ATOMIC-BEAM

STUDY

OF T H E S O L A R

LINE AND THE SOLAR

7699/~ POTASSIUM

GRAVITATIONAL

RED-SHIFT

J. L. SNIDER* Jeff'erson Physical Laboratory, Harvard University, Cambridge, Mass., U.S.A.

(Received in final form 13 January, 1970)

Abstract. Time shape and red-shift of the solar potassium resonance line (4eP~/.,.- >4~S~;~) at 7699/~ have been studied by an atomic-beam resonant scattering technique. Light fi'om the central 10% of the solar image fell on a potassium atornic beam whose scattering wavelength was shifted in a known way by a magnetic field. The line profile was obtained by measuring the scattered light intensity as a function of magnetic field. The time required for a single profile of the line core was 30-40 rain. Most of the observed profiles were asymmetrical and the character of the asymmetry varied in an erratic way from profile to profile. The mean red-shift of the 40 profiles which showed small or no asyrnmetry was : (~ 2) ......., -- ] 0 - 1 m,~ = (0.6] : :: 0.06)(A ,;.)g...... where (A)-)grav is the gravitational red-shift predicted on the basis of the principle of equivalence. This result, together with those of other recent experiments, is consistent with the previously observed correlation between the red-shift of a solar line and its strength. Various checks of timeexperimental method are discussed, including preliminary measurements on the solar sodium D I line.

1. Introduction M a n y years a g o E i n s t e i n e m p l o y e d the p r i n c i p l e o f e q u i v a l e n c e to predict a d e p e n d e n c e o f the w a v e l e n g t h o f a spectral line on g r a v i t a t i o n a l p o t e n t i a l (Einstein, 1911). T h e d i s c o v e r y o f the M 6 s s b a u e r effect m a d e it p o s s i b l e to verify this p r e d i c t i o n in terrestrial e x p e r i m e n t s ( P o u n d and R e b k a , 1960; P o u n d a n d Snider, 1965). O v e r thc y e a r s a g r e a t deal o f careful w o r k has been d o n e on solar lines, f o r w h i c h the p r e d i c t e d f r a c t i o n a l w a v e l e n g t h shift r e l a t i v e to the c o r r e s p o n d i n g terrestrial line is t o w a r d the r e d by a b o u t 2 p a r t s in 106. T w o g e n e r a l c o n c l u s i o n s h a v e e m e r g e d ( A d a m , 1955, 1958, 1959, 1962). First, m o s t solar lines are i n d e e d red-shifted, but by a n a m o u n t c o n s i d e r a b l y s m a l l e r t h a n p r e d i c t e d w h e n they arc o b s c r v e d at t h e c e n t e r o f the solar disk, t h e shift i n c r e a s i n g as t h e l i m b is a p p r o a c h e d until it b e c o m e s e q u a l to, o r e v e n cxceeds, * Present address: Department of Physics, Oberlin College, Oberlin, Ohio 44074, U.S.A.

Caption to frontispiece on pp. 350-351 : The importance 2b flare photographed with the 40 cm refi'actor (f/12.5) of the National Observatory of Athens the 2nd Novernber 1968, by means of an lt'x Filter, pass band 0.5/~. Film: Kodak SO 375. The diameter of the original negative is 155 ram. This flare was accompanied with strong radioemissions throughout the whole radio-spectrum. (1) The flare before maximum, at -- 1.0 A, from the center of Ha at 10~L02 '~ 52~; (2) the flare at --0.5 A from the center of H:x at 10~' 07 TM 45~; (3) the flare near maximum in the center of 1--Laat 10h 10''~ 38~; (4) the active region after the flare (0.0 A) at 11a~ 12TM 07"-'. (By courte,~y (~["C. J. "Waeris, National Observatory r thens)

Solar Physics 12 (I 970) 352-369. All Rights Reserved Copyright (r 1970 by D. Reidel Pttblisking Company, Dordrecht-Holland

THL7699 +~POTASSIUMLINEANDTHERED-SHIFT

353

the predicted value at the limb. Second, there is a correlation between red-shift and line strength, stronger lines having a greater shift than weaker ones at a fixed position on the solar disk. The deviations of the solar observations from the gravitational effect are believed to be mainly due to Doppler shifts produced by radial currents within the photosphere, but quantitative understanding is still lacking. For white dwarf stars the predicted shift is to the red and roughly 100 times greater than for the sun. The white dwarf data do show qualitative agreement with this prediction (Greenstein and Trimble, 1967). The motivation for the work reported here was provided by two recent experiments on the sun. In 1.961 Brault used a grating spectrometer with an elegant oscillating-slit method to show that the solar sodium DI line had no significant center-to-limb wavelength variation and was red-shifted relative to a laboratory sodium absorption cell by an amount equal to 1.05 + 0.05 times the predicted gravitational effect (Brault, 1962). Also in 1961 Blalnont and Roddier used an atomic-beam resonant scattering technique to study the solar strontium line at 4607/~ (Blamont and Roddier, 1961 ; Roddier, 1965). They found a large center-to-limb effect for this line, similar in character to that discussed above. In the present experimcnt the atomic-beam technique was used to study a solar line whose origin and behavior were expected to be similar to those of the sodium line, in the hope of obtaining additional unambiguous evidence for the solar gravitational red-shift. 2. The Atomic-Beam Method and the Solar Potassium Line

