CRITICAL FREQUENCIES, SUNSPOTS,A•D THE SUN'S
ULTRA-VIOLET
RADIATION
BY C. W. ALLEN
Abstract--Monthlyvalues of el0, the critical frequencyrelative to the critical
frequencyat zero sunspots,have beenaveragedfor a numberof stationsand tabulated
for the eleven-yearperiod1937-47.The variationsof el0 for the E-, Fi-, and F2-regions
have been correlatedwith the solar data for sunspot-numbers,
bright Ha and Ca
floecult,faculae, and the coronal-lineintensity. The variationscorrelatedare found to
lag behind the sunspot-numbervariations by the following parts of a month: Ha
fiocculi,0.15; Ca fiocculi,4).3!;ef0•, 0.43; faculae,0.56;rføFx, 0.66; eœør2,0.68; coronal
line, 0.87; and this is interpretedas givingthe orderof increasingmeanlife of the relevant
solar features.
In the expression
eS -- (1 -[- bR) -- (•œ0)•relatingrelativeultra-violet intensity•S
to sunspot-numberR and critical frequency,the adoptedvaluesof n and b for the regions
E, F1, and F2 respectivelyare n -- 4, 4, and 2, and b = 0.0097, 0.0124, and 0.0200.
Values of n determinedfrom the relation betweencritical frequency and the Sun's
zenith-distancewere 3.72 for the E-region, and 4.90 for Fl.
The values of •r• are shown to vary with time, season,and station. The noon
values however do not vary greatly and are generally closeto the diurnal mean. A
method of choosingstationsreasonablyfree from the F2-anomalyis given,and the
recombinationand electronsdecaycoefficientsare determinedfrom thesestations.The
number of quanta per cm• per sec outsidethe Earth's atmosphereat zerosunspotsis
givenas:E, 5 X 10s;F1, 1.9 •( 109;andF2, 2.3 X !09.
The variation of critical frequenciesfor a selectionof ionospheric
stationswas studiedfor the period of decreasingsunspot-activity193744
in an earlierpaper [see1 of "References"
at endof paper].In the present
papermorerecentionospheric
and solarobservations
are addedto the
earlierdata, and the inter-relationof theseobservations
for an eleven-year
cycleis discussed.
The mainobjectof the workis to seekevidence
on the
variations and sourcesof the ultra-violet radiations which produce the
ionosphericlayers.
(1) Monthlyionospheric
andsolardataduring1937%7--The
methodof
analysing
andexpressing
thecriticalfrequencies
has•ready beendescribed
[1].Fromthepub!ished
monthlymeans
wedetermine
the "relativecritical
frequency"
z/ø,whichis the ratioof fo the actualcriticalfrec/uency
to
z/øthecriticalfrequency
at thesamehourandseason
extrapolated
to zero
sunspob-ac•ivity.
Thevaluesof aføaretherefore
purenumbers,
and,with
certainexceptions
discussed
in Section
4, all Stations
givethesamevalues.
Themeans
ofthesevalues
aretherefore
excellent
measures
ofsolaractivity,
andareindependent
of unRs.In thisrespect
theyaresuperior
to thewell
used"sunspot-number"
for whichthe constants
needcarefulmonitoring
by the originators
at the SwissFederalObservatory.
The analysisof the four originalstationsWashington,
Huancayo,
433
434
C: W. ALLEN
[Vo,. 5a,No.4]
W•theroo, •nd C•nberra (Mount Stromlo) h•s been continued.For these
stations we use noon and 09•-15• means •or the E- •nd Fl-regions, and
noon, midnight, and 2•-hour means for the F2-region. It was evident
however that the inclusion oœmore stations would eliminate some oœthe
fortuitous v•ri•tions •nd give a better representationof world conditions.
Accordinglythe six stationsFairbanks, Brisbane, San Juan, Maul, San
Francisco,and'Baton Rougewere added,but in these casesnoon values
only were used.The resultswere extractedfrom •onosphericdata published
by the CentraltLadioPropagation
Laboratory,Washington.
zføfor these
stationswasfoundby dividingthepublished
fo by the•fo determined
from
the four original stationsmainly in the years 194!=16. The mean values of
zføsofoundwerethendividedintothenoonfø-observations
to redetermine
the valuesof •fo fromthe sixnewstations.In thisway the newvalueshave
been fitted onto the old.
TABLE
Year Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec. Meat
1938...........
