AD-A155 214 SOLAR CONVECTION(U) COLORADO UNIV AT BOULDER DEPT OF 1/i.

ASTRO GEOPHYSICS J TOONRE ET AL. 30 APR 84

UNCLASSIFIED AFLT-483 1687--i4F/6 3/2 NEIIhEU~hhhhhIIIhEEIEhmhhhhhmmhuIIIIIII

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1111 1.25 1. h6

MICROCOPY RESOLUTION TEST CHARTNATIONAL BUR[AU Of SlANDARDjS 1961-A

AFGL-TR-84-0130

SOLAR CONVECTION

qd- Juri Toomre

Katharine B. GebbieN

Lfl

V Department of Astro-GeophysicsUniversity of ColoradoBoulder, Colorado 80309

Final Report

Period Covered 1 Mar 77 - 30 Nov 83

Date of Report 30 Apr 84 0

Approved for public release; distribution unlimited

-DDTIC

AIR FORCE GEOPHYSICS LABORATORY JUN12 1985

AIR FORCE SYSTEMS COMMAND SUNITED STATE AIR FORCE- GIANSCOM AFB, MASSACHUSETTS 01731

k, T .

"This technical report has been reviewed and is approved for publication"

Stp Keil, Captain, USAF Stephred 7eil Captan, USAF

Contract Mianager Solar Research Branch

FOR THE COMMANDER

URITA C. SGLDirttor-Space Physic Division

This report has been reviewed by the ESD Public Affairs Office (PA) andis releasable to the National Technical Information Service (NTIS).

Qualified requestors may obtain additional copies from, the DefenseTechnical Information Center. All others should apply to the NationalTechnical Information Service.

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6 NAME OP PERFORMING ORGANIZATION 6c. OFFICE SYMB~t )a NAME *)E VMN I

Depar tment: of As tro-Geophvsics 1f 1 I-

U IjVerS ity V Uf ColIorado {______________ _____

6-> ADDRESS ,,il, ,Iat and /11' C~d.') In ADDRESS .5.

Boo I (cr, ColIorado 80309 l:n..' .

aa NAME OF F JN(JING,SPONSQRIFIG 18b. OFFICE SYMBOL 9 PROCURE ME N I .Nt5 I t N' ,k'S t1' ~.,IIORGANIZATI(ON (if .pphicabl.'.

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sc AORIESS it. . tollvrd /11' C,,d.') 10 SOURCE OF FuNDiNG NOS -

PROGRAM PROj C T SAtK W)HKuNI T

SELE ME NT NO NO) NI>

I I 1 a a . I~I S,5 I aI', ., sft ca Non, 61102F 2311I(dSolar Con1vct ionl

12. PL RSONAL AUTHOR(S)

J ur ii 'I omrI2 and Ka thar jne B. Gebbie13a, T \1PE OF REPORT L7b. TIME COVERED 14. DATE OF REPORT (Yr. Mo., Doy7 15 PAGE COUNT

Final P ROM _147 TO 1 W313 94 pi 3616 SUPPLEMENTARY NOTATION

19 ABSTRPACT -vI~~e ,,',' - lrtssa and idenitify by block? number) .

A hrog suyof covciepenetration into the solar atmosphere and convectivemotions in sub-atmospheric layers on the sun was made. Non-linear anelastic andBoussinesq modal equations were developed and solved to describe solar and stellarconvection. An explanation was developed for the lack of penetration of large-scaleconvective notions into the observable solar atmosphere through the discovery ofhucyancy braking near the top of a supposedly unstable layer. Observations of

* motions in the solar atinosphere led to the discovery of a new scale of solar motion, -

thI2 so-called mnesogranulation. A technique was developed to use changes in thesolar five-minute oscillations as a probe of internal solar structure. Using thistechnique, large-scale, subatmnospheric convective eddies were discov?red.

10 r I'ii RUT'(N "VAIi A tI11 f IF A I3 PAC T 21 ABSTRACT SECURITY CLASSIFICATION

*'. 'I jF .4 N " . 1 41 III IN IVINIJA 22t, TELEPHONE NUMBER 22c OFFICE SYMBOL

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.-- 7

3

A. OVERVIEW OF RESEARCH GOALS

The research supported by this contract has been directed

toward improving our understanding of the turbulent convection

that is present below the solar surface and of the penetration of

these motions into the solar atmosphere. The dynamics of this

convection has a critical role in determining the magnetic

activity of the Sun and thus is fundamental to all studies of

solar-terrestrial relations. The work during the first two years

of effort as Part I of this contract concentrated partly on the

development of nonlinear anelastic and Boussinesq modal equations

to describe solar and stellar convection. The solution of such

highly nonlinear equations required the use of major computing

facilities and of asymptotic analysis. The research dealt with

observational studies of supergranular scales of convective

motion over a broad range of heights in the solar atmosphere. It

also lead to the discovery of apparently a new discrete scale of

convection on the Sun called mesogranulation. The coordinated

ground-based and satellite observations utilized the Sacramento

Peak Observatory (SPO) diode array and the Orbiting Solar

Observatory 8 (0S0-8) satellite's ultraviolet spectrometer.

The work during the next three years of effort as Part II

turned to coordinated observations of persistent flows ranging

* from the photosphere to the transition region using the Solar

Maximum Mission (SMM) satellite's UVSP instrument and the SPO

diode array. The studies dealt with supergranular and

* mesogranular scales of motion within and outside magnetically

active regions. The height variation of the flow amplitudes,

.1 V%

. -ZP ~-

4

their correlation with magnetic structures, and the degree of

isotropy were of primary concern. A major effort was also

initiated to use the five-minute oscillations inherent in our

Doppler velocity data sets to search for the presence of large

scale, spatially periodic flows (akin to giant cells) below the

solar surface. The oscillation studies required the development

of inversion procedures to be able to deduce the variation with

depth of giant cell flows. The continuing theoretical work on

anelastic modal descriptions for solar convection concentrated on

the time dependence achieved when multiple modes are introduced

into the representation, and dealt with the essential issue of

implementing subgrid modelling of the turbulence. Such

theoretical modelling of convective flows in the subphotosphere

yielded predictions of mechanisms that serve to prevent the

largest scales of convection from roaring into the atmosphere.

It also predicts that strong horizontal flows may well be present

at relatively shallow depths below the surface.

B. RESEARCH ACCOMPLISHMENTS

The research work supported in substantial part by this

contract has resulted in 20 published papers in refereed

scientific journals, the cover pages of which are attached as

Papers A to P. A further 18 published abstracts of talks at

national conferences have also been cited in the quarterly

rep)orts, and there have been over 22 other seminars given

describing aspects of the research. Of equal importance are the

6 Ph.D. theses (Theses A to F) that have been completed at the

;niversity of Colorado under the supervision of the Pi's of this

5 .

contract; this is of considerable significance to the long-term

development of such research endeavors in solar physics.

The Ph.D. thesis studies supported in part by this

contract are entitled:

Thesis A. "Mesoqranulation and Supergranulation in the Sun",

L.J. November, 1979.

Thesis B. "Internal Gravity Waves in the Solar Atmosphere", S

B.R. Mihalas, 1979.

Thesis C. "Convection in Rotating Layers with Thermal Winds

and Applications to Jupiter", D.H. Hathaway, 1979.

Thesis D. "Mesoscale Entrainment Instability as the Cause of

Mesoscale Cellular Convection", B.H. Fiedler, 1982.

Thesis E. "Oscillating Probes and Direct Observations of Solar 5

Convection", F. Hill, 1982.

Thesis F. "Nonlinear Compressible Convection with Penetration",

N.E. Hurlburt, 1983. S

The published research papers that serve as the primary

reporting of the scientific results from this contract are

conveniently reviewed by considering four groupings of the papers

and the theses:

GROUP 1. (Papers A to D; Theses A,E)

Observations and Interpretation of Large-Scale Persistent

Velocit Fields in the Solar Atmosphere:

Coordinated SPO. OSO-8 and SMM Observations

.. . , I.T LT•LL.L T[ i-.• T[ i -L"• . . . ....... •- " . . . . . . . . . . . . ' -" ' .. ... .. '

6

The calibration of theoretical models of solar convection

requires high quality data about the variation with height of

persistent flows in the solar atmosphere. Since observations may

well lead such theory, we believe it essential that there be a

close interplay between these two disciplines and therefore have

accordingly organized our research programs. Thus we have sought

to measure and interpret the manner in which convective flows are

able to penetrate upward into the photosphere, chromosphere and

transition regions. Velocity observations in the upper portions

of the atmosphere have required the use of ultraviolet

spectrometers aboard spacecraft like OSO-8 and SMM. Doppler

measurements being made simultaneously from the ground at SPO

permitted us to link these flows to ones in the photosphere and

nea-- the temperature minimum, thereby yielding a coherent

saimpling of the velocity fields over a broad range of heights.

Papers A and D, and Thesis A, showed that persistent

fi'ws of supergranular scale can be traced all the way up to the

transition region, with such velocity patterns able to penetrate

well over 11 density scale heights. The character of the flows

has changed with height, with horizontal rms flow amplitudes

in:reasirig from about 400 m/s in the photosphere to over 1500 m/s

in the middle chromosphere. A distinctive change also occurs in

th- flow structure: although horizontal flows predominate in the

photosphere, the flows become increasingly isotropic with -!

height. These properties suggest that supergranulation

experiences strong braking of vertical momentum in the

subphotosphere, while the horizontal shearing flows in the

chromosphere must be shear unstable and a source of internal

-. o,

7

gravity waves. Thus convective flows of large horizontal scale

have a remarkable ability to penetrate into the atmosphere, and

hardly have a benign role there.

Paper E reports studies with SMM of persistent flows in

the transition region, revealing that their spatial rms increases

to over 4000 m/s as sampled in C IV. There is a striking

correlation between intensity and vertical velocity acr-ss the

field of view that often shows two distinct branches when these

variables are plotted against each other: the sites of strongest

emission in the UV often possess vertical velocity amplitudes

substantially lower than those on the primary branch. This led

us to discover that such a signature is associated with regions

of emerging magnetic flux. This will serve as a means of

predicting sites that should show substantially enhances soft

X-ray emission known as X-ray bright points, and such

observations will be a key aspect of SMM operations after the

repair of the satellite. We should emphasize that all of the

coordinated observations have been very demanding, requiring

extensive development of procedures and calibrations on both the

OSO-8 and SMM satellites and their spectrometers, along with

considerable improvements on the SPO echelle spectrometer and

diode array.

The study of persistent flows also requires careful

filtering out of strong contributions from five-minute

oscillations. We devoted considerable attention to this

question, and as a consequence discovered a new scale of

convective flow, with its horizontal scale of 7 Mm being

iriterrne(pdate between that of granulation and supergranulation.

S_ . .

p~ - - -7 1: ,!1 7

8

Papers B and I, and Theses A and E, discuss the properties of

such mesogranulation possessing spatial rms vertical velocities

of about 60 m/s. Mesogranulation my represent the missing scale

of convection driven largely by the He+ ionization zone.

Paper A.November, L.J., Toomre, J., Gebbie, K.B., and Simon, G.W., 1979,"The height variation of supergranular velocity fields determinedfrom simultaneous OSO 8 satellite and ground-based observations",Astrophys. J., 227, 600-613.

Paper B.November, L.J., Toomre, J., Gebbie, K.B., and Simon, G.W., 1981,"The detection of mesogranulation on the Sun", Astrophy. J.Letters, 245, L123-L126.

Paper C.Gebbie, K.B., Hill, F., Toomre, J., November, L.J.,Simon, G.W., Gurman, J.B., Shine, R.A., Woodgate, B.E., Athay,R.G., Bruner, E.C., Rehse, R.A., and Tandberg-Hanssen, E.A.,1981, "Steady flows in the solar transition region observed withSMM", Astrophys. J. Letters, 251, L115-L118 (1981).