In the atomic-beam method of studying tile intensity vs. wavelength profile of a solar line, solar light is resonantly scattered by a beam of the appropriate atoms. A magnetic field applied to the bealn atoms shifts their absorption wavelength in a known way by means of the Zeeman effect. The intensity of scattered light as a function of magnetic field gives the line profile directly. The great advantage of this method, in addition to its high resolution, is that it gives an absolute measure of the wavelength shift of the solar line relative to the free atom wavclength, since the beam atoms are essentially isolated. No laboratory comparison light source, which may be subject to pressure or other shifts, is involved. The main disadvantage of the atomic-beam method is its limitation to spectral lines corresponding to transitions to the atomic ground state. Also, any hyperfine structure complicates the Zeeman effect and reduces the resolution. For this reason Blamont and Roddier limited their work to strontium and other Group II elements whose isotopes have predominantly zero nuclear spin. A search of the solar spectrum (Minnacrt et al., 1940; Moore et al., 1966) for other suitable lines showed only two: the sodium DI line at 5896 A~ already exainined by Brault and the corresponding potassium line at 7699 ~. The latter line is free from blends and quite symmetrical, while a beam of potassium atoms is easy to obtain. The naturally occurring stable isotopes are K.39, with an abundance of 93~ and K 4a, with an abundance of 7~o. Both isotopes have a spin of~- and show hyperline structure.

354

J.L. S~[DER

Perhaps the most appealing feature of {hc potassium liJl.e is the fact that although, it is considerably weaker than the sodium line it is .presumably still formed high up in the photosphere where convective motions are small (Lain bcrt and Mallia, 1968). This is a consequence of its low excitation potential and large resonance cross section. An estimate of the wavelength shift produced by collisions with h.ydrogen atoms, based on the work. of Biermann and ktibcck (1.948) and Hindmarsh et al. (1967), shows that it sh.ould be at most of the order of 1 m/~. assuming that the line core originates at a continuum optical depth of 0.l or less. An optimistic guess would therefore bc that the potassium line should show the full gravitational red-shirt, 16.3 m ~ for a wavelength of 7699 ~,, free of complicating Doppler or collision shifts in the same way as sodium appears to do. Figure 1 shows the hyperfine structure and Zeeman effect for the states invol.ved in the 7699/~ line. The hyperfine structure of the ground state corresponds to a splitting ENERGY

~

m~

A i

! ~ F -

g ,,~i"/3 ,

~G9si

~ oi

H IN

UP

i b

k

,!'1 ;!

+ 112 I/2

IELD DOWN

GAUSS

Am0.=O TRANSITIONS EXCITED BY

SOLAR LIGHT WITH VERTICAL INPUT POLARI~.ATION

AmT= d- I TRANSITIONS DETECTED USING CIRCULAR A NALY:;=ER

Fig. 1. Zccman effect in. potassium. of roughly 9 m~, while that of the excited state is negligibly small. For fields greater than a few hundred gauss each of the ground state m.~= -t-89levels is split into a set of" four evenly spaced, equally populated levels whose separation rernains essentially constant, giving an overall spread in absorption wavelength of about 7 m,~ for each set. In. this strong-field region the sets or transitions a and b have absorption wavelength dependences of - 18.4 m ~ / k G and + 18.4 mA/kG, respectively, relative to the zerofield center of gravity of the two ground state hyperfine levels.

3. Apparatus A 4" diameter clock-driven plane rnirror mounted on a shelf outside the laboratory window directed sunlight along an axis parallel to the earth's polar axis to a stationary

THE 7 6 9 9 X POTASSIUM LiNE AND THE RI-D-SHIFT

355

4" diameter flat mirror inside the laboratory. This second mirror sent the light downward into a vertically mounted J. W. Fecker 4" reflecting telescope which formed a solar image of about 0.4" diameter at its Newtonian focus. The stationary flat m i n o r could be adjusted so that the solar image was accurately centered on a -~-"diameter aperture in. the telescope's focal plane. The light admitted by the aperture travelled horizontally, first through a glass microscope slide used as a beam-splitter to reflect some .light to an intensity monitoring system, described below, then through a lens, a sheet ot" HN7 linear polarizer, a second lens, a second -.~" aperture, a Thin Films interference filter which passed 7699 A with a halt'width of 16/~, and finally into an evacuated charnber placed in. the 21" gap of a 12" diameter clectromagnet where it fell at right angles on the beam of potassium atoms. Light which was not scattered by the atom.ic beam entered a blackened tube where it was largely absorbed. The two lenses were adjusted to locus the image of the first aperture on the second aperture. Figure 2 shows the apparatus schematically.

