A C O M P A R I S O N O F S O L A R E U V I N T E N S I T I E S

A N D K - C O R O N A M E T E R M E A S U R E M E N T S

GEORGE L. WITHBROE

Harvard College Observatory, Cambridge, Mass. U.S.A.

(Received 4 January, 1971)

Abstract. Characteristics of the emission observed above the solar limb in four EUV lines, Sixn 4499, Mgx 2 625, Nevni 2 770, and O vt 21032 are discussed. The mean temperature of the corona derived from the ratios of the intensities of Sixn 4499 and Mgx 2625 is 1.8 million K. There do not appear to be significant temperature differences in regions with low EUV intensities and those with high EUV intensities, suggesting that the EUV emission from the lithium-like ions depends primarily on the integral of ne 2 along the line of sight.

The EUV data are compared with K-coronameter measurements in order to yield new estimates of the abundances of Si, Mg, Ne and O relative to hydrogen. Within the uncertainties of the analysis, these coronal abundances are in agreement with the corresponding photospheric values.

1. Introduction

Measurements of the radiation emitted by the Sun at wavelengths not accessible to

ground-based equipment are providing valuable new data on the chemical compo- sition and structure of the solar chromospheric-coronal transition layer and corona.

The present paper describes how extreme ultraviolet (EUV) observations made above the limb can be used to derive coronal temperatures and densities. The observed

ratios of the intensities of lines from the lithium isoelectronic sequence, Six11 2499,

Mgx 2625, NevIII 2770, and Or1 21032, were used to determine coronal temper-

atures and relative abundances of Si, Mg, Ne, and O. The absolute intensities of the EUV lines, temperatures determined from the line ratios, and electron densities

derived from K-coronameter measurements were used to place these abundances on a scale relative to hydrogen.

Ivanov-Kholodny and Nikolsky (1961, 1962), Pottasch (1963, 1964a, 1967) and Athay (1966) have demonstrated that in principle it is not difficult to derive relative abundances of different chemical elements through the use of extreme ultraviolet flux measurements. Their techniques have been used in a number of investigations of the

chemical composition of the corona (Ivanov-Kholodny and Nikolsky, 1961, 1962; Pottasch, 1963, 1964a, 1967; Athay, 1966; Jordan, 1966a; Dupree and Goldberg, 1967; Jordan and Pottasch, 1968; Nikolsky, 1969). Some of the results are summa-

rized in Table I. Differences in the coronal abundances determined from EUV data are caused primarily by differences of opinion about the relative weights that should be given to spectral lines formed in different levels of the atmosphere and/or different parts of the EUV solar spectrum.

Determination of a reliable absolute scale for coronal abundances from EUV data is a somewhat more difficult problem than determination of relative abundances.

Solar Physics 18 (1971) 458-473. All Rights Reserved Copyright �9 1971 by D. Reidel Publishing Company, Dordrecht-Holland

A COMPARISON OE SOLAR EUV INTENSITIES AND K-CORONAMETER MEASUREMENTS

TABLE I

Relative coronal abundances

459

Element Photosphere Corona GMA a LW b Athay Pottasch DG e Withbroe (1960) (1968) (1966) (1967) (1967) (1970)

This study

Si 100 100 100 100 100 100 100 Mg 80 85 100 60 80 98 80 Ne - - 100 70 - 60 80 O 2800 1700 1300 500 2800 980 1300

a GMA -- Goldberg, Mailer and Aller (1960). b L W - - Lambert (1968), Lambert and Warner (1968a, b). e DG = Dupree and Goldberg (1967). a Calculated by assuming A~g/Asi = 0.8 (see text).

I n f o r m a t i o n a b o u t the s t ruc tu re o f the solar a t m o s p h e r e in a d d i t i o n to tha t p r o v i d e d

by the E U V d a t a is r equ i red . P o t t a s c h (1963, 1964a) and D u p r e e a n d G o l d b e r g (1967)

h a v e used a c o m b i n a t i o n o f E U V a n d r ad io obse rva t ions to d e t e r m i n e an abso lu t e

a b u n d a n c e scale. T h e abso lu t e scale de r ived by this t e c h n i q u e is accu ra t e to a b o u t

a f ac to r o f 3.

