太陽内部熱対流と磁場の数値シミュレーション

千葉大学堀田英之

1

QUCS2019@京都大学基礎物理学研究所2019年12月16日背景動画：ひので観測

2

光球 彩層

コロナ

右上：太陽標準モデル(Model S)Christensen-Dalsgaard+1996

右下：VAL Cモデルを参考に手書きVernazza+1981

太陽

遷移層

放射層

対流層太陽半径：70万 km

太陽物理学の問題：コロナ加熱・太陽風

3

Suzuki+2001Shoda+2019

光球にある膨大なエネルギーの0.1-1%をコロナで散逸させれば、コロナ加熱、太陽風加速は達成される。多くの数値計算でコロナ加熱達成。散逸の詳細過程が焦点(Solar-C EUVSTの課題)

観測(SST)

太陽物理学の問題：フレア

4Cheung+2018

観測(SDO) 数値シミュレーション

磁気リコネクションにより発生する爆発現象。発生の大枠は理解され、忠実に現実を再現したような数値シミュレーションが行われている。

現在では、大フレア発生の事前予測などより実学的な側面へ移行中(Kusano+2012, 新学術PSTEPなど)

太陽物理学の問題：11年周期・ダイナモ

5NASA/NAOJ

ガリレオ以来、400年以上に渡る観測から太陽の黒点数は11年の周期を持って変動していることがわかっている。

その意地のための物理機構はいまだに明らかになっておらず、太陽物理学最古の問題となっている。

地球から見える面に占める黒点の面積

熱対流による太陽の磁場生成

6

対流層

放射層

味噌汁@松屋

放射層からのエネルギー注入により、対流層は乱流的な熱対流に満たされている。

この乱流状態になっている電離したプラズマと磁場が相互作用することで11年周期を維持。

磁場生成から黒点形成

7

放射層

対流層

光球(太陽表面)

乱流による磁場生成(ダイナモ)

熱対流・磁気浮力による磁束輸送

光球の熱対流・放射による黒点形成

これらの過程をできるだけ正確に数値シミュレーションで再現することで、11年周期を理解する

太陽内部で解くべき方程式

8

磁気流体力学の方程式Magnetohydrodynamics (MHD)

質量保存則

運動方程式重力

ローレンツ力 コリオリ力

エントロピーの方程式or エネルギー保存則

輻射磁場の誘導方程式

状態方程式(電離の効果を含めるOPAL)

@⇢

@t= �r · (⇢v)

@

@t(⇢v) = �r · (⇢vv)�rp+ ⇢g

+1

4⇡(r⇥B)⇥B + 2⇢v ⇥⌦

⇢T@s

@t= �⇢T (v ·r)s+Qrad

@B

@t= r⇥ (v ⇥B)

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これらの方程式を格子法で解く(格子が多いほど正確)

どんな状況を計算するのか(したいのか)

9

輻射エネルギーフラックス(よく知られた量)

対流層計算領域

L� = 3.84⇥ 1033 erg s�1

11年周期で0.1%の変動あり輻射エネルギーフラックス

太陽表面から輻射として出てくる輻射エネルギーフラックスは精密に観測で得られている。

ある静水圧平衡の大気に下部境界から輻射エネルギーフラックスを注入し、上部境界から同じエネルギーを抜く(抜ける)。

対流層の中では、熱対流がエネルギーを運ぶので、その熱対流と磁場の相互作用を調査する。

磁場の初期条件は非常に弱いものから始めるのが慣例

太陽内部の成層：初期条件

10

モデルと観測の差(Basu+1997)

熱対流・磁場の分布は観測からはわからないが太陽標準モデルと日震学により、太陽内部の密度、圧力、温度分布は非常に精密にわかっている。

数値計算を行うための初期条件、インプットパラメタは精密に決まっている

dr

dm=

1

4⇡r2⇢dp

dm= � Gm

4⇡r4� 1

4⇡r2dv

dt

dT

dm=

8><

>:

3rL

256⇡3�r4T 3(Radiation zone)

✓dT

dm

◆

mlt

(Convection zone)

dL

dm= ✏n + ✏g � ✏⌫

dXi

dt=

✓dXi

dt

◆

burn

+

✓dXi

dt

◆

mix

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日震学(MPS website)

太陽標準モデル

日震学による差動回転推定

11差動回転

データ提供Howe氏

太陽では、赤道が極よりも速く自転していることが知られているが、現在では日震学により詳細な内部構造が明らかになっている。対流層、低緯度では誤差1%程度。Schou+1998など