IO

I" - ~ " - - I' 'p,9

~' . . . . . . . . . . . . . .

F ' ~ ; ~ - - B"--5,

I

I

ttBtFII o

! ,i

I 2

'/8 DIAMETER APERTURE IN TELESCOPE FOCAL PLANE BEAM SPLITTER

25

2" FOCAL LENGTH LENS

4

HN7 LINEAR POLARIZER

5

4"FOCAL LENGTH LENS ii

6

Fig. 2.

I/8 DIAMETER APERTURE

7

INTERFERENCE

8

LOCATION OF I/8 DIAMETER DETECTOR ENTRANCE APERTURE

FILTER

9

ATOMIC BEAM

I0

VACUUM CHAMBER

II

BLACKENED TUBE

Schematic top view of input optics (not to scale). The magnetic field in the scattering region is perpendicular to the page.

With. the linear polarizer oriented to polarize in the vertical direction, parallel to the magnetic field, only the two sets of Am.j = 0 transitions a and b shown in Figure 1 were excited in the atomic-beam atoms. Light emitted by the atoms downward, parallel to the magnetic field, was analyzed by an H N C P 7 circular analyzer and reflected by a mirror into a 2~' long horizontal lucite light-pipe to an EMI 9558 photomultiplier tube connected to a conventional pulse counting syslem. The sense of the circular analyzer was so chosen that when the magnetic field was directed upward, only the Am a = + 1 radiation emitted by atoms which the solar light had raised to the re.r= _:i_ excited state, by transitions a, was detected. When the field was downward, A r e s = - 1 radiation, was detected, emitted by atoms which had been raised to the m j = + z~- excited state by transitions b. This meant that if the magnetic field was upward initially, was then reduced in magnilude, reversed in direction, so that it was

356

J.L. SNIDER

downward, and final.ly increased in magnitude, keeping its magnitude in the strongfield region throughout, the atomic-beam absorption wavelength, of the transitions which gave rise to detected scattered photons became progressively longer, since transitions a and b have wavelength dependences of - 1.8.4 mA/kG and + 18.4 m/~/ kG, respectively..It follows that the dependence of the scattered light intensity on magnetic field reproduced the shape of the incident intensity vs. wavelength profile. The strong-field requirement was fulfilled by taking data only at fields greater than 500 G. The only effect of hyperfine structure is to reduce the resolution by broadening the absorption profile. For potassium, the overall width of each set of levels is about 7 m/~. as mentioned above. To summarize: the region around the Free potassium. atom mean. absorption wavelength was explored with a window of about 7 mA width. whose wavelength dependence was 18.4 mA/kG, relative to the center of gravity of the ground state, for fields greater than 500 G. It is interesting that if the linear polarizer is rotated through 90 ~ so that the incident light polarization becomes horizontal, Ants= __+l transitions are excited and the Zeeman shift in mA. per gauss should be just twice as large, with. the connection between field direction and direction of shift just the reverse of that above. Several line profiles taken with. this sense of polarization, which confirmed these predictions, are discussed below. Figure 3 shows the scattering chamber schematically. The potassium, beam was produced in a stainless steel oven, O, heated to roughly 250~ The beam emerged through a 0.030" diameter orifice, was collimated by a-8~" diameter hole, passed through a buffer chamber where it could be blocked off by the stop, S, and a second 1 tt hole into the scattering region and finally struck a surface ionization detector, D,

TO PUMP

//

TO LIGHT TO PUMP TRAP TO PUMP

0

S

/

'

TO seA.

GAUGE /7

~=~

ON

5)8

/7 GAUGE

/ C

p

TOP

I

SOLAR ' LIGHT

. . . . . 7

COVER

i

SIDE Fig. 3. Top and side views of scattering chamber drawn to scale, with details omitted for clarity. The magnetic field in the scattering region is perpendicular to the page in the top view.

