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- ikfilicli-FORMATION AND EVOLUTION OF THE SUN . no f ER- -- - I . . . - ./ tr--
ROBERT R. BROWNLEE
University of California, Los Alamos Scientific LaboratoryLos Alamos, New Mexico
I. INTRODUCTION
In these days of renewed vnd vigorous interest in the origin,
structure, and past and future histories of the solar system, detailed
knowledge of the formation and evolution of the sun has become of.vital
importance. For example, knowledge of the rate at which radiant energy
was streaming from the solar surface, and the extent of that surface2
at the time of the formation of the planets is basic to any realistic
theory concerning their formation. Coupled with this new and wide-
spread interest in the time-history of the sun has been the advent of
the high-speed electronic computers and the development of techniques
which enable the astronomer to investigate many complicated relations
which heretofore had been considered beyond reach. It is my intention
to discuss briefly the present state of knowledge concerning the history
of the sun, what investigations are currently going on, and to indicate
some of the' fields of knowledge in which uncertainties and difficulties
continue to emist. - -LEGAL NOTICE
States, nor the Commission. nor any person acling on behalf of the Commus/M:
TWs report was prepared as an account of Government sponsored work. Neither the Un ted
- A. Makes any warranty or representation. expressed or implied. Mth respect to the accu-
As used in ure above, 'peraon a/Ung on behalf of the Commission' includes my em.
racy, completeness. or usefulness of the informaUon contatied in this report, or that the useof any inform.Uon. app....8, method, or pricess $../.led I 'W. report may oot Infringe
1privately owned righta; or
B. Assumes any ilibililes with respect to the use of, or for damages resulting from theuse of any blformation, apparatus, method, or process sclosed in this report.
ployce or contractor of the Commission. or employee of such contractor, to the extent thatSuch employee or contractor of the Commlision, or employee of Buch conlactor prepares,disseminates, or provides access to. any information pursuant to 88 employment or contractwith the Commission, or hle employment with such contractor.
DISCLAIMER
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.
4, .
KNOWLEDGE OF STELLAR FORMATION
A great variety of astronomical observations support the view
that stars are formed from the interstellar medium. As can easily
be shown the most luminous stars are emitting radiant energy at such'.
a rate that they cannot possibly be very old, and these stars are
invariably found in intimate association with clouds of gas and dust.
' . This is true within our own and other galaxies. In some instances
the space motions of such stars can be measured and are found to be
too small relative to the surrounding clouds of gas to be mere pass-
ersby. The conclusion seems to be unmistakable that these stars were
born from the surrounding material.
There ts a class of stars known as the T Tauri stars whose
spectra and light variability suggest that they are passing through a
short lived phase of their evolution, and these stars are aleo
imbedded in clouds of interstellar gas and dust.
In a number of places in the sky, dark spheroidal globules can
be seen projected against luminous clouds and the obvious interpreta-
tion is that these are' protostars which will at some time in the future
contract sufficiently that they will begin to glow, and thus become
stars.
I hasten to point out that there have been many theoretical
difficulties in providing good quantitative explanations for the above
observations, but nevertheless the observations appear to give great
confidence to' our belief that stars are being born from the interstellar
medium.
2
BASIC SOLAR DATA
We may well ask if the sun contains information within it which
Will tell us anything of its birth and its aging processes. The
obvious fact about the sun, of couree, is that it is shining. An
inevitable result is chat it must evolve, for its supply of energy
can not be infinite. As this energy source must lie in the deep
interior, what can we say about it?
At first glance the deep interior appears to be less accessible
to scientific investigation than any region of space around us. How-
ever, if we ask the correct questions, we find that certain information
about this important region of the. sun is being communicated to us quite
directly. First, a gravitational field is emanating from the sun and
the motions of the planets and minor planets within this field allowI.
us to determine the solar mass. Secondly, the solar radiant energy
crossing a unit area of the earth's surface can be measured, and theluminosity of the sun, i.e., the rate at which energy is being emitted,
is easily derived. Thirdly, the diotance of the earth from the sun
, . being known, the size of the sun can be determined quite easily. Thus
we determina the three basic ·stellar quantities for the sun .. the mass,.
the lurninoeity, and the radius.
' There are yet three additional bits of information which should
be mentioned. First, through spectroscopy, something of the chemical
composition of the outermost layers can be determined. This problem is
fraught with difficulties but even so such derived information is veryimportant to our understanding of what has gone on in the interior.