太陽の差動回転は、太陽内部の熱対流による非線形効果で生成されると考えられており、数値シミュレーションによる熱対流の再現の答え合わせの一つになる。

子午面上の流れ(～10 m/s)も観測されているが、差動回転(～2 km/s)と比べて遅く観測が収束していない。こちらは現状では答え合わせには使えない。Zhao+2013など

太陽内部研究の難しい所：スケール差

12

温度 密度 空間 時間6000 K 10-7 g/cm3 1000 km 数分

太陽表面

対流層の底温度 密度 空間 時間200万 K 0.1 g/cm3 20万 km 1ヶ月

対流層

対流層内部で大きく変わる空間・時間スケール

当然、磁場周期は11年なので最終的には数十年まで解きたい。基本的に、太陽深部と表面は別々に研究されている→太陽表面付近のみの研究から紹介

光球計算：計算設定

13

Convection zoneCalculation region

一般的に計算領域 6 ‒ 30 Mmほど(対流層の厚み：200 Mm)

計算時間は数時間から数日

下部境界での上昇流のエントロピーを太陽標準モデルの値にすると自動的に光球から太陽フラックスとほぼ同じ値が出ていく

6 Mm

700 km

光球計算：輻射輸送

14

比較的精密に輻射輸送を解かなければいけない灰色近似(波長積分)・散乱無視・局所熱平衡(LTE)は光球では許される。(彩層では、散乱・non-LTEを考慮しなければいかず難しい, Bifrost code)

Vögler+2005

典型的に18-34 本の光線を解く

100 km以下の構造に興味がなければ2本の光線を解けば、粒状班の熱対流速度は間違えない。

光球の計算例

15

コード間(CO5BOLD, MURaM, Stagger)で結果は高いレベルで調和的(Beeck+2012, R2D2, RAMENSコードでも確認済み)。10 Mm程度の小さい計算領域ならば観測と非常に高い調和性天文学で最もうまくいっている数値シミュレーションの一つ

数値計算観測

R2D2コードの結果

吸収線幅による数値計算と観測の比較(Nordlund, 2009)

光球計算：黒点

16Rempel, 2012

観測を非常によく再現するような黒点の数値シミュレーション。

半暗部の成因に謎が残っているがほとんどの物理は明らかに。

観測(SST)

太陽内部研究の難しい所：スケール差

17

温度 密度 空間 時間6000 K 10-7 g/cm3 1000 km 数分

太陽表面

対流層の底温度 密度 空間 時間200万 K 0.1 g/cm3 20万 km 1ヶ月

対流層

対流層内部で大きく変わる空間・時間スケール

当然、磁場周期は11年なので最終的には数十年まで解きたい。基本的に、太陽深部と表面は別々に研究されている→次に太陽深部のみの計算を紹介

深部計算：計算設定

18

対流層計算領域

下部境界：0.71Rsun

上部境界：0.96-0.99Rsun

計算領域は典型的に対流層の底(0.71Rsun)から表面付近(0.96Rsun)。最高でも0.99Rsun (Hotta+2014, 2015)

計算時間は典型的に数十年から千年。光学的に厚い領域なので、輻射輸送は拡散近似。Model Sに従い、下の境界からは3.84×1033 erg/sのエネルギーが入る。上の境界からは人工的に同じエネルギーを抜く

深部計算：音波

19

音速

対流速度

対流層の深部では、音速が熱対流速度に比べて数千倍速い。陽的に解くと時間刻みへの制約が厳しい

対応策は二つ- 音速無限大の仮定(アネラスティック近似)(全体通信多い、表面扱えない)

- 音速抑制法(Hotta+2012, 2015)(局所通信のみ、表面含むことができる)

音速 対流速度

アルフベン速度

格子間隔

時間刻み

深部計算例

20

Hotta, 2018Velocity amplitudes increasewith radius due to the density strat-

ification, with horizontal velocity scales reaching over 200m s!1

near the surface (Fig. 15a). In the mid-convection zone the ve-locity field is nearly isotropic, with a characteristic amplitude ofabout 100 m s!1 for all three components.