THI-

7699 X POTASSIUM

LINF AND THE RED-SHIFT

357

which was used to determine when the beam intensity had stabilized at the start of a run. The detected current corresponded to an optical thickness of the beam roughly equal to 1 at the resonance peak. One filling of the oven with potassium lasted for about three runs. The pressure in the scattering region was maintained at a few times 10-s mm of mercury. Each of the three separate chambers in the apparatus was pumped by a separate 2" oil diffusion pump. The scattered light which was detected first passed through a -~" diameter hole placed 7 { ' directly below the intersection of the atomic and light beams as shown in Figure 3. It then went through the circular analyzer, CA, and was reflected by a small 1 " dialneter entrance aperture on the end of the 58-i~ diameter plane mirror, M, into the -~] ,'r 89 horizontal lucite light-pipe. The path length between the two -~- holes was The photomultiplier was cooled with dry ice and acetone to reduce the dark rate. Typical count rates were: dark rate, 10-20 cpsec; solar rate with no potassium beam, 100-200 cpsec; solar rate with potassium beam, 200-500 cpsec at 10 kG. The solar signal, the beam-on minus beam-off count rate, was thus li'om 100..300 cpsec at 10 kG. The observed red shift and line asymmetries had no sign.ificant dependence on the density of the atomic beam, indicating that the beam was indeed not optically thick so that saturation was not occurring. Further support for this was provided by the Osram lamp profiles discussed below.

4. Experimental Procedure A brief description of the details involved in setting up for a run and taking data naay be useful here. Data were taken only oll clear, cloudless days. The oven was turned on and brought to equilibrium using the surface ionization detector to monitor the beam. This took 1 to 2 hours. During this time the photomultiplier tube was reaching equilibrium at dry ice temperature. The solar tracking mirror was placed on the outside shelf and aligned. As soon as the atomic-beam intensity and background count rate were stable, the magnetic field was set at its 'standard' value of 10 kG in the upward direction. The solar image was aligned on the input aperture and a 100-sec count taken with the atomic beana on. Then the beam was cut off, the image was realigned and a second 100-sec count was taken at the same field. "The beam was now turned on again, the field was decreased, the alignment readjusted and a 100-sec count taken at the new field. Counts were then taken at gradually decreasing field strengths, still in the upward direction, until after reaching the lowest field of 500 G two counts were again taken at the 10 kG standard field, one with beam on and the other with it off. This enabled correction to be made later for variations in the solar and atomic beam intensities. Next, the field was reversed in direction and counts taken at successively higher fields starting at 500 G. Finally, the field was returned to its standard value in the upward direction and two counts taken, with and without beam. Field measurements good to a few tenths e r a percent were made with a Rawson model 824 rotating coil gaussmeter whose probe tip was placed close below the scattering region. The time was recorded for each point, and frequent checks of the oven temper-

358

J.L. SNIDER

nature stability were made with a copper-constantan thermocouple. Usually lhe sweep through the line was restricted to the central region, but when data were taken over the full range of magnetic field additional standard counts were taken halfway through each side of the line. It took 30-40 rain to complete a profile consisting of about 15 points.

5. Data Analysis G o o d data were collected on 22 different days during the months from January through May of 1969. The first step in data analysis was to average the beam-off counts for successive standard field points. This average was then subtracted from the beam-on counts taken at the different fields between the standard field points to givc the resonantly scattered signal at the various fields. Next, the difference between the beam-on and beam-offcounts was found for the standard field points. This difference represented a resonantly scattered signal which was presumably proportional to both the solar and atomic beam intensities. The signals for successive standard field points were averaged. Finally, the signals for the various points taken between successive standald field points were divided by the appropriate average signal at the standard field. These ratios of the signal at different fields to the standard field signal were then carefully plotted as a function of magnetic field, a separate plot being made for each of the sweeps through the line. The eri'or introduced into the ratios by the above method of correction was only a few percent. Originally, a Jarrell-Ash -~-m monochromator, a photomultiplier and a chart recorder were mounted to monitor the solar intensity in the vicinity of the 7699 A line by detecting the light from the beam-splitter already mentioned. A comparison was made at the standard field between variations of the monochromator output and variations of the solar count rate, after the atomic beam had reached equilibrium. The monitor system did not accurately follow the variations in the standard field count rate. For this reason and because the self-consistency of the data was improved, the standard field counts were used to correct [br solar and atomic beam intensity variations as described above, rather than using the monitor system output. To determine the observed shil't of the line minimum relative to zero magnetic field, which corresponded to the free atom reference wavelength, a smooth curve was first drawn by hand through the points of each line profile. Then the axis of symmetry of the core of the line, between the half intensity points, was located by finding the centers of horizontal lines drawn through the profile at regular intervals and joining them with a line. For some profiles the symmetry axis was vertical, indicating a symmetrical line. In these cases the shift was read off the plot directly. For many proliles the axis slanted one way or the other, showing asymmetry. The shift of these lines was taken to be the shi['t indicated by extrapolating the symmetry axis to the line minimum. Further discussion of the line shapes is given below. The method of correcting for the motion of the earth about ils own axis and about the sun was as follows. The mean time was found for each line profile and from it was deduced the mean hour angle relative to the local time at which the sun crossed the

TIIE 7699 X POTASSIUMLINE AND T H E RED-SHH:r

359

meridian. The shift produced by the earth's motion about its own axis was then found from the expression:

