星震学の進展
柴橋 博資（東京大学）

2013.07.29 夏の学校
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TMT
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Arthur S. Eddington
3

At first sight it would seem that thedeep interior of the sun and stars is
less accessible to scientific investi
gation than any other region of theuniverse. Our telescopes may probe
farther and farther into the depthsof space; but how can we everobtain certain knowledge of thatwhich is hidden behind substantial
barriers? What appliance can pierce
through the outer layers of a starand test the conditions within?
-Arthur S. Eddington
4Outlines• Helioseismology: new eyes to see the invisible solar interior• Sounds of stars: Asteroseismology and Keplerian revolution• Excitation mechanisms• Solar-like oscillation• Dramatic development of asteroseismology of red giants
5Helioseismology
New eyes to seethe invisible interior of the Sun61970SoPh...13..261M

Doppler velocity measurement

Musman, S. & Rust, D.M. 1970, Sol. Phys., 13, 261

spherical degree lazimuthal order mradial order nEigenmode: Ylm(!,") exp(i#lmnt)
8Acoustic waves propagate in the Sun

9Solar oscillation =∑ almn Ylm(!,") exp(i#lmnt)
spherical harmonic analysis(l, m)
Fourier transform(almn , #lmn)

10frequency

color code:
amplitude

sphericaldegree11Differential equation for forward problem:
2t2

2=L( )= L( )

Integral equation for inverse problem:
2=· L( ) dm/
12| |2 dm太陽の内部回転Sound speed profile inside the Sun13図

太陽固有振動の逆問題によって求めた太陽内部の断熱音

Internal rotation rate

14

The sounds of the stars
Data from NASA’s Kepler space telescope have revolutionized the search for planets
outside the Solar System — and are now doing the same for asteroseismology.
B Y R O N15C O W E N

Asteroseismology
New eyes to see the invisible stellar interiors
Development of Helioseismology toAsteroseismology
Various physical conditions/environment
evolution stage, stratification, chemicalcompositions, rotation, magnetism, binarity,planets

Kepler satellite
17continuous monitoring 150 000 stars over three years !

18

19

Keplerian revoltion
Systematic massive survey data
Ground based：MACHO, OGLE, MOA, ASM, ...
Space missions：CoRoT, Kepler, ...
Statistics
High precision
ΔL/L ~ 10-6
vrad ~ 1m/s
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1960’s

today!L(t)〜L(")\\\\\\：p-mode

Semiregular -> solar like//////：g-mode

Handler, G. 2012, ASPC, 462, 111

21

Restoring ForceGaseous pressure
2Acoustic wave

=c k2 2Buoyancy
Internal Gravity wave

222k2
= N 2 kh2

A. Ogorza≥ek: Helio- and asteroseismology

2frequency

khc
"="=N

horizontal wavenumber

Figure 3. Relation of dispersion. Two asymptotes are depicted
as dashed lines. For wave to propagate its frequency has to belarger than both N and kh c, or smaller than both of them at23

units of their maximum value.

Only
will bing ’tions:

0.6
0.5

Ll20.4s 2 0.3
GM/R3

N2ad+µwhereTo soditionof the0.2
0.1
0.0
0.0

0.2

0.4

0.6

0.8

1.0rR
Figure 8. Propagation regions for polytrope model. N is depicted

Secon
24
surfa

acoutic mode：#nl≃!# × (n+l/2+%) -dnl!# = [2 ∫ c-1dr ]-1
dnl : sensitive to the corefrequency ~ (sound travel time from the center to the surface)-1~ (GM/R3)1/2
sound wave: fast in the deep interior, less sensitive to the corerefraction due to the temperature gradient induces thesensibility to the core, evolution stage
25

small spacing '&large spacing%&
26

Christensen-Dalsgaard, J.1993, ASPC, 42, 397

Excitation mechanisms
Self-excitation
Thermal overstability:
opacity mechanism working in an ionization zone
Stochastic excitation due to turbulence:
waves generated by turbulence resonate in thecavity of a whole star
Tidally forced oscillation

Solar-like oscillation

http://bison.ph.bham.ac.uk

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A stack of power spectraof nine red giant
pulsators

J. De Ridder et al. 2009,Nature, 459, 398

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Future prospects for solar-type stars

3!"