The horizontal divergence PDF shown in Figure 14d is nearlyidentical to the v0r PDF in Figure 14a at r ¼ 0:98, but as with thespectra in Figure 13d, this correspondence breaks down by r ¼0:92 R#. In the mid-convection zone the! PDF becomes moresymmetric with nearly exponential tails (S ¼ !0:13, K ¼ 9:2at r ¼ 0:92 R#). Non-Gaussian behavior such that K > 3 forvelocity differences and derivatives is a well-known featurefound in a wide variety of turbulent flows (e.g., Chen et al. 1989;Castaing et al. 1990; She 1991; Kailasnath et al. 1992; Mieschet al. 1999; Jung & Swinney 2005; Bruno & Carbone 2005). Inparticular, the PDF of velocity differences between two pointsseparated in space is often modeled using stretched exponentialsf (x) / exp (!jxj! ), where ! approaches unity for small spa-tial separations (as sampled by derivatives) and becomes moreGaussian (! $ 2) as the spatial separation increases.

The vertical vorticity PDFs shown in Figure 14e also exhibitnearly exponential tails. However, near the surface (r ¼ 0:98 R#)the distribution is bimodal with prominent tails signifying anabundance of extreme events (K ¼ 180). These tails arise fromthe intense, intermittent cyclones that develop at the intersticesof the downflow network at mid- and high latitudes as discussedin x 3. By r ¼ 0:92R#, the bimodality is absent, although the PDFis still highly intermittent (K ¼ 25). This is consistent with Fig-ure 2b, which suggests that the high-latitude cyclones are confinedto the outer few percent of the convection zone (rk 0:95 R#).

The signature of high-latitude cyclones is also present inthe PDF of temperature fluctuations as a prominent exponentialtail on the negative side at r ¼ 0:98 R# (Fig. 14f ). As with theradial velocity PDF, the bimodality disappears by r ¼ 0:92 R#due to entrainment, and the negative tail becomes unimodaland exponential. The asymmetric shape of the temperature PDFsarises from the asymmetric nature of the convection noted in x 3;cool downflows are generally less space filling and more intensethan warm upflows. The temperature PDFs remain asymmetric(S < 0) and intermittent (K > 3) throughout the convectionzone, becoming most extreme near the surface where S ¼ !1:6and K ¼ 12. The standard deviation of the temperature fluctu-ations ranges from 0.4 K in the lower convection zone to a max-imum of 4 K at r ¼ 0:96 R#.

Correlations between vertical velocity and temperature fluc-tuationsmay be investigated further bymeans of two-dimensional(2D) PDFs (histograms) as illustrated in Figure 16 for r ¼ 0:98R#.Althoughwarmer and cooler temperatures are associated with up-

flows and downflows, respectively, the relationship is not linear.Upflows exhibit a prominent maximum at v0r % 20 m s!1 andT 0 % 2 K, whereas downflows are more distributed, both in therange of velocity amplitudes and in the spread of temperaturevariations for a given v0r. This spread increases somewhat towardhigher latitudes due to the preponderance of intermittent cyclo-nic plumes, but the average correlation shown in Figure 16l isinsensitive to latitude. The reversal in the sense of the tempera-ture variation at high radial velocity amplitudes is due in part topoor statistics (few events), but it does have physical implica-tions. As noted in x 3, the strongest upflows occur adjacent todownflow lanes. Cool regions associated with downflow lanestend to be more diffuse than the lanes themselves as a result ofthe low Prandtl number (Pr ¼ 0:25). Thus, the fastest upflowscan be relatively cool. Similarly, the fastest downflows occur inlocalized regions adjacent to warmer upflows such that the tem-perature fluctuations are diminished by thermal diffusion.Correlations between the horizontal velocity components v0"

and v0# are of particular interest because these may be comparedwith analogous correlations obtained from local helioseismology.Such correlations not only represent a potential diagnostic forgiant-cell convection, but they also reflect latitudinal angularmomentum transport by Reynolds stresses, which plays an es-sential role in maintaining the differential rotation profile (x 4).However, the 2D PDFs in Figures 16a, 16d, and 16g appearnearly isotropic, implying that the horizontal velocity compo-nents near the surface (r ¼ 0:98 R#) are only weakly correlated.At high latitudes there is a weak positive correlation signifyingequatorward angular momentum transport, but at mid-latitudesthe sense of the correlation reverses (Fig. 16j). At low latitudesthere is no clear systematic behavior, as expected if horizontalvelocity correlations are induced by the vertical component ofthe rotation vector.The lack of prominent horizontal velocity correlations in the