A n o t h e r m e t h o d o f e v a l u a t i n g the abso lu t e scale is to use the c o r o n a l i r o n abun-

dance d e t e r m i n e d f r o m the analysis o f f o r b i d d e n l ines in the vis ib le p o r t i o n o f the

s p e c t r u m (cf. Po t t a sch , 1964b, 1967; J o r d a n , 1966a, b). H o w e v e r , because o f the

i m p o r t a n c e o f o b t a i n i n g re l iab le c o r o n a l a b u n d a n c e s , use o f E U V d a t a to de r ive

a b u n d a n c e es t imates w h i c h are i n d e p e n d e n t o f the f o r b i d d e n l ine analyses w o u l d be

p re fe rab le .

A th i rd t e c h n i q u e for de r iv ing abso lu t e c o r o n a l a b u n d a n c e s was used by W i t h b r o e

(1970). H e used c o r o n a l e l ec t ron densi t ies de r ived f r o m a v e r a g e d K - c o r o n a m e t e r

TABLE II

Absolute coronal abundances (logAE) ~

Element Photosphere Corona GMA b LW b (1960) (1968)

Athay Pottasch DG b Withbroe e This (1966) (1967) (1967) (1970) study

Si 7.5 7.55 7.5 8.0 7.5 7.7 7.5 Mg 7.4 7.48 7.5 7.8 - 7.7 7.4 Ne - - 7.5 7.8 - 7.5 8.6 O 8.96 8.77 8.6 8.7 9.0 8.7 8.6

a AE = abundance of element E with respect to hydrogen where l o g a n = 12.0. b Definitions of GMA, LW and DG same as Table I. o Corrected for an error of 0.24 dex (0.24 dex= 10 TM) in original paper resulting from neglect factor of 1.32 needed to convert HAO K-coronameter measurements into the same units used by Van de Hulst (1950).

460 GEORGE L.WITHBROE

measurements and EUV limb brightening observations to construct a model for the equatorial chromospheric-coronal transition layer. A comparison of observed EUV intensities with intensities calculated from the model yielded the absolute abundances given in the 7th column in Table II. Photospheric and coronal abundances deter- mined by other authors are also given in Table IL Abundances derived in the analysis described below are given in the last column. The latter are the first abundances derived from EUV measurements in the corona above the solar limb where the electron density could be independently estimated from K-coronameter measure- ments made at the same position on the same day.

2. Observations

The observations consist of K-coronameter data, kindly supplied by Hansen, ob- tained by the HAO instrument (Wlerick and Axtell, 1957; Hensen et aI., 1969) located at Mauna Loa in Hawaii; and of EUV data acquired by the Harvard College Observa- tory experiment aboard OSO-IV (Goldberg et al., 1968; Reeves and Parkinson, 1970) in October and November 1967. During its useful lifetime, the OSO-IV instrument generated approximately 4000 spectroheliograms at over 50 wavelengths between 300 and 1400 A. The spatial resolution of the observations was 1 arc min. The field of view was a square area 36 arc min on a side. The instrument could obtain obser- vations at one wavelength during an orbit, the wavelength was usually changed once per orbit or every 90 to 100 min.

For the present study all the good quality spectroheliograms in a selected orbit, usually between 5 and 8 in number were averaged together to produce a mean spectroheliogram. The intensity at 2 arc min above the solar limb was determined at 5 ~ intervals around the limb using 4-point logarithmic interpolation of appropriate data points in the EUV spectroheliogram (each one a 40 • 48 array of intensity measurements). These intensities were then directly compared with K-coronameter measurements made at the same height on the same day.

Figure 1 is a plot of intensities of SixlI 2499, Mgx 2625, NevIII ~770, and Or1 21032 plotted as a function of T, the angle between a given solar radius vector and solar north. The gaps at the north, east, and south occur because the interpola- tion procedure used did not permit determination of intensities close to the edge of the field of view. Also plotted on the graph are the corresponding values of pB measured with the HAO K-coronameter, where p is the polarization and B is the brightness in units of 10-8 of the radiance of the center of the solar disk. As expected, there is an excellent correlation between the brightness of the K-corona and the EUV intensities, since both depend upon the number of electrons along the line of sight.

Data such as those presented in Figure 1 can be used to derive absolute coronal abundances for chemical elements having coronal lines in the wavelength range accessible to the HCO spectrometer, 300 to 1400 A. Four coronal ions had sufficiently large signal levels to accurately measure the emission at 2 arc min above the limb,

A C O M P A R I S O N OF SOLAR E U V INTENSITIES A N D K - C O R O N A M E T E R M E A S U R E M E N T S 461

I 0 5 ] 0 5

,<d El: LL1102 l-- r r)

qP LLI LF)

~ 1 0 t c )

u3 Q9

>-

(/3 z U

z

I

- - S i Xl l k 4 9 9

- - MQ X X 6 2 5

i ~ i ..... ~.~ / . - i s t r /

/ , ~..,.