(A./.)I.O[= N.80(COS(5)(sin H) mA, where (5 is the solar declination and H the hour angle. This expression assumes ).=7699 ~ and the local latitude. The declination and the time of local noon were found from the l:armer's Almanac. The expression shows that the morning hours correspond to a wavelength shift of several m)k to the violet, since H is then negative, consistent with the fact that the laboratory is then approaching the sun. The shift in the afternoon becomes several rnA to the red since the laboratory is then moving away from the sun. From the earth's orbital motion there follows a shift: (A).)orb

=

(4.45 x l04) Ar m A ,

again valid only for 2=7699 A, where At" is the change in the earth-sun distance in astronomical units in one day. Values of At" were found fi:om the American Ephemeris and ,Vautical Ahnanac. During the entire period of this experiment the earth was moving away from the sun so that a red-shift varying up to a maximum of 13 mA

NORMALI~':ED SIGNAL ( NORMALI~'ED TO VALUE WITH FIELD UP AT IOk GAUSS)

-~-i-

SYMMETRY

f0.5 ;I/ I k GAU$S=IS.,or m A

[~k.. I0

;

L~..__

n S

DOWN

0 FIELD

i..--I

i .. t 5

i

;

I 10

uP

IN k GAUSS

Fig. 4.

Sample lirte profile over full field range, taken o n J a n u a r y 12 with vertical input polarization.

360

s.L.S.xtoFR

resulted. For each line profile these two shifts were added to give a total shift due to the earth's motion. The last step in the data analysis was to convert the observed line profile shift measured in gauss to a shift in i~aA,using the Zecman slope of 18.4 mA per kilogauss. From this shift the total shift due to the earth's motion was subtracted to give the true shift, corrected for earth motion. No correction for the rotation of the sun about its axis was made, since the input aperture was centered on the solar image. This is one source of possible systematic error which is discussed below.

6. Results A total of 70 line proliles was obtained with vertical input polarization. Of these, 13 were profiles of the line over the full range of field strengths up to 10 kG while the remaining 57 were limited to the range of fields below about 5 kG. The mean depth of the profiles was 15-20% of the intensity at 10 kG where the intensity was probably ~90% of the continuum level. Their mean full width at half minimum depth relative to the 10 k G point was 8600+200 G or 158+4 mA. Each profile was assigned an

NORMALIZEDSIGNAL ~-I.0

!

9. r .

,i - 0 5

!iik G A U ~ ~ io

g DOWN

o FIELD IN k GAUSS

5

io

uP

Fig. 5. Sample line profile, taken on February 6 with vertical input polarization.

THI- 7 6 9 9

k

361

I'OTASSII.M LINE AND THE RED-SHIFT

asymmetry, this being a qualitative indication of the degree to which the symmetry axis of the line core deviated from being vertical, togcther with the direction of this deviation. 'Red' asymmetry means that the symmetry axis deviates toward the long wavelength direction as one moves from the wings of the line toward the core. Lines of different asymmetries and field strength ranges are shown in Figures 4-7, with their symmetry axes indicated. The errors shown include counting statistics and the uncertainty introduced by the method of averaging as discussed above. The corrected shifts of all lines showing the same asymmetry were then averaged. There was no significant NORMALI'~ED SIGNAL I '-I.0

i

MMETRY

,, i i k GAUS -4--~. i I I0

[

=

I

I

I

5

DOWN

;

I

I

i

I

0

FIELD

I

I

i

I

5

I

I

I

[

I

I0

uP

~N k GAUSS

Fig. 6. Sample line profile, taken on April 4 with vertical input polarization. correlation between asymmetry and time of day or date. The results are shown in Figure 8 and in Table I. In this analysis 6 lines have been omitted because they displayed large asymmetries. A rough estimate of the error involved in drawing the line profile, extrapolating the symmetry axis to the minimum and determining the shift is 2 mA, as shown in Figure 8. The errors tabulated in Table I are this number divided by the square root of the number of protiles. 'Medium' asymmetry corresponds roughly to three times as large a shift of the line minimum, relative to the line center at the 0.5 intensity level, as does 'small' asymmetry, roughly 5 mA and 2 1hA respectively. The mean shift is plotted vs.

J. L. SNIDI-,R

362

NORMAL[~'EDSIGNAL 1.0

O.S

MEDIUMVIOLET ASYMMETRY

I I0

r

I

I

I

I 5

I

i

I

I

i 0

DOWN

FIELD GAUSS

!

!

I

I 5

I

~

t

i

I I0

up

IN K Fig. 7.

Sample line profile, takcn on May 27 with vertical input polarization.

SHIFT IN m,~ I NONE

SMALL RED

ASYMMETRY SMALL MEDIUM VIOLET RED

MEDIUM VIOLET

20

l-,~t~.~?-~!~i~ ~:~-?_ ~~~!!i~i,tt:~ Fig. 8.

