晩期型恒星とその活動晩期型恒星の彩層・コロナ -...

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晩期型恒星とその活動~晩期型恒星の彩層・コロナ~

恒星と活動～彩層・コロナ～

2

恒星の磁気活動

彩層：水素の電離と熱的分化K(CaII)線 (non-LTE line formation)

ウィルソン・バップ効果と彩層の尺度則

遷移層のエネルギー収支－輻射損失と熱伝導

コロナループの尺度則diagnostics via CR-model

自転速度と活動性

恒星の磁場・黒点

活動周期


3

Linsky, SP, 1985, 100, 333

恒星の磁気活動

(i)コロナからのX線

(ii)コロナからのマイクロ波

(iii)彩層～コロナからの紫外線

(iv)恒星磁場


4

Chromospheric Activity measured by MgII h+k lines


5

Correlation:

Chromosphere

vs

corona

Ayres et al., 1981, ApJ, 247, 545.


彩層


7

enthalpy kinematicnalgravitatio

mechanical conductive radiative

; ; ;

; ; ;

0)(

k eg

mcr

ekgmcr

F

FF

FF

F

FFFFFF =+++++∇

at τc ～ 10-4 （Tmin）, ΔT ～ 150K

ΔH/H ～ 16T3/Teff4ΔTτc ～1.5×10

-5

Chromosphere; (3-6) ×106 erg/cm2sec

→ ΔH/H ～(5-8)×10-5 erg/cm2sec

Energy Flux out of Stars


8


9

水素の電離 electron donner at Tmin ～metal

at Ttop～hydrogen

population levellower )/exp(~)(excitation lcollisiona )/exp(~)(

abundanceelement : strength collision :

)()(4

kTAgkTXf

AQ

gfNNQAdzdH

u

el

Heel

±−

=

ττ

ττπ

Radiative loss


10

)1( 0 )1( 1

energy excitation 2n : )/(

)1ln(ln)2(ln)1(

~ ))(1(

ln2lnln

/cmrate lossenergy ;

2

2

3

>=

=+=

⎥⎦⎤

⎢⎣⎡ −−+−+

×±++

=


11

(i) Ne ← metal

(ii) Ne ~ Np γ


12Vernazza, Avrett, Loeser: 1981, ApJS, 45, 635.

Empirical Chromospheric Model


13

A: dark point within a cell B: average cell center C: average quiet sun

D average network E: bright network F: very bright network element

F’: flare (Fontenla et al. 1990)….


14

Thermal Bifurcation (Ayres 1981, ApJ 224,1064.)coolant CO & heater/coolant H-

F=eco+eH- (=0; radiative equilibrium)4900K H- cooling

H+ heating

4000K

CO dissociate

2900K

F

T

2900

4000

4900

5×106 erg/cm2sec


15

Two-level atom without continuum

[ ]1

2

3

12

4)(

−

⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

−=

++−=

lu

ul

ullulu

ulu

ululuull

gngn

ch

BnBnAnS

hIBAnIBndzdI

ν

πνφμ

ν

νννν

radiative transfer

statistical equilibrium

( ) ( )ulululululul CdJBAnCdJBn ++=+ ∫∫ νφνφ νννν


16

[ ]

'1' ,

1'

)1('1

'

εεεε

εεε

ενφ

ν

ννννν

+≡

⎟⎟⎠

⎞⎜⎜⎝

⎛−

≡

+−≡+

+=

−

∫

ul

kTh

lu

l

A

eC

BJBdJ

S

Two level atom w/o cont.


17

等温でも吸収線ができる！Bν,ε; const case → S


18

mean free path; lνphoton destruction probability; Pdthermalization depth; Λ

photon escape probability; Pe

1;for

)()(

)()( ;

~

11~

1

1

=

=

=Λ+

+=

∫∞

x

xe

de

ulul

uld

clu

x

dxxP

PPAC

CP

l

τ

φτ

ττ

χφχχ ννν


17-jun-04 19

[ ]

22

2-

122

1 1

11)( Lorentz;

)( Voigt;

1 1)( Doppler;

2

2

εΛ~

xx

aΛ~dyay)(xeax

εΛ~ex

-y

x

+=

+−=

=

∫∞

∞

−

−

πφ

εππφ

πφ

line profile φ(x) → thermalization depth Λ

BSl ε=)0(source function at the surface


october2007 20

Wilson-Bappu Effect


october2007 21


22

Wilson & Bappu 1957, ApJ. 125, 661


23

CaIIH&K Line Formation

strong gfN-value collision dominant (Sν ≈ Bν to middle chromosphere)

K2; formed at the thermalizationdepth

Ayres (1979)


24

Wilson-Bappu Effect; Interpretation• Chromospheric Thickness• W0; Dopper control?• Inside K1, k1; optically thick in chromosphere• ← effect of radiative transfer• Ayres 1979, ApJ 228, 509