/", ] ,, ,., .--,d ,j ',,

i o o ^ i f \

/ ~ . " t\ / \

IC] 0 9 O N E

I 1

. . . . N e vi i i k 7 7 0

....... 0 v i k 1 0 5 2 m

t

/ ',j

I \

t \ I1

l/ ..i

\ ~ I A I \

I ] 1 8 0 2 7 0

S W

D E G R E E S )

% \

\ \ \ / \ j

4 0

O3

c~

<~

0 u )

L 0

[K hu t- Z LO

I 03 o LL. 0 ImJ (D Z

0 2 ~ o2

u~

W Z

t F-- �9 I

5 G O ~

N N

Fig. 1. EUV intensities observed 2 arc min above the limb on November 23, 1967 as a function of ~t, the angle between a given radius vector and solar north, and the corresponding polarization and

brightness parameter pB from the K-coronameter data.

the lithium-like ions SixII (2499, 2521), M g x (2625, 2610), N e v m (2770, 2780), and OvI (21032, )~ 1038). Other coronal lines within the wavelength range covered, such as F e x v )~417 and FexvI 2335 and 2361, were very weak because of the use of normal incidence optics in the OSO-IV instrument. Furthermore, the absolute sensitivity of the instrument to radiation with wavelengths shorter than 450 A is poorly known. The iron lines were much better observed with the subsequent HCO OSO-VI instru- ment, and will be discussed in a future paper.

3. Analysis of the EUV Intensities

The intensity of an EUV emission line (cf. Withbroe, 1970) is given by the expression

oo

f 2 dr/s~ > I(0 ) = 1.73 • 10 - 1 6 AfK #G(T~) '~(tlp) ne (1) oR D

where ~ is the distance from the center of the Sun in units o f the solar radius R o ; A is the abundance of the chemical element producing the line measured with respect

462 G E O R G E L . W I T H B R O E

to the hydrogen a b u n d a n c e ; f is the oscillator strength; g is the Gaunt factor; G (Te) is a function that depends upon the fraction of atoms in the state of ionization producing the line, the temperature, and excitation potential o f the line; n e is the electron density; K ~ (t I#) is a parameter that depends upon the line optical depth; # = ( l r ) x / ( r 2 -- (pR| and r is the distance from the center of the Sun. For the lines considered here, the optical depths at 2 arc min above the limb were found to be sufficiently small to set K ~ ( t / # ) equal to unity. The error introduced in the abundance determination by making this assumption is small, o f the order of 10~ or less. Since this error is much less than errors caused by other uncertainties in the analysis, Kq~ (t/l~) was set to unity in order to simplify the calculations.

Another assumption made to simplify analysis was that the coronal gas along the line of sight is isothermal. This implies that the ratio of the intensities of two different spectral lines, for example 2499 of Sixti and 2625 of Mgx, observed at the same position above the limb will be given by (see Equation 1)

I(~)si xH Asl [ fgG (To)Is i x1~ 2 499 Asi I (r -- AMg [ fgG (Tc)]Mgx 2 625 -- AMg f (To) (2)

where f (T~) is a known function of the coronal temperature T~.

~ . 1 0 o v

= I0 ~r

jO z

i i i

I 6 . 0 6 . 2 6 .4 6 6

L O G T

r~ 2 .<

N o

~ i o -I

o

.<

>

z

m m

~ 10-I

~5

io -z t. 6 0 6.2 6 ,4 6 .6

L O G T

I

Fig. 2. Theoretical ratios I(Sixii 2499)/l(Mgx 2625), I(Sixl[ 2499)/l(Nevni 2770), and I(SixII 2499)/I(Ovi 21032) as a function of temperature. The assumed relative abundances of Si, Mg, Ne

and O are respectively 1.0, 0.8, 0:8 and 11.2.

A C O M P A R I S O N OE S O L A R E U V I N T E N S I T I E S A N D K - C O R O N A M E T E R M E A S U R E M E N T S 463

An earlier paper (Withbroe, 1970) showed that the intensity ratios I(SixH)/I(Mgx), I(SixII)/I(NevnI),andI(SixH/I(OvI) are very sensitive to temperature. Theoretical values for these ratios are plotted in Figure 2. The f-values are taken from Pottasch (1967), the Gaunt factors from Bely (1966) and the ionization equilibrium calculations needed to compute G (To) are from Allen and Dupree (1969) and Dupree and Wood (1970). The ionization equilibrium calculations include dielectronic recombination. The relative abundances used,

Asi'AMg:ANe:Ao of 1.0:0.8:0.8:11.2,

%

k 2 0 -

'.:2 ..........