1.209 !.217•1.2171.222 1.264 1.252 1.224 1.209•1.2451.254 1.22•
19391.2431.2151.158!1.184
1.2141.2!4 1.2001.1941.2171.2001.1871.194 1.203
1940 1 149 1 170 ! 170 1 172 1 157 1 1641 161 1 1811 180 1 172 1 154 1 138 ! !64
1941 1.121 1.122 1.121 1.101!.081 1.0921.108 1.!23 1.128 1.113 1.108 1.141 1.11•
1942 1.112 1.109 1.122!1.130,1.107 1.062 1.048 1.0341.041 1.042 1.053 1.062 1.077
1943 1.0521.0661.071•1.0711.0531.051,1.0371.0241.014 1.0061.008 1.034 1.04(2
1944
!945
1946
1947
1.026 1.028
1.059 1.064
1.091,!.158
1.283 1.328
1.041:1.037
1.061 !. 083
!.193,1.196
1.313•1.378
1.018
!. 074
1.194
1.400
1.020
1.099
1.182
1.329
1.006
1.085
1.215
1.334
1.028
1.082
1.229
1.302
1.022 1.044 1.040
1.078 !. 127 1.125
1.19'8 1.204 1.242
1.3241.428 1.408
1.038
1.104
1.317
1.408
1.03•
1. •
1.2•
1.35•
SOLAR EFFECTS ON CRITICAL FREQUENCIES
435
Year Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec. M•ean
1937 ..........
1938 1.74 1.86
1939 1.72 1.74
1940 1.48 !.52
1941 1.44 1.42
1.87 1.72
1.84 1.86
1.67 1.64:
1.57 1.57
1.36 1.30
1.62 1.77 1.78 1.87 !.97
1.74 1.73 1.80 1.84 1.77
1.80 1.76 1.70 1.69 1.73
1.46 1.53 1.56 1.55 1.63
1.26 1.35 1.35 1.37 1.34
1.83
1.73
1.72
1.57
1.34
!.76
1.75
1.64
1.52
1.33
!.71
!.74:
1.581
1.441
1.38
1.86
1.72
1.7(•
1.5•
1.3•
1942
1943
1944
1945
1946
1947
1.39
1.20
1.12
1.22
1.66
1.92
1.34
1.17
1.07
!,29
1.60
2.06
1.12
1.01
1.17
1.41
1.67
1.92
1.18
1.02
1.12
1.44
1.80
1.90
1.22
1.I1
1.14
1,40
1.83
1.88
1.2•
1.14
!.1(
1.3(
1.64
1.94
1.34
1.16
1.07
1.19
1.30
1.88
1.34
1.16
1.04
1.20
1.58
1.91
1.41
1.22
1.07
1.26
1.68
2.00
1.26
1.21
1.11
1.35
1.59
1.90
ThemonthlyvaluesofaføB,rf•,
1.22
1.20
1.09
1.33
1.68
1.96
1.16
1,13
1.14
1.29
1.70'
1.98
1.14
!.05
1.10
1.27
1.64
2.00
andafør•.
from1937to 1947aregiven
in Tables 1, 2, and 3. The earlierdata have beenadjustedslightlyas follows.For the E-regionthe valueswerereducedby 0.6 per centin order to
make the extrapolationreach1.0 at zerosunspots,
and the Fl-figureswere
reducedby 0.2 per centfor the samereason.For the F2-regionthe rangeof
variatiqn for the ten-stationmeanwas6 per centlessthan for the original
four-station mean, and the earlier resultswere adjustedby this mount
to makethe data homogeneous.
The evaluationof zføfor eachionospheric
layer dependson the extrapolationto zero sunspotsshownin Figure 6. In
due coursewe are sureto experiencea much lower sunspot-minimumthan
that in 1944,and only a very smallextrapolation,if any, will then be neces-
sary.It mightthenbefoundthat thevaluesof zf, and•erefore aførequire
a slight modification.
Figure1 showsthe monthlyvariationsof rfo for the threeregionsE,
F1, and F2 during the period 1937-47,and for comparisonthe relevant
solar variablessunspot-nmber, Ca fiocculi,faculae,and intensity of the
coronal line are also shown.
Zurich
finalrelative
s•spot-numbers
havebeen
used,
andthecharacter figuresof flocculiwerefrom the Q•rterly bullstinof solaractivity.For
the purposeof Figure! andthe correlations
to follow,the character-figures
have been convertedinto numbersthat were more nearly proportionalto
areasof fiocculiand appro.xima•lyequalto sunspot-numbers.
The convertionis givenin Table 4. The areasof faculaehavebeengivenme in
advance
ofpublication
by...the
Astronomer
Royal.
Thecoronal-line
(5303
•)
intensitiesare from •e Harvard Stationst Climax, an.dmany of •'•uhe
se data
have alsobeensentme ;madvice of publication.Daily valuesof meM•an
coronal
brightness
wereprepared
by averaging
thefourbrightestmeasurementsin eachsolarqu•dr•t, combing •ese, and then addingor sub-
436
C.W. ALLEN
[Vo,•.53,No.4]
FIG.I•]WON7'HœY
T•B LE 4
3
Character-figure
Ha fiocculi number
Ca fioccu]i number
19
48
96
150
2O4
16
.41
8O
136
204
tracting sevendays from the date to representconditionson the meridian.