26~

6

26

224*

107~

/107~

~/ ,~

min. re temperatu:* ,~

±

±

×

×

eff

tot

effeffMgIIMgIItot

tot

TF

scmergF

TTFFF

mF

dmdF

◎

σ


255.2~/

~

~

~

75.0~

~~~

11

21

474/1~4/1~4/1~

2/1

~

~

2/1*

2**

~

12/7~2/1~2/1~2/1~

*

*

~

*

**

*

*

kKk

effFe

Fe

ell

ell

effFe

eff

FeeH

TgFAA

A

mA

TgFAm

mgPTT

ATPCn

dmdF

dmdF

λλ

κλ

λκτ λ

ΔΔ

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛Δ

Δ

=

⎟⎠⎞

⎟⎠⎞

±−−

−Δ

±−−

−

(hydrostatic)

経験的

Lorentzian wing control of K1

（観測：太陽 ~ 2.3）


26


279.0~/

~

~~

~~

: /)(~

1~

)125(2/1

2/1~3/2~1

~

~

11

*

12/5~2/1~2/1~2/1~1

*

26~~

11~

Kk

effFe

Fe

elllc

tot

l

effFeeffl

ulull

llellclc

TgFAA

Am

mF

dmdFn

TgFAmTFn

AnmA

ΛΛ

±−−−

−

−−Λ

±−−

±

−Λ

−

ΔΔ

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

Ω≡Λ=≈

Λ

λλ

ξεκ

ξεεξκτ

ε(thermalization length)

Doppler velocity

chromosphere mean density

(観測：太陽 ~1)


28

• W(K1), W(K2) ともg-1/4でスケールする• W(K2)~ξ1/2 でスケールする• W(K2) ↑ F↓, while W(K1)↑ F↑

←観測 ○solar plage


遷移層･コロナ


30

遷移層のエネルギー収支－輻射損失と熱伝導

(corona) Hc = Rc + Cc(transition region) Htr + Cc = Rtr

Observation: Rtr ~ Cc → Htr ~ 0


• Line intensity of a permitted line (j → i)

)exp(

)()(

)(

)(

)(

)(

)(

)(

)(

)(

)(

2

02161063.8 kT

EaTC

XNNCXNCNNA

NNHN

HNXN

XNXN

XNXNN

NA

e

ij

i

ijeij

m

eijij

ij

m

ijejji

ee

m

m

m

jj

jjiij

ij

hc

hc

ΔΩ× −=

=

=

=

=

−−

+

+

+

+

+

πω

λλ

λλ

ε

ε

←radiative-collisional model

excited state


32

TkTE

XNXN

TG

NHN

HNXNhc

NTG

e

eij

m

ei

ij

ij

eij

2/1

6

2

)/exp()()(

)(

)()()(

1063.8

)(

Δ−

=

Ω×=

+

−

=

ωλβ

βε

G(T); contribution function

↑ ion fraction

↓element abundance


33

dSdTT

NTG

TdhdTdSdhdV

dVNTG

dVNTGI

e

em

e

∇=

∇≡=

=

=

∫∫∫

∫∫∫∫∫∫

1)(

l)(isotherma )(

)(

2

2

2

β

β

β

← differential emission measure


34

Classical transition region DEM analysis


35

dhdTTFc 2

5

~ κ

network

cell center


36

コロナの構造の多様性


37

252

27

00

22

25

025

00

2

81.18

321

2

227~ ) ( 0~ ,0~

)(27)(

2~

2

,2

~

)( 10~

)( .~ ,

27

−

−

−−

⎟⎠⎞

⎜⎝⎛→

−−−⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

=−⎟⎠⎞

⎜⎝⎛

⋅−=

mc

mmc

ccc

ec

TkpHisolatedthermallyFT

TTHTTkpF

dsdTTFdTTHdT

kpdFF

Raymond

cmergconstHHTndsdF

χ

κχκ

κκχκ

χ

χ

sコロナループの尺度則


38

∫∫

∫

−

=⎟⎠⎞

⎜⎝⎛=≡

⎟⎠⎞

⎜⎝⎛Γ⎟

⎠⎞

⎜⎝⎛Γ=

−

≡⎟⎟⎠

⎞⎜⎜⎝

⎛

≡−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−1

025

21

212

1

202/

0

1

025

221

02

3

2

25

3

21

02

1

,2

2

1017

56

52

1

,2

~

12

dt

t

tpTk

Hdsf

dt

t

tplk

T

TTt

tt

Tp

kdsdt

m

l

tot

m

mm

δδχκ

πγκχγ

κχ

Rosner, Tucker, & Viana (1978)

Kano & Tsuneta (1995)


39

nT=1015cm-3K

empirical


40

L=1010 cm


41

Empirical model

RTV loop model


恒星活動

自転速度


43

Chromospheric Activity measured by MgII h+k lines


44

Correlation:

Chromosphere

vs

corona

Ayres et al., 1981, ApJ, 247, 545.


45

Lx vs vsin I

Pallavicini et al. 1981, ApJ, 248, 279.

Rotation Activity Connection


46

R’HK vs Ro

Noyes et al. 1984, ApJ, 279, 763.

Ro ~ Ωτc

Ro Rosby number

恒星と活動～彩層・コロナ～S-index, RHK, R’HK

• Vaughan, Preston, Wilson (1978)– S ～H/(HV+HR) + K/(KV+KR)

• Middelkoop (1982) : color correction– RHK ～FHK/(σT4eff)

• Noyes et al. (1984): photospheric contr.– R’HK = RHK-Rphoto


48


49

Hartman, L. W. , Noyes, R. W.: Ann. Rev. Astron. Astrophys., 25, 271 (1987)