- - T ( S i xtt X 4 9 9 / M g x X 6 2 5 )

- - - T (Si xit X 4 9 9 / N e vm X 7 7 0 )

...... T ( S [ xtl X 4 9 9 / O v l ) , ,1052)

o . o I I 0 90 180 N E S

( D E G R E E S )

I I

-. .-

I 270 560 W N

Fig. 3. Temperatures derived f rom different line ratios observed on November 23, 1967 as a function of ~,.

are logarithmic averages of the coronal abundances given in columns 4 through 7 of Table I.

Figure 3 shows temperatures derived from the intensity ratios I (Sixn)/I (Mgx), I(Sixn)/I (Nevm), and I(SixI1)/I(OvI) for data acquired on November 23, 1967. As is apparent, the variation of T c with 7 ~ is relatively small in spite of the large variation of the corresponding EUV intensities. (see Figure 1). The temperatures computed from the three different line ratios are also in reasonably good agreement. This is significant because the ionization potentials of the O vI, Ne VHI, Mgx and Sixn ions range from 138 V to 523 V. The mean temperature determined from all of the SixII and Mgx observations (see Table III) is 1.8 millionK. There appears to be no significant difference in the temperatures of regions with low EUV intensities and those with high EUV intensities. This is illustrated in Figure 4 where temperatures

464 GEORGE L. WITHBROE

TABLE III

Summary of dates and orbits during which data were acquired

Date (1967) Orbit during which data were acquired

Sixu Mgx NevooI OvI

Nov. 2 220 227 226 225 Nov. 3 242 233 - - Nov. 4 259 253 248 - Nov. 9 322 326 - 332 Nov. 15 417 416 - - Nov. 15 426 425 419 422 Nov. 16 434 433 436 432 Nov. 21 514 513 515 - Nov. 22 521 520 522 525 Nov. 23 537 536 538 541

Fig. 4.

6.4

~96.2 0

6.0

[ ] [ I I i I l i

�9 " .~ . . , ", "." r i . . . . �9 �9 . . . . . : . ~_~ - . :4~ . = : . .

. , ..o..:, : 7 ~ . - . ~ . ' : . . ' ~ . ~ . . ~ : ~ . , ~ . ~ . . : o . ' . o ' . ' ~ ' ~ . ' . , . . ' " ; . $ . , .~ . ." .

�9 . I J " � 9 � 9 . - . . . ~ % , o , e - -

o * i , �9 ee �9

i i I i i i I I i I0 I 10 2

T(Mg x X625 )

O

Temperatures determined from the ratio of Sixu 2499/Mgx 2625 as a function of the intensity of Mgx 2625.

computed f rom the SixII and M g x data are plot ted as a funct ion o f the intensity

of the M g x line. The lowest E U V emission usually occurs in the polar regions while

the highest E U V intensities occur when the line o f sight passes th rough active regions

near east or west l imb passage. These results suggest that the assumpt ion that the

corona is isothermal a long the line o f sight is probably not too inappropr ia te and

also that the coronal emission f rom the l i thium-like ions depends pr imari ly on the 2 integral o f ne along the line o f sight.

A COMPARISON OF SOLAR EUV INTENSITIES A N D K - C O R O N A M E T E R MEASUREMENTS 465

Several of the ratios of lines from the lithium sequence are insensitive to temper-

ature for the range between 1.4 and 2.5 millionK. These are the ratios I(Mgx)/I(OvI), I (Mgx) / I (Ne viii), and I(NevHI)/I(O vI). Since the temperatures of most coronal gas

seem to fall between these extremes, these ratios can be used to derive relative abun-

dances AMg/A o, AMg/ANe, and ANe/Ao (see Equation 2). In Figure 5 the observed ratios I(Mgx)/I(OvI), I(Mgx)/I(Nevln), and I(Nevm)/I(OvI)are plotted (points)

as a function of the temperatures determined from the I (SixlI)/_/(Mgx) ratios�9 The relative abundances of Mg, Ne, and O have been adjusted so that the theoretical

curves pass through the means of the observed ratios�9 Values for these abundances

are given in the last column of Table I. The abundance relative to Si was determined

by assuming that AMg/Asi=0.8, a value consistent with both the photospheric and

the coronal determinations of the relative abundances of Si and Mg. One disturbing aspect of the data presented in Figure 5 is the, large amount of

scatter of the observed points. Some of it is due to statistical noise in the measure- ments and changes in the corona occurring in the time between the observations of

different spectral lines�9 A more important cause of scatter is the difference in the

I O I

0

0

~ i00

oJ s .<

x

I0

I I I I I I

".%�9 �9149149

~ : . �9 .,.:.