November, L.J., Toomre, J., Gebbie, K.B., and Simon, G.W., 1982,

"Vertical flows of supergranular and mesogranular scale observedon the Sun with OSO 8", Astrophys. J., 258, 846-859.

Accession For

NTIS GRA&IDTIC TABUlannounced ]

J' -sti i clat 1on

Distribution/

Availability Cqdeu

Avail and/or-Dtt I Special

.i

9

GROUP 2. (Papers E and F; Thesis B)

Internal GravitV Waves in the Solar Atmosphere:

Thoy and Observational Consequences

This work represents a detailed assessment of how S

internal gravity waves (IGWs) propagate through the solar

atmosphere. Paper E and Thesis B describe the first reL arch

effort to calculate IGWs within a realistic model of the vertical I

stratification, and thus clears up many misconceptions about

partial reflections and diffractions that arise when modelling

the solar atmosphere as a sequence of slabs with abrupt changes

in properties. The paper provides explicit predictions about

wave amplitudes and relative phases betwen velocities and

thermodynamic fluctoations. Further, it discusses criteria for

the nonlinearities that must come about as the waves travel

upward and increase their velocity amplitudes (due to

conservation of momentum). These criteria lead to estimates of I

heights at which IGW with differing horizontal wavenumbers and

frequencies may be expected to break and thus deposit their

energy. Paper F expands the analysis to include effects of I

radiative dissipation on such waves, and reveals that IGWs may

survive the coolinrg effects of H- ions as they propagate upward,

provjded the wave. are either produced by shear instabilities in

the photosphere or provided their wavelengths fall within a

specific range. Thus our work, contrary to previous predictions,

strongly sugie'-ts that IGWs should be a substantial component of

velocity fields within the nrhntosphere, chromosphere and

10

transition regions. However, explicit observations of such waves

through Doppler measurements of spectral lines may well be

inconclusive, since IGWs often have vertical wavelengths short

compared to contribution functions for many lines. This leads to

line broadening rather than simple shifts; phasing relations in

thermodynamic fluctuations further produce asymmetries and

skewness that may confound spectral line measurements. The IGWs

are likely to be one of the main causes for the observed line

broadening, and thus micro/macro-turbulence may largely be a

superposition of many wave modes that are just not being

resolved. Further, the breaking of these waves over a r e Uf

heights in the chromosphere may provide a significant f .tion of

the mechanical energy deposition needed to sustain the

c-h r-omosphere.

Pper E.Mihalas, B.W., and Toomre, J. 1981, "Internal gravity waves inthh solar atmosphere. I. Adiabatic waves in the chromosphere",Astrophys. J., 249, 349-371.

Paper F.Mihalas, B.W., and Toomre, J. 1982, "Internal gravity waves inthe solar atmosphere. II. Effects of radiative damping",Astrophys. J., 263, 386-408. .J

......................... ..-.............. ....................% ...-..-....

i

GROUP 3. (Papers G to P; Theses C, D, F)

Development of Nonlinear Modal Descriptions for Solar

and Stellar Convection: Theory Incorporating Effects of

Penetration, Rotation, Stratification

I

We hj',e cari-ied out a broad collaboration cn the

devc lopment , > ., Knear convection theory that has inv "ve'i

Drq. Jin .t.. . r ani lean-Paul Zahn from Observatories of Niw_ . .

and! Pi> 1" Mili at TouLouse, Edward Spiegel from Columbia

'rviersity, Dowilas Gough and Nigel Weiss from University o

C'wr : lgw, Peter Gilrma from HAO/NCAR, and Daniel Moore from

1''Ie al College. Since the salaries of our collaborators are

t,,m< "a1el'v hy their home institutions, and because we have

0,A.in access to large computers without explicit charges co

tK . ntr °ct, we oelieve this major aspect of our research

prniram has been especially ,ost effective.

In Papers G and H are considered the development of p

.-irary conditions for convection penetrating into stable

srur :)i ings, and the consequences of this on loss of angular

r-omoritum. Papers I and J discuss the major issues of what occurs p

w ,c conr'tive motions are explicitly treated as being

r):r-.-;sibi-. The rules of rotation, curvature and north-south

: ... ,': ';,.., tne preferred forms of convection

,, -l i ]e:, _,n i'apf -ri K and L. This work is vital in

V ._ ,;4nth th,. oiant cel ls on the Sun should be

S, :, t ;%' t:n 1- 1n.., O, n, iiqne] with the rotation axis, as

'an, 1 Q , xrt'.;:r ,t . rc.ls aligned in the east-west

. "t ,i' ,1ie, t , or, jupiter. Papers M, N, 0) and

• , • "

PAPER J

C'.F~ki t TX +k0 71 POVCT [ONO AN! THEIR ROLE IN

Jutr I Ti)) unre)e; ! ire -101 '1! sr ro-'>ahV!slICS and Joint InSt rtit' for

<-r,,;':sicu, Pivers'itv of Coloro'-' Ind i ni

03i' ' .. rt,f d-r, 1b.oulder, .O 8f.09, U.S.A.

(Thrui., :WI (oonae in stars appear to require viguorur:;co uve, tlAtheL4 thle surface. If we Wish to LUnder: -tnd hA)

va uos '''; :tblte contribute to the iechanica' onuthi t, i-:; ir' c c hr ocosoher es, then ..e must be tnin,

)in the atmosphere and wtith the naru-ri of th eird One cannot really separate these, two;, s rib

r- [:;hi e this l ink, we will raise somehst i vo fV t ')- j~ i a s tell1ar e nvelIo pe a nd o tn inI !)nI-

t ' p I. The si.-nificant pulsbetwe i 'whit isobin r)f t. ioret ira lIv exol,)aimed should servye i ni I -

rt e so sin'( th~it n eed to he pursuted . We will c on cen tra te o(nthe Slu, inl or I! l i the observat icas here are suf fic ien t I1':o

t ae i 1t raIIe nn2es t o t he o ry u n ava ilablhet- in no: 2 -

o)ther >r r a I also turn t'o A-type stars to) '1 bu.rr ire

t 'or r cribing, convection that maw, do- h, rr t1;,in7 MjiT 1- r ~o .' iped ic t in the ver ticalI struLc tureF inT t'11'

f I ows

r) ''''' O)I'POVECT ION ZONE WITH THE ATMOS PH1ER

T! 1 r t,- ,irru lmi tho convection zone are linked hiv a nuiriher

o f d i dI r- 1' pr Om ess es thait have thme po tentrialI for d posi t -

im '' ' n),rnm ph ' The p)r in c ipalI c ou plingPs a re p)r uI LedC

by! )........' v;'rmVrraMO act ion deep within tire r'Orrvrmt ioiizon 0. ' i' r i)(ii i mpad shaping the obse r vii mp in

f 1I,- 1va Oft niassocijated mavnot in irinut 0-.i i i t is

a ''-' 5 flve 00 majr rulte in Inca Illv httu io

.1 ~ ~~~~ T t-Io I)r,''(Ii c t the12o ret i callIy r ow :i.l; i i ifin Il 'i- ' 'or r'iv rume as)Out Or wha1t COn t ro 1) "

-i r2.. ;dis re still Imovmind 'or inre t).

fn) u t lh ihn n ow ha ve bf en i dIe nt i ! i I n (s sin

Io L [i -I pe ad 1 argo lv eva-nescciit wi vms inlt

it ' tu, i.n hetwio(n these two reginors.

571

.au ... .. ts'i i i. 5, 171 W8 .

is?~~~~~ ......~iii~i I im

PAPER H.

G ~ h . , h i'. -. , 19'3 Vol 9. pr, :41 2350 o , n -J U~- LIJ 1 Ua078~

On the Angular Momentum Loss ofLate-type StarsB. R. DURNEYNational Center for Atmospheric Research~t Boulder, Colorado, U.S.A.

J. LATOUR

Joint Institute for Laboratory Astrophysics, Boulder, Colorado, U.S.A.and Observatoire de Nice, Nice, France

(Receii ed Ju~ne 23, 1977)

The observed surface ancular 'elocily of main-sequence stars shows a sharp decrease at aboutspectral 1)pe F f ,uc' mral stars mole massive Than V-r cannot experience an appreciabfleangular niowintim los bccau, c their consecti zofl~s cannot su~talfl a mag-netic dynamo:without a m.i iict,, a hie anrcjar [irom, ntuni l,s io ,cry small. The ini uence ol rotation on tileconsw.isc r~L, .r> c-en t;aj ,or Lixe exeicrl,c ' ~a ,olar tv pe dJ. nanlo. Rotat,on can inueiice

these e)nsect is c rmotions Al the tspicat om,);SicI tImei iS s arger than the rotatior time. iif

11u, > 1, 11, wshr andt L Are t~ ra l~of Wc, con',ectl'.e selocily andI~ milnvl leninh in the

lower part of the ,' ~e.r zone ard 12 1, ithe: star s anigiiar seiocltv. For man-C4uece S( Str oifdifferent ma-yc, ard chenica coip'~It,ois ssc, esajilate the ilmensionie, paramleter u, Q I anid

show that it In~rcr-es-, ris tor stii, hrose mass, M. exceceds that defined b"Iog(AIf, Af - 1 (U I TI l nt I re tic str ankuia r.Oi and mass. %recttViyi). Thus evenfor large aiguLar se',icillsn, mailmetic dsnarnos are tit)t (castrite it togk."M,) Iappreciably exccds

L INTRODUCTION AND THEORY

Figure I (front K-raft, 196r)l Ih bovss the v af at Ion of averag-2 aneVular momentumn

moMent U tfl.,,UIMI'L',(I 2 s l (J "l rolt t n, Of niail-sequenestars ssI Wi d 2_11 etlmass, disldcd b' thle sta r' t Ms.A, and 1 I.l).I he extra polated 1:11e.

_1~x 1 2 w kas added h-, Dlsle 09701. The strikine featurc about hel.. I is -

the sharp dccre c trt In for ,t ars iess tntssi c than about I.5M, l -Schatzman(1962) attrikitcd this htcak in <.1_ > to the an1gular nionlentumi li-s-experieiL.AI % tI ith conseettlolt 70f125 accordlni to the follov. iriiconcept for- thle -UtI la - .i er-s Of C,)cn et ]Of)1 7(-11(.1, are elfIictIt tn icenerat intLsound A!,s C ts ri pro pa,,,.te ups's ards. ,hock, and depostt their cnergy in the

tihe Nalioll !cr fir Atrti-plieric Rescari~h is sponsored by thC, National ScierceFound a Ii i

241

-4

23

PAPER G,

o aU W, *n h '-, Ld. 1 97KPi~t,.i v, m 0 1 8'.q-

On the Boundary Conditionsa Imposed by a Stratified Fluid

JEAN LATOURtJoint Institute for Laboratory Astrophysics. University of Colorado andNational Bureau of Standards, Boulder. Colorado 80303

anid

JEAN-PAUL ZAHNObservatoire de Nice. B.P. 252. 06007 Nice, France

(Receit ed VNo ember 2, 1977. in final form February 27. 1978)

Generatring, the results ovbia'ned bY Stix 101 and by Whiitehead (1971). %%e present the-homogeneous~ boundary conditions that are imposed by a fluid of table but oihertxi~c

arbitrary strititication. 1htese penetratise conditions are strictly valid only in) he liil 4

steady lineiicd floss, but tinder ome conditions they cun also be applited it) nonariir

problems%. An cs~imple of kicnar peneurahitse conscctton is treated in order to illustrate the: u'.e

of these boundary conditions.

1. INTRODUCTION

In many problems encountered in geophysicai or astrophysical fluilddynamici. the unstable region which gives rise to the motions is relativelysmall coimared Ai~s, for eyamnple, the w&hole atmosphere or the wkholestar. When one deals numerically with those motions. one is thereforetempted to describe them only in the unstable region and its immediatevicinity. JTs hottcser raises the o uestion of what conditions are to beimposed at the bounidaries of tile computational domain.