Corrected shifts of thc potassium linc grouped according to asymmetry. The horizontal lines show the mean of each group as listcd in Tablc I.

THe;

7699 ;k i,otassiuM L.UN."~ANDTIIE RED-SHIFT

363

TABLE I Mean shifts for various line asymmetries Asymmetry

Number of lines

Mean correctcd shift in. m/k

none small red small violet medium red medium violet

13 19 8 ~16 8

9.8 10.9 9.1 12.7 6.7

I- 0.5 I 0.4 L 0.7 =!=0.5 :: 0.7

MEAN RED-SHIFT IN R1A

GRAVITATI ONAL RED-- SHIFT

15-

I

"MEDIUM"

"SMALL"

[~ONE

-'=----RED

!

"SMALL. . . . VIOLET

I

MEDIUM" ~.

ASYMMETRY

Fig. 9. The mean corrected red-shift of the potassium line vs. line asymmetry. See text for details.

a s y m m e t r y in Figure 9. There is a very clear c o r r e l a t i o n between the line a s y m m e t r y and the estimated shift. A total o f 5 line profiles was taken with horizontal input polarization. A sample profile is shown in Figure 10. The m i n i m u m was indeed shifted in the o p p o s i t e direction fi'om t h a t observed with vertical i n p u t p o l a r i z a t i o n , by an a m o u n t in gauss closely h a l f as much, a n d the observed m e a n line width in gauss was close to o n e - h a l f as large, in a g r e e m e n t with the p r e d i c t i o n s m a d e above. F r o m these profiles it is difficult to tell whether the c o n t i n u u m has been reached at I0 k G and how m u c h o f

364

,f.L.SNIDER

the apparent structure in the wings of the line, which was somewhat variable, is real. Together with the 13 full tield range profiles taken with vertical input polarization these protiles show a mean equivalent width close to the 154 m A given by Moore et al. (1966). In addition to the above solar data, the profile of the emission line from an Osram potassium lamp run at low power was observed several times. An example is shown in Figure l 1. The most interesting feature of this line is that it appears to be shifted to the NORMALI~'ED SIGNAL /.0

I k GAUSS.36.GmA

I0

S

OOWN

0

FIELD IN I( GAUSS

5

I0

up

Fig. I0. Sample line profile, taken on May I with horizontal input polarization. red by about 100 (3 or 1.8 mA. This result was observed to be independent of the input power to the lamp. At higher powers the line broadened and showed selfreversal, but the shift remained the same. Essentially the same shift and width was observed for a second potassium lamp, with an atomic-beam density about a :factor of two smaller. This was additional evidence that the beam was not optically thick. As a check on the operation of the system, the 'profiles' of white light sources, supposedly flat, were studied. A Sylvania 100 Watt arc lamp and a G E 200 Watt tungsten standard htmp were used. The signals were only ~: 100 cpsec and ~ 4 0 cpsec respectively. The arc lamp gave inconclusive results, with signal variations of 10-20~,, which did not seem reproducible. This may have been due to the effect of stray mag-

THE

7699 ~ POTASSIUM LINE

365

AND "IHE RED-SHIFT

NORMALIZED SIGNAL ( NORMALI~'EO TO VALUE WITH FIELD UP AT ,500 GAUSS )

I.O

FWHM ~-,~4 5 mA

I k GAUSS-18.4mA

5

DOWN

o

FIELD

5

uP

IN K GAUSS

Fig. 11.

Sample potassiuln Osram lamp lilac profile taken on Marcia 17 with vertical input polarization. The lamp current was 0.35 Amp.

netic field on the arc or variations in the lamp current, which was not monitored. The G E lamp current was monitored and held constant. With the magnetic field down the count rate from the GE lamp was reasonably independent of tield while with it up it Ol appeared that the count rate showed greater fluctuations and was perhaps ~-10,...,, higher in the 5-8 kG region. This may explain the fact that a number of solar line profiles showed the long wavelength side to be quite smooth while the other side was somewhat bumpy. Even if this were a real instrumental effect, no signiticant shift in the location of solar line profile minima should have resulted. -

9

7. Possible Systematic Errors There are a number of possible sources of systematic error in the determination of the red-shifts which wc will now consider. (a) The uncertainty in centering the solar image on the input aperture and the irregularity of the tracking mirror drive meant that the solar image may have been displaced on the average relative to the aperture by several per cent of the image's diameter. The aperture's diameter was roughly -} that of the image. The magnitude of