6.0 6 .2 6 .4

L O G ( T c) I I

oJ

0

h-- b-

~0 z

- - I I I i I F ~ 1 0 0 !

�9 �9 �9 � 9 �9

1.0

6.6

I I I J

�9 �9 �9 J

x

6 . 0 6,2 6.4

L O G ( T c )

6.0 6 .2 6 4 6.6

L O G ( T c)

6 .6

Fig. 5. Observed ratios l(Mgx 2625)/I(0vi Z1032), l(Mgx 2625)/l(NevnI 2770) and I(Nevlii ).770)/I(Ovi 21032) (points) as a function of the temperature determined from the Si Xli 2499/ Mgx 2 625 ratios. Crosses mark prominence observations. The curves are theoretical ratios computed

from the abundance ratios given in the last column of Table I.

466

I01 ' I

G E O R G E L . W I T H B R O E

i i r ) [

Fig. 6.

i f ) O

c~J

x

i0 ~

iO-)

�9 . . . . . . . . . ; - . - �9 , . : . . v . . 4 . - " e.

. , . . ; ~ . . . ~ , . . , , ~ �9 ,

�9 �9 e o l �9 �9 �9 % ~ �9 . . . ~ . . ~ .a~.. -.2...

�9 * S , ~ l ' ~ , ~ , e e I " "% �9 �9 . '~ . , : .~"- .~ ,~ ' . "; �9 .

�9 - . ; . ~ ; x : , .. �9 q?�9

J I n ~ , i I I I0 ~ i0 2

I (Mg X k 6 2 5 )

Observed ratios l(Mgx 2625)/I(0vi 21032) as a function of the intensity of Mgx 2625. Crosses mark prominence observations.

observed ratios dependent upon intensity. This is illustrated in Figure 6 where we have plotted the observed ratios I(Mgx)/I(OvI) as a function of the intensity of the M g x line. The ratio systematically increases with increasing Mgx intensity. The ratio I(Mgx)/I(Nevn 0 shows a similar trend. I f the coronal temperature in both quiet and active regions were between 1.4 and 2.2 million K, as indicated by the ratios I(SixzO/I(Mgx),I(SixzI)/I(NevI.), and I(SixH)/I(Ov O, then we would expect that the I(Mgx)/I(OvI) and I(Mgx)/I(Nevn 0 ratios would be independent of the intensity of the M g x line. The fact that the ratios are not independent of the intensity of the M g x line may be evidence that there is material in the line of sight whose temperature falls outside the limits over which the theoretical ratios are constant. An alternative explanation is that the theoretical line ratios contain systematic errors.

Prominences provide one type of inhomogeneity that can have a significant effect on the ratio I (Mgx) / I (OvI). The crosses in Figure 6 mark some observations of a large prominence. Prominences emit substantial OvI radiation because they contain some gas at temperatures of a few hundred thousand K (Kirschner, 1970; Kirschner and Noyes, 197l). Gas at this temperature emits Or1 21032 two order more efficiently than gas at coronal temperatures. Therefore a small amount of cool material, such as that contained in prominences, can significantly enhance the intensity of O vl 21032. Since Nevii l 2770 is also emitted most efficiently by gas with temperatures below one

A C O M P A R I S O N O F S O L A R E U V IN T E N SIT IE S A N D K - C O R O N A M E T E R M E A S U R E M E N T S 467

millionK, its intensity can similarly be affected by the presence of small amounts of cool gas along the line of sight. Since SixlI 2499 and Mgx 2625 are emitted most efficiently by gas at coronal temperatures, their intensities are unaffected by the presence of cool gas unless the quantity of cool material becomes sufficiently large to significantly reduce the amount of coronal gas along the line of sight. It is possible to account for the relative behavior in quiet and active regions of the intensities of the SixII, Mgx, NevuI, and OvI lines by introducing approximately 5 to 10% of 600000K gas in the line of sight in quiet areas and 0% 600000K gas in active regions.