Since the motion- are damped in tile stable region, one might try tocompute a numerical model on a domain large enough, so that theamilplitudeI (If thC SOILutIOn would be very small on its boundaries. J hiscould be aclticvcd t.%ith a computational domain encompassing sc~eral e-foldin,- distanices of the solution in the region of stabiility. Stres.s-free or

rigid botundary conditions could then be applied at these potnts, but withthe shortcoming of irno stnu ph steal constraints that arc quali lati~eci

different from those prevailing in thle stably stratified fluid, w&here no

ltin Ic.isc of jbsen~c tuorn Oifuersatirc dce Nitc, Nic:e. France

U 3117

PAPER FTHE AsritolHYstCAL 10k IKN&I 263 It't6 4()XVW 141fCCciprCI

INTERNAL GRAVi r' W.*VI'S IN rifE SOLAR \rmosmilI RI:If EFFECTS Of- RADIATIVE I)ANPIN(;

BARBARA WI t1o1 1 Min si *V,Adtoanced Sidt Prerini. -tin.i ( cizc ii \rnit~i-livric Rcirachi'

and Depattinicii of .\,it,)O-copho~i- ail Joilt li:liitc lor I .1o.tor~\irophNsic,.I.ntrisof (jAorid'

AND

JIJR Txslkt-Deparirncnt of -\soro-Gcoplis inid joint tn~itout ioi tihorator,, Xtropi isi

U!noacrit5 ol (- olotidoRecened 1982! Mi.o.*ap 19.'! Mali 26

ABSTR ACTRadian' e daminping of internali eravit\ WaS Ces in the solar atmosphere is considered inI a IticarietA

approxititatton kt oh a height-dependent Ness tonian cooling time. A linear fit 1,, made to Sil\damping tine,, for the. photosphiere. and this [!near relation is siiply extended into the chromospht:Initial energes tli\C s 1 10"I, 10 .and 10" erus em s are assumed for monochromatic gras it.waves wioth a solide rantie ol Irequencies and horizontal siasen urnbers. 7

It is fotind (Ili? damI ne11 hals thle least Cired oil woats s with small ,a lues ol th lie crtical wa n neFor such si as es nereLv tlu'tes of 1 0' I 0" criz> cm - s S- Can reach the tCImpera ir ittinintunifrom an initiail flu~x (it 10' 10" ergs cm 2 s 'in thle low photosphere. Thle energY thix of iltegras ity wa sat chrom"Tospheric heighlts appears to be limited by development ot nonihnearittemore than hv radiatise darmping.

Gravity, Aiase.s hase larizer horizontal than vertical velocities: radiative dampine CaU',es thle ratioof the velocities, to increasec and the selocity amplitude,, to diminish vith hete'lt froml thle lossphotosphere to the temperature minimum reg-ion. These waves may play an im1portant role inI thebroadening and ,trenothening of pholospheric ,pectral lines: like 2ranulation tloss s. thle cetitei-to.limb variation and the liciulht dependence of thle velocities have thle same sense as., those dcdueedLfrom obser at ions.

Phase laL's between vertical s elocitv and thle pressure, temperature, and denoit v perturbation,are strongl\ alected bht (lie damiping. A ko altered are vertical si avelcngth. grouIp s loci t. and rispath. Amplitudes, of thle thermodyn-amiL pert u rat ions change relative to one another miid to hievelocity ampiti td cT hese effects arc discussed both in terms, of tile comparison hens cen adiahit tand damped gras. itv si is 1 and in relation to the effects of w.-at es on sp'.ctral line,..Suhjec-t licadiis eras it iton Sun: atmosphere - - Sun: atmospheric nmotion.,

Sun -chromnosphere

1. IN Ro[ l UttON exponentialiN w ith hei allt : its scale liei i1 isaboit 60 ki.In thle solar ph 'tosphere. temnperalture t1I nt nations and thus about halt thle densiv scale hei li1 it inc fle

assoctilicd Als thI c ~ii ea is se ntar" he raipidl'o rate of energy loss is, direct I proprortial it) ih,-isrmooftwd hr thetratiftertlf raiat~iion betkween hlottero and erntssisit'i. the effects of raidiatise damptn.,ei C LcstxCCtecooler re ' iot, III u~tldw. itih entisitoitics ni thle to be- greatest loss in thle pholospiiere I nltci thecpresenose ol ain Te~ln hiliudirv itiiis rapid loss of simrphitytng: isstiinptioln that the gas v, iipii( iil tlio.raidiitioii to spac.u ssitit;!ter recions, r. diattinL more isotropic, and isothcrniil (Spic-e ll)s', Sri\I 1-M mlicstIronglr thain cooler lc i-I lie tti''t iniprrint con- obtains damping titces thait are i1kts rlsCk ii 'itrihutor, to the hie-h 41), 1 '.111,1t in isi in the lowA, to the opacity and thiu increasec raipidl% wilt licicliiphoto plecre ire po-s in-~, :e thle 11 ion. Radiatike ilaipitiv is, a iisiptis piocs thut -1ipririi sitnple did r,,stnation aroorktibtatinstdi Jirectlh to iitninisl thc itittitle of the ietiu iitiiieaccompnsiitu ih p i ndi ctiiiiotl (t continliuum perturbation associated kil lie siaseci In -t 11 irddiation ie opiiirII iite phiotoxplicre d-crecases decreases thle wise :iitlphIll Int t~ - itd rchs li11t stis\

as well. Beccause the %c,,ktonwin ,oineri ILi11 tI. I- 1.%

to R~ fr, -f '. terns to thle lllL.tiiCari~elcce liiiilIt 1, .,n, I I * Mm'dtrieS tile dispertin rel 11idi1tllilL tii:: ' T1

3 8 6 i l ' f a m o n g p e r t i tr lh t t io n q u a i i t i e s, M H j hi r tl it.U 1 1 , ! I ilc : t h

2]

Titit ASTROUlYI~ rusi-& Rliii 1s.&i- 349 VIt. IMI October I PPR E4 1911 Tls 14- S- All,. ,SII"jhl' - - Iir d U 5' iA

INTERNAL GRAVITY WAVES IN THE SOLAR ATMOSPHERE.1. ADIABATIC WAVES IN THE CHROMOSPHERE

BARBARA WFirNI.MlkAAd~anctd SitidN Proeri.

National Center for Alilophcric Her'crh.' adDepairiment of -ooi.~~ c

and Joint Institute o 1at iraiun 5'irorh%,ic,.-Univrsav of CoXlor.ao

AND

JURI TooMREDepartment of A~tro-6cophs'ics

and Joint Institute for Lahoraior% \,iroph.%sic.. 2Urui'ersiiv of( olorado

Receired 1981 .Voiemher 2v6. ac~epred NI~5 April 3

A BSTR ACTProperties of adiahatic and linear internal gravity waves propagating in a solar model are presented

and discussed. Nolnaiscriteria unique to grasity wases are employed toetiae s-beknheights, anid the results are used to deduce information on the possible role of &gras itx vwaes in thechromospheric eneres balance.

We find that in thle photosphere and low chromosphere the ratio of horizontal to% Crtical %elocltv is,large, and thus line-o-slighlt %eloci ties ofizgras itA wa% es are much greater near the solar limbh than at( diskcenter. rlus ratio. s. hich is approximatll. proportional to the Brunt-VaisaUa lrequencN, i. idcd hs Ohewase freu'.. 7xN. ),comes much smaller and may approach unity in the upper chroinosphere. %%herethe Britrit-Va isalaI frequency is ser~ small. This prohahl\ implies much strotteer center-to-limbvariation oflie hroaleniniz low in the atmosphere than in the mid-chromosphere. Masmu)Lm serticaihvelocit% amplitude, for gras ity waves are estimated to he of the order of 2 ksm s or less. indmaximum i I-/olI'al 5 elocir) anmplitudes are around 6 k~m s -or less. Mv ille temperature pert Urha-tions mas ie a, L~tree: a I~ i )21 Hit) K. Substantial phase laueN eist between the thuid % elocit N and thete mPe ratIUre a t d d eni t y pe rt urba t ions. a nd thle heig h t ir:i it ion s o f t hese phasae la gs I.ica aI I sow aninterfercnce_ pattern that results from partial reflection.

We estimiate that izras ty %kases with ain incident enerigy flux of 10" erg~s cm :s- can propa ' ateupw ard to a nias nmin height of aroundm '(X) 1000 kmn al os e the oisible surlace before i-,.ml~nineaitieslead to was e brealsinu, while thosce sith an energs flux of 11W ergs cm- -' can .ttliin maswiniuheights of aroutid I -i) I(X) km., Comparison \sA ith estiniate'J cnerg losses indicates thiat rltwaVe's could coiiui ate ,ienicinils to the energrs balance in. tie !os4 and mid clii oophere. hut arcnot likel\ to be Lill impjOrtant source ot heating at eatrhetehts.suhji'r Imr'~imtqs eras lation Sun* atmosphere .- San chromosphere

1. IN Itiii)i (- I 1(N the propagating acoustic was es that first receis ed iticn -tion. largelyr because thie a1)pcaired to be Lcap.ihI bc

The acou nc- r;i% Its %k.. i spCtra n1 in the -olar atlmo- transporting meclianicat encrv . iips %atd and dpsit isphere cotupri-c- %k.e ti fl~e thui permit free in' he Throinosphiere and it ,iii..uioll ren'un h'e . ~Imlpropagation wii lic aiu hi..iIe ihatare uc eane- man 1949, LIlrnsclineider 19 1. 19-4. Siuii .iid'I c .uici

scent thiro ,iehiOUt iiihichl ,r 11 ot hIe au i he e nd 19 4 ) ! no %y app ar , that the smC CuimieCII 111 11e- , 1propa '.i1ieL 'A, I. 1 1'i i LC Ice 1i1 t1c IL -Ili sp1ILeicL period skascs into stuicks Inas IclkI set~ s0 to ct10and thins 1111 ust:;X ' sc~ hc li, 1. 111, - Iouer chromiiosplieie hutll 1,1 he'. cAummio)t l' ~(p-mnode- ii -i -- it it e: aiur r. C ind ueIces-um h lcauuit. IIIi if) Ihl mIII usplc I Pii,itIunterrl~ll 11' t ~ (~i'),! 1 it1 I i.4 ' i ' 'ii ( r on I'- \fluai Aiiid Whi I rs , )i.Ias-.i .. ol Iii' 1)k c\ .s it. d iu l l 1!ii' I tiulii'uuleii \liu' roe n~m tlN, cst:n..use stuiit MiC .is~u ~I'iic)Iim 't: III II l.- !'!, i C J-1d '. til ' .it . 'f 1101 'i .s lhis bee:n ilslireutd hs is siii-lo9 ti i i ltliii: till)ii'1i, 111' .~ l) .I'% .. lii p i It I, 'i-iinUtC ( CI 11AuODib l:,seruId"e siti]cikIissu 111 11 pl I

and tIcnpioil (4 _. I,)) po\Ai pct fl 0-~ i 1',', 4

*~w '1... * . I Rhodes. t !rikh, ind Simion 19 '. I )CUbi'cki I IIl )IIi

141)

2(0

PAPER D.

TmF Asttiwivim. mA Jul RNAI . 2CJA '46. 04). It')52 JElkI

C 199 2 Thc An-~. .n I A, I, ..... 5. . . All ~ a , ".- A',w

VERTICAL FLOW)%S( 1 SUPE R(IR \\. lAR A\NlD) \ISOG;RAN T[A R SCA IT OBSFRV E 1)ON 1 IlL SU.N W\'I II OSN

LAt R IN( J. N(s I I1 I tK .' -11k I 10() M k I. AN I \lI IARIN i B. (I 1 11111

j~ ~ Lhcrpjr *rr~pts.I1 . v'crit of (nj Vll~ im ,.,,d Uni -0%i oil (iC.L ol.ido n i,111:I,

ANDI

CIEOR61I W. Sj\ (1\

Satrameni' Pc~ik 4)'~ i!

