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)