366

J.L. SNIDER

the Doppler shift produced by the sun's rotation rises linearly from zero at the center of the image to a value about equal to the gravitational shift at the location of the edge of the aperture, the shift being to the red on one side and to the violet on the other. If the aperture is exactly centered on the image, no net Doppler shift will result. For a few percent relative displacement there will be a net Doppler shift of a few percent ol the gravitational effect. Each point on a profile may be shifted systematically by this amount so that the location of the line minimum may be systematically in error by a few percent. (b) A Doppler shift may have resulted from lack of perpendicularity between the light and atomic beams. This angle was carefully checked on several occasions and found to be 90 ~ within a few hundredths of a radian. The vacuum chamber could be reproduci bly replaced between the magnet poles after being removed to rctill the oven. The mean speed of beam atoms was such that the maximum possible Doppler shift, that with light and atomic beams parallel, was roughly equal to the gravitational shift. Therefore the maximum possible error from this source is also a few percent. (c) No special precaution was taken to center the interference lilter's passband, peaked at 7704 A and with a 16 A F W H M , exactly on the solar line. The effect of operating on the shorter wavelength side of the transmission curve would be to make the line asymmetrical to the red, according to our definition, without signiticantly changing the location of the minimum. A red asymmelry in the small to medium range could have resulted. (d) The stray field of the magnet, a maximum of 5-10 G at the photomultiplier position, could affect the detection sensitivity in a field-dependent way. To test this, with the light-pipe removed a flashlightbulb and interference filter wcre mounted atthe photomultiplier input, keeping the tube in its usual position, and the count rate fi'om the bulb studied as a function of field. Shielding the tube with several layers of Conetic foil reduced the variation in count rate over the full range of fields to 1-2%. As a further check, the light-pipe was remounted and a Sylvania 100Watt arc lamp substituted for the telescope. With no atomic beam and with the linear polarizer removed to increase the count rate, the variation of counts due to light from the arc lamp which was scattered from the walls of the vacuum chamber was again only 1-2~; over the full field range. This should have a negligible effect on the solar line profiles. It is not clear why the arc lamp was stable for these measurements while it did not appear to be for the measurements discussed in the last section. (e) Another source of error is misalignment of the linear polarizer. If its polarization direction was not accurately parallel to the magnetic field, then the unwanted Ares= __+1 transitions would be excited, with Zeeman shifts twice as large as the desired Ams=O transitions and with reversed sense relative to the direction of the magnetic lield. Distortion and shift of the line would result. For a maximum possible misalignment of several degrees, an estimate of the shift of the line minimum gives at most a few percent toward the violet. (f) Allowance should be made for the fact that the detection solid angle is finite. We have assumed throughout that the detected photons arise from only one of the

~sE

7699 .~. POTASSIUM LINE A N D

367

THE RED-SHIFT

two excited atomic states populated by the two Am.j= 0 transitions a and b shown in Figure 1. Ideally this would be the case if the detected photons were travelling exactly along the field direction, since then only Amj = _+ 1 photons would be involved and the circular analyzer would reject one sense of circular polarization. At finite angles with respect to the magnetic field the Area= 0 intensity becomes non-zero and such photons will not be rejected by the analyzer. Undesirable photons from the Ams=O decay of the other excited state will therefore be detected and lead to line shift and distortion. From the dimensions given in Section 3 the ]naximum angle involved is about 88radian, corresponding to a Ams=O intensity of a few percent relative to Ares= __+1. This corresponds to a shift of the line minimum of a few percent to the violet. 8. Conclusion

Until the origin of the asymmetry of many of the line profiles is understood it is difficult to know what significance should be attached to their mean red-shift. The

-•x

I0 e

"1"O.B r

-I-0.4 ~I

0.0

-0.4

o! --I,2

-I.6

Fig. 12.

I

I

0.6

I

0.8

]

I.o

I

I

1.2 1.4 LOG{~XIO 6 )

I

1.6

I

1.8

i

2.0

I 2,2

Tile residual red-shift,/$, of various solar lines as a function of their equivalent width, W. All unlabelled points are from Adam (1958). See text for details.

368

J.L. SNIDER

fact that each profile is a timc-average over almost I hour and a space-average over the central 10'.',."~of the solar image makes the marked variations in the asymmetry of the line seem rather surprising. No source of instrunaental error which would give both directions of asymmetry, as well as the observed correlation between shift and asymmetry, is apparent. It is hard to imagine that conditions in the earth's atmosphere are responsible. Tiais points to a real solar effect which it will be very interesting to investigate further. For the present it seems reasonable to quote as the most significant number the mean shift of the 40 lines which showed either small asymmetry in the line-core or none at all, and to compare it with the predicted gravitational shift. This mean shift is 10.2+0.3 mA. Adding the various errors discussed above linearly would give ~ 1~/.o -< ' as" the limit of error. We w'ill adopt as our final result: (A)0 ........ = 10 _+ 1 mA (for lines showing small or no asymmetry) which gives (A;.) . . . . . .

1

-- (0.61 _+ 0.06) (A2)g,~.