Rel',! ed I1'J t~u ria 11,. ', / 2h,,a

ABSTRACT

Stead'. fltm. .hi'.c ber ohser- ed at d:s k (enter oin the quiet SuitIn ' a the U~nis critIs of Colorado

Ultra,, 'l'.i SpLc i icr on 0S\( ) N aind Ilhe diode arrai.. ir1itrmcri at SI( raiiicntoh Ik.A ()hr'ar

Sirylilt~oicoui oh r\ations ill Fe I X§Y'n. Mg I\ ' V itd Si 11 \ V I - .illo%\' ii III i,,hllp IIC

time- a% cr.igcd Dopplet \cloci tics oser ainet zht rangc ot 1400i kin fr 0o1 11C phlolther 14' tthe ;niddli.chrornosphcre It 1, !isi\n thait paitterns (if jstcJds sertical e'c twh.. i thc larici -. d 1Li1 I'.

supe~r~i Illai itt' pe ti the tn 0ll lroniosphtrc. '.5 tIrC 11112 C0'.oireae '. \ itl hos 110 C n

Iov~er Ii thc iwib '-: her S!01h 'wen Alre WC11 t' pCr-:'1l or ait ILLt'4h. ,Nsiih bi'k nilwe teii

sp IAt Il tesin l i ; x Vai wl tni:. 5.o tw attplitice inerease fro mt ah -it ',() iii ill I L. I Aind M Icrrn ir i '. n ie 't :. t! t. i i up o.s te d k r ar s (hs r d '',h liIit) ahoul *,I' i In Si it Ilich r rmat.iI rkeso1litii'n reseals tlt~it .1rito 1 'l Iille-t hoiiion iscales Of J" (IL I 'ire ' 1111present in (tiC Sf 1 C11 k.' ft'. J.!t, aith n theeI (10 10 no 'Of?'.iW irck liiwithl ihc m iniliiin -ccn in i-c i and Nl, I 'il 0'C restn'n h sai [ill, It OW

[;MC asrct sJ v. iOUt -'1 11 , conaretl '.srth abuit 41) Iis Ill I c .Iand I IIl,, At

.'jta I i. itlu s'11i atllospltri: miotion, Suin ctirontosphcrc Sun vranifiatin 7.iI l , t i n :.: c I nt l, tf.'ire lit tihI Th'.F ret Ita 1 011,0 ri r. .1 01 v01C~l~l 1 tI 1

th all'I A .1 i H- I i 1 Illt< %tilti pei~li ne u11,. i ne -Ie \P tis I , -~ ;Iiiro

hi'th th, 11 -1f.11 -11 111,, the -I r ~ oti 'I[ II 1 t %1 - 1 1' Jj

C : f-ICi i. d l . 1 1 ; iI I I

h , cf 1 1 11. i t I I ) t ll Ii 1 Lj! X i ' L L I ' l 1 I ''

the~~~~ ~ ~ ~ ~ ~ .tw I -.' i, . ; f111 111~ ld1 II . l i:IIII

%- l - - - -

PAPER CTHr ASTROMYI, ktI IMt ~~ ~ Q m Oct~cwhtr IV

STEADY It (M'-, IN I IIt Sol-AR TRI IIN l(jO 0131URVEDW) I~ lIii

KA~I AR I 113 (011 ,Iti I . FRANK 11111 A-,~ 1 i-Ri Too%wgDpitnc'ii ,f A- i IN ii> Lin icr . I rad \jiwriaI Iijt,-atj -f 'sI. Ind ard". a d liii ItII itic [., I -Ik.,rtr

I.AURI N( I J NiI \1141t R .-XNi (11 tpw0 \V SiIMONSa tri~'nt ~diI h,cr\ i r Suntp,, Ni' Nicx!,, i 141

Jositi B (iiR ,-\N-\r'' R, d N'. -ccl N ASA td'imrd SpattC f14ii _C'.i : t iC O& ct 409. (IT N ' M r" Itnd 7

Ri(IIARD A' Sili0 -\I) BR'(It - .\U,,

R. (iR..N ArIH,-\N

El MrO C, 13RI' R, JR ALNi) R .1, R. A Ri ii"'Ict Al".i~ !' .l ' i( ,rh 1 12'ri r'.. Hint ,ir PtIh' Ali,. ( h ' 14 4

AND)

EINAR A. ' \iRC,-IIAsSt NN mSA Mir'hjli Spa-:c I I..tc ( enc!Lr. i dc PNOt tf,~i4c A1.1ihmi ~

A13STRA('1Stead% ;lx. it Ihc t c t~1 r,;n'iItn rcpiln have hc.cn ohserx ed \Aiih hei UhIrxji let

Spectr(TInCIrc Ind P' 1 i t. S11 -Nr un men? oni 1!1'-' i !aunz AftN"? tutu N' 4 jIt'l

The per, ''';:t~.', m . ut~P cc t Jk vittev hav pat~l Till, .mplmiutic, -1 1 4 kin N 1" IhLC 11 litc. ]1i 11 's I - mli k in III C 1" !tic Z11IMiIde t lit-e more hotrviontal l.Seen 10 . I i e ci it TIc !)L i' A ttitt h c~r lts ol siid .rt!Ial Nelooi\ .Cr~ls ifn .ii\ -'

seen IT ~ 01d -& P1t Ow 5: At!ii h~tit di~inct niancN.

S lhj hi 'NX 11101j~eit. ntilti Sun. dicrom.i.srhlere Sun. corolm

I I N Pt) I tlit'chrornosphecre We hlk\fltu'wx eIndcd tickc obh.,j

The reuli r'. -': 1 Ior lic P '~ti- i rcijt lions~ At slcad\ ~t it the ltt%%cr IrriNiliti c.

"etc - : f nd , I . , I ii * -,. - II- it Ki, u,,ing the UA SP VXpcr':ITIIt- I Ol ' )"i t NtOl StUd, ORme hi t.' t 1 111%k' 'It (it, sateillite File results prc,,cntet.1 hecre \\crc t'Fti.tii-I Pittm

quiet Sun andI ncir I if ticr c ci'-'r.. 'o'sert. tion, in C ij A 113( 1 2 1 o ' K I. Si I N\ hition-. V.k: it Iid ic - i t. tt'l t Il the I-c I 414 t - I c 1 K). antik IN MX 5V 4S I II K)

* ~~A5576, N14 i ji, ; .- nIN I Li'. I-iO rsious rnea.- Lrenicn. ttf "it,ik fli,\ ilteh,'I ii ti

the Smjr~ijiwt'i P I -' tod hi.N.pt tio re.:: tn haic been made h\ Ic' i- wi d H' 'f, tj~-.i

n'.iruwit aril t'i'c n ific' it.Pdc h Lltrtittct S;'tt rtuteL'k ttnt eUN ) ' 1111 m It T.I.i, dSpe~~tiimitr it Vt. itt -. ,i.:~t t '.ettht.i u '.eietr~ JII,Ce'i- Si 1% XI -ilt') 0b'.er\CtL \\101 .'I'

1979,~~~~ Ti~~ t t 2 t !7 -! 'jm,-t-' rIp- *.ItII 'm i t'.'~it rc't-~c 'i~c per~t.'icl tim

ijh t '-1'A, kit) I'ii I!, Ti:- t" f,*~ i tir~i IIc ~rtt IV kl' At" lt P tu w~

NP cmI td f)Ii ~ )L IIIH-~I N N I i' 1 1) 1 '1 IL "t!t'

*~~~~~~hv Vuttr .. ic h- .IA t 0& xi*, ,ih , ir'-trmmIsae tti.itt t

h~~ thu N1976) t. hipma lutrait 19- is. l Btpl ruc iit~h ( I i Ind A0.1

4

11 0 M10\IW ' '1 IM 11

18

PAPER B

Tim ASTROPH(YSICAL .ttliti. XL 245 Ii2-. 6 IM Mayv IQ 9 1The A..,kenaf A .1 t ,t Ii t) i k it tetiset I V tttt in U S A,

DrI;[ETFICTIIN OF1 \1lSO(;R.\\VL.\iH)\N TIF Ni: j

IDcparivic'itof \eilro (cph~sic,, Lritivtrsilvi Gtemrat it ald J-1t1i Iititt f-r 1,-L 1 t r.Cniversity of CoIirAdO andt Nauiit Qli~ti" Siull.

AND

GEORGE W~. SIMION

A~ir Force GeophYsics Laborator, Sacranwit J (I'v fl.r vii,'r\

Rectived 9QSO Vozembehr 3, accepled 1jStV 'fawirl 13

ABSTR ACT

'rinit avtraj~ts of vclocit\ measurements at disk cuntt r on Ihe quict Suit rcvctil hI tit- itnm1fairIv statittnir \ jAtt I1 'I I Celiuiar tl, -,% ith a spatial scaile 44 3 10 \till. Saio t l:,.t.rtYia spatial rins \-,rtit Li v -b)cty Itintlit wlvlt o liut 00) nis - sliepisetd )n thc kirger i 1;1 1 trgranular tlti\i . [hei Ii-imc -e f nin, irinuhcs appear to) be at icast 2 hr.

Subject hlea~litl,2: sn till msplicric moittionls -_ Sun: granulaioin

1 . IN rRor~tw:lioN wSvteniatio, e-lItilir floe. it diusk t rilt r hlitc t(

One (if thc strIkat! jtr;trtlis )i the Jt crvvdi etir; lar.vei inIt(nilIniyt 11,11k It- .I ein\

\1 ti ( I k r, In L tr: 1n t. fi lt r~~p lrii r r1er 1.) 1ii Tv hIx vi ;ni~ 1111

cellsma biixitef rtIrr 1;() Min m,,rr-ttr th'i Wl'itIht i tit 111 iltiittri 1--,;1~

cellular peiteris f ljiti ~li' antI , T)UtrLiit- ilu ' 1I -1 ~r u l -n i,tion sliiu a rainvc ,f i/., ilLr, tit riul -ti ilc I

d tiffer h\ a fot tttr of ;1I) Th t xit nit -f ( i ill 11 il !tl:u. I nI- it m ,isiurlI I~ h, lai_, " dr . ii Wi a'.

held ~ ~ ~ ~ ~ ~ ~ 11 jtLtvt- .iii-il \r in.i v crn ii ~ j;r.Kqimi ltl i Iit: id-.[( kh V t t ''I

rotation.Wec riutirt litre retO lit tl-cvx itin, of I.t ol\ vtrtitt a;.11LtIt an oritr 4 iiuintil:I iuir~vr. 1-t tii a

velticit\ thait i -trilnv vxii~~ fmr ,t inot tir it-ri %U1 h tr ime , i t-11 rI-i

sicae of t S it ilit ti lit w ",i t h, (r I it -kt i or. 111t

P'eak ()lt-,t rvi',ttr\ 7itI 1

i I l TInt rIt ii if. MilstRk\AIIN5

SIgnI III a s it It lle Of 3 110 I th inIp r.t r at Fh 'SI~ li I t rritV t Ie ~ t", it t-.\i I I f i I -.

r ~ least 2 Itr. ThiIt-c stu toi II:rt bI i t - I,- I ailel V( h- ll' l I) tIrO'rdLp ath I li it I i - vi li-:,11 i

-. in a t-;ttr tmbn I i- i L hr lir-i- tl-r Muom k [maL-t-s V),T 5 h r or -triitil ib-~ t Iti . It,

li e or -d iit kk ,, t 11:1 , iI ~r T a ra s It i j- Iin o v(it!- r iz , i I1.1, li

717

PAPER ATHE ASTROPHYSICAL JOULRNAL, 2227:(A)-t 1 , 1974 Janiary 15

C 1979. The A',eiic in Aw-o - Ail rlji re-vred Printed n U.S.A.

