sec

ICARUS 8, 160--165 (1968)

Observations of the Beaming of Jupiter's Radio Emission at 620 and 2650 Mc/sec J. A. R O B E R T S AND R. D. E K E R S

Radiophysics Laboratory, Commonwealth Scientific and Industrial Research Organization, Sydney, Australia Communicated by J. G. Bolton Received July 14, 1967 At frequencies above 1000 Me/see the radio emission from Jupiter varies by approximately 10% as the planet rotates, but at 408 Mc/sec no variation has been detected. Observations at the intermediate frequency of 620 Mc/sec reported here show variations similar to those found at the higher frequencies. This confirms results at 610 Me/see reported by Barber. A new series of observations at 2650 Me/see defines the variation with rotation very clearly. The results can be explained by synchrotron beaming in a dipole field with the axis inclined about 15° to the axis of rotation, whereas the tilting of the plane of polarization requires an inclination of 10°. I. INTRODUCTION I t is known t h a t the decimetrie radio emission from Jupiter varies as the planet rotates. The variation of the intensity is ascribed to the beaming of the radiation towards the magnetic equator of the planet combined with a tilt of the magnetic axis relative to the axis of rotation (Morris and Berge, 1962; G a r y , 1963; Bash et al., 1964; Roberts and Komesaroff, 1964). Roberts and Komesaroff (1965) (hereafter referred to as R. & K.) found similar variations of intensity at both 2650 M e / s e c and 1410 Me/see, but at 408 Mc/sec a n y variation appeared to have considera b l y lower amplitude. To help clarify this m a t t e r observations were made in 1964 at the intermediate frequency of 620 Mc/sec. These results are reported here and show similar beaming effects to those found at t h e higher frequencies. This agrees with results at 610 Me/see reported by Barber (1966) since these observations were made. Measurements of the total intensity at 2650 Mc/sec made a few months after the 620-Me/see measurements, and intended as control observations, are also reported

here. I n these measurements the radio emission from Jupiter was compared repeatedly with the emission from another source only ~ o away. With this technique the Jovian intensity variations could be measured with considerable precision. The results in the present p a p e r were briefly reported in a review p a p e r (Roberts, 1965). I I . OBSERVATIONS The observations at both frequencies were made with the C S I R O 210-ft radio telescope at Parkes, I~.S.W.

A. 620-Mc/sec Observation~ The receiver was a crystal mixer with a noise temperature of 400°K. Complete linear polarization determinations were made using the "on~off" technique to measure the flux density in six polarization angles at intervals of 30 ° of position angle (see R. & K.). The data were digitally recorded and computer processed to obtain the best fitting (least squares) sinusoid of period 180 ° . Observations were made from August 18 to August 22, on August 160

BEAMING ON JUPITER'S RADIO EMISSION

25, and on September 23 and 24, 1964, (UT dates). The August observations were made between 04h and 08h local solar time (18h-22 h UT) and the September observations from 02 h to 05h30m local solar time (16h-19~30m UT). The system gain was monitored by injecting noise from an argon discharge tube after each polarization determination, and by observing the source CTA 21 twice during each period. On each night the noise calibrations and the CTA 21 deflections were consistent to within ± 2 % so the Jupiter deflections were normalized to the mean CTA 21 deflection for the night. The scale of flux density is based on an assumed flux density of 8.7 X 10-26 watt m ~ (cps)-I for the source CTA 21. This figure was derived from observations of the relative flux densities of 3C17, 3C444, and CTA 21, an d using flux densities for 3C17 and 3C444 obtained by interpolating between the values given by R. & K. The contribution of the background to the Jupiter observations was determined after Jupiter had moved to another part of the sky. The corrections made to the total intensity for the contribution of the background did not exceed 3%, and the errors due to uncertainties in this correction are thought to be less than 1%. On the other hand, the correction to the polarized component was often as large as 50%, and uncertainties in these corrections could lead to errors of ~ 2 0 % in the degree of polarization and errors of ~ 5 ° in the polarization position angle.