Monthly meanswere preparedfrom the daily values.The data beyond
April 1, 1947,weremultipliedby $ factorof 1.4 in orderto keepthem
consistent.Dr. W. O. Roberts of Climax has kindly informed me that a
changein the measuringroutine at this t/me justifies the use of such a
factor.
The ordinatesof all data in Figure 1 have been adjusted so that the
difference between the value at R -- 0 and at R -- 100 is the same.
(2) Correlations--Figure
i doesnot showany featuresthat differin any
important respectfrom thosepublishedearlier [1]. The detailedagreement
between
the various
factors
c0ntizuues,
andthisnowapplies
alsoto the
intensityof the coronalline 5303A. The similaritybetweenthe curvesfor
the coronalline and •f0• is rather striking.
SOLAREFFECTSON CRITICAL FREQUENCIES
437
A closestudyof Figure 1 showsthat the featuresof all the curvesare
delayed
a fractionof a monthwith respect
to the sunspot-curve.
The
addition
of moredatanowenables
usto determine
thisdelayandthe
sequence
in whichthephenomena
occur
withmoreaccuracy.
Forthispurposeweplotcorrelation-coefficients
withthedatadisplaced
by 0, 1, or2
months.The numbers
correlated
axethe departures
fromthe 12-month
smoothed
curve,andtheresults
of thecorrelation
areshown
in Figure2.
I-l• •LOCCUI.!
½8 FLOCCglI.!
,
c,••'Loccvu S
t
!
....I
/.o•
Z--CORRELATION
OF MONTHLYDœPARTURœ$
FROM SMOOTHL:D
CURVE;VALUœ$
CORRELATED
ARE DISPLACED
BY
O• I• OR • MONTHS
The pairs of phenomenacorrelatedare shown,and in each casethe phenomenonon the left precedesthat on the fight. The probableerrors of
the correlation-coefficients
are indicatedin the diagram,and theseare taken
into considerationin fitting.the resultsto a Gaussiancurve which has fallen
to half-value for a displacementof onemonth.
The sequenceof two phenomenawith about the same delay may be
determinedmuch better by correlatingthem againstone anotherthan by
correlat•g all featureswith sunspot-nmbers.All the pairsof c•)rrelations
have beent•en into consideration
,to obtainthe delaysgivenin Table 5,
wherethe probableerrorsmustbe about -4-0.'05
month.
It is quite clearthat thereare real time-differences
betweenindividual
solarphenomena
aswellasbeEween
solarandionospheric
phenomena.
The
natural explanationis that all phenomenaare associated
with sunspot-
438
C. W. ALLEN
[VOL. 53, No. 4]
TABLE5--Delay of correlated
featuresbehindsunspot.numbers
in month
Sunspot-number .................
Ha flocculi
...................
Ca fiocculi ....................
•f0• .......................
Faculae .....................
Rfør• ......................
•før2 ......................
Coronal-lineintensity
0.00
0.15
0.31
0.43
0.56
0.66
0.68
0.87
groupsbut that somehave a longerlife than others.It might be presumed
that they wouldall start togetherand that the greaterthe delaythe longer
the life. If an ionospheric
regionwere causedby the radiationfrom a particular solar feature it shouldhave the ss•e delay. The data in Table 5
would suggestthat: (a) •he E-regionradiation comesfrom the chromosphericleveland is associated
with the appearance
of fiocculiand faculae;
(b)the F1- andF2-region
radiationcomes
fromfeatures
witha longerlife,
•d by comparison
with the behaviourof the coronalline we wouldexpect
the source of radiation to be in the lower corona.
.Thisresultmight be comparedwith that of Kiepenheuer[2] who attributes the F2-regionto faculae,and •e E- andthe Fl-regions to the corona.
(3) Relationbetweensunspot-number,
critica•frequency,and ultra-violet
intensity--Forthe purposeof determiningthe relationbetween•fo and
sunspot-numberR without too much scatterwe usethe 12-month smoothed
valuesof each.Furthermore,
sinceit hasbeenfoundthat the •fø-variations
lagabout
halfa month
behind
R weplo•each
smoothed
valueof•foagainst
the mean smoothed value of R for that month •nd the month before.
The resul!sare shownin Figure 3. The valuesfor the decliningyears
1937-44 are seen lo agree fairly well with those for •k•eincreasingyears
1944-47. In each casethe relation is linear enoughfor many practical pur-
poses,
andthevaluesat R -• 100become
•føz -- 1.185,rfør, - 1.223,and
•før•---- 1.73.
