Focus is given to possible variations in solar luminosity and accurate methods of monitoring it. Aside from direct bolometry, one methodology for this type of research makes use of measurements of the solar diameter and limb darkening function as indirect indicators of the solar luminosity. This approach was reviewed

Bos, R. J.

Caudell, T. P.

Hill, H. A.

English

NASA Technical Reports Server

PRECb'DI_iGPAGE BLANKNOT FILMED
SCLERASOLARDIAMETEROBSERVATIONS1
HenryA. Hill,ThomasP. Caudelland RandallJ. Bos
Departmentof Physics
Universityof Arizona
Tucson,Arizona 85721
ABSTRACT
The accuratemeasurementof the solarshapeand diameterhas provento be
a very difficult endeavor, as evidenced by the large scatter in the data
record. Althoughobserverbias, c_nging environmentand atmosphericseeing
havebeen identifiedas the major sourcesof this scatter,attemptsto correct
for these still leave disagreementregardingthe constancyof the solardiam-
eter. Most data have been derived from solar meridian and Mercury transit
timings,withtotal solareclipseobservationsaddingsome additionalinforma-
tion. Interest in the time dependence of the mean solar diameter has been
revive_latelyas a means to infer indirectlyvariabilityin the solarlumi-
nosity. However,theoreticalresultsregardingthe relationshipbetweenthese
two propertiesare stronglymodel-dependent,demonstratingthe needfor inde-
pendentmeasuresof diameterand luminosityvariationsbeforeinferencesabout
the lattercan be made. The recentuse of computer-controlledphotoelectric
devices has led to the systematic removal of observer bias and atmospheric
seeingfrom measurementsof the solardiameter,but a new set of problemshas
surfaceddue to variationsin the sun itself. Carefulattentionmust be given
to the definitionof an edge on the solardisk in orderto distinguishbetween
observeddiametervariationsdue to physicalshape changesand those due to
variabilityin other solar prope_ies which affectthe edge definition. For
example,the discoveryat SCLERAz of differencesin the solar limb darkening
functionbetweenequatorand pole requiredthat specialprecautionsbe taken
to extracta visual oblatenessdeterminationwith minimal interferencefrom
such effects. Therefore,programs which proposeto accuratelymeasure in-
trinsicsolardiametersmust not only guard againstthe classicalsystematics
mentionedearlier,but must be preparedto detectchangesin other properties
of the sun at the extremelimb.
IThe work was supported in part by the National Aeronauticsand Space
Administrationand the Departmentof Energy.
2SCLERAis an acronymfor the SantaCatalinaLaboratoryfor Experimental
Relativityby Astrometry,a facilityjointlyoperatedby Wesleyan University
and the Universityof Arizona.
1982009140-122
https://ntrs.nasa.gov/search.jsp?R=19820009152 2020-03-21T10:57:37+00:00Z
\INTRODUCTION _'
With regardto man'sapparent desire for stability,i.e.,constancy, in I
the structureof the universe,the sun has been a considerabledisappointment.
Variabilityseems to occur in each observedsolarpropertywhen it is examined
with sufficientcare. The adventof the telescopebroughtaboutthe discovery
of the sunspotcycle; later the magnetic cycle was _ound and recently,with
the additionof new observingtechniques,variationhas been detectedin the
apparent solar shape. Focus is now being giv._nto possible variations in
solar luminosity and accurate methods of monitoring it. Aside from direct
bolometry,one methodologyfor thistype of researchmakes use of measurements
of the solardiameter and limb darkeningfunctionas indirectindicatorsof
the solarluminosity.This approach,which is currentlybeing used at SCLERA,
will be reviewedhere.
DIAMETERVS. LUMINOSITYVARIATION
A changein the solar diameterwill occurwhen a change in energyoutput
or a redistributionof energywithin the sun occurs. Some recenttheoretical
work has beendirectedtoward attemptingto identifythe funda,nentalphysical
processesaffectingthe relationshipbetweena change in radius and a change
in luminosity. Reference1 and, in more detail,reference2 describework to
derivesuch a relationshipby varyingthe convectiveefficiencyused in local
mixing lengththeory. Reference3 uses changesin magneticflux tube buoyancy
to alter the radiuswhile holdingthe luminosityconstant. The argument is
put forth in reference4 that variations in lower convection zone magnetic
fieldswith the solarcycle could alter the differencebetweenthe actualand
adiabatictemperature gradients, thus affectingthe convective flux. The
resultsof these models vary considerablyin the predictedmagnitudeof the
relationshipbetween radius and luminosity variation,evenpredictingdif-
ferent signs in some cases. Comparisons between the variousmodels can be
found in references5 and 6. It appearsat thistime that independentobser-