A second type of inhomogeneity that can affect the EUV line ratios is a coronal condensation (cf. Newkirk, 1967) which can have temperatures two or three times larger than the 1.6 to 2.2 millionK temperatures derived from the ratios I (SixI0/ I (Mgx) , l(Sixn)/I(Nevm), and I(SixH)/I(Ov O. Although the behavior of some line ratios can be explained by introducing hot (more than 2 million K) material into the line of sight, other ratios cannot easily be accounted for in this way. If the behavior of the ratios I(Mgx)/IOv 0 and l(Mgx)/I(NevnI) is caused by temperature in- homogeneities, the most likely explanation appears to be the presence of small amounts of cool (less than one million K) gas in the line of sight in quiet areas.

One possible source of error in the theoretical intensities is neglect of density- dependent effects in the calculation of the ionization equilibrium. Since the Mgx intensity depends on the integral of n~ along the line of sight, the trend observed in Figure 6 could possibly be a density effect. The results of the calculations of Burgess and Summers (1967) and Jordan (1969) suggests that density-dependent effects in the ionization equilibrium can cause the ratios I(Mgx)/I(Ov 0 and I(Mgx)/I(NevxII) to increase with increasing density. However, until more theoretical calculations are made, it will not be possible to determine if the observations can be fully explained in this manner.

We intend to study the problem of the O vI and NevIII emission more thoroughly with the OSO-VI EUV spectra obtained at the solar limb. These data have a signifi- cant advantage over the OSO-IV data in that nearly simultaneous observations (within 15 min or less) of the intensities of lines from the lithium isoelectronic sequence (as well as many other lines) were obtained above the limb in both quiet and active regions. Also of importance in the OSO-VI spectra are the Fexv and FexvI lines, which are most efficiently formed at temperatures of 3 to 4 millionK and therefore can be used to estimate the amount of high-temperature gas along the line of sight. The OSO-VI spectra may be instrumental in resolving the question of whether the peculiar behaviors of the ratios I(Mgx)/I(Ovi) and I(Mgx)/I(Nevn 0 are a conse- quence of density differences or temperature differences between quiet and active regions.

4. Comparison of EUV and K-Coronameter Data

To place the relative abundances given in Table I on an absolute scale, it is necessary to determine the electron density along the line of sight. Assume as a first approxi- mation that the coronal gas in the plane defined by the line of sight and the center

468 GEORGE L.WITHBROE

of the Sun is isothermal, with a temperature defined by the ratio of the SixII and Mgx lines. Also assume that the variation of the electron density with radius along any radius vector in this plane is given by the hydrostatic equilibrium formula with this same temperature. Then Equation (1) can be rewritten as

where I ( ~ , ~) = 1.73 x 10 - ' 6 AfgG(Te) <ne2 (~, ~)) C ( ~ , ~, To) (3)

: , ) d r c ( e , Q, :re) = ( e ,

oR|

can be integrated numerically. If there are density inhomogeneities along the line of sight, the average (n~ (7 t, ~)> gives greater weight to coronal material of high density than to coronal material of low density. Because of the rapid decrease of n~2(7 j, r) with r, the average also gives greatest weight to material at the position where the line of sight passes closest to the solar surface. Given the assumptions given above it is a simple matter to calculate values of Asi @2 (tp, Q)> from the observed Sixn intensities. If we know (n~ 2 (5 ~, ~)), then Asl can be determined.

Information about the mean electron density as a function of position around the solar limb is contained in the K-coronameter data. The definition of Equation (3) depends upon the assumption that the electron density along any radius vector in this plane is given by the hydrostatic equilibrium formula. Since the mean variation of n e (r)/n~ (9) for the corona in 1967 is very similar to that in van de Hulst's (1950) model (Hansen et al., 1969) and since the brightness of the K-corona, pB, varies directly with the mean electron density along the line of sight, we would expect that

<l /e( }t~t, e )> = 4 .~ PB ( 7t' e) , , PBVH(e5 nete)VH (4)

where pB(7', ~) is the HAO K-coronameter measurement, pBvH(Q) and ne (0)vrt are given in Van de Hulst's (1950) paper and the factor of 1.32 converts the HAO measurements to the same intensity scale used by van de Hulst (see Newkirk, 1961). If there are density inhomogeneities along the line of sight, the average (nr (~, r gives greatest weight to coronal material at the position where the line of sight passes closest to the solar surface.