3
4 *
-
Secondly, sonie kind of lower limit can be Bet to the age of the sun,
for certainly it cannot be younger than the earth. Furthermore the
surfacd of the earth contains information which suggests that the
luminosity of the sun has been relatively constant for very long periods
of time . The third obseryation ie 80 obvious that it can easily be
overlooked, but it is of basic importance to the theory of stellar
interiors. That is the fact that the sun is essentially spherically
symmatric and in hydrostatic equilibrium -. it is neither pulsating
mor blowing up, at least not on a very fast time scale.
The combination of all of the above information leads to many
interesting conclusions. For example, from the known size, i.e.,
volume, and mass, the mean density of the sun 18 immediately obtained.
The fact that the sun is in' hydrostatic equilibrium means that the total
pressure ac any point muat be just suffidient to support the weight of
the cverlying material. Making various assumptions about the density
distribution, we can regulate the pressure at every point by adjusting.
the terapsrature at that point until hydrostatic equilibrium is achieved.
Naturally, an arbitrarily chosen density distribution will undoubtedly
result in a temperature distribution which will in no way correspond
to .8 realistic flow of the energy such that a correct luminosity will
..be achieved. Obviously there needs to be a simultaneous solution for
all parameters of the problem 16 order to match what ia so "casually"
observed:
·· 4
A
Perhaps the most striking conclusion concerns the energy, for the
average rate of energy releaBe is about 2 ergs per gram per second,
and apparently there have been no marked changes in this rate for four6, I
or five billion years.-'.,7.
The proposed sources for this energy have been varied. Perhaps
4.the oldest suggested source is that of combustion. But proportioning
the mass in the most ideal way into carbon and oxygenD the maximum
age of the sun would only be about three thousand years. Clearly,
another source must be sought. It has been suggested that solar material
might be supplemented by an infall of meteoric -material, but the density
of the material in the vicinity of the sun is quite insufficient to be
held responsible for any significant contribution to the solar energy.
A little more than a century ago H. von Helmholts proposed that
gravitational contraction was the source of energy for the sun and stars.
The gravitational energy stored in the sun is approximately equal to
155 x 10 ergs/gram and if contraction were responsible for the luminosity
of the sun, the solar diameter would be decreasing at about the rate
of 40 meters/year, or about 4 kilometers in a century -- a rate which
is not observable. (Good angular diameter meaeurements of the sun can
be obtained only for about the last two centuries.) Howevers the length
of time for the solar material to contract from an infinitely large
size to its present dimension would be only a few tens of milliond of
years. This is also an interval of time which is much too short.
D
5
Finally, increased knowledge of the atom has led to the relation
20between mass and energy, 2 e wt2. or approximately 9 x 10 ergs/gram.'
. This is a source so plentiful that in four billion years and at the
present lumingsity, the eun would have decreaaed in mass only about
. 0.02 per cent. It is clear that the sun is feeding upon its mass and
at., the present ratd of consumption, apparently has a long life ahead.
II. BASIC DIFFERENTIAL EQUATIONS OF STELLAR STRUCTURE
From the above information, and with the assumption of spherical
Symrne try, the following differential equations can be derived.
1. i&41 = .G *(r) 9(r)dr 2 Equation of Hydrostaticr Equilibrium
dM (r) 22. ----- = 4-1 r p (r) dr Continuity Equationdr
Conservation of M:ass
dL(r) 23. - = 4u r p (r) e Luminosity Equationdr
1
&I =- .3 K o (r) L(r) Energy Transport4. a. Radiationdr 4ac 3 4 2 EquationsT. (r) 41- r
b dI = 13-1 I dE'dr r P dr Conduction
' '
6
:.1
5. a. P = k. P(r) T(r) + T4 Equation of State H -
. .5/3 or 4/3b. P p Const ( 2, i
electron W /
I .
