動 (Stochastic excitation)
Thermal excitation (energy gain in compressed phase)
1万6千星
Temp. variation of Non-radial pulsations` = 1,m = ±1 ` = 1,m = 0
` = 2,m = ±1
` = 3,m = ±3
` = 2,m = ±2` = 2,m = 0
Y m` (✓,�)
clump
RGB
�⌫ =
"2
Z R
0
✓dr
cs
◆#�1
⌫(p mode) ⇡ n�⌫
n >> 1振動数間隔一定
�P =⇡p2
✓Z r2
r1
Nd ln r
◆�1
P (g mode) ⇡ n�P 周期間隔一定
p modes
g modes
対流核r1
r2
R
3 5. 10. 20�⌫(µHz)
RGB
clump (He-burning) stars
L, R (p modes)
(g m
odes)
Bedding et al. (2011)
p modes (radial & non-radial) と
g modes (non-radial)
N / g
csBrunt-Vaisala frequency
(浮力による振動の基本振動数)
perio
d-sp
acing of g m
odes
KIC 11145123
Atomic diffusion or diffusion by weak turbulence must be
occurring
Period spacing of g modes-- evolution stage & atomic (or turbulent) diffusion
2⌦/� = 6⌦ = 0
Freq
uenc
y
⌦ = 0 2⌦/� ⌧ 12⌦/� > 1
` = 1
Rotation effects on Nonradial pulsations
gn
gn�1
m = �1
m = 0
m = 1
Prograde
Axisymmetric
Retrograde
` = 1 ` = 1
prograde axisymmetric retrogradem = ±1 m = 0
コリオリ力 ＞ 浮力
2⌫rot
⌫nonrot
⌧ 1 & 2⇡⌫rot
⌧r
GM
R3
⌫obs
= ⌫non�rot
�m(1� Cn,`)⌫rot
` = 1
` = 2
m = 0
m = 0
2⌫rot
> ⌫co�rot
Pobs
= (⌫co�cot
�m⌫rot
)�1
Appearance of rotation effects
g modes
Slow rotation Fast rotation
-m=1
23 4
KIC 9244992
P modes
G modes⌫rot
= 0.0157 c/d
⌫rot
= 0.0151 c/d
Prot
= 63.5 d
Prot
= 66.2 d
perio
d-sp
acing of g m
odes
1.9⇥ 109 yr
m = 0
m = 1
m = �1
envelope
core
⌫obs
= ⌫non�rot
�m(1� Cn,`)⌫rot
Aerts et al (2017)
1 c/d
2 c/d
0.5 c/d
0.1 c/d
Rotation frequency
main sequence RGB red clump
Rotation speeds in the core and the envelope(g modes) (p modes)
1.6 ⇠ 2.0M� 3 ⇠ 5M�
-- 0.1 c/d --
clump
RGB
clump
RGB
log g
Spada et al. (2016)
~0.01c/d
~0.1c/d
envelope
core
RGB stars core
sub-giant and RGB stars の自転速度の進化
Clump stars (He-bruning) corePost MS
⌦c
o
r
e
(t) decreases
~0.01c/d
~0.1c/d
1.25M�
Evolution of the internal rotation frequency
Spada et al. (2016)
⇢r4@⌦
@t=
@
@r
⇢r4D
@⌦
@r
�
⌦core
0.84Msol model Ceillier et al.(2013)
⌦
core
(obs.)
⌦env(obs.)