B. 2650-Mc/sec Observations The 2650-Mc/sec total intensities are taken from the series of position measurements made in November 1965 [Roberts and Elkers (1966)], supplemented by 19 "on~off" observations at two orthogonal polarization angles made on November 15 and 16, 1964 (UT). The observations were made between approximately 22h and 02h30m local solar time (12h-16h30m UT). At the time of these observations Jupiter was only ~1~o from the source CTA 21 so that each source could be measured alternately. This proved an excellent

161

method of calibrating gain changes. As seen from Fig. l ( a ) , 9 0 ~ of the total intensity measurements of Jupiter lie within ±1. 6% of the mean curve. The 2650-Mc/sec flux density scale is based on an assumed flux density of 5.28 X 10-26 watt m -2 (cps) -1 for CTA 21. This value was determined from measurements of the ratio of CTA 21 to 3C17, 3C444, and 3C454.3 using the flux density of these sources adopted by R. & K. These estimates agree to within a few percent. I I I . RESULTS

A. Total Intensity In Fig. 1 the total intensity (sum of two orthogonal polarizations normalized to a polar semidiameter of 22":75 arc or a distance of 4.04 a.u.) is shown as a function of the longitude of the central meridian of the disk. [IAU System I I I (1957.0).] The variations at the two frequencies are seen to be quite similar, and to be similar to the variations found previously at the higher frequencies. Thus, in agreement with Barber (1966), we find that the highfrequency form of the variation detailed by Roberts and Komesaroff persists at least down to frequencies ,-~600 Mc/sec. If, as suggested by R. & K., the behavior at 408 Mc/sec is quite different, then the change must occur below 620 Mc/sec. Such a change over a wavelength range of 3:2 is surprising. The scatter in the 408-Me/see observations of R. & K. is less than the expected variation in intensity and it is difficult to see why any such intensity variation would not have been seen. However, further lower frequency observations should be made to check the 408-Mc/sec result. R. & K. fitted their total intensity observations to a relation of the form I = Io cos n ¢~,

(1)

where ~m is the zenocentric magnetic latitude of the Earth and is given by sin Cm = cos ~ sin Dz + sin ~ cos Ds cos(/~i1 -- l°m).

(2)

162

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Here fl is the angle between the magnetic axis and the axis of rotation, DE is the tilt of the northern end of the axis of rotation toward the Earth, a n d / ° m is the longitude of the northern hemisphere magnetic pole. Taking fi as 10 °, the value needed to fit the tilting of the plane of polarization, R. & K. found different beaming north and south of the magnetic equator. A similar result follows from the present data. Both the 620-Mc/sec and the 2650-Mc/sec results require a value of n in Eq. (1) of about 3.5 for northern magnetic latitudes, but for southern latitudes a value ~13 is needed for the 620-Mc/sec data and a value ~ 7 for the 2650-Mc/sec data [Fig.

2(a), (c)]. M. Komesaroff pointed out to the authors that this asymmetry could be removed by

adopting a larger value for fl, the tilt of the magnetic axis. More recently we have seen a prepublication copy of the review by Warwick (1967) in which this same interpretation is discussed, and indeed in several earlier publications in which intensity (but not total intensity) data were fitted to such a model the deduced tilts of the magnetic axis were greater than the 10° needed to fit the tilting of the plane of polarization (Bash et al., 1964; Barber, 1966). To test this interpretation for the present data the 2650-Mc/sec results were fitted to Eqs. (1) and (2) with D~ equal to the Ephemeris value of 3?3 and with four free parameters, fl, n, Io, and l°m. The leastsquares solution was computed using a program supplied by D. E. Shaw based on

BEAMING

OF

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a simplex method for function minimization (Nelder and Mead, 1965) in which all the parameters are fitted simultaneously. The best values for the parameters are given in Table I. TABLE I SYMMETRIC

MODELS

WHICH

t~EPRODUCE

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INTENSITY VhRIA~ONS 2650 M e / s e e

620 M e / s e e

1577

(15.7)

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RADIO

163

EMISSION

with these larger tilts result from the larger values of ¢~ reached as the planet rotates. The 620-Me/see data are insufficient to d e t e r m i n e fl so a v a l u e of 15.7 was assumed when deriving the values of n, Io, and I°~H given in Table I. That the observed total intensities are adequately represented by this model is shown by Figs. 2(b) and 2(c), in which the results are plotted as a function of magnetic latitude with a 1577 tilt of the dipole. The agreement with the fitted curve is seen to be within the errors. Whether this method of representing the total intensity variations will lead to a clearer understanding of the departures of the magnetic field from a dipolar form remains to be seen.