The definitions of the variables in the above equations are:
r radial coordinate P total pressure
G gravitational constant p density
, M(r) mass interior to a sphere L(r) energy crossing the
of radius r surface of radius r
energy generated ,gram-lsecond-f T temperature
a radiative constant c velocity of light.,
K Rosseland mean opacity B mean molecular weight
Ik Boltzmann' s constant a average mass/electron
r adiabatic exponent H mass of unit atomic
weight
Three quantities, u, the mean molecular weight, K, the Rosseland mean
opacity and 9, the energy generated per gram per second, have been l
introduced in the above equations. Each of these ia a function of the
chemical composition, the density and the temperature, and all are presumed
to be known. The calculations of the latter two quantities, while quite
feasible with electronic computers, are enormously complicated and require
elaborate machine codes and experimental results. However, assuming
them to be known, the object is to determine the temperature, pressure,
density, mass interior and the energy crossing the sphere at every point
' 7
.
: r within the star. Since there are, in effect, five equations in
five unknowns, a model for the sun or a star is obtainable.
The boundary equations for theoe equations are as follows:
At r = R= the radius of the stm, the pressure, the density and the
temperature are presumably knowa. At r = 0, the mass interior,
M(r) and the net flow of energy across thaC Bphere, L(r), must equal
zero. These ' conditions are two too many, and some freedom ofI .
choice in their use is poasible. In practice, the two are veed as a
cheek upon the calculations. In general, the history of the e'ntire
i problem has been the changing application of these boundary conditions.' To obtain a model of the sun, or any star, one needs the mass ,
luminosity, radius, and the chemical composition. In general these
.are a function 02 time, hence a model of the sun represents the sun
for only one moaent in time. However, since the. temperature, density
and chemical composition are finally known for every point within the
model, the rates of conversion of mass to energy are known for every
Point, and therefore the rate of change of the chemical composition
is also knewa. Such a change will alter the molecular weight, the
opacity and the energy generation and these will in turn alter the
structure of the model. Thus, having a model for one moment in time,
themodel for a subsequent time is determined.
The calculation of a model on a desk calculator is an exceedingly
laborious and time-consuming effort. The wide-spread use of electronict'
8
..
..
computers has made possible the calculaticn of such a model in· 8
few seconds and a number of different techniques have been developed. '
Because of the great interest in the sun, models for stars of one
solar mass have race ived a great deal of attention.
III. EVOLUTIONARY SEQUENCES FOR MODELS OF ONE SOLAR MASS
EARLIER RESULTS
The first detailed calculations of a vequence of models which
represented the contraction phase of the sun were made by Henyey,
Le Levier, and Levee*. Somewhat later, using a different cortiputational
technique, Brownlee and Coxi calculated evolutionary sequences uaing'
idproved opacities and considering the role of an outer convection zone
and all sourcea of nuclear energy generation. Among the latter, the
possible role played by deuterium was investigated. The results are
shown in the theoretical Hertzprung-Russell diagram in Figure 1.
Prom tile initial model for these tracke, when the radius was approxi-
Istately thirty times that of the present auni the contraction was traced
ubtil the transmutation of hydrogen luto helium in the center of the
motlel yielded enough energy to cause the rapid contraction to cease.
At the outset, about 97 percent of the gravitational energy was still
present. Thus calculations ranged over a tine during which almost all
*· Henyey, L. G., Le Levier, R., and Levee, R. D. 1955, Pub. Astronom.Soc. Pacific, 67, 154.
1 Brownlee, R. R. and Cox, A.N.,·1961, Sky mid Telescope, 22, 252.
1.
t.
, -
.P.. I
-
. *4.../'.,1.:
"»r l e 24, 3 S „t L
1.:41 3- ---- NO DEUTERIUM
' ti.
f v' 4 DEUTERIUM2,
5 ' DEUTERIUM& 3.1 5 UNMIXEDI 1.1 0 64 95 ...
6 1 «,4 7 -Ill 01. 'i
gr' .08 DEUTERIUM. m-I .1
a2 9 MIXED' *' : nu 1'1# 1 1 1 1 114 ,
4 1r-- 3.8 3.6 3.4 3.2 3.0 2.8 2.6.. ., 11 I.
4 1-11
LOG Te °Kk4%4*-_
.
1
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LOS ALAMOSPTI' '.,0 LABORATORY
A- 627931ELE.iSE RE-ORDERC Ai,OVE NUMBER
- ---
.
'.,t
-.
\
[
of the potential enargy was converted into internal energy Bad
radiated energy.. When no 8euterium was presents this period of
time was greater than 100 million yearm. When deuterium vac added
iri an ame',mt eqi:al to that found in the earth and in metooxiteso
about 2 huadredths of a percent by mass, chere was a significant
pause in the *entraction at the moment the de:itral temperature 'and
density Were sufficient for the proton-deuteron reaction tc occur.