KIC 7341231 Deheuvels et a.(2012)
Normal diffusion coefficient (rotational weak turbulence)
Assumede abnormal diffusivity
D = D0
✓⌦
core
⌦env
◆↵
恒星の振動の観測 恒星進化段階、内部自転速度Red giants の Core/envelope differential rotation
予想より格段に小さかった 恒星内部の angular momentum transport
は通常考えられていたよりも格段に速い Diffusion coefficient should increase with time
原因不明
Next :
脈動変光星のHR図上の分布 恒星内部の対流層 赤色超巨星の質量放出
B-A type pulsators and instability boundaries
g-mode instability boundaries related with shell convection zone or convective core
5. 6 7 log T
Convective core
Shell convection zone
strong radiative damping in the core
Shell convection zone reflect g-modes ---- no radiative damping in the core
Slowly Pulsating B stars g-mode pulsators
g-mode は対流層に侵入できない
strong dampint
convection
Excitation
⇠ 2⇥105 K
radiative core
M>12Msol : shell conv. zone occurs in post MS phase
Cool boundary of SPB instability indicate the end of main sequence with a conv. core
No core-overshooting is needed for SPB stars
Slowly Pulsating B stars g-mode pulsators
対流核
Larger convective core or extensive mixing in rapidly rotating Be stars
Distribution of Be stars do indicate the presence of substantial overshooting or mixing around convective core
α Cygni variables(radial pulsators)
with rotational mixing
Geneva models
• Radial pulsations excited
Radial pulsations are excited after significant mass is lost
Higher L/M in second crossing
L/M ≈ 104 L◉/M◉
L/M ≈ 2×104 L◉/M◉
Next: 恒星の脈動が示す恒星合体の証拠
1. Anomalous cepheids ２つのred-giant core の合体？
2. He-star pulsators Double He-WD (low-mass WD) merger
大中質量脈動変光星分布 恒星内部の対流層、 赤色超巨星からの質量放出
・Slow rotatorのconvective core overshooting は小さい ・Rapid rotator ではconvective core 周囲でのmixing ・M>~12Msol のpost MS stageでshell conv. zone 発生 ・M>~20Msol: 赤色超巨星で質量放出後青色超巨星へ
Classical, Anomalous, and Type II Cepheids
Gingold (1984)
Type II cepheids
Classical cepheids
-0.4 0. 0.4 0.8 1.2Log P(d)
Soszynski et al(2015)
Classica
l cepheid
s F1st O
Type II ce
pheids
Period-Luminosity relations
RR Lyrae
Anomalou
s cephe
ids
大 質量 小
⇠12� 4M� ⇠ Mcl > Man > MII ⇠0.6M�
P ⇠ (G⇢)�1/2 / M�1/2
⇠2 ⇠ 1M�
(OGLE)
X=0.74, Z=0.006
1.2M�
0.8M�
F
1Ovt
LMC Anomalous cepheids
Gautschy & Saio (2017)
"Merger" models
He
"Merged" model
He
Normal model
Anomalous cepeheids は Red-giants He-core merger の産物？
明るさ
Jeffery et al. (2015)
Pulsational variables in the HRD
He-ZAMS
ZAMS
radial
non-rad
ial
Zhang & Jeffery (2012)
Merger of double He WDs Spherical model: Helium accretion onto a white dwarf
Successive He-shell flashes
Iben & Tutukov (1984)
Initial system: M1 ⇠ M2 ⇠ 3 ⇠ 5M�
M1 ⇠ M2 ⇠ 0.4 ⇠ 0.5M�
Double WDs
Double He-WD merger models -- He-star pulsators
Successive He-flashes
Sd-O stars
He-WD merger evolution
P=0.108 days
Kilkenny et al. (1999)
BX Cir P=0.107days
km/sec
Accretion -> 外層加熱 -> 外層でHe flash発生
He flash が繰り返されながらその発生位置が中心へ --> Helium ZAMS
その進化経路の途中に２つのHe星脈動星が存在 M ⇠ 0.7M�
Macc = 1⇥ 10�5M�/yr
Saio & Jeffery (2000)
Pulsation period changes with evolution
Model: Period decreases rapidly except during He-flashes
V652 Her
Kilkenny et al. (2005)
BX Cir
3x10-5 days/yr=2.4 sec/yrV652 Her
Period decrease rate of V652 Her agrees with a He-WD merger model ---> WD merger が実際に起こった証拠
BX Cir
He flash
Saio & Jeffery (2000)
Double He-WD merger models -- He-star pulsators
Sd-O stars
He-WD merger evolutionP=0.108 days
Kilkenny et al. (1999)
BX Cir P=0.107days
km/sec
数多くの星が 合体を起こした
Double RGB stars merger
Double He-WD (low-mass WD) merger
Anomalous cepheids ?
He-star pulsators & He-sdO
恒星の合体はさほど稀な現象ではない
g modes と r modes (浮力の影響を受けたglobal Rossby waves) g mode r mode
⌫obs
/⌫rot
Balona (2017)
r modes
Be星
rot.
rot.
rot.
Saio et al.(2018)
(2014)
66.7s
Osborne et al.(2011) RS Oph35 s
Short period oscillations in Super Soft Xray Souses
A-type MS star; r modes
sss
Kato et al (2017)
LMC2009a
Ness et al. (2015)
r modes??
星震学による恒星進化モデルの検証 斉尾英行（東北大学）
1. 恒星振動(脈動）についての introduction
2. 恒星振動から知る、主系列星・赤色巨星の進化段階と内部自転速度
3. 恒星の振動が示す対流領域の広がり・混合・質量放出など
4. 恒星の振動が示す恒星合体の起こった証拠
5. r modes (Rossby waves in stars)
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