Ninety percentile errors are given for Io and l°m which affect the sum of squares independently. The error quoted for I0 does not include any error in the adopted flux density of C T A 21. Values of fl and n arc not independent. At 2650 Mc/sec, to the 90% confidence level the values may range from fl = 13.2 with n----2.3 to fi----19.3 with n = 1.4. The lower values of n found 7-" @'0

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The 2650-Mc/sec total intensity at magnetic latitude zero given by the present observations (Table I) is 2% greater than the value found by R. & K. one year earlier. Such a small difference could arise from errors of scaling. The results certainly demonstrate a long-term stability of the radiation

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BEAMING OF JUPITER'S RADIO EMISSION

The 620-Mc/sec total intensity at magnetic latitude zero is found to be 6.39 X 10 -26 watt m -2 (cps) -~ (Table I), whereas the value found at 610 Me/see some 8 months earlier by Barber (1966) was 7.05 X 10-26 watt m -2 (cps) -~, or 10% greater. However, since different calibrator sources were used in the two sets of observations this difference could arise from scaling errors.

B. Degree o] Potarization (620 Mc/sec) As indicated in Section I, uncertainties in the corrections for the background result in considerable uncertainty in the 620-Mc/sec polarized flux density. This is thought to contribute substantially to the scatter in the observed degree of linear polarization [Fig. 3(b)]. The mean linear polarization is 0.20 with an uncertainty of _+_0.05, mainly due to uncertainties in the background corrections. Any dependence on longitude is masked by the scatter in the data.

C. Direction o] Polarization (620 Mc/sec) Since the ionospheric F a r a d a y rotation at 620 Me/see was ~ 1 0 ° the observed position angles have been corrected for this effect. On the advice of Dr. F. F. Gardner we have computed the ionospheric F a r a d a y rotation from a formula for a plane stratified ionosphere, namely = - 3 . 6 t (f0F2) 2

(degrees).

Here ]oF2 is the ionospheric critical frequency in Me/see and t is a thickness factor. The constant involves average values for the zenith angle and for the 'ingle between the direction of observation and the Earth's field. For the thickness factor t we have used the average value for the local solar time as given by Munro (1962). For the August observations the winter value was used; for the September observations the average of the summer and winter values was used. The values of foF2 were taken from the Australian Ionospheric Prediction Service Series D publications. For the time

165

of day at which the August observations were made both the thickness index and foF2 were varying rapidly with solar time. The effects partly compensate, but by virtue of the way in which they were derived the values of ~ must be relatively uncertain. The corrected position angles are plotted as a function of l,~ in Fig. 3 ( a ) . Within the errors they appear to be consistent with the higher frequency results which have a peak-to-peak variation of 20 ° with the downward crossover occurring at Im ---183 °. The mean direction is some 2 ° different from the normal to the axis of rotation but uncertainties in the ionospheric F a r a d a y corrections could perhaps account for this. REFERENCES BARBER, D. (1966). The polarization, periodicity and angular diameter of the radiation from Jupiter at 610 Mc/s. Monthly Notices Roy. Astron. Soc. 133, 285-308. BASH, F. N., DaAXE, F. D., GUNDERMANN, E., AND I=IEILES, C. E. (1964). 10 cm observations of Jupiter, 1961-1963. Astrophys. J. 139, 975-985. GARY, B. (1963). An investigation of Jupiter's 1400 Mc/s radiation. Astron. J. 68, 568-572. MORRIS, D., AND BERGE, G. L. (1962). Measurements of the polarization and angular extent of the decimeter radiation from Jupiter. Astrophys. J. 136, 276-282. MUNRO, G. H. (1962). Dirunal variations in the ionosphere deduced from satellite radio signals. J. Geophys. Res. 67, 147-156. •ELDER, J. A., AND MEAD, R. (1965). A simplex method for function minimization. Computer J. 7, 308-313. ROBERTS, J. A. (1965). Jupiter, as observed at short radio wavelengths. Radio Sci. 69D, 15431552. ROBERTS, J. A., AND EKERS, R. D. (1966). The position of Jupiter's Van Allen belt. Icar~ts 5, 149-153. ROBERTS, J. A., AND KOh~ESAROFF, M. M. (1964). Evidence for asymmetry of Jupiter's Van Allen belt. Nature 203, 827-830. ROBERTS, J. A., AND KOMESAROFF,M. M. (1965). Observations o ~ Jupiter's radio spectrum and polarization in the range from 6 cm to 100 cm. Icarus 4, 127-156. WARWICk:, J. W. (1967). The radiophysics of Jupiter. Space Sci. Rev. 6, 841-891.