Thia caused a total increase in the Contraction time' of a factor of
about two. An additional calculation was made on the assumption that
the deuterium was constantly mixed throughout the model, and again
the contraction time was increased.
Figure 2 shows plotted the radius of the model va time. The
momant the deuterium began to burn is quite apparent, as wall aeI.
the moment in which the resulting enargy release stopped supperting
the outermost layers.
Figure 3 shoes plotted the Ener#y Balance as a function of time.
Figure 4, ie addition to showing the radius vs time plot and
the change of the potential and internal energies with times shows
the temperature changee vB times as well. Of pmrticular interest in
thie figure is the abrupt halt in the increase of the temperature in
the center indicated as Bone one. A abort time later the temperature
Changes £811 to zero throughout tlie modelp. and this is. said to be tile i· 1time of the primordial solar model cr the initial sun.
,\
11
...
2.0
SOLAR GRAVITATIONAL CONTRACTIONZONE INTERFACE POSITIONS VERSUS TIME
1.5 DEUTERIUM BURNINGNO DEUTERIUM BURNING
\ 20/
EC' 1.0- iN
-
9 20- \\\6 1\ \ 10
\ \0.5 ' '
i \90 \
': 4 ... :.\
. \\ . \ -\\, .\ -
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f (106_YEARS)1
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18
LOS ALAMOSPHOTO LABOR,1 TORY
NEG- 60341 6NO.
PLEASE RE-01:DERBY ABOVE NUMBER
..
fi. fi,·T
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4 1 1
3-------- ENERGY RADIATED- ENERGY PRODUCED---- POTENTIAL ENERGY
If
2- INTERNAL ENERGY .Iilii
TOTALENERGY
1- 4/4.0-..
0 ----------E \\- -1 - \00 \\\
-2 -
\\/\\\
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-3 - SOLAR GRAVITATIONAL CONTRACTION \\\
ENERGY BALANCE VERSUS TIME \\
-4 - \\\\\\
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-6 1 10 50 100 150 200 250 300
f ( 106 YEARS)=-
.L... 13 \:
1., «1. . 4 . 9 2 Ji. Pig:.3. , C'
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LOS ALAMOSpHi'"0 LABORATORY
)ps 603413RO.
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1 Dr ALOVE NUBIBER
'...'
A B CD18 - 1 1 1 1 1 1 1 1 Ill - 18
16 - - 16ZONE 30
14 - - 14
RADIUSU)
a.12 - - 12
W1-
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,
58- -80 ZONE 22
-06- -6
4- -4
ZONE 14
2- -2
_ZONE 6
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+2 - FNERGY RADIATED - +2INTERNAL MINUS PRODUCED
Ul
80- - . - il ---) TOTALW - ..
: -2 - 00 - -2-
0 \- \
-4 - Fig. 4. Changes in the solar model --4\originally containing 0.02 1,er cent 'g POTENTIAL
-6 - deuterium. Zone 30 is the outside - -6
surface. Some of the gravitational po-tential energy during the contraction
14 - is converted to internal heat energy,ZONE I - 14
and the rest is radiated. Teml,eraturesare those midway between the bound- ZONE 6
12 - - 12
z aries of each shell, except for zone 15 which gives the temperature at a pointJ 10 - - 10w midway between the solar center andf the first interface. The letters at the ZONE 1408- top indicate four el)ochs for which de- -8
W I.-W tailed information is given on page 256.H 6- -6
80
4- -4(D
o TEMPERATURE ZONE 22
- f2- -2
ZONE 30==-- --- -
0 0
200 180 160 140 120 100 80 60 40 20 0
MILLIONS OF YEARS
'-9
LOS ALAMOSPHOTO LABORATORY
5 6 1 Al 9 31;0.
L U .6.*v.U; RD ORDERD C A*.01'E NUMBER
,.