The intensity of ultr•-vio!et light responsible
for the v•rious ionospheric
!•yers c•a be rela•ed[1]to sunspot-numbers
a•d criticalfrequencies
through
the relation
•S = (1 -]-b/•) = (M'ø)
'•...................
(1)
Here •S is the relativeultra-violetintensityor numberof quautacm-0•
sec-x expressed
in a manneranalogous
to aft. It will be recalledthat (1) •
based on the argument that sincethe variable part of the Sun's ultra-violet
radiation comes from active areas the amount of that radiation. will be
proportionalto the number of active groupsand thus proportionalto
sunspot-number.
SOLAR EFFECTS ON' CRITICAL
FREQUENCIES
439
For the interpretation of ultra-violet intensities in terms of critical
frequencies
it is desirableto determinen by whatevermeansareavailable.
Oncen is fixed b canbe determinedwith someaccuracyfrom the data in
Figure 3.
The theoreticalvalue of n is 4 for an ionosphere
composed
of electrons
recombining
at the rate aN •., wherea is the recombination-coefficient
and
N, the electron-density
[3, 4]. The value of n is 2 ff electronsdisappearby
a decay-process,
that is, if they disappearat the rate fiN, with fi the decay
constant.Althoughthe basicreactionsof the ionosphereare still under
o
Q
Q
.
.
.
discussionthe value of n must be between 2 and 4 if the electronsdisappear
by an atomic process.
Waldmeier[5] has givena methodof determir_•ng
n empacally.He
showed that since
Cf')""'-'S cosx
wherex istheSun'szenith-distance,
if thevariations
ofS canbeeliminated
n can be determinedfrom the relation betweencritical frequencyand x.
In thiswayheobtained
n: 3 fortheE-region
fromobservations
at Mount
Herzogstand.
Themethod
isonlyapplicable
whenthereisa clearrela½ion
between
foandx. Waldmeier's
method
isnowapplied
totJae
E- andFl-data
from14stations
up to theendof 1945.Solarvariations
havebeeneliminatedby usrmg
zJ•, andto e.'•a• thevariation
ofsolar•db.
rancewep!ot
thisag.ainst
(cosx/d•),where
d istheSun-Earth
distance
relative
to the
mean.Whenx was!argecosx wasreplaced
by [i/f(R, x)] fromChapman's
440
C.W. ALLEN
I I' I
½AN•œ•tA
I
I...........
I '• "'I
WA?*!tϥ00
!
HUAiVCAI•O
•oJ
o
[Vo•,.5s,No.4]
I
i
I
I
ß '• ,
I
I
'
' : NO0•
•
OB•ER•AT/ON•
•h A• /5h M•AN•
0[4
0,3
0.8FO•
FIG. •--RELATION
CAH•ERRA
BETWEEN
•A THKRO0
B•I•BAN•
COS X A•D
E CRITICAL
FREQUENCY'
N•A NCAYO
TRINA
WA•HIRGTON
BATOR
•OUG•
CNIL L
--o.,
-'•
o
•-o.7
.
-0.8•
I
•
o=N•N
o=9AAND
•A
•-o.• •
• • .o•(,.•.)
.I
I
I
I
, i ,,,
I
•
I
) ..........
.•---.,I
i
!
I
I
SOLAR EFFECTS ON CRITICAL FREQUENCIES
441
tables[6]usingR = 650for the E-layerand300for the Fl-layer.In this
expressionR is the distanceof the Earth's centre in terms of the scale
height;ekewhereR is sunspot-number.
The dataare plottedlogarithmicallyin Figures4 and5, andtheslopes
of thecurvesgivethe estimates
ofn
which are collected in Table 6.
In Figures4 and 5 the noonobservations
are distinguished
from the
meansfor 09hand15h,but all •hevaluesareusedfor obtaining
the results
givenin Table 6. There is a tendencyfor the noonobservations
aloneto
T•
6--Valuesof n, andzf øat x = 0øfor E- andFl-regions
E-region
Station
Fl-region
Declination
n
W't
logzf ø
n
W't
log zf ø
o
Canberra
Brisbane
Watheroo
35.3 S
27.5 S
30.3 S
3.65
3.60
4.05
1:6
11
20
0.518
0.512
0.508
4.00
5.23
4.72
16
9
20
0.643
0. 646
0.643
Washington
Huancayo
39.0 N
12.0 S
3.52
2.84
22
12
0.528
0.543
4.78
7.13
18
10
0.636
0.653
San Juan
Fairbanks
Maul
Great Baddow
Ottawa
18.4
64.9
20.8
51.7
45.5
N
N
N
N
N
4.98
4.07
3.58
3.70
4.31
5
14
5
9
5
0.522
0.495
0.524
0.503
0.511
5.30
5.10
7.82
3.52
4.18
6
13
3
7
5
0.644
0.626
0. 659
0.643
0.648
Baton Rouge
30.5 N
4.10
5
0.503
4.31
4
0.651
Churchill
Trinidad
San Francisco
58.8 N
10.6 N
37.4 N
4.85
3.01
3.62
3
3
7
0.526
0.534
0.515
5.42
7.04
4.80
8
2
6
0.632
0.649
0.632
0.517
4.90
Means
.......