THE H-JIGHT VARIATION OF SUPFRGRANULAR VELOCITY FIELDSDETERM\INEtD [lZOM SIMULTANEOUS 050 8 SATELLITE AND

GROUND-BASED OBSERVATIONS

LAURLNCE J. No.VrEN1111RJURI Too-IRE, AND KArt1AR1NE B. GEBBIE*

Department of Astro-Geophysic-i. Untsc-sity of Colorado: and i)nt Institutle for Laboratory Astrophysics,Uniiersuty Of Colorado ana; Naional B~ureau 4.1iStandards

AND -

GEORGE W. SINIONAir Force Geopthysics Laboratory, Sacramento Peak Observatoryt

Receit ed 1978 June 5; accepted 1978 July 20

ABSTRACT

Simultaneous. satellite and :,round-based observations of superpranular velocities In the Sunwere made usimne the ljniscrsirtv 4t C.oiorado UV Spectrometer on 050 8 and t,ic SacramentoPeak Observators diode arrav instru-ment. We comp~are our observations of tl'c' steady Dopplervelocities seca tow.ard the limb in the middle chromosphere and the pheotosphere: the observedSi it AI8I7 and Vc i *' 576 spectral lines differ in height of formation hy about !4 hl kmn.

The strikn! reSulr'S of' th ee observations are that supergranular motions are ahK to penetrateat least I I dcn,,it'. >xIde heic hts and that, in dolig so, the motion increases from anout Soo) in sin the photo'phere to a t lea' t 1000 m s - Iin the middle chromociphere. Further. i~ distinct chanLcappears to occur in the floss structure: whereas the horizontal :oinponent of tlic velocity pre-

doiates in the los photosphere. sucnte.;ting strong braking of' .ertical momentum, th io t i)nihigher in :,i'e ativophcre are more isotropic. These ob,'ervations imply that supergranularvelocities should hec es dent in the transition reigion.

The strong horizontal Thear lavers In supergranulation must produce turbulence- .nd internalgravity waves. I-s-e smaller scale motions have bearing on chromospheric heatingL_ and non-thermal lintc broadenine.Subject heading;. ca nsection -- Sun: atmospheric motions - Sun: granulation-

Sun: spectra - ultraviolet: spectra

1. INTR()IC[;0N the region of greatest convcctlise driving in the Sun, as'

Observations of velocit', ficlds o~rig-inatinti, deep in determined by, The Rav!eie2h number based on the locailthe solar interi or %souid erc atls aid :he oretical model., uea-btcerdetadtednst cl eet

of ola covecionandn~nneic vnao~.If nsie- The details of the con',cction may be fairly sensitivelengh dse r ptons4 s e'in ae na gude, to the structure of the layer between this depth and thie

cengthtise riptions 0i til _,ir-.ccin ar ran stalies surace, and supergranular motions may therefore:originate ~ ~ ~ ~ ~ ~ srv asee~ inaeieir hssie~sta probe of this intervening region wsell. IForI

observations of the eIict% fth1d-, of' oiait cels -mid ,uch probing to be effective, measurements of s upe,,r-super-ranUleS Vssoud be parI.1 mmarlv u'fLC11. the forme granular velocities are needed oxer a broad rainee ofbeing of glol h al andti k!e h;i tir has a, hoti/ontlt heights in the solar atmosphere, requiring' bo th liero L I.d -

based and satollite observations In a number of ,pectralscales of about 10,1i1) k. m. I lie iint andO asso- lines, The Nertical variation oi' the velocities and ! heciated varnatio)iis in direni n1t~liun Mn the SunT

haveprued i thuliI ncr5 eca~e t thtr ery intensity fluctuations Could then be used as heach-lowvelcit aml:~iii- Si rriai~i ''hicty iels, marks against which to calibrate the functional forms

whcra. tc- e~I. r'ramitds r that may soon become available from a,idancedmhire re, e I a ur,': -t i s r cniae theories; of convection, based for Instance on aficlisticfore deaild ora,tl ;ii,! I, prlihc 2ors ainly~~c' modal equations tTooinre et al. 1976, Nelson andforerai ir Musman 1977, 1978).by buoyansiar~e P!in n- d iU i 'trie mainl Supergranular motions are also of ( nsiderable

helium a ;i iorcea iri eihti -,ii w hk.iiiis isn alof interest for theories of chromospheric ncatl nii.helum t ; nni~i i .i17.if)krn I is ,, i~o Theoretical solutions for convection ,ulngest that

*Staff Mcuuhcr. N\'l'hi il tic! i o srrdl . cell .ular motions with the large horiz'ontal 'cailet Oera'~Iby h N'. -'I ~i c ic. hr P~cach typical of suipergranulation should penetrate rni rch

in Asirn f,-., t: ,_ ':r r ' -- ith ttc Natroiii ifct higher into the stable atmosphere than thioe wit theF-u und at~ori smaller scale (about 1000 krnl of granulation. It S

600

16

Paper R.Gough, D.O., and Toomre, J. 1983, "On the detection ofsubphotospheric convective velocities and temperaturefluctuations", Solar Phys., 82, 401-410.

Paper S.Hill, F., Toomre, J., and November, L.J. 1983, "Variability inthe power spectrum of solar five-minute oscillations", SolarPhys., 82, 411-425.

Paper T.Hill, F., Gough, D.O., and Toomre, J. 1984, "Attempt to meassurethe solar subsurface velocity", in Proc. Conference on SolarOscillations, (ed. G. Belvedere and L. Paterno), to appear,(Univ. Catania Press).

00D

15

GROUP 4. (Papers Q to T; Thesis E).

Solar Five-Minute Oscillations as Probes of Dynamics

and Structure in the Subphotosphere Observations and

Theory

Our work with the five-minute oscillations of the Sun has

sought to use these wave modes to probe the structure oL large

convection cells and of differential rotation below the surface

of the Sun. The necessary Doppler velocity data sets have been a

natural adjunct of our observational. work on the persistent

flows. The results to date appear very promising, for we believe

we lhave been able to detect strong flows below the surface that

may be evidence of giant cells there. The results of the

observations are reported in Papers Q, T and S, and in Thesis E,

and the necessary theoretical analysis of the advection of waves

by large-scale flows is discussed in Paper R. This will be a

major area of inquiry in solar physics, and we have enjoyed being

present at its beginnings. However, there is a great deal of

work to be done with inverse theory to help interpret the rapidly

improving observations, and thus this subject is also one of

lonq-term research investments, much like convection theory

itself.

P~zpe r Q.Hfill, F., Toomre, J., November, L.J. 1982, "Solar five-minuteosci]lations as probes of structure in the subphotosphere", inPulsations in Classical and Cataclysmic Variable Stars, (eds.J.P. Cox and C.J. Hansen), pp. 139-146, (JILA).

Paper 0. 1

Zahn, -J.-P., Tooxnre, J., and Latour, J. 1982, "Nonlinear modalanalysis of penetrative convection", Geophys. Astrophys. FluidDynam., 22, 159-193.

Paper P.Latiour, J., Toomre, J., and J.-P. Zahn 1983, "Nonlinearanelastic modal theory for solar convection", Solar Phys., 82,387-400.

medium below the solar convection zone. This has major

implications for magnetic dynamo models, for it may permit dynamo

action in this region and thereby overcome many of the

difficulties with magnetic buoyancy of the evacuated flux tubes.

I

Paper G.Latour,J., and Zahn,J.-P. 1978, "On the boundary condj 'ionsimposed by a stratified fluid", Geophys. Astrophys. Flui I Dynam.,10, 311-318.

apaer H.Durnev, B.R., and Latour, J. 1978, "On the angular momentum lossof late type stars", Geophys. Astrophys. Fluid Dynam., 9,241-245.

Paoer I.Tounire, J. 1980, "Overshooting motions from the convection zoneand their role in atmospheric heating", Highlights Astron., 5,571-58C.

Paper J.Zahn, J.-P. 1980, "Stellar convection theory", in StellarTurbulence, Proc. IAU Colloq. 51, (eds. D. Gray and J.L. Linsky),Lecture Notes in Physics 114, pp. 1-14 (Springer).

Paper K.Hathaway, D.H., Gilmam, P.A., and Toomre, J. 1979, "Convectiveinstability when the temperature gradient and rotation vector areoblique to gravity. I. Fluids without diffusion", Geophys.Astrop*Lys. Fluid Dynam., 13, 289-316.

Paper L.

Hathaway, D.H., Toomre, J., and Gilman, P.A. 1980, "Convectiveinstability when the temperature gradient and rotation vector areoblique to gravity. II. Real fluids with effects of diffusion",Geophys. Astruphys. Fluid Dynam., 15, 7-37.

!aper M.Latc ur, J., Toomre, J., and Zahn, J.-P. 1981, "Stellarconvection theory. III. Dynamical coupling of the two convectionzones in A-type stars by penetrative motions", Astrophys. J.,248, 1081-1098.

Paper_ N..Toomre, J., Gol,,h, D.O., and Spiegel, E.A. 1982, "Time-dependentsoilutions of multimode convection equations", J. Fluid Mech.,125, 99-122.

12

P tackle the highly nonlinear descriptions of solar and stellar

convection using modal equations, and are essential ingredients

in the development of our theoretical approach that promises to

unravel the flow structures with depth in the solar envelope.

These constitute a wide series of papers, and it may be

best to summarize the main results of our theoretical work to

(late. Firstly, compressibility yields considerable asymmetries

between upward and downward velocities within three-dimensional

convection cells. The fluctuations in pressure, ignored in

Boussinesq and nearly incompressible treatments but not here, can

even lead to buoyancy braking near the top of a supposedly

unstable layer. Thus penetration upward, as into the stable

atmosphere, can be either impeded or sharply diminished, whereas

penetration below the convection zone can be very strong indeed.

The role of buoyancy braking should lead to the lateral

deflection of rising motions within the giant cells as they

* approach the He++ and He+ ionization zones at depths of about 20

Mm and 7 Mm below the surface. Thus we may expect to find strong

horizontal motions there, and possibly only very feeble

counterparts in the atmosphere itself. A similar lateral

dleflection of supergranular flows would occur at shallower depths

below the surface, and thus a greater horizontal velocity would

be evident in the photosphere. Our work has revealed the very

nonlocal character of nonlinear convection, unlike what has been

assumed within mixing length treatments. We also find that

penetrative motions are much more vigorous than predicted by

* linear theory, and can serve to modify the mean stratification

very significantly over the extent of penetration, such as in the

*° '- - - --- * "y w c- . v ° J .v - - -- , . .. . . - •. .. % . D . ° . o i .

--. W.r •

"'' - -... "- "" .. -- . ..... ''-- " PAPER J I, '----

>.v-

STELLAR CONVECTION THFORY

Jean-Paul Zahn

Obser-vatoire de Nice

06300 Nice, France

I. INTRODUCTION

This meeting, which deals with turbulence in stars, opens with a review on ther-

mal convection. There is no better way to state from the start that among all insta-

* bilities that are likely to arise in stars, it is thermal convection which is the

most firmly established as a cause for the turbulence that we observe on their surf.ce.

Our confidence in this comes mainly from the theoretical preoiction that convective

instability sets in whenever the density stratification becomes superadiabatic, as is

expected in late type stars whose outer layers are very opaque, due to the ionization

of the two most abundant elements, hydrogen and helium.-And, in these stars at least,

thermal convection occurs close enough to the photosphere to influence, be it indi-

rectly, the profile of spectral lines.