Aft€r the wadel has reached the main sequence of stars its
path in the Solowatrio Magnitude 400 Effective Temperature diagrad
ts drastically aleer*d. Changes in structure still occur, but on a:5
much longer time voi.le. As ths hydrogen in the central regions i a
0942,tedd to helium, the mean molecular weight increases, the central
regions collapse slightly, the opacity decraaeee,.and the density
and temperatitre are increased. The energy preduction is thus enhanced
and the luwinosity of the modul rises. The oVeer rezions actually '
ex'patid during elds phase, so that the radius and lominosity of the
.7todal slowly increase. (The decre*Be in mass dwing this phnse is
easeotially negligible.) After sote period of tima the model should
- pass through or nttar the positioa Of the present sua, depending upon
ita re*emblance to the sun.
All of the above mentioned calculations were sade with an assumed
chemical composition of 74.4 percent by weight of liydrogen, 23.6 percent
by weight of helium and 2 pescent by weight of the, heavier elegents.
It vaa fowld that the model took entirely too much ti*re to reach the'
I
lumineaity and radi.us of the present sun--a period of about 11 billion
years. An altered chemical composition waa suggested, since a decrease
in the initial abundance of hydrogen and a corresponding inorease in
the abundance of hellwa would serve to shorten the time betwe*n ·'the
initial and present solar donditions.
15
RECENT RESULTS
In the earliest stellar models, the simplest possible surface
boundary conditions were used, i.e., that the pressure, temperature ·
and denoity all vanished at the surface. While these conditions
were quite adequate for making preliminary and general calculations
of atellar interiors. experience has show'n a need for greatly refined
boundary conditions. In fact, it is now clear that nothing short of
a *11 determined model stellar at; aesphere will suffice to establish
a proper surface boundary condition. This is proving tolbe especially'
true for the study of calittracting solar models.
HayaShi* wae the first to point out that the calculations de-
sci'ibed above for the earliest phases of the contraction would have
resulted id an entirely different history had tHe convection in the,
outermost layers been handled dorrectly. Hle prediction was th# result
of his study of the importance of convection in the outer envelopes of
the late-type giant stars. In the models just desc:sibed the boundary
condition used was derived from atmospheric madels by Swihart and Fisehel t,r
and with an assumption of constant gamma between the point of the onset
of convection and tile outermost mass point of the interior. The assumed
value of.gaewa was apparently toe large and the envelope structure and
.,
* Hayaahi, C., 19610 Pub. Astran. Sos. Japan.131 4501
t.' Swihart, T. L., antd Fischel, D., 1961, Ap.J..Suppl. 5, 291
.
. I
.
16
f
..
I
..
the depth 02 the conmection reston are very sensitive to the value
of ggmma. u,ed. The correct bcundary condicioe should consider the
variable gauna ond the eenvactive efficiency, as liayashi has done.The result ** a lower temperature .for the Itermbet maes point of the
. laterlor, a correspobding change .in strueeure, and a mueh deeper
cotivective resion.
Recent reaults verifying Slayashi' e prediction have been re-
ported by Eser and Cameron*. dad Weymana and Moore. f Ezer and.Cmneroa
calculated twenty-seven models by .a technique which did not yield
a st:lek evolutionary sequence but which ser· d to delineete such a
sequence. They found thit for all •aodels above 2.5 solar rsdii,
the convection w#Is cmmplete all the way to the center. The
efficieney in carrying anergy by convaction is 80 muth greater than that
by radiation flow chat tha luminoot tios of the models are very high
when compared with the previously reported results. Further, since theenergy im ewitted at auch 3 great rate, the collapse of th,3 model ia
greatly hastened and the corresponding conversion 09 gravitational
energy la dreatly adeelerated. The final result is a grgatly ohortened
calculated titi,e for the andel to reach the initidl r.ain ecquer.co of
stars, 8.e. , i t s prittordial 13**te.
8 Rzer, D.5 and Cameron, A. G.W., 1962, The Early Evolution of the Slm.
preprint
9 Reymanno A.9. and Moore, E., ·1962, The Abmidance of Lithium and theSthucture. of Gra*itatte:lalbt *mtract#49 Stars of ddeSolar Meas, Peepriat
\
13 7
)„
Recent work at Los Altmos is in qualitatite· agreement vith
that of Bayashi and Ezer and Cameron. Since the te¢liniques used
and the various assllmptions necess&:y to the determination of
boundary conditions, the convective energy flow and die chemical
colzposition are B'imilar but not necessarily the sawe, exait sigiree-
neak is tert:einly neR to be expected. l
·The chealieal Composition for the re,ults described below was
59.6 percedt by WBight hydrogen, 3:.4 percent by weight helium, and
2.0 percent by weight heavier elements.