3.72
..
..
0.643
givesomewhat
greatervaluesof n, but thisisnotalwaysthe case,andthe
agreement
between
noonobservations
andthosefor09a and15hisgenerally
well wi•_.hin
the scatter.It is seenthat our evaluationof n is basedmainly
on annualvariation,whereasWaldmeier'sis basedon diurnalvariation.
Comparison
of thenoonvalueswith thosefor 09hand 15• in Figures4 and
5 showsthat an evaluationbasedon diurnalvariationwouldhave given
approximately
the sameresult.Carehadto be takenduringthe months
whencosx wassmallandvaryingrapidlythroughout
themonth,.Therewas
a tendency
in suchcases
foronlytheMghercriticalfrequencies
to bemeasured and the mean thus increased.To counteractthis tendencyto some
extentthe cosx usedfor eachmonthwasobtainedby averagingthe begin-
ningandendofthemonthandusingthemeanofthisandthevalueforthe
442•
....
C. W. ALLEN
[Vo,..
•a,:No.
middle of the month. Months when this devicewas unsatisfactorywere
omitted.
The valuesfound for n are' E-region,3.72 q- 0.09; Fl-region, 4.90 q0.18. With'these exponents(1) becomes
•S•
=(1
+0.0088
R)
=(•/o•)a.,o.
}................
(2)
•Sr• = (1 + 0.0168R) =
PIowever,the departure of the measuredvalues of n from the theoretical
(recombination-!aw)
n = 4 doesnot seemlargeenoughto justify discarding
the theoreticalvalue. With n = 4 (1) becomes
•Sz
=(l+O'0097
R)
=(rføz)•
}.................
(3)
=
+ o.m2 R) = (d%0 '
and the relation betweenR and S on this basisis plotted in Figure 6. The
relations(3) are adoptedin preferenceto (2).
FOR THœ œ•F/• AND F•-R•'G/ON$
Figures4 and 5 give a rather convem.'ent
basisof comparison
of the E-
andFl-regionsat severalstations.The valuesof zføfor x = 0 mightbe
regardedas fundamentalconstantsof the ionosphere.
The valuesactu•y
obtainedfrom Figures 4 and 5 are given in Table 6 and plotted against
latitudein Figure7. The decredeof z/øwith latitudeis smallbut quite
general,andthe resultsweobtainfromFigure7 aresummarised
in Table7:,
The value of n for the F2-region may not be determinedby the same
methodsincethereis no clearrelationbetween
før• andx. Howeverequation (1) shows•
that thereshouldbe a linearrelationbetweenR and
SOLAR EFFECTS ON CRITICAL
FREQUENCIES
TXSL• 7--Valuesof zf øwiththeSunat z•ith
Place
Equator .....................
Pole
.....................
Mean
•f observed
stations
E-region
F!-region
Mc/s
Mc/s
3.47
3.10
4.53
4.24
3.29
4.40
(rfør•)",
•ndfortheF2-region
•hevariation
of•joiss,•ffi:ciently
large
to
test•helinearity.
Thesmoothed
values
areplotted
forn 1i• Figure
3,
a•dn = 2 in•gure6.When
themore
recent
results
of1944-47
aretaken
intoconsideration
it canbeseen
tl•t thecurve
forn = 2 ismuchmore
line• ths•n' 1.Thevalue
n = I published
eaxlier
[1]onthebasis
of
observations
of i937-44is therefore
abs•doned,
andwe adoptn = 2.
ActusJ/y
n = 3 wo•dfit theo•ervations
R • 120,butwould
notbe
linear
in therange
R•( 120which
isobserved
much
better.
Theresults
forR • 120appear
tobera•her
erratic
inalllayers.
Probably
equa•on
(1)
does
notapply
aecurate!y
when
•ereaxe
soma•ysunspots,
andalso
the
Fl-region
has
atendency
tobecome
submerged
inflxe
F2-region
attimes
of
highsunspot-activity.
With n = 2 for •e F2-regi.on(1) becomes
sr2 =
+ o.oo
= (før2)2
...............