A whole IAU colloquium has been devoted three years ago in Nice to the topic of

stellar convection, and one finds in its proceedings an extensive account of what

was the state of the problem. Some progress has been accomplished since then, and

naturally I will spend mo3t of my time describing recent work, and even work in progess

that I am aware of. But on the assumption that some of you are not too familiar with

the subject, let me first recall some generalities.

2. A HIGHLY NONLINEAR PROBLEM

Thermal convection is described by a set of well-known equations, which state the

* conservation of miss+ V.pv - 0 (I)

at (-)

that of momentum

t+ (VV) -VP + 1 +1(2)

"0m

- .

27

G-ph. 4-i- -h.. , d J 1). 1 .YN I 1 1 ; 2X5J 116

0 (;' -", ii 'd: H'-i t'1,1 PAPER K.

Convective Instability whenthe Temperature Gradientand Rotation Vector areOblique to Gravity.1. Fluids without DiffusionDAVID H. HATHAWAY

Departrnent of Physics and Astrophysics and Laboratory forAtmnospheric and Space Physics, University of Colorado, U.S.A.

PETER A.. GILMAN

High-A 'ttude Observatory, National Center for

Atfrospheric Resea3rch, U S.AT

JURI TOOMRE

Departmnefir of Astro -Geophysics and Joint Institute forLa)boratory Astrophysics. University of Colorado. US.A.

Receite Do re wiher, 197't

We carry out a linear stahility anialysis of fluid layersi under uniform rotation whichi po~sessboth %rtical arnd hoirizmntal temperature gradients. In order to represent artous latitudessitf 6,:,e piatie rpitillel lasers we use a rotation sector wnich is gtererail oblique t, t r;m~ty

We n idclJe flud k ittiout dill usion within a flotuNines.q approximation. IIII, .inplificd

c(.ih.iqrratuoni us'e (,rt oa~ tire preferred Loneeti-,e modes as a function of latituide on aplanct lik~e Jupiter [he tilted rotation vector introduces a preference for roll-like distur-bance, withI i ri fih-siuith oruettion,, while the horizontal temperature gradient prOdUce. d

thermal wind .hear w hicht Lasors coentstise rolls oriented parallel to the flow in anr east-westdirection 'iA'01 h- th thuee cihc i present wec find that t le horizontal teriperature gradient

needed to produee .i prelerecnce for the axiss nirnetrie or east-west rolls iricreases withinci':.airug rutiii'n raec and dccuea-i. laltade I1fe results also indicate tltat shuells with,watrftnt-qi it.ur ht - C -t MoeI IOI A otu prefet ence lot e ast-wecst rolls than do shells withf colequuit'rs, InI .diuluto we fuind that the tilted roitation sctor serve-, to make the svminietric

tfle Naitionuh entr for \t niospheric Research is sponsored by tire National Scece

2f99

28

PAPER L(,~~~~phI1" %,,1 .. I ~ ~ I . IS pp 7 17

0 G"'d' rId li-0., \ N. I CI.h IrV I'l

VPiI~d III i-a (CI Hua

Convective Instability when theTemperature Gradient and RotationVector are Oblique to Gravity.11. Real Fluids with Effects ofDiffusionDAVID H. HATHAWAYt

49 Department of Physics and Joint Institute for Laboratory Astrophysics~t* University of Colorado. U SA

JUR! TOOMREDetjartment of Astro GeophysIcs and Joint Institute for LaboratoryAstrophys'cs, University of Coloradlo. U S.A.

PETER A. GILMANHigh Altitude Observatory. National Center for Atmospheric Research§

i 'lle etj 0. i,,hrr '(,.I I)-())

I he I ineui ihI~ tNij!.i (;, ~IIh % I\ a~ht~ n di Too mire 1 19NI ilcrc, I te.r ieleriicd I,,

a, 11aper 1)1 r[j'it j !.,t fb3'l-uicC4 hliiJC Cith r~iitA d 1hertiil -~!iCi7 \, if, i'.Ipcr

I the fluid 1, 'niix d heIIecil p.iflie ;,if.LjdcI anktidi iC i1. tfe 7Il,111117 %CeIt :H 1ihl 1 ic [o'

grw~il I hi' 7.'LI.'i 'I.7 .'di 1 e iererCicc fo oitt l-Iikc diT,jI~hii CjIIIC

he pie '.i ,t .1 Iii id.i ic.77.71..Iturc c7..d.7it proIIJ' cI~ ,i heii l ti~ d h a r~ei "hih

the irwt"Hd -1111C luriIrd cI PA.i-r I I o7 liet IliiCli larver OtIMIIC;tC 1 71 . F1I-C I

partlI uL 11. 11 t rl IIlk- II h 1,11t..c 1 I Icl rlit I re ;.I r I . fI d p~flhlC2 I oI (the P'i ittdtl

n1 h rIh7ii. W! Ii I,' .'i Vi, .hti' ti irve . :7 i. i t ItI.C 'retII It .1 Ilt~i. '

I~~~ IlliIfIt

Sxe dI'j 1 , - t '

0 I ii- h i

Till Asli-w,t,;ln 1 iw P. 248 1 "1 1'sI -;ric-,,r PAPER. M

STELLAR ONA VI ( H~( )N'A I If 010 111II. D YN.,1 [CA L 1 PEE IN( 01 F I FI L I WO) CON VI (A IN1'N I S I \- IN' PE STFARS BY PEN I RA.I IEVE MO [l( NS

JUAN I-ArotH()hser~jt,,is 'If %!c I :,r .-: Of N1,c. .ant J.n institute for Lahorarors AmrruphNic..' Un.'.crsir. If ( 'I'raidI

JERI TowwISJ,rrr En.imi, 'or i0s: r oih D.e~'Ic1-aritment ,[ Asir..'-(.phsue. Uru.'cr,riti ofI'rad.'

AND

JEAN-PAtI. ZA1I NObser\ aror,, of Nicc. Un.i cr-i is of Nice

R ci c J Y5 h! N) )..."iiwr /, at eti I Q,,? tfjr it

ABSTRACT

Anea~t.; i Vc it! :. ins arc usedI to examinc thermal con'c ction occurrn, ne over mians detisi i>Ncale cightlii i i th,' critrrc ot'utr c.-iclopt: of .in '\-t~pe star. ec~1ottpassiui both the hsdropcri rtildhcllurn co.1"1"1i- ic~tre Si n2.ie-10h mode aaStIC solUUion fo r such COnpre's+ ' Y~displa ' strone_ ';C o Inof tlc inotions into adjacent radiative Lone>. Such rni\n e \%wuilE

precl!ude di: f.:'.%t Of~aj~ cicmcents in the supposedik. quiescent rceuon hetccu the i'' 0unstable i mc' I ndecd. the anchisti- solutions reveal that the two zone" 0 o sei e ta Ii,,dymnnncafl ~k pc i's the us ersh, 'otin_ fictions The nonlinear single-mode equait:u, atiflit t~k,solutions fo r ihe -awlw 'ii rid si e n nd these are distinautshed by- the crisc (if ici %crt~lvelocitN at tic Ornitcl ,I tIc 1h ce-6ti enal ceil. The Llps> ard directed floss> ,llL esk uelrpressure cftce!s I. licri t lies pceitrite inito reaa 'ns where the sertic:al \scale heigoht has I., oine smtallcomnparedt i i hoiz .e itril sale Ilie f 1lCuctatng prcssuire can utodikt the denisi tv !Iti .iitils 5(.

that the o i reh . icfoeislandw~lth buo~anc:\ braking actuadll JOCies d ne ir thetopl of ite ,c'ion c. Csen fhinJi the mean stratiti,:ation is :,tilt superidiah-itic [hlc IiLl

anti btoo an.. rk ti rLe scrN cs to dc(clraitc the %ertical mnotions and deflect them latcr . I. lad.to St rona. ho relw~ ootwA1 I' .uiC. t hus th shatllow but h IIh.untable hs droaen ion' it ilo 11i1t.i

mas~~~~~~~~~~~~~ ser1 tto cj ietois h I etlsaec arablec tI supcr~ratlait'n ir,: i'2i

throach! mi:. li .n .\hre ith :iri di.n portom of its .'r_,itimi it0MioMitut. Il:i]~eithat 1-t rton, i :ii~'e'Ar fl1Ws liu'1,li ) C present just beo~the -'arface of the stAr. anid sIiiili Is Sthat tielt: r..a.2 estendiniit :0 he stable atmrosphere Amild appear inainls as iotizwlita

Nuhdis ( fIi~ .COMn>cetion - otar,, atmospheres - -stars: interiors stars! nietallic lineI

1. INHW t (' 1 [ts, about 61~ of the total flux. .t ,1I a blue ho (I,% o0 der, I

Tvpiealis A tvpc lOir, p;-.css Es>o cowrlctof l on'.s, magnitude 2,reater than in mo 't m ine m netl n10 :0,Cl

one dirtisl- :1w iii..c .lr'.i , (L~ iin~nl 5 IIatoiur I1970i). rhouili ttixino-!ecthrer,4z0tiri

th Imeo/t di , f~tit aol :iIc tcpr dt'>ti be adisl to I' eId comllpara'ble flirses Mli\iic

drisecn hs the, k:,, ;id './,t .n it h-in:u .'t.diO 1977, Nelson I19781 These anelat s oluv oti hitw

mot m:inn-l.ii kri-ti dels. c tvo ,on h c ,te are reveCaled th'It the (conseetise mions nli.iti

sepair.i t d ihs Lvp i : Ciri .I a se c~ 'I hi.C11 are not jLust 0111111CLI to the rciown I Iu.al 11110k 11-I I

StUdird In It; P ii i- 11 1 1!C ,J On. j t*~ ure igradents Rather, (tie flms penectiate ,~e~ .,.. 0

* ~niotwi in ill klct; rK I' 0ti .,jej:si. hits hoth up~idand dossriwkard int., if, K 1

nroda; njii ii : r mn t5r i >*<W raterial surronrdine til ree~ion andi es-rt di i kti~

d~nii,, (MIi -, 11 :....Lbiilt.l5 iie' f tountcr, xlls We 1.otrelir(]dd(a oscI> ilittorisl

fr.'ir th'se i ct! it ; i en tr..Onieirs u r I\ . r the deeper- unstahle /one s tuidl estild it 11t,,.

iturri eOT,ti.i~ lo ii ie ck'ld 0er,1>1t'r1 11RN %t oscrling hIrt-,cn conseetise /ire.at'. 011: - -cwas not explitls icludeil in tile anakls i I h,'- I',

w ~.-~ - .- s4 * uwgests that fi the ro conteetise lone, tin ini \ spe I I .I1

Niit' ntd 11w'. I Y- mi lh .arc d~nammallsl 'Ilp]Cd, a lFCY111 contrars, to iiot iw\.

PAPER N,I'vint,, in ',-d' lh'b ,

Time-dependent solutions of multimode

convection equations

ByJ U RI TOOMR E,

.fii14'tiri' Si~ww- riVn~iNtt, of ( ''I''rotifui l~iider. (''I'rotou S0304ii V' S

D. 0. GOUGH

. i rr of(d Cairid'i . S'iIr S'tiret. t iitridg (B 9-16t " iij.Ilid

AND E. A. SPIEGELDepart niilt o t C''i i .(olumbima I 'riversit .% New~ York. Ne York I (K27, U S,:\

(Received :11 Main-h I I)SiI and in revised formn 65 JulY 19s25)

4 Truncated iwtdal vquifti iris arv used to study the timie evolution (i' therriinivonvvction In fiht ii~~ tpoiito hs olna qa os1 b~iiby expaufiihi! _2 th b tiiic(ltill! \(ikcit 'v andi t enperatutie fiel(Is Ii a finite si-i ofplanforro of tii liiriziiu! ciqiiates. Hevre %e report on nnierical stidievd(-;ihnigwith t~ko it hr,-' filuule, \iti triad interactions. We have found rich tire itit--doicein thez.,e ca~o-. jwriliew and apeiodic soit owns can he( o)btaine~d. along 'A ith NarlmovMt( ail 5011114 ii Tl ri. Inob 1 oinorv repro(11uce4 tile (qualitaIt ie j;I wfr (it'

spoke pirtevrn 'rieonas o)bseirved Ii experiments at high l'rairi imrni-,.Tho)ugll the \.-iwi' 4t ft- 1siiouI of' tile titlif it-wxdellt ,olitloins do4 not fue Ait 11those A'tfi I,\ Iin'iit,, their %; flit on \% it i 1 i,,rih nnicoil piriso- (-(II taoural\E~xcept at t Ill- hi,_tl-t IRal\ jit i winiiIT A r c nisidcdre il), tlihe b oretwaolINuaselt n1111110,4-1-, %%"'1 i c\ Fwr' ilerit.