vationsof solar diameter and luminositywill be necessaryto resolvethese
differences.
Another problem, and one which is commonly overlooked,relatesto the
observationaldefinition of a solar diameter and its relationship to the
theoreticallymodeled perturbations. Adiscussion of the use of the solar
diameter as an indirect measure of luminosity makes little sense without
careful consideration of this matter. We will deal with thi_ in a later
section. Nonetheless,historicalrecordsof diameter have been analyzedfor
variationand these analysesare reviewedin the followingsection.
HISTORIC_ RECORDOF THE SOLARDI_ETER
Attemptshave been made for overthreecenturiesto measurethe diameter
of the sun. Theseobservations,which consistof meridlonaltransits,Mercury
transits,and solareclipsetimings,havebeen reviewedr4centlyin an effort
124
1982009140-123
i,i
to determine the long-term character of the solar diameter. Reference 7, in
an analysis of the Greenwich meridian circle data, initially reported a de-
crease in the solar diameter of nearly 2" per century; this figure has recent-
ly been revised downward to about 0.'Iper century (reference 6). An analysis
of the record of Mercury transit timings from the late 1700's to the present
has resulted in the conclusion, at the 90% confidence level, that the solar
diameter has decreased by less than (7:3per century and, within the stated
error, probably not at all (reference 8). References 9 and 10 employed a
large sample of published solar semidiameter determinations taken between 1660
and 1978 and f_und no indication of a substantial secular variation, although
a variation with solar cycle may exist. Finally, timings of eclipses made
near the limits of totality in 1715 and 1925 show that the sun was larger than
it is currently by _ and (77, respectively (references 11 and 12).
It is clear from the above summary that the historical record provides no
clear interpretation. Changing environmental conditions, observer bias, and
errors in correcting systematics like irradiance, lunar limb shape, and sea-
sonal changes in refraction partially contribute to the "scatter" in the
observations. The salient point, however, is this: the weight of these
studies indicates that the solar diameter is variable at the 0.1% level over
time scales of 10-100 years. Modern observations and techniques will be
necessary for more detailed conclusions.
MODERN OBSERVATIONS
The use of photoelectric devices to determine the shape and diameter of
the sun allows greatly increased precision. The usual observer biases are
immediately removed and the systematics can be controlled for. Even so,
controversy has arisen from the intercompariso_ of modern measurements of the
solar shape (references 13 and 14), primarily because of differing definitions
of the solar edge used in the diameter determinations. In fact, this intercom-
parison led to the discovery of changes in the solar limb darkening function
on time scales of several months (reference 13). These changes are manifested
as an excess equatorial brightening and were detected through the use of an
edge definition which distinguishes between physical changes in radius (i.e.,
a rigid translation of the limb) and changes in the shape of the intensity
pattern used to define the edge. This definition, which also demonstrates a
markedly reduced sens ivity to seeing effects, is referred to as the finite
Fourier transform definition or FFTD (see reference 15 for a more complete
description). When the FFTD was applied in an observing program to measure
solar oblateness at the SCLERA telescope during the early 1970's, the oblate-
ness was found to contain a time-varying component. The properties of the i
FFTD allowed the differentiation of those periods of time when the excess !
equatorial brightness was minimal, i.e.,when the equatorial and polar11mb i
darkening functions were most similar, resulting in a determination of the i
intrinsic visual solar oblateness.
These measurements have far-reaching implications. Changes in the solar
limb darkening function must be accompanied by changes in, for example, the
temperature and density profiles throughout the photosphere and chromosphere.
Alteration in these properties will change the energy flux associated with
125
o,
1982009140-124
T(
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various energy transpo_ mechanisms.The existenceo_ a time-varying excess _:
equatorial brightness implies, then, an antsotropy in the solar flux. The
accuracyto be expectedfor direct bolometrlc measurements of the solar con-
stant will be stronglyaffectedby this anlsotropy,since any observationof
that typeworks in a very narrow solidangle.