It isevident,
ofcourse,
thattheestimated
variation
inintensity
ofsolar
ultra-violet
light
:m
most
sensitive
totheevaluation
o•n.Kie••euer
[2]
has
used
n-- 3,4,and
4forE,F!,and
F2,respectively,
and
obtains
amuch
larger
F2-radiatiOn
.v.ariation
..:/ ithat
repre•nted
•m(4).
Bradbury
[7]hassuggeste•d
•at thetwoF-layers
arise
from
a s'mgle
process,
and
are
segrega..•d
by...the
•ange
ofrecombination-coefficient
with
444
C.W. ALLEN
[VOL.
ss,No.4
height.If thisweresotheywouldhavethesameconstantb. The twovalues
quotedin (3) sad (4)'of 0.0124for F1 and0.0200forF2 aresufficiently
at
variance
to makeit unlikelythattheyareactually
thesame.
However,
the
ev•uation of n is not accurateenoughto provethis point.
(4) Abnormality
of theF2-region--Itis wellknownthat the F2-region
departsverywidelyfromtheidealconditions
of a Chapman
layerin regaxd
to the distribution
of criticalfrequency
throughout
theday,theyear,and
overthe surfaceof the Earth. However,for all times,seasons,
andgeographical
locations
thereis a fairly regularvariationoffør•.with sunspotnumber,andwith sufficient
datafør2canalwaysbe extrapolated
to give
zfør2at zerosunspots,
•før2canthenbedetermined
in relationto thisvalue.
For ourpurpose
it is importantto knowwhethervarioustimes,seasons,
and stationsgivesimilarvMuesof •føF2.
In orderto studythispointthe diurnalvaxiations
of criticalfrequencies
for the fouroriginalstationsWatheroo,Washington,
Husacayo,aud Canberrawereplottedona logarithmic
scale.For eachstationonediagramwas
madefor eachmonthof theyear,andthe curvesfor eachyearin the period
1937-44wereplottedon thesediagrams.Knowingthe sunspot-numbers
it
was possibleto interpolateand extrapolateamongthe individual curves
andobtaina curvefor eachmonthandeachstationrepresenting
R -- 100
smd"R -- 0. The montltly curvesso obtainedwere averagedinto three
seasonal
curvesasfollows:Northernsolstice,
May, June,July,andAugust;
equinox,March, April, September,and October.;and southernsolstice,
November,December,January, and Februby. The resultingcurvesare
:---'"%.
WA
T>IœRO0
NOON
FIG.a--DIURNAL
VARIATION
OF •'•-•?ANOee•
•_.,
SOLAREFFECTS ON CRITICAL FREQUENCIES
445
shownin Figure8. If aførais to havethe samevaluein all cases
the curves
forR = 0 andR = 100should
beparallel
andseparated
by thesamedisrance.In orderto illustratethe factsthe verticaldifferencebetween•e
curves
for R = 0 andR = 100hasbeenmeasured
andplottedoneach
diagram;
it represents
the diurnalvariation
of af%,.for R = 100on a
logarithmic
scale.
Themeanvalueof 1.73hasbeenquoted
in Section
3,
butit is nowseenthattheaføra-vMues
varyconsiderably
throughout
•e
day.Thesecurves
showthatthegreatest
departure
ofaf%afromthemean
comes
at thehours
ofsunrise
andsanset.
Themostconstant
houroftheday
is noon,and it was for •is reasonthat noonvalueswere usedfor all new
stations
in thedetermination
ofafø.In theearlieranalysis
[1]it wasfound
that the noon,midnight,and24-hourmeansgaveverysimilarvaluesof
a:fo.
It cannowbeseen
thatthisisduetothecomplementary
nature
of•e
curvesfor the Southern
and NorthernHemispheres.
Thisis shownvery
clearlyfor thenorthern-solstice
curves
for Washington
andWatheroo.
The curvesreproduced
in Figure8 are interesting
in themselves
as
showing
a remarkable
uniformity.The curvesvary fromthe extremesummer type best represented
by the Washingtonnorthernsolsticeor the
ttua•cayo southernsolstice,to the extremewinter•pe bestrepresented
by theWateroonorthernsolstice.
Theopposite
typesarecomplementary
as
regardsdiurnalvariationof afø•. We seealsothat the abnormalities
of the
F2-region,for examplethe 18h-maximum
and very severepre-sunrise
minimumof the sum_met
type andthe post-sunset
minimumandnocturnal
increaseof the winter type, are muchmoresevereat sunspot-minimum
than at sunspot-maximum.
(5) Numberof ultra-violetquanta--Thenumberof ionisationsand therefore the numberof tonisingquantaresponsible
for the ionospheric
layers
havebeendiscussed
by BatesandMassey[4],an.din the E- andFl-layers
it is only necessary
to relate •e• data to the phaseof the sunspot-cycle.