1. IntroductionIll thel i~i'~il t til 'tw ki~ii \'etti-inniref to doribt Ilw ufo) toiliiro, of1

Tr i f-ii l,7i',o honriiitt-i r,-trin1 to, a I b)iniri. (Guitrh & Spi--tl 1')7'fiirvirila ti 1 11) W o iiui fit, Ilthr iii fu to1i I 'ft ille mill \i' I li t#rrni i)f

the pilitilii tin i''i- fi - U-;l '1i11h kcpt iii' a tvit, firii-. 'if %%> I .

rnlnr'r .i I u Fi" I It f f lit , IO A .)ti-i oi i lftiii II.ffiil t, i ~m hut

nv ,- ffw o tl',l t 1-i-1 Il 1 t a -~ w 11 l;(J 1

* ifr- rit f li - Ir il Ii ~if' ' iiu l t '. 11i4,1- -fui- I w %% I ' Il , I'iiiod iu-ruapu- i it.

4i w l , l t b tI 0 .-( i l i , 1 1 1C 1 - - r ' l ~ i - i t tl r ( c il

31 J

PAPER 0.o iii' 'I"' A, 92 : ii2 i 0-- I52 VA 22 1 9

j .... d '..' ", II 195t2Pnid ,mt. H ...

Nonlinear Modal Analysis ofPenetrative Convection

JEAN-PAUL ZAHNt fObservatory of Nice, University of Nice, F06007 Nice Cedex, France

JURI TOOMREDepartmnent of Astrophysical Plan'etary and Atmospheric Sciencest1, wd JointInstitute for Laboratory Astropltysics§, University of Colorado. 8 ijitfr,CO 80309, US A,

and

JEAN LATOURIJoint (nstture for Laboratory Astrophvsics '. University of Colorado. BouleorCO 80309, USA, anti Observatory of Nice, University of Nice, F0600,- VicfCedex. Frarce0

(Ret eve,1 Januarv N., '982, in final 1,,,m June 25, 19821

Thc :iodai exp-insion proc-,durc ha, been -,sed to analyze penetrative convection thai jrisc*'V. hC) a tl~in uninle~~5c ivter Is eivOCddcd tIcLVcif ivo whsicl reg~ions fhe ou Fl 1k4t

approximi-nton is appl; c.1 in A.h;cri OI l A Ofcc wIt nnPI C1biI:tV LndI strita(IIAII01 II

rieglectcd-( Various C~ilcjAlt;OIIS l~ive been rraLde, %ith one andik tw~o modes. toi RaslIctirlnurnber, ringiiz from [he Lr)),.il Vdluec to more i.an to' tines critical I he etlckidecreasing the Pr;indtl nwnIa.r hi,ii also been ne-siieaid

It is found thct: in the Pnilinc ir recime', the c0flscctivi rfotiiln, penetrate suhs; it ilkInto' the stable: rcn.)ns. 1 h, 1LIX of kinetic e'nergy p~t'.s a1 crUcial role in sush Pcneaiotn.andI its existence f pit; sot112 rt, uitenints on the motiions: III the single-miode sei. thce')ic.'Ato be three' dimeinjouil fhe' cxtiflt of penetration aitunts to ahirut halt 4f thc ithiekites oIthe unstihle lhier -,n eacth side Of i1 When the ticiiree of instabilitv and that eli sitbilit. ii,comiparable in ife' 1,w o ouiins. :t increases as the ,ibiliv,~ of the outer rectfis) I% s eThe peti.t tion 1epth .ippcar, to he indepcrendcrnt of all otnvr paranietcrs de'tinin. (iproblemn

tPrescrit . Oirs~(bsrr i sty 4 Pie dlu 10i. 5200 flae'nere's de Bigorrte, U-rince

1JI A I, opcr.il 1,m!1 hy (tie I fisersity of Coloradt) anid the Naitilnal FiurC31u (If

159

PAPER P.

I NONLI\FAR ANELASTI( MIODAL. THEORY FOR SOLAR

CONVE.CTION"

(In tited R e vkii

JEAN LATOUR

lin in rie. i'ii c I,/ 'r,,icrA rrccph i oi% L iiiereine e liii Cc rtido. cuedo(hee reti 'iri e e' ice BP2 5:.

F0600-h .e Cfl/SEX. E-,i;,,e

j SJURF TOONIRF

Depacrccew 4i.',r'phi'cc.;1' P/'iecciiri w3,, Si'riei ' ~'' aii Jlle Inslate for Lehwal-eere-

4stroephiiiii. Lmciepsii ,I Co/loraedo. Houliader. C'0 'cI.,tlv L'S,4

and

JEAN-PAUL ZAHIN

4 ~~~~~Ob' eri at ire di Pi'-c-uA/idiei dIJrci 'Ca ce. F6520 '(.iBai~ere3 tie Bciiore frce

Absiract. Piciu.,,r' ~ erciocflupe rnidci haie beeni ciinipcleed u'ciee the singic-mccd aclc. e icc

ai .c de'rij~ci, 0! a .lhcnic;'t 10lC'iwnii I illprrnaLch pri)\ides ce'.ijcs for the C.iii.iiion~ %%:!i ,IL'IIII oI

the lariree't Lwi'c il'. ;:!1,ei'jr floii'. akin I, i,int celk, %eett hoc:ri tal 'is ccecpcrachl ic I the toiad il l~

oftthe Comce, flo'ii /ncI lcc 'li ceI''i tl Ctnrent, are cap ,t'cc Of ileichiei comrtIihstlc w ,W

ocecurrine ciscr imci, -dci~t' '.cew,''i Seviu-Ic miidc aefLeI'ii'',,i ha~e beeccil rece i c'c

enteiloe Mi-. ii-i 1,l'> iS'i c .iiiC -iaiti~ii owrF Int a i : \ccriil exicet hec:auee.i iliceriillp

(Ocr c,'Iiset'.i I tll.\ C,'':,lTI' crk h% till 1)11- 7Cil. a1 ec-ILI -. 1 r reeni1n tir'iln Ii

rITI ,''ri 11 llrk '0 13it~ HI(' til i , i i 't irir the Iur-Lic the''. mcerri c equaitio 'i i t ! -Ika'.'iiiiii

for the Iiiii~c i''i l ,sc'eeiiii ii~ n~ rc :thii~ii:ett c i 'cnrc t the ocrTi-al 11~.t 111,i

Leflier ?If th c' i~zimi,wt~ciA -cIi It II !ha~ 'it.r tile Up'svcd !;rctcdt t~cis, c\perriice laic ipcel cts M C11 *Ih c''''ct ii' t, rcrii'. cre thLrc.crticcal scale i-c, -!It li cecccnie sTllil cactj i rcditoo thve

lr.'rc;'ci !.. I C c ,, tii,.ciiit'' -''c'i ,III in'diI. III- det'ecit' !I'i12i.Cili,' o 0"cc thu ilc se Mi Zhr

huo',\,ii. t-ce~c i, car'to- Pa.Ctii~,cii' rckiit'i iciiiijs lacc nccir the top ,I tihe cieiii/c

[thc prc-u .,i IC I-I, \a n %' re\r , itr t ace 1 11 c.11io hl;t IM I t.10 I c111u1d IIe eci~tZ ci t ve01 iiCI ci CdII C r \C

I() jccli'ric ltie t i cliii cc inc.nd cietCLe: them i~iierailI' eier Is irongr hocrizonetal 'heaiiiirnc,'iii

It appce rs III,"' ii', h dii.kniccl priic'csews i1ii1\ e\PI;IIci ceii\ (Ilek:npt at'IIIIIINO tlonic recaed to' tie ktrr--lscale, cc c' iic rc ,c feeble cci the Iclcr atmosphrere

1. Introduction

The st ruIcture ofIic solar atnmosphere is (let ermined largeI% bN the con ection lust heli.,,tile SUrface and the % s that it can c'cncrate, The cotupling of these tuirbulent moionccls

wkith intlict uc ttlc urit canse mos~at (if wkhat is observed on thle Sun111. Ices e er,thcorcti,,:,l ()Ie ncie the df ritics of the solar convection zone and associated

4 fli~otions ini itr ibn.ichre i, ,tull \'ec\ Incomplete. For in stance, no detailed theorcudtal

Pr'''' ''''c'':, I -1-i~ P, fi eiec ' 'i c l~recdSeAr(~i/cecield cc tle ( rinc.ic

il J'c. r , !h, ~l and~ the Nationial Beirecm Of staniids'F-crc. ;;IC'P t I \t'(c'' i'

t Noces i (ii., ' , III, dI 'i CrCNI'i ct dc I w'ulic.

twher I'll, 92 1 - ;1 1., It'll i,l it .0 i is c c.2

i3

1$c i

the I ' c.cnercwl'ct IS a~itccrizedtoi rerc~cicei anri 'ait ihis report.C,ctrips',iri P lo iiher roerodrucifl by otihers crocisi he obtained trom

4tOliih ~lr

in Pul , ti .... ; 1 s .1 rid c v,','ic -c

pp. 1 31- 14 -, A - .H uldor, CO) (192Z) PAPEk ,

SOLAR FIVE-MIN!TE OSC[LLATIONS AS PROBES OF STRUCTURE IN THE SUBPHOTUSPHLI.t(F

Frank HILL, Jur TOOMRE

Department of Astr~physical, Planetary and Atmospheric Sciences,

and Joint Institute for Laboratory Astrophysics,

University of Colorado, Boulder CO 80309

and

LPurence J. NOVEMBER

Air Force (;trphvs1,_-s Laboratory ;ind AURA, Sacramento Peak Observatory,

Sunspot, W., 88349

ABSTRACT AIL

Power spetri of solar five-minute oscillations display prominent ridvge

structures in (,,) spare, whore k is the horizontal wavenumber and -w is thetenporal frer-ncv. The pos:itions of these ridges in k and w are s.nsitive tolarge-s cle velocity and tenperature fields over a range of depths below the

surface. We have compared observations on separate days to search for shifts ...in the ridge centrolds that can be related to different velocity ano

temperature patterns having been brought into our sampling region by solar

rotation. The results suggest that we may have detected convective flows withscales akin to giant cells. Comparison of ridge centroids on two ohservin!

days separated by 27 days, or about one solar synodic rotation period', show nosignificant ridge displacements. Other pairs of days generally display Smeasurable differences in ridge centroids, with these corresponding roughly to

changes in horizontal subphotospheric velocities of order 50 m s- . Our

limited data suggests that the horizontal pattern scale of the cells is about5/27 of the solair circunference, or about 800 kn.