Variabilityof the limb darkeningfunction may well pose the dltlmate
limitationon the precisionto which a solarr_;ametercan be determined,and
progress must be made in understanding its rf6ects on measuremer,ts of the
solar diameter. On the other hand, changes in the limb darkening function,
rather ihan in the absolute solar diameter, may turn out to be the domirJant
source _f information on the solar d-tvtng function for the earth's climate.
SCLERA'SOBSERVINGPROGRAM
At SCLERA, an active program is planned for 1980-8)ireference 8) to
studylong-termsolar variabilityand its effecton solar energyoLtput. For :
the firsttime the full astrometrlccapabilitiesof the SCLERAfacilitieswill .
be utilized. A reviewof the variousaspectsof this programfollows.
To accurately measure changes in the shape and diameter of the sun, a
Michelson interferometerwith a He-Ne laser source is used. This device
continuouslymonitors the separationbetweenthe detectorswhich gatherthe :
limb intensityprofiles used in the FFTD definition of the edge. To study
long-termsolarvariability,extremestabilityof this Interferometerand its _
supportinghardwaremust be maintainedthroughoutthe plannedobservingperi-
od. To meet this goal for the short term, approximatelythe firsty_ar, the
observinginstrumentwill perform in a "frozen"configuration.This implies
thatno modificationsor improvementswill be made to the hardwareduringthis
initialperiod. To allow the comparisonof diameterobservationst_ken fr:m
day to day, a white light interferometerhas been Impl__nted which coexists
with the Michelsonim,Lerferometer.The measurementof the white light fringe
with respectto the laser fringe providesthe necessaryday-to-dayfiducial
for the short term.
The balancebetweenfreezingan astrometricinstrumentto Insuroconsis-
tency of resultsand the necessityto respondto new technologicaldevelop-
ments, thus stayingat the frontierof the field,representsa major dilemma
in astrometry.A calibrationschemeis currentlybeing developedat SCLERAto
avoidthis predicament.The new deviceuses g,'atingopticsand laser lightto
producereferencefiduclalsin the telescope'sfocalplane at a stahdardangle
of separation.Thiscalibrationsystemwill allow absolutediametermeasure-
ments to be made with high precisionin a historicallyrepeatablemenner. In
addition,its incorporationintothe observingprogramwill removethe neces-
sity to maintain the detectors in a frozen state and permit technological ;
upgradingwhen appropriate.
Anotherfeatureof SCLERA'sobservingprogramis the continuousrecordof
the 11mb darkeningfunctionwhich is made simultaneouslywith the diameter
measurements. The FFTD edge definition is then appll(;to these intensity
profilesoff-lineto generatea sensitive"barometer"of changesin the llmb
!26
1982009140-125
rl• darkening. This will provide the necessary informationto separate physicaldiameter changes from those due to changes in the shape of the limb, thus
avoiding the possible misinterpretations mentioned earlier. ._
The 1980-81 observing program calls for daily operation of the telescope, :
weather and equipment permitting. The analysis of these new observations
shouldprovide,among otherthings,an improvedvalue for solaroblatenessand
a new measureof the long-termvariabilityof the sun. It is anticipatedthat
, this program at SCLERA should launch a new era in the study of the global
propertiesof the sun.
REFERENCES
1. Sofia, S., O'Keefe, J., Lesh, O. R., and Endal, D. S. Science, vol. 204,
1979, p. 1306.
2. Dearborn, D. S. P. and Blake, J. B. Astrophysical Journal, vol. 237,
1980, p. 616.
3. Thomas,J.H. Nature,vol.280, 1979,663.
4. Spiegel,E.A.and Weiss, N.O. Nature,vol.287, 1980, p.616.
5. Gilliland,R. L. AstrophysicalJournal,1980 {submitted).
6. Gough,D. Nature,vol.288, 1980, p.639.
7. Eddy,J.A.and Boornazian,A.A. American AstronomicalSocietyBulle-
• tin, vol.11, 1979, p. 437.
8. Shapiro,I.I. Science,vol.208, 1980, p.51.
9. Wittmann,_ Astronomyand Astrophysics,vol.61, 1977, p. 225. :
10. Wittmann,_ Personalcommunication,1981.
11. Dunham,D. W., Dunham,J. B., Fiala,A. D., and Sofia,S. Solar Constant
Workshop. NASACP-2191,1981.
12. Dunham, D. W., Sofia, S., Fiala, A. D., Herald, D., and Muller, D. M.
Science,vol.210,1980, p.1243.
13. Hill, H. A.and Stebbins,R. T. AstrophysicalJournal, vol.200, 1975,
p. 471.
14. Dicke, R. H. and Goldenberg, H. M. Physics Review Letters, vol. 18,
1967,p. 313.
15. Hill, H. A.,Stebbins,R. T.,and Oleson, J.R. AstrophysicalJournal,
voI.200, 1975, p.484.
127
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16. Hi11, H. A. Proceedingsof Workshop "Solar Instrumentatlon-- What's
Nnxt," Sacramento Peak National Observatory, Sunspot, New Mexico, 1980.
1982009140-127


Sclera solar diameter observations

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