The formulafor the numberof quantaper cmapersecoutsidethe Earth's
atmosphereat zerosunspots
becomes
zS = ella(1.24X 10•)=(zfø)
• .......................... (5)
wherezføis in Me/s andrefersto the caseof verticalSun,H is the scale
height,a the recombination-coefficient,
ande the Naperianbase.U•g the
valuesof H and a quotedby Batesand Masseywe obtain the numberof
quantafor the regularE- and Fid:ayersgivenin Table 8. Thesenumbers
may be multiplied by •S to give the quantafrom .anactive S•.
In the caseof the F2-regionit is e•dent that (5) cannotbe consistent
with (4) sincethe exponentof .•e criticalfrequencyis four in oneeaseand
two in the other. The d•c•ty can• overcomeif we assumethat in the
F2-1ayerelectronsdo not dis.
appearby the usual recombination-process
446
C.W. ALLEN
œVo,..
55,•ro.•i
TABLW.
8--Ionospheric
dataandnumber
of ultra-violet
quar,
ta emitted
by theSunat
zero sunspot-number
Item
E
F1
F2
Scale
height
H (cm).......
1.0X 106 3.0X 106 7.0X I06--
zf øfor vertical Sun (Mc/s) ....
• (cm• sec-•) ..........
#(sec -•) ................
3.29
1.0 X 10-8
Quanta at Sun'ssurface(cm-• sec-•)
Quanta from wholeSun (sec-x) . .
2.3 X 10•
1.4 X 10S•
4.40
4 X 10-9
ß
zS(quanta
cm
-•-sec
-•)......
5 X 108
6.9
....
2.1 X 10-4
1.9'•'109
2.3 X 109
9 X 10•
5.3 X 10•
11 x 10TM
6.5 X 10•
[3, 4] represented
by (dN./dt) - (q - aN]), q beingthe rate of electronproduction;but by • dec•y-l•w of the form
(dN,/dt) = (q - •5N,)....................
(6)
Mohler[8]hasshownthatthisdecayqaw
givesa bettergeneraldescription
of •the.characteristics
of •e F2-region•au •e reeombination-!aw.
Exam-
piesof thisimprovement
eaualsobeseenin Figure8. Forrecombination,
thelogarithmic
decrease
offoat nightt'nneshould
befasterforthehigher
electron-concentrations
at R - 100tlxauforR = 0. For decay,the decrease
rate shouldbe the same,and the decay-constant
# shouldbe measurable
fromtheslopeof thenight-timecurve.In Figure8 thetendencyistowards
a fasterslopeat R = 0, but for the moreregularcurves(for example,
Canberraequinox)the two slopes
are aboutthe sameas requiredby the
deeay4aw.
Bates and Masseyhave summarisedthe valuesof a obtainedfrom vari-
ousobservations,
andquote8 X 10-x• cma see-• asa daytimevalue.The
sameobservations
eaube interpretedto givevaluesof/S. In particular,
Appleton'smethodof determininga from diurnalvariation [9] can als.o
be appliedto • and gives
'
IS- \(..d/Va
dt -- _d•t
•)/(Nr - Nz)........................
(7)
whereNa and Ns are electron-densities
equallyspacedbeforeand after
noon.The maior uncertaintyin the applicationof Appleton'smethod
either a or/• is that the diurn.a!variations are influencedto an enormous
extent by the F2-anomaliesmentionedin Section4. From the 12-hour-wave
character
ofthe•yør•-curves
in Figure8 theanom•eswouldappear
to
tidal effects[10],and thesewouldseverelydistortthe electron-decay
process.To apply Appleton's method we must therefore seek for a station
SOLAR
EFFECTS
ONCRITICALFREQUENCIES
447
where
these
effects
aree!iminated.
Forthisselection
weturnagain
to
Figure
8where
wehave
seen
thatthediurnal
variations
offør•change
from
a characteristic
summer
typetoacomplementary
winter
type.
Inbetween
thesetwoextremes
is a typeof diurnal
curvewhichhasa minimum
of
abnormality.
We,therefore,
base
ourfurther
analysis
onthistype,
anduse
asourexamples
theCanberra
equinox
curve
andthemean.oftheWatheroo
equinox
andsummer
solstice
curves.
Theni•t curves
give/?
= 3.5X !0-5
ingood
agreement
withMoblet's/?
-- 2.9X 10-• fromWashington
data
[8].However,
daytime
observations
us•g(7)give
much
.greater
values
of/•,
andthesearesummarised
together
withestimates
of a • Table9.