INTRODUCTION ,1

Two-dimensional power spectra of high degree (100 < X < 1000) solar

oscillations possess striking ridge structures. Such concentrations in power

for the flve-minute oscillations appears to arise because these acoustic modes

are resonantly trapped in the convection zone (e.g. Ulrich 1970; Leibacher and

Stein 1971; Deubner 1975; Rhodes, Ulrich and Simon 1977). As reviewed inthese proceedings by Christensen-Dalsgaard (1982) and Gough (1982), theobserved horizontal wavenumber k and temporal frequency w of the modescontributing to such ridges provide information on the mean stratification ofthe Sun; they can also serve as probes of large-scale velocity and thermalufields in the ;ubphotosphere. Indteed, Duhner, Ulrich and Rhodes (1979) -

sought to probe h'ow soliar rotation variei with depth by using the five-minuteoscillaitions ot high degree, tlouch Gough (1978) cautions that the inversionof such data Involve- considC:rdibl dellricy. Here we report on some aspect' Kof our ,'ntlnki rq; program of obs-ervation-s designed to search for variations inthe position of tlc ridges that may be due to different large-scalesubphoto!;ph,,ric cnvectlon patterns being brought into view of our observingwindow by solar rotation. We ,shall show thit the possible presence ot giant

" " i " '.:i :. . .Ll. 7 . - • ' -. .2 . --:-:: -. -... . - .- . - '.1" .. '-.< - "'"" :, -- i.;,,,,, . ,, ,0

34

PAPER R.

0ONT Iv IF1) FEKT10N 01F S V 1IOT0S P1I ERI C

CO0NA FCTl VE N~ F 1, 0CI1A FiS AN!1) TE F 1 PERA"I' F

F 1, U (IU %T 0l N S

D 0) GOLGil

and

)(wit )~l.l. I j". .u I Jr.phli ,,:i Dc;,,r,'n'ir t-' pfil a! I'!ari.i o id *lz''''' i, ri,

So en e L 'utcrwt lora,, H, (!' i.1o t SI

Ab.,Irat:. \pt~-, jorc is . ,~ ti cIir j i :ic .:l1ncQ (1t !,11C- 11,2 L(Mt' cddc 011l tile NkAI c

f!CIrc 1 Icrl , I i ~j c -1 , rjjjhCr k. 'it.: PhIiu.p IIr.r1l tkltropic ..ocr 1IF'T " hlci it 1, p'1" Cd ", ""k auliriitiIc

cvn~ctl5c 9-s I he ic ,ijtitiui t Ow'. - ,sct u11,1 ha, "t nt:.c i ic dclp1,ol ii .c ri ;utlii

compfll ricill ot 0!, -1[%; '. ;1 9 .. i 1 , .. 1 i hcI ' cA ~ c uCC11 111 s 11L-1121 1 4 tic 'lrh cr '-,!sd

on iv'ifir.!': il~tL i I k 1,Ol I ,I ' ,cr tlic , i t the [S l1 ''!JJC A OIt t i t 41;i'l 1

tc h 1:11.14 ;-s-cl] 1 'l t!u!~ u t t 1h (ittcrc .s reisoral lc ~ i [ it i! .1 ,2 pi,-,Ic torecci

,ime a~c it, M Sc i.:-cc ibit ii it the solar ':01tSCitioll Loiud

1. Introduction

[htrLICtire of-the xs as that produce the five-minute tilatijoits'the Suin depend

prirtc:ipaflk )nf the nmean -ertical stm~tlioccttlon of temperaiture. Fiat str,ititic.11101 dtetflhlfe\ ak burl. sell deined 'enuenee otirelAtion'-bt' e I u tri ad thechorvitilstase nitti of the 'lcilhations. I1,hi' ha , hei e'.hihtetd !or the teail SuIT Int 1 ~e,pcctrakof lDippicr ttcusrntnsI .1ehner cia.. 19r')h. and il'tpimicd'A itt therni

to detclrttiitte the 'idi'h;It It the isentropic: part ot theconvectuolt I~ IcI cL, Hhtt'tttel

e t. i t It uh( is ei X e% c~ xr. t hese re, Li~tfs are titt pert ects1. miititit d

frcluciiy I s It, t prei Icil ioetermnned hiceau se the mto)des do not persistI rii it l.it,

the \-,a% c pat terns, are d isto( rtedi h,, rot at ion anrd the in homogenenies c .~i,it vd it 1th

c c( e(tini I t Is dite parposec() i i Is pa per to) report a prelinti nar\ ti ioreIticIt: (I IesC\l111121il

of the imivenitudc 1 l the di ioriio n,, xsith i % iet ill the e% entul esuemn In. 1,ilCII t Ihei

vcIoclt\ antd teltl 1rir It lu Ittit Ionts i n iticecelin .eetlon i oe. In ir i a pclttlpll\ Iiin 1i, Imit

I( ll eir ol, , 1 ) ,31 ohsrvi it 1 es. idece fo r such d isoiIon s is- presen tedt

We relstric t ,aI r it tit )it to itidest ( It hiih degree. I n tflt lt: wa~ the osc IlI iti *fl in-tre

trapped in I al hiii. %it ave Ctd 2.ILClis t hcet ih the photosphere. Ithe !ase Ic 1 t ttIt Ippli

region ls at a depth or Aih mtit I R . shere it and I are the order and deet cc , t te lit It:

*Pro"ccti -1 1 ic i1t I At I .'i't u'l: P-Nm,hb m S'ar;? it! , lw ilan w. hedit lt Iw im,

Aslhropi Ph 6 1, iI I Sit. 11" 11 trttc 0isz

7, nh ' I h 1 1) cidI " I'l, ( \;I-:, i,h, lit /I s, Pj~ /1 't I S -

The u.S. Govearniment IS atithor'ii to rewwlouce al sell t his report.

Per 0,sO'l for further repr()djo,~, cb v othiers mus t e outilind fromI

th ,pyih ow e. - -- ------ '~

PAPER S

VAR I AHI LI N I N I'll 110%N IR SPEC iTRUM X OF SOLA R

MIE-NIINUTF OSC'ILLATIONS*

(Invited Review)

FRANK FttL ind Jt'R I 100MIR

AV; F Phi V:. l'. ':i,f 'Fill . , huf Ru'( ol(d 1 0 i NOW9 1, . 4

and

L AUREfN CE J. N 0VE %IB I R

.1.' '''. .. I a rir r, ,% Al RA, .Sat ~r'mn Peal, Ot,,erm,,t, .5im,jj,. A5 1I t. Si I

Abstract. I %,!r ;la A' At-eor I A ;Ii nnnt ~iJif~ Ip primireil i, ri ia. X

II It :ic i . (' A t ri i'zn:t l ise cw rher antd (:, is tlie i.-milril frek~iiicii.' I hc 1 ". 11 ,'

'~cri~uc. a-:1~t Oc .,> [o prohc tetanlt t j Itr s f, trm iJc Ill.--'F'.,e , -- : 'H'a .t.. .tr 'Ti 'Ohi i ii' itt II 0t)scfJt.,t ,I I\C-:1ritltc~a m ta

Arrisl !-'let 'ar F t r .. aa e It N aIcr~reuro '2 (P)Ixvrsmtors (SPi, 55a>.to ea, hci h, t-p a r'c trt kon ori scpa~rume do los r its Ii ridve li'cjitwns. toic~c mI,,I, -tfront dilc ti' Ip't'ralra hater lisng hccr, hromtluhi Mutu ItLir ,inwhnri -Ix'iri,tan''r P ;- '' f-- -iamcd ir i\ Lik, o ohSv,%jlatiri ": t)opr C1a. a , c

N~g ' I ~ i tei1c mor~ dCit.i set cosars i( t, I I hr Ii time anid sanip! .

''1 A!! a'Li-I rL"Ainiii ot 2 .Ind temporal i mphrnp re' t 01' hi,.0

dcrat. . . . . 0' Ic n , % Iin tdmid Wcs %%htCfl ire St,11T'sIa-mI( sia'trrric,1rIT I hn. ht .i,(~crOt tre,, 1ll1!\/-A 1' i i t eat a r, amid %kc~tV~atd prop.tn,i m;un wi ,- t

aII - . It I , nt:I o it1.t 11 CIC I t tI Id~ I L, erknrV r I II i o i hscr, 1, 1 .. %kn1:! . is% hsir i,!,s I- hie on Ili, order of [()I) rn %'c rni n c ~ tm'

thle J1,111i\ . ~i to '.inrl :C!1,s

1. Introduction

'Tda-~r..ce idnr pti dand temporal (k. (fpo%%er spectra of the olbsers edlis c-n t tm 1 ' 0: haSu ce , [)eubner ci al.,. 1 979 l. Such ridge-, in po.. crarehecatasa ~ ~ t . . a., ~trlpCd in the thermnal.structure bel w thie solar surf ace possess

a 'a url% so :! ' I ' ip hct skvcn their frequencN .:i and horizontal waventimnher kSin--- '1, IcVr i!iion' ', I, deter-mined larel hv the vertical straticatorof ;ic k)!-iia suirice, the o~bserxed positions of' the ridges Lould he

tel(,I ti a' r dterrn~ne at least the adiahat in the isentropic part of the:consc 'i-: io I - i'' lBard' nritua 1..ICi d- Libo% ct al. .1980)). I Iolsever, the

(i i C .. r' b perturbed hr temperature and %clocitv

1"( \I.; rtel. air li in. and so t)o bt diflerential rotaition. ThePit I 1- 1 ;I) Lukkl vid it attempt to detect shifts in ridge positions thit

* F n I ~ t i ,, ~ . .. , / ' 5, and Si h,4 Ow ...hmi',i. uhf 1 it 1 the ( ritlimeti

lit~~~ ~ Ik 1 1 . , , 1 in tii Ii N.itiomnal Ilurtim of Stird~trd,

* ,, , 5 ~,i nt is a ,ihnor/ t 1 11"-t, , -l t i.,!It this repti i

r T~l 1. Ut I ~ y "t'U . I -,' rIt i ell i rrn m

Pr c o f rci,.ce on .,.i.r 0 c l a tio n r,

(-d . , -" - , ! -. , ! 1 : . . , ,, , : " i r . t ,

ot Car.1niu iarc:) to apptar in 64 PAPER T, -

ATTE.MPT TO MFAS11RE THE SOLAR SUBSURFACE VELOCITY

FRANK HILL

National Solar Observatory, Sunspot, NM 88349, U.S.A., andJoint institute for Laboratory Astrophysics, University of Colorado,

DOUGLAS GOUGH

Institute of Astronomv, University of Cambridge, Cambridge, CB3 0HA,England, and Joint Institute for Laboratory Astrophysics,

University of Colorado

and

JURI TOOKRE

D pcartient of Astrophysical, Planetary and Atmospheric Sciences, and,oint Institute for Laboratory Astrophysics, University of Colorado

Boulder, CO 80309, U.S.A.

ABSTRACT The five-minute oscillation modes will be advected by-,:iz,.: . ' Citi05 below the solar surface, and thus can be used as

prc bes thr, of rotation and large-scale convective flows. Results ofv , t ..... r" a.ied to observations of high-degree modes carried out

x ,:r d,.>- rev-isl variations in horizontal velocities with.. " -v ta,: ray r h- the result of giant conv ction cells,

t . , n t u iati r.a' es this interpretation somewhat tentative.

1. INTRODUCTION

This paptr rep;-rts a preliminary attempt to determine the sub-ph, tenh¢ric vel:citv fi e!d from the positions of the ridges in the

,,v ) p wor sp-ctra of five-minute oscillations, where k is the hori-zontal wavknumber and w is the temporal frequency. An optimal averag-i I inversion procedt.re, used originally by geophysicists and which wass,:'estei yv the work of Backus and Gilbert (1968,1970), is applied toth, perturbations to thie rid- positions that we believe are induced bvlarge-scale horizontal flo. The motion is composed primarily ofd'pth-dp.ndent rotation and possibly a contribution from giant

convection cells.

Previously Deubner, Ulrich and Rhodes (1979) sought to determinefron the ridv' position how solar rotation varies with depth. Similara:qlvsi< ar ried to subsoquent obrvations (Rhodes, Harvey and DuvallI183) failed to r,prodnce the earlier results. Hill, Toomre and

FILMED

7-85

DTIC