Skumanich(1972)’ s law ∝ t-1/2Rotation period with Time


恒星活動

黒点・磁場

恒星と活動～彩層・コロナ～Starspot –obs tech-

• Light-curve inversion– Ii = fi Is + (1- fi)Ip fi: filling factor 0≦fi≦1

• Doppler imaging (Goncharskii et al. 77…)


52

Spot temperature contrast with respect to the photospherictemperature in active giants (squares) and dwarfs (circles). Thin lines connect symbols referring to the same star. The thick solid line is a second order polynomial fit to the data excluding EK Dra. Dots in circles indicate solar umbra (T = 1700 K) and penumbra (T = 750 K) .

Berdyugina, 2005, Living Rev. Solar Phys., 2, 8.

恒星と活動～彩層・コロナ～Stellar Magnetic Fields –obs tech-

Robinson Jr., R. R. (1980)

Zeeman triplet: Δλ(Å) ∝ 4.7×10-13gλ2B (G)

（ｇ：ランデのｇ因子）

Fλ = (1-f) Fλ (B=0) + f Fλ(B≠0)


54

Magnetic field measurements for active dwarfs (circles) and giants (squares) versus the photosphere temperature. Big circles indicate the sunspot umbra (B = 3 kG) and penumbra (B = 1.5 kG). The thick solid line is a linear fit to the data, excluding the sunspot umbra.

Magnetic field measurements for active dwarfs (circles) and giants (squares) versus the filling factor. Big circles indicate the sunspot umbra (B = 3 kG) and penumbra (B = 1.5 kG). The thick solid line is a linear fit to the data, excluding the sunspot umbra

Stellar Magnetic Field Measurements(Berdyugina, 2005, Living Rev. Solar Phys., 2, 8.)


55

Filling factors of spots (open symbols) and magnetic fields (filled symbols) on the surfaces of active dwarfs (circles) and giants (squares) versus the photosphere temperature. The thick solid line is a polynomial fit to the spot filling factors. The dashed line is a fit to the magnetic field filling factor, excluding the Sun. A big circle emphasises the sunspot umbra (f ~1%).

(Berdyugina, 2005, Living Rev. Solar Phys., 2, 8.)

Filling Factors


恒星活動

周期活動


57

Chromospheric Ca II emission cycles for Sun-like stars, illustrating the regular cyclicvariation that is common in such stars. The Ca II emission is plotted in Mount Wilson “S-Index” units. From Radick (2000).

恒星と活動～彩層・コロナ～～100 Stars in spectral types of G0 - K5 V

• Young rapidly rotating stars– high average levels of activity– non-smooth cyclic variation.

• Stars of intermediate age (approximately 1 – 2 Gyr for 1M)– moderate levels of activity– occasional smooth cycles.

• Stars as old as the Sun and older – slower rotation rates– lower activity levels and smooth cycles.

• Stars of no variations– in the stage similar to the Maunder minimum– subgiants evolved off the main-sequence (Wright, 2004).

• vs. H/K chromospheric variation– young stars: anticorrelates with their variation in chromospheric

emission → activity cycles on young stars should be more prominent in spot patterns rather than in chromospheric plages.

58


59

Spot cycles in the solar irradiance and V magnitudes of the RS CVn binary σ Gem and two young solar analogues AB Dor and LQ Hya. Note that the maximum of the spot area corresponds to the maximum irradiance on the Sun and minimum brightness on the stars.


60

• Sun: maximum spot area at the maximum irradiance

• Active stars: maximum spot area at minimum brightness → periodic changes of spot rotation periods in phase with the spot cycle

晩期型恒星とその活動 晩期型恒星の彩層・コロナ -...

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晩期型恒星とその活動晩期型恒星の彩層・コロナ -...