near-surface downflow network may be attributed to the rela-tively small spatial and temporal scales of the convection. Theeffective Rossby number here is greater than for the larger scalemotions deeper in the convection zone, implying weaker rota-tional influence (x 2.2). Coriolis-induced correlations are con-sequently weaker. Since the differential rotation is maintainedprimarily by horizontal Reynolds stresses (x 4), weaker horizontalvelocity correlations help account for the decrease in latitudinalshear found in our simulation near the outer boundary.A near-surface shear layer is also found in helioseismic in-

versions, but its structure is quite different than that found in oursimulation (Thompson et al. 2003). The radial angular velocitygradient appears to be positive at all latitudes, and the latitudinalshear remains roughly constant across the layer. As discussed in

Fig. 15.—(a) Standard deviation, (b) skewness, and (c) kurtosis of the three velocity components are shown as a function of radius, averaged over a time interval of62 days. The solid, dotted, and dashed lines represent v0r, v

0", and v

0#, respectively. Horizontal dashed lines show skewness and kurtosis values for a Gaussian distribution

(S ¼ 0, K ¼ 3) for comparison.

MIESCH ET AL.572

0.71Rsun 0.98Rsun

Miesch+2008

達成される熱対流速度は、太陽標準モデルなどで使われる混合距離理論と調和的

赤印は混合距離理論

規格化したエントロピー

最近20年の進展：差動回転

21

602 MIESCH ET AL. Vol. 532

FIG. 5.ÈSnapshots of the radial velocity Ðeld in simulation TUR are shown at a level near the top of the convection zone (r \ 0.95 The time intervalR_

).between each successive image is about 9 days, one-third the rotation period of the coordinate system, P (\ 28 days). Each surface is tilted 20¡, such that thenorth pole points out of the plane of the page, as in Figs. 2 and 3. Light and dark regions denote upÑow and downÑow, respectively.

for each simulation is illustrated in Figures 5 and 6. Notethat these snapshots are taken with respect to the rotatingreference frame.

In case TUR, the convection structure is very time depen-dent, making it difficult to identify any persistent featuresover the course of a full rotation (28 days). As noted in ° 4.1,strong downÑow lanes aligned with the rotation axis oftenoccur at low latitudes, but they typically persist only fordays or weeks and are continually advected by horizontallydiverging Ñows and di†erential rotation, making them diffi-cult to track. The downÑow network at the poles is gener-ally more isotropic, is characterized by somewhat smallerspatial scales, and, again, evolves substantially on time-scales of weeks.

In contrast, the convection pattern in case LAM does notvary strongly with time. Banana modes persist for manyrotation periods at low latitudes and propagate in a prog-rade direction (increasing longitude) relative to the rotatingcoordinate system at a rate faster than the local angularvelocity of the Ñuid (see Table 2). A weak, smaller scale,more rapidly Ñuctuating Ñow component is also presentnear the outer boundary, visible in Figure 6 as a ““ cobbling ÏÏor ““ dimpling ÏÏ superposed on the dominant banana struc-ture (see also the upper images in Fig. 2). It is possible totrack individual downÑow lanes for many rotation periods,although snapshots such as those shown in Figure 6 oftenleave some ambiguity in discerning among similar features.Periodic, persistent modes also occur at midlatitudes, buttheir longitudinal propagation rate is slower, caused, inpart, by the local di†erential rotation, and they continuallybreak and recombine with the lower latitude banana modes.At high latitudes, low azimuthal wavenumbers dominate,

and they tend to propagate slowly retrograde. As men-tioned in ° 4.1, the transition between the low-latitude,rapidly propagating banana modes and the slower high-latitude modes occurs at a latitude that approximately coin-cides with the cylinder tangent to the base of the convectionzone and aligned with the rotation axis. It is generally alongor near this tangent cylinder where the breaking and recom-bining of low- and high-latitude modes occurs.

The longitudinal propagation and persistence of velocityfeatures can be better demonstrated using images of theradial velocity Ðeld as a function of longitude and time, asdisplayed in Figures 7 and 8 for several chosen latitudes inthe mid convection zone of each simulation. Each imagespans the full 360¡ in longitude and covers a time interval ofthree rotation periods (84 days). A characteristic propaga-tion speed for the patterns shown was obtained by Ðrstdetermining the predominant azimuthal wave mode at eachlatitude, deÐned as the wavenumber corresponding to thepeak of the time-averaged Fourier spectrum in longitude. AFourier transform in time was then used to compute a cor-responding phase velocity for the predominant azimuthalmode at each latitude. The results are listed in Table 2.