From Equation (4) and the observed K-coronameter measurements <ne (~, 0)> can be calculated. If one makes the additional assumption that (n~ (~, ~)) derived from the K-coronameter data is equal to (n~ 2 (~, 9))1/: derived from the EUV data, it is possible to determine the absolute abundance of Si. Since active regions are contained, in the line of sight for many data points, we expect that (n~ (~, Q)),/: will often be greater than (n~ (k~, if)). Thus the Si abundance estimated by this technique may be too large.

Figure 7 compares values of (n e Oe, ~)) computed from K-coronameter data with values of (n~ Og, ~)),/2 determined from the Sixn data using the procedures outlined

F i g . 7.

A COMPARISON OF SOLAR EUV INTENSITIES AND K-CORONAMETER MEASUREMENTS 469

Q) v

Z JOE

�9 t " ~ I / ' ,

I 0 90 N E

Ne ( S i x l l X 4 9 9 )

. . . . Ne (WHITE L I G H T )

I 180 270 560 S W N

~/ ( D E G R E E S )

Mean electron densities computed from the K-coronameter and SixII 2499 measurements as a function of ~u for data acquired on November 23, 1967.

above and Asl = 3.2 x 10-5. Both densities are plotted as a function of 7 j, the angular

position measured from the north pole of the Sun. The agreement between the two curves is clearly very good.

Figure 8 compares values of (n e (7/, ~)) computed from K-coronameter data with values of [10 4.5 Asi (n 2 (7 ~, ~))]1/2 determined from all of the SixII data used in the analysis. A description of the data is given in Table III . Also drawn on the graph are the lines [10 r Asl] 1/z (ne(~ , Q)) for Asi = 10 -5, 3.2x 10 -5, and 10 -4. The line for Asi = 3.2 x 10-5 fits the data very well. Since we expect that (nZe (~F, ~))i/z is greater than or equal to (ne (7 j, e ) ) because of the presence of density inhomogeneities, these results suggest that

Asi ~ 3.2 X 10-5

This differs from the result of Pottasch (1963, 1964a, 1967), who found Asi--10 -4. I f As~ is assumed to be 3.2 x 10-5, then the relative abundances in the last column

of Table I can be placed on an absolute scale. The resulting abundances are given in the last column of Table II. Because of the good agreement between these abundances and the corresponding photospheric values, it seems reasonable to assume that the photospheric and coronal abundances of Si, Mg, Ne, and O are identical. Our results do not justify the conclusion that the coronal abundances of these elements are larger

470 GEORGE L.WITHBROE

d

/x

v

c,l eo

Z

v •

x

%

I0 8 I0 9

~ a e (~,p) ~

Fig. 8. The quantity [104. 5 AsJ <ne 2 (~u, 0)>]1/2 derived from EUV data (see text) as a function of the corresponding mean electron densities derived from the K-coronameter data. The solid lines are plots of 1104.5 Asi] 1/2 <ne (~', 0)> as a function of <he (N, 0)> for different values of Asi.

than the photospheric values; rather, they suggest that the coronal abundances might be smaller.

The major sources of systematic error in the derivation of the abundances given above are uncertainties in calculating the exact position of the solar limb in the EUV spectroheliograms; in the effect of temperature and density inhomogeneities along the line of sight; and in the absolute calibration of the EUV intensities. The absolute scale of the EUV intensities is accurate to about a factor of 2. The uncertainty in the position of the solar limb, coupled with the steep gradients in the EUV emission above the limb (cf. Withbroe, 1970), result in an uncertainty of 0.2 dex (0.2 dex-- = 10 o.2) or less in the abundances. Another source of systematic error is the uncer- tainty in the mean temperatures derived from the ratio of the intensities of Sixn 2499 and M g x 2625. This uncertainty depends upon the assumed ratio of the abundances of Si and Mg, which appears to be known to an accuracy of about 4- 20% (see Table I). The net effect of the uncertainties in the calibration, position of the limb, and the coronal temperature is that the absolute abundances quoted above can be systematic- ally off by a factor of about 2.5 to 3 (0.4 to 0,5 dex). dances, the results of the present investigation suggest, as we have indicated earlier, that the EUV emission from lithium-like ions depends primarily on the integral of

A C O M P A R I S O N OF S O L A R E U V I N T E N S I T I E S A N D K - C O R O N A M E T E R M E A S U R E M E N T S 471

It is difficult to obtain a reliable quantitative estimate of the effect of inhomoge- neities in our results. Inhomogeneities in temperature provide a particularly difficult problem with respect to the Ovi and NevnI emission. As we have already indicated, the intensities of these lines are very sensitive to the presence of small amounts of coronal material with temperatures below one million K. If present, such material would enhance the Neviii and OvI emission relative to the Mgx and Sixn emission. Therefore, use of mean temperatures defined by the SixII/Mgx ratios would result in over-estimating the Ne and O abundances.