Tx]•xm
9--Daytime
estimates
ofa andgfromdiurnal
variation
offfraforselected
curves
from Canberraand Watheroo
Station
Canberra
o
!oo
Watheroo
o
lOO
Mean
3.!
1.6
2.3
0.9
X
X
X
X
10-•ø
10-•ø
!0 -x0
10-•ø
2.0 X 10 -•
3.0 X 10 •
1.6 X 10 -'•
1.8 X 10 -'•
2.0 X 10-zø
2. ! X 10 -4
At thedailymaxim.
m wehave(dN,/dt)= 0 in (6), andthefluxof
F2-radiation
becomes
S = eHqo
= eH•N,secx, where
qo= qsecx isthe
maximum
rateof electron-production
fora vert{cal
Sun.Takingvalues
fromthecurves
weob.• thenumber
of quan•.per•' per-.sec
for zero
sunspots
zSr•= 2.3X 1'0
•. It mi.gAt
be•rked thata similar
procedure
usingthevalues
of a 'mTable9 averages
to •S•, = 1.7 X.....
!0"quota
cm sec
-x,and•emfore•e •o'.i1•bergena or• isnotverysignificant
--2
in practiceat sunspof•m•um.
.in •dependent
estimate
offf•.2maybemade
from•e observa%ion
by
Berkner
andSearch
[11]ofthegrowf•oftheF2-re•onafterit hadpractically'disappeared
ina •turbance.Theirsolution
isnotverysensitive
to
(which
theydeterincas1.66X !0'•ø).Theyob• q0= 218,giving
S=
eHqo
= 4.1X 10".Table
3 •ves•for,atthattime(March,
19'40)as
1.57,
whence
zS•, = 4.1 X 10•'X 1,57-'- !.7 X 1:0"
quan• cm-'sec
-•.
Eclipse
observatio•
can.also
• an•,ed to give/?instead
ofa, andan
approximate
treatmentof .theeclipses
s•udied
by I-Ii• [12],Wells•d
Shapley
[13],andDenise,Se•:..
between5 X 10-• :and3 X !0".
The c.o•tantsadoptedfor •the.F2-region
am givenin Table•.8.•e
resulting
zer.•unspot,
ultra-•oletem:msions
forall tamelayersareve•
closeto •e valuespu!b!i..•shed
by Bates.andMassey.
448
C.W.
ALL•N
[Vo•,.•s, No. 4]
(6) Solaractivity--Wehaveseenthat ionospheric
criticalfrequencies
canbe usedasa significant
andaccuratemeasure
of solaractivity[15,16].
From their relation with sunspot-numbers
it is evident that criticalfrequencychangesare associated
with the individualsunspot-groups.
Criticalfrequencies
are,therefore,
anothermeasurement
of a solar-surface
phenomenon,
andarenobetterthansunspot-numbers
in representing
the
internalrigourof the process
whichcauses
the sunspot-cycl
e and which
obviously
variesfromonecycleto another.Thisrigour,whichshouldbe
the most fundamentalindicationof solaractivity, canstill be determined
onlyby thestatistical
process
of counting
sunspots
ormeasuring
quantities
that dependon the numberof sunspots.
[1] C. W. Allen, Terr. Mag., •;1, 1 (!946).
[2] K. O. Kiepenheuer,
Ann. d'Astrophys.
8, 210 (1945);Mon. Notices,106,
515 (1946).
[$] S. ChapmanandJ. Bartell,"Geomagnetism",
p. 505,1940.
[4] D. It. BatesandI5. S.W. Massey,
Proc.It. Soc.,187,261(1946);192,1 (1947).
[5] M. Waldmeier,Helv. Phys.Acta, 17, 168 (1944).
[6] S. Chapman,Proc.Phys.Soc.,48, 483 (1931).
[7] N. E. Bradbury,Terr. Mag., 48, 55 (1938).
[8] F. L. Mohler,Bur. Stand.J. Res.,25, 507 (1940).
[9] E. V. Appleton,Proc.it. Soc.,162,451 (1937).
[10] D. F. Martyn, Proc.It. Soc.,189,241 (1947).
[11] L. V. BerknerandS.L. Seaton,Terr. Mag.,45, 393(1940).
[12] i. J. Higgs,Mon. •qotices,102,24 (1942).
[13]
H.W.Wells
and
i. H.Shapley,
Terr.
Mag.,
$1,401(1946).
•
[14]F. I)enisse,
P. SeligInann,
andIt. Gallet,C.-R.,225,1169(1947),
[15] O. Burkard,ActaPhys.Austria.,1, 98 (1947).
[16] M. L. Phillips,Terr. Mag., $2, 321 (1947).
COMMONWEALTHOBSERVATORY•
Canberra,Australia, July, 19g,8