I f we plot this result, together with. those for Na (Brault, 1962) and Sr (Roddier, 1965), on the graph of residual shift vs. line strength shown, by Adam. (1958), the results are as shown in Figure 12. Here iS is the residual red-shift in m/~, this being the observed shift minus the predicted gravitational shift, and W is tfic equivalent width of the line in mA. Values of Wwere taken from Moore et aL (1966). The unlabelled points shown are those given by Adam (1958), the line being a least-squares :fit to them. The correlati.ola between shift and strength, which Miss Adam observed is certainly supported by the three additional points. The strength of a solar line does appear to be important in determining its shift. Qualitatively this makes sense since the stronger lines are formed higher in the photosphere where con.vective velocities are smaller, but no detailed explanation exists. All we can at present say is that, contrary to our hopes, the solar potassium line is affected differently than the sodium line by the dynamics of the photosphere. T.he "additional unambiguous evidence for the solar gravitational redshift" mentioned .in the Introduction has not been found. To check the operation o.f the apparatus, several runs were made with a sodimn beam, using a Spectrum Systems thin-fihn filter to isolate the D I line. On the basis of limited data it appears that the sodium line is indeed shifted by the full predicted amount. A run was made on an Osram sodium lamp as well. Contrary to the ~: 2mA red shift of the potassium lamp, the sodium lamp showed g 2 mA shift to the violet. The existence of such shifts underlines the fact that the measurement of small line shifts relative to such a comparison source can be subject to large errors. It may seem that a source of systematic error is the presence of the 7<)/,;abundant isotope K r in the atomic beam..l.ts Zeeman shifts are the same as in. K 39 but its zero-tield wavelength is shifted to the violet by ,~:4 mA relative to K 39 (Jackson and Kuhn, 1938). From these data we lind that the presence of K 4~ w'ill shift th.e apparent minimum of a line profile by ~0.3 inA to the .red relative to where the minimurn would be located if the beam. were pure .K39. Assurnillg that the isotopic abundan.ces are the same on the sun as in the atomic beain, however, it is the zero-field wavelength

rw:

7699 X POTASSIUM LINE

AND 1I-112RED-SHI1-T

369

of the atomic beam consisting of both isotopes with respect to which the solar wavelength should be compared, so that the question of the shift relative to the K 39 wavelength is irrelevant. At the present time a 12~" diameter solar telescope is being built to study the asymmetries of the potassium line further as well as to look at the red-shit't as a function of disk position. The tracking drive will be much improved and the larger aperture will give an order of magnitude increase in signal. A more powerful magnet will make it possible to take data ['urther out on the wings of the line. Further work will also be done on sodium. It would be gratil),'ing if this experiment stimulated further theoretical work on the line profiles and red-shifts of'potassium and sodium.

Acknowledgements

It is a pleasure to thank Costas Papaiiolios for helpful discussions and the loan o f apparatus, Brian Smith for help ~vith the sodium runs and discussion of systematic errors, the members of the Department of Astrophysics at Oxlbrd University for much valuable advice and encouragement and tlarvard University for financial support. References

Adarn, M. G. : 1955, -~lonthly Notices R~O'.Astron. See. 115,405. Adam, M. G. : 1958, MonthO," Notices Roy. Astron. See. 118, 106. Adarn, M. G. : 1959, Monthly Notices Roy. Astron. Soc. 119, 460. Adam, M. G. : 1962, Prec. Roy. Soc. London A270, 297. Biermann, L. and Li.ibeck, K. : 1948, Z. Astrophys. 25, 325. Blamont, J. E. and Roddier, F. : 1961,Phys. Rev. Letters 7, 437. Brault, J. W. : 1962, Thesis, Princeton Universily. Einstein, A. : 1911, Ann. Phys. 35,898. Greenstein, J. and Trimble, V. : :[967, Astrophys. J. 149,283. Hindmarsh, W. R., Petford, A. D., and Smith, G. : 1967, Prec. Roy. Soc. London A297, 296. Jackson, D. A. and Kuhn, H. : 1938, Prec. Roy. Soc. London A165, 303. Lambert, D. L. and Mallia, E. A. : 1968, Solar Phys. 3, 499. Minnaert, M., Mulders, G., and Houtgast, J.: 1940, Photometric Atlas ~/ the Solar Speetrum.[?om ).3612 to ).8771, Ltrecht. Moore, C. E., Minnaert, M., and Houtgast, J. : 1966, Secomf Revision of RowlandS' Preliminary 7?lble ~['Solar Spectrum Wavelen~,ths, N.B.S. Monograph 61. Pound, R. V. and Rebka, G. A. : 1960, Phys. Rev. Letters 4, 337. Pound, R. V. and Snider, J. L. : 1965, Phys. Rev. 140, B788. Roddier, F. : 1965, Ann. Astrophys. 28,463.