Solar-like oscillations
detected by Kepler

Teff"max

W. J. Chaplin 2012, ASPC, 462, 527

Teff

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!# ∝ M1/2R-3/2#max ∝ g Teff-1/2 ∝ MR-2Teff-1/2∴R#max !#-2

M ∝ #max3 !#-4!#

http://bison.ph.bham.ac.uk

31

Listen Songs of Stars

Bats see the world with sound.
32

\\\\\\：p-mode//////：g-mode

33

coursety: J. Christensen-Dalsgaard

Dramatic development ofAsteroseismology of Red Giants
gravity wave：buoyancy as restoring force
buoyancy: stratification of light element above heavy element layer

practically, gravito-acoustic wave

N2

Christensen-Dalsgaard, J. 2012, ASPC, 462, 505

34

Stellar Physics to Understand through Seismic Investigations
232

Astrophys Space Sci (2010) 328: 227–236

Fig. 3 Brunt-Väisälä frequency
N, hydrogen content X, andperiod spacing !P in three
evolutionary states of a main
sequence 6 M! star (Miglio etal. 2008)

panel while the corresponding period spacings are drawn
in the right panel. As
1/2
gravitynl = [l(l+1)]0(n+l/2+%)shows up in
sharp featurein Nmodemoves out in buoyancyPradius,a periodicPcomponent
with a decreasing period in radial order as the star evolves.
Astrophys Space Sci (2010) 328: 227–236

ncyet16

Noels and Montalbán

Karoff, C., Arentoft, T., Glowienka, L., Coutures, C., Nielsen, T. B., Dogan, G., Grundahl, F.,& Kjeldsen, H. 2008, MNRAS, 386, 1085
Kjeldsen, H., & Bedding, T. R. 1995, A&A, 293, 87
Maeder, A., & Meynet, G. 1991, A&AS, 89, 451
Mazumdar, A., Briquet, M., Desmet, M., & Aerts, C. 2006, A&A, 459, 589
Miglio, A. 2012, Asteroseismology of Red Giants as a Tool for Studying Stellar Populations:First Steps, 11Miglio, A., Chiappini, C., Morel, T., et al. 2013, MNRAS, 429, 423
Miglio, A., & Montalbán, J. 2005, A&A, 441, 615
model with a moderate overshooting parameter of the orsive stars remains unclear at present. More observations areMiglio, A.,
Montalbán, J., Baudin, F., et al. 2009, A&A,503, L21
needed with well-identified modes available, especially inder of 0.1. Through a fitting of five identified modes in θMiglio, A.,
Montalbán,J.,&Dupret,M.-A.
2007,
MNRAS,
375,
L21 stars, to help clarify the problem
slowlyrotating
β CepheiOphiuchi, Briquet et al. (2007) found a much larger overof P.
the 2008,
extra-mixing
in such stars.
Miglio, A.,
Montalbán,
Noels,A., &Eggenberger,
MNRAS,
386, 1487
shooting
parameter ofJ.,
0.44.
The situationis lessconclusiveinother
βCepheistars.
In12
Lacertae
forinstance,
DesmetMontalbán, J., Miglio, A., Noels, A., Dupret, M.-A.,
Scuflaire, R., & Ventura, P. 2013, ApJ,
6.2 Solar-like stars
et al.118(2009) found an upper limit of about 0.4
for αov while!
766,
35
Dziembowski and Pamyatnykh (2008) performed a prelimLow
mass starsP.(M2010,! 2 M!ApJ,) have 721,
a convective
envelope
Montalbán,J.,
Miglio,A.,
Noels,A.,
Scuflaire,R.,&Ventura,
L182
inary analysis with models computed without overshooting.
which can stochastically excite acoustic modes. Here theMorel, T.,The& case
Miglio,A.
2012,
MNRAS,
419,
L34of ν Eridani is even more challenging. Pamyatsituation is drastically different from that of massive stars
Mosser, B.,
Barban,C.,
Montalbán,J., ofetovershooting
al. 2011, A&A,
532, A86nykh
et al. (2004)
advocatea small amountsince regularities
in the frequencies are to be expected due≤ 0.12) while Ausseloos
et al. (2004)
could(αovBelkacem,
the asymptotic
Mosser, B.,
K., Goupil,
M.-J.,
et notal. find2010,toA&A,
517,behavior
A22 of the modes. In an analysis ofa satisfactoryon the fittingof fourmodes.
Bootis, Di540,
MauroA143
et al. (2003) showed how overshooting
Mosser, B.,
Goupil,solution
M. J.,based
Belkacem,K.,
et al.
2012,η A&A,

Figure 3. Brunt-Väisälä frequency N, hydrogen abundance X and period spacing∆P in three evolutionary states of a main sequence 6 M star (Miglio et al. 2008).