The epacideo for this eompcoiticn ae calculated, by Stewart amd
Cor :12 los Alazoa *re shown in Flattrcs 5 and 6. '1114 coda whiah
is used Co calculdee these opacities coasiders baued-boufd, bound-
free, and free -free absorption, electron statterillg End negative ion
absorption. For the data shown, the ranse in temperattlre is fron:
4.343 x 10-4 kilovolts (5040'K) to 10 kilovolts (1.1603 x 108.K).
The range in density is fro,·1 10-14 gm/cra3 to 103 dns/(2 •
The equation of state data used haze also bean Computed by Stewart
mid Com for the identical ranges 02 temperflt»re and density.
Soma of the .results of the most recent calculations, .are shown
in tha figureE which follow.
In Figure 7 eha luminonity an a function of r#diuM is Chaun fee a
particular model with R/tle = 24.2. As the boundary coaditions be*48
used are considered Preliminary, the actual value of tha luminoaity ia to
64 given little weight. Note that each particular region 0£ the model
is contribucing Buwa 9 f ita sifevitational energy to the luminosity. 4..
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d-1.-.... -1- 1 .....$: 84 1.4 - \f #- E. . . . . . . \\\
----»_s. . . . . . . I
:
-* mw- 1 ' =. i i - 6-wrif-.=i- 1 Tr 1- * d 4 * +- - -
0 - . - 6 O 0 0- - - -- 'O/ T
24Fig. 7. The Luminosity (in units of 10 ergs/sec) vs Fractional
Radium for a Model with a Radium Equal to 24.2 Times thePresent Solar Radius
./
-- t.t ,S .'.1.A'•It)S . ,1 , . 1 , „. ':' 'ORY
6 z ·C u w D
i .,., 3,1_:.'li 'ILL__11
Figure 8 shows the pressure profile *or 4he oaze zelel. Thu
.16 3pressure is in units of LJ crsdicm. .
Figures 9 an€ 10 ahm, the temperature (in kilovolts) and the
log of the density va radius, respectively. These two fiBuree are to
be coipared with iisures 11 and 12 which show plotted the arme2
quantities, but for a model of radius R/11 u 1.29. The great increase
in temperatlize ard density throug)tout the itar during t:lia course of the
contvaction can easily be noted.
Figures 13 cid 14 show simi tar results derived from the earlier
work dene at Los Alamos. When theae arc cominred with tho four preceding
figures, thu different to=pereture and density distributions are quite
stribirt. The differencd ig wiraply that in (IR initial solar e:>del,r
the convection rosie;n does not extend throughout tlie star but is rather
gonfined to an cuter region and a swill central core. The model
whi<li is convective throushout shows quite flat profiles.
' It is of interast CO se,3 11JW the actual temparaturc gradient differs
from the adiabatic scadiant of the model with R/il' = 24.2. I'ltis caa beseen in Figure 15, vite:e the excess af the tesrerature gradient OVUr zhe
adiabatic is plotted versus the radius. As the successive models approach
th* radias of the preaent 340, this difference becomea less and less.
Eventually tho opacity in the central reglcus becomes aufficioutly low that
the cotriection ceases. In the outer regions the temperature graliaut
betomao that of the adiabat.
· 22
-0101SERIES 4 PROB.EM 30
-01" 1
1 1 1-024
-025
-030
-035"
-040'
-045·
-050·
L0 -055-
f I --065.
am $--.....4-075·
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-100'\
-105·'
-110-01•000-02' 4/ *01 •015 •02( +02k •030 +03g +040 +049 +056 +055 +060 +065 +07(1 +075 +08 +085 +09 +09 7io/
Fig. 86 Log Pressure vs Fractional Radius for Model R • 24.2 (3.*
-Z
LOS ALAMOSPHOTO LABORATORY
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-
' Fig. 9. - Temperature vs Fractional Radius for Model R = 2.4.8 0 . ,
P
9'1
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LOS ALAMOSPHOTO LABORATORY
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*200SERIES 4 PROO.EM 30
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350
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Fig710.-Log Dengity vs Fractional Radius for Model R 24.2.0.
f:/1 -'
LOS ALAMOSPHOTO LABORATORY
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91:1
... F. . ,Fig: 11.- Temperature vs Fractional Radius for Model R = 1.29-0 -. 11 1-
i
LOS ALAMOS
PHOTO LABORATORY
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BY Al,OVE NUMBER
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*150'
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-200
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-450
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-90'
-650
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: R/00 -
Fii. 124 Log Density vs Fractional Radius for Model R : 1.29 0 - « j
3
9 --
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.