Another important type of inhomogeneity is coronal condensation, whose proper- ties have been determined from emissions in the visible and X-ray portions of the spectrum (cf. Billings, 1966; Newkirk, 1967; Gabriel and Jordan, 1969; Batstone et al.,

t970). These features can have temperatures ranging from 2 to 6 millionK and densities from one-half to several orders of magnitude larger than the densities found in the present study. Calculations with the data of Batstone et al. (1970) indicate that introduction of one of these features into the line of sight will increase the root-mean- square density determined from the lithium-like lines by a larger factor than it will increase the mean electron density. Consequently, abundances derived from EUV observations will be over-estimated, probably by a factor of not more than 2 to 3.

It is of interest to consider the problem of coronal inhomogeneities from another viewpoint. If we assume that the photospheric and coronal abundances of Si are equal, then the results presented in Figures 7 and 8 suggest that in both quiet and active areas the root-mean-square electron density and the mean electron density are very nearly equal at a distance of 2 arc rain above the limb. We note that Sixn is formed over approximately the same temperature range as Nelx, for which Batstone et al. (1970) found densities on the order of 10 ~~ in active regions on the disk. Our results indicate that densities this large are not normally found at 2 arc min above the limb, if they were, the coronal silicon abundance would be smaller than the photospheric value by a factor of 2 to 3. We shall consider this problem in more detail in a future paper. To properly evaluate the difference between the root-mean- square and mean electron densities it is necessary to consider also the horizontal and vertical density structure in the different regions along the line of sight. Towards this end, we are evaluating techniques for using spectroheliograms made several days apart. Hopefully, we will be able to place upper limits on the difference between the root-mean-square and mean electron densities in both quiet and active regions.

In addition to providing information about the absolute scale of coronal abun- 2 no along the line of sight. Consequently, spectroheliograms in these lines, particularly

Mgx 2625, serve as excellent maps of the distribution of coronal electron densities across the solar disk. The Mgx 2625 observations provide the best data for this purpose, since the SixII 2499 emission from the disk is contaminated by chromo- spheric radiation from the He1 continuum, the Nevln 2770 emission from the disk is contaminated by chromospheric radiation from the hydrogen Lyman continuum, and the chromospheric-coronal transition region contributes significantly to emission from the disk in both Nevm 2770 and Ovl 21032. We point out these facts because

472 GEORGE L. WITHBROE

of the existence of a large number of daily Mgx 2625 spectroheliograms that were

obtained by Harvard experiments on OSO-IV and OSO-VI. Based on the above considerations these spectroheliograms contain a wealth of synoptic information about coronal electron densities. The OSO-IV spectroheliograms which cover the

period October 25, 1967 to November 29, 1967 have been published by Reeves and

Parkinson (1970). The OSO-VI data, which cover the period August 14, 1969 to

May 12, 1970, are still being processed and should be available at the National Space

Science Data Center by late 1971.

5. Conclusions

This investigation demonstrates that there is a strong correlation between the emission

in EUV coronal ions and the emission in the white light K-corona. Within the un-

certainties of the analysis, the absolute coronal abundances derived from a compari- son of the two types of data are in agreement with the corresponding photospheric values. The mean temperature of the corona derived from the ratios of the intensities

of SixH 2499 and Mgx 2625 is 1.8 millionK. There do not appear to be appreciable

temperature differences in regions characterized by high and low EUV intensities.

Consequently, the coronal emission from the lithium-like ions provide a convenient

tool for measuring coronal electron densities.

Acknowledgements

I am indebted to L. Goldberg, R. W. Noyes, W. H. Parkinson, and E. M. Reeves,

who contributed so much time and effort to making the Harvard OSO-IV experiment a success. I thank them, A. K. Dupree, and R. T. Hansen for many stimulating

suggestions and comments. I am also indebted to R. T. Hansen for the K-corona- meter data. J. C. Flagg and D. Bechis provided computer programming and compu-

tational assistance. This work was supported by the National Aeronautics and Space

Administration through contracts NASw-184 and NAS 5-9274.

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A COMPARISON OF SOLAR EUV INTENSITIES AND K-CORONAMETER MEASUREMENTS 473

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