In case TUR, the (/, t) diagrams of Figure 7 reÑect thecomplexity of the velocity Ðeld, suggesting the super-position of many coupled azimuthal modes propagating atdi†erent longitudinal phase speeds. New downÑow lanesare being created and destroyed continually, and althoughfew persist for the entire interval, many last longer than arotation period, in contrast to the more rapidly evolvingnetwork near the surface. At low latitudes, most of thevelocity features clearly propagate in a prograde directionrelative to the rotating coordinate system but with varying

FIG. 6.ÈSimilar to Fig. 5 but for case LAM

Miesch+2000

604 MIESCH ET AL. Vol. 532

shown in Table 2, this mode is actually propagating slowlyin a prograde direction and is being advected backward bythe local di†erential rotation. The high-latitude m \ 7 modeis also propagating slowly prograde, boosted by the localdi†erential rotation.

In case LAM, the persistence and propagation of bananamodes is evident in the (/, t) images of Figure 8, particularlyat low latitudes. The mean azimuthal wavenumber spec-trum of the low-latitude image exhibits a strong peak atm \ 9, and this mode has a relatively well-deÐned progradephase velocity that is faster than the local angular velocity(Table 2). In contrast, the dominant features at high lati-tudes are of signiÐcantly larger scale (m B 4) and propagateretrograde relative to the rotating coordinate system andrelative to the local angular velocity. At midlatitudes, thepattern is more jumbled, with greater time dependence,more contributing azimuthal modes, and a phase velocitythat is less well deÐned. Still, the analysis described abovereveals a dominant, prograde-propagating m \ 8 mode(Table 2).

We emphasize that the velocity features in Figures 5, 6, 7,and 8 are not simply advected along with the di†erentialrotation. Rather, they represent traveling convective modes,each with a characteristic phase velocity. The propagationcharacteristics of the low-latitude modes are similar to theRossby-like waves described by Glatzmaier & Gilman(1981a), which arise from the near-conservation of potentialvorticity in the presence of a density stratiÐcation. Forfurther results on the propagation of linear convectivemodes in rotating spherical shells, see Gilman (1975), Busse& Cuong (1977), Soward (1977), and Zhang (1994).

Persistent downÑow lanes, such as those exhibited byboth simulations LAM and TUR, are associated with hori-zontally converging Ñows in the upper convection zone andare therefore potential sites for the large-scale concentrationof magnetic Ñux. Such structures may help to explain per-sistent regions of enhanced magnetic activity observed onthe Sun and other stars, commonly referred to as ““ activelongitudes ÏÏ (e.g., Jetsu et al. 1997).

5. MEAN FLOWS AND THERMODYNAMIC VARIATIONS

5.1. Di†erential Rotation and SpeciÐc Entropy ProÐlesIt was mentioned in ° 1 that thermal convection under

the inÑuence of rotation tends to redistribute angular

momentum and that this redistribution process is likelyquite di†erent in laminar and turbulent Ñow regimes. If therotational inÑuence is strong and baroclinic e†ects areweak, the resulting di†erential rotation proÐles tend towarda Taylor-Proudman state in which angular velocity con-tours are parallel to the rotation axis. Previous simulationsof solar convection in spherical shells generally gaveangular velocity proÐles of this type (Gilman 1977, 1979 ;Glatzmaier 1984, 1985a, 1987 ; Gilman & Miller 1986).Departures from such cylindrically aligned Taylor-Proudman states can occur because of baroclinicity(latitudinal entropy gradients) or Ñow components notstrongly inÑuenced by rotation, such as small-scale vorticalmotions that are part of a turbulent cascade.

Helioseismic results imply that the angular velocityproÐle in the highly turbulent solar convection zone is notcylindrically aligned (Thompson et al. 1996 ; Schou et al.1998). Figure 9a illustrates the main features of the internalsolar rotation proÐle as inferred from helioseismology,obtained from six months of p-mode frequency measure-ments by the GONG network of solar telescopes(Thompson et al. 1996 ; see also Fig. 11). Midlatitudeangular velocity contours tend to be radially aligned ratherthan cylindrically aligned, and sharp radial gradients areconÐned to narrow shear layers near the base of the convec-tion zone and just under the photosphere.