Extra-mixing changes the chemical composition profile. Il the star is massunits of their maximum value.

Only
will bing ’tions:

0.6
0.5

Ll20.4s 2 0.3
GM/R3N2ad+µwhereTo soditionof the0.2
0.1
0.0
0.00.20.4

0.6

0.8

1.0r
R
Figure 8. Propagation regions for polytrope model. N is depicted

Secon36surfa

dual character :acoustic wave in envelope,
while gravity wave in coreprobe for stellar coreMontalban J. et al. 2010, ApJ 721 L182
Bedding T.R. et al. 2011, Nature 471 608
Beck P. et al. 2011, Nature doi:10.1038/nature10612

frequency separation

mixed mode :l=1 modes are sensitive
both to stellar core andenvelope and detectable#nl≃!#( n+l/2+%) -dnl!# = [2∫ c-1dr]-1

radial order37

Stellar Physics to Understand through Seismic Investigations–7–16

9Noels and MontalbánKaroff, C., Arentoft, T., Glowienka, L., Coutures, C., Nielsen, T. B., Dogan, G., Grundahl, F.,& Kjeldsen, H. 2008, MNRAS, 386, 1085
Kjeldsen, H., & Bedding, T. R. 1995, A&A, 293, 87
Maeder, A., & Meynet, G. 1991, A&AS, 89, 451
Mazumdar, A., Briquet, M., Desmet, M., & Aerts, C. 2006, A&A, 459, 589
Miglio, A. 2012, Asteroseismology of Red Giants as a Tool for Studying Stellar Populations:First Steps, 11Miglio, A., Chiappini, C., Morel, T., et al. 2013, MNRAS, 429, 423
Miglio, A., & Montalbán, J. 2005, A&A, 441, 615
Miglio, A., Montalbán, J., Baudin, F., et al. 2009, A&A, 503, L21
Miglio, A., Montalbán, J., & Dupret, M.-A. 2007, MNRAS, 375, L21
Miglio, A., Montalbán, J., Noels, A., & Eggenberger, P. 2008, MNRAS, 386, 1487
Montalbán, J., Miglio, A., Noels, A., Dupret, M.-A., Scuflaire, R., & Ventura, P. 2013, ApJ,Fig. 1.— Upper766,panel:
118 density distribution and the ` = 1 propagation diagram for a 1.5 M
Figure star
6. withUpper
distribution= 1 propagation
Montalbán,
Noels,A.,
Scuflaire, andR.,&!
Ventura,P. 2010,
ApJ, branch
721,diagram
L182
radius ⇠panel:
12J.,RMiglio,
atdensity
twoA.,
different
evolutionary
states:ascending
red giant(RGB, for aMorel,T., of& Miglio,A.!2012,
MNRAS,
419,dotted
L34 the1.5 M! left)
withradius∼ (He-B,12R
when
ascendingRGB
and during
Heandacore
He-burningright).
Horizontal
lines
denote(left)
the frequency
domaincoreofMosser, B., Barban, C., Montalbán, J., et al. 2011, A&A, 532, A86

38

Stello et al.

Stello, D., Huber, D., Bedding, T. R., et al. 2013, in ASP Conf. Ser., in press

39

Stello, D., Huber, D., Bedding, T. R., et al. 2013, in ASP Conf. Ser., in press40

At first sight it would seem that thedeep interior of the sun and stars is
less accessible to scientific investi
gation than any other region of theuniverse. Our telescopes may probe
farther and farther into the depthsof space; but how can we everobtain certain knowledge of thatwhich is hidden behind substantial
barriers? What appliance can pierce
through the outer layers of a starand test the conditions within?
-Arthur S. Eddington
41Asteroseismology
Songs of Stars
42