LOS ALAMOSPHOTO LABORATORY 1
NEG. 6 2 7 9 2 5NO.
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2,-'.... 9 f
F.
20
18-- INITIAL SUN
16- TEMPERATURE VERSUS RADIUS- C CONVECTION
14 -C
9 12 -00 10--4 -8- 8-
6-
4-
2-
0 1 2 3 4 5 6 7*-t '-10 -- 1 -----:I
ELI+J'Jd-M (guvu U
r
Fig. 13. Temperature vs Radius for a Model of the Initial Sun... --
. -0=---,- - ... ......
- --
LOS ALAMOSPII/"0 LABORATORY
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861 603414
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C INITIAL SUN2- 1LOG DENSITY VERSUS RADIUS
C CONVECTION
AlA
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.F 0
-1 i c
-2
0 -1 2 3 4 5 6 7/ 10 \
- r / 10 m'
Fig. :14. Log Density vs Radius for a Model of the Initial Sun -·
.
--
... ... I.
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Ii - _ . . . ... - - . _- - · -· ·I 'trl-.-
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Fig. 15. The Excess of the Temperature Gradient over the AdiabaticGradient vs Fractional Radius for Model R 9 24.2 0 '.
*·-
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I. 3
TRE, SOLAR FGTU94
·Finally., a tew egamvznte should be maile abouk the future/
..
bittory of 14 sua. From work' done by many workers' in the past and
iroe Calculations currently beins wade at #he Univarsity of Galifornia
by Manyey, at the California Institute of Tdghnoil*·Jy by R. 6. Saars,
at Priweat#a by SchwZI.rjechild, at the NABA Institute for Space Studies
6, Eze* and Coaeron, at the Los Alamos Scientifie Laboratory* and a
ninber of other places, it is clear that the amouat of information regard-
ins tile total life hiotory in the eun has jowt begun te acqpmulate.-
Even 60 we can state with come certainty whar the "imwidiate" ruture/ I
of the ste, will be .
Dy Cottlpering the "age" of the model wilen it *mt closely repressn#s
the sun with tlte age of the sun as derived by other muthods, it is
poseible to select a chemical compeaition which will give the "correct"
age. Thie compooition, depending on the opacltles one aess, etc., appears,
to be about 63 to 65 perceut by weight of hyflrogen, 2 to 3 pergoat by 1.weight of tile heavier clemente, the remainder beivg helium. Thuo an
\
1 additional "observed" fact is used to determine an additional model para- ,
6,2 ter.
Currently, the bent models seem to suggest that in the centleal
re$*ana of the Present sun about one halt. of the 'original hydrogen has
been converted to lielium. Thic proce3$ will continue until all of
hydrogen is illi:ned, at which time the cant:al regiums begin to contract
8081078 at mor e rapidly. Ths outer regiona gradually accelerate in their.. expansion and finally--curnnit modela buggest al ter gbout six or seven
*
31r
i.>t..1
litlizes *re yeare--the sun.e.it'l turn. a-*4 6:em the.main. eequeice...
rattler whruptly (16 1/*0-40 a giart gte.
She centrbl tekiperstars& a:0 6%*gities will h#*e l,Come
4.,Q p f E 4 fLY·:· 1.q 4·4· *4• P•:· -, - ·;i' helium vili iteelf bogin to be. tratle--w-:i -41--6-9 -*6* .*#w.. -na
mutod Lato carbon. Ther# gill follm a colowfbI voried of tbe sus,
as a giant Stag, making *sny ulttmente within ic. Unfor'*State ly,''
for 6% pirament the''theeretidal taile:totantjins of this epoell, cli 1
thes# fjo £0110W, bowevar encciti*g, te rather impes fectly held. The
'·i. abticip.fee.d iaeraaees of ot,e kz ladae in tim nqar futtlee. promiae to
meke thii field of Ateller mddeld n vety prefitkble ene.
1·
*
..
.
./
32
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