The lower shear layer is known as the solar tachoclineand represents a narrow transition region between the dif-ferential rotation of the convection zone and the approx-imately solid body rotation of the radiative interior.Although the analysis is complicated by accuracy andresolution limitations in the helioseismic inversions, thetachocline seems to be centered at or slightly below the baseof the convection zone, with a width and little[0.1 R

_latitudinal variation (Kosovichev 1996 ; Wilson, Burton-clay, & Li 1996 ; Basu 1997 ; Corbard et al. 1998 ; Antia,Basu, & Chitre 1998). Theoretical models suggest thatintense horizontal turbulence and global-scale circulationsdriven by shear instabilities and magnetic e†ects producepoleward angular momentum transport in the tachoclineand keep it relatively narrow (Spiegel & Zahn 1992 ; Elliott1997 ; Gilman & Fox 1997 ; Gough & McIntyre 1998).

The upper shear layer near the surface is most pro-nounced at low latitudes. It is likely produced by the vigor-

FIG. 9.ÈLongitudinally averaged angular velocity proÐles : (a) the solar rotation according to an RLS inversion of p-mode frequency splittings from theÐrst six months of GONG data (Thompson et al. 1996) ; (b)È(d) the rotation in simulation TUR; (b) at one time step ; (c) averaged over one rotation period ;and (d) averaged over 10 rotation periods. The color tables and contour levels used for the helioseismic and simulation data are indicated. Note that thecomputational domain does not extend all the way to the photosphere, as discussed in ° 3.

太陽成層で- 赤道加速(Miesch+2000)- 対流層内部で回転軸から傾いた分布(Miesch+2006)- タコクライン(Brun+2011)- 表面角速度勾配層(Hotta+2015)

最近20年の進展：磁場周期 (1/2)

22

Brun+2004高解像度計算乱流的な磁場が支配的で周期は再現できず。

Ghizaru+2010低解像度にすることで、乱流的な磁場成分を抑え30年程度の周期を達成

最近20年の進展：磁場周期 (2/2)

23

低解像度

中解像度

解像度高い<Bφ> at r=0.72Rsun

高解像度

乱流が支配的な状況でも磁場周期を達成、小スケールの乱流状況が大スケールを決めている(Hotta, Rempel, Yokoyama, 2016, Science)

なぜ大規模磁場が再度つくられるのか

24

高解像度にして、小スケールダイナモが効率的になることになることによって、小スケール磁場エネルギーが小スケール運動エネルギーを超えるほどになる。

その結果、ローレンツ力が小スケールの運動を抑制する。

破壊をしていた小スケール乱流が抑制されたので、大規模磁場が維持できた。

一方、現状ではまだ太陽のような規則正しい11年周期は得られていない。より高い解像度でより効率的な磁場生成を達成することが必要か？→富岳での課題

磁場をどうやって生成しているか

25

基本的には、低解像度と高解像度で磁場生成の機構は変わらない差動回転による引き伸ばしと回転による乱流非線形効果

磁場生成に関しては、太陽深部のみで閉じている→その結果としての黒点形成

深部計算と表面計算の接続：動機

26

Babcock, 1961

対流層内部での磁場生成の結果、太陽表面で黒点が形成されていると考えられる。

しかし、磁場生成そのものにも黒点の存在が重要であるというアイディアがあり(Babcock, 1961)、最近の観測はそれを支持している(Cameron+2015)

一方、これまでの深部数値計算には困難さから太陽表面が入っておらず当然黒点もない。

太陽の磁場生成を真に理解するためには、太陽表面を取り入れることは必須→達成

太陽対流層⇄表面一貫モデル熱対流の様子

27

エントロピー擾乱 放射強度

Hotta, Iijima, Kusano+2019, Science Advances

今後の展開：磁場生成⇄黒点

28

磁場生成から黒点形成、黒点形成の磁場生成の影響を自己無撞着に計算→富岳の課題

まとめ

29

ü 太陽の11年周期理解には、太陽内部の熱対流を理解することが必須

ü 非常に大きなスケール差のためにほとんどの研究で太陽表面と深部が分けて計算されてきた。

ü (表面計算)：10 Mm程度の小さい計算領域ならば、観測との調和性が非常に高い。黒点などの特徴も再現可能

ü (深部計算)：乱流の自発的な磁場生成により、大規模磁場や周期が再現可能に

ü 表面深部を両方含んだ計算も実行可能になってきた。