The effect of the horizontal extent of Aurorae on the apparent luminosity-altitude curves

Research

notes

RESEARCH

NOTES

The effect of the horizontal extent of Aurorae on the apparent luminosity-altitude curves (Receioed 13 November 1953) $ 1. The identification of lines of atomic hydrogen in amoral spectra by VEGARD (1939) and their subsequent study by GARTLEIN (1950)and MEWEL (1950) show that fast protons must certainly be a component of the incoming stream of primary particles. Furthermore the recent quanta1 calculations of BATES and DALGARN~ (1953) indicate that the electron capture process presumed to be operative is, in fact, a very inefficient source of the lines, which suggests that fast protons may actually be a major component. It is a simple task to derive the luminosity-altitude distribution that would ensue from the entry of protons into the Earth’s atmosphere. Except perhaps in the case of the higher aurorae the calculated curves for a mono-energetic incident stream (cf. BATES and GRIFFING 1953) are very much sharper than are the curves obtained from photometric measurements (cf. HARANG 1944, MEINEL 1952, BERKEY and GARTLEIN 1952): in particular it has been shown that the hydrogen line emission from an aurora located near the 100 km level would be confined to a vertical interval of only 1 or 2 km, which is a far narrower range than the BATES and GRIFFING (1953) have pointed out that the predicted observations indicate. curves could be reconciled with the measured curves by arbitrarily assuming that the incoming protons have a wide energy spread. However there is the possibility, to which MEINEL (1952) has drawn attention, tha,t the finite horizontal extent of aurorae along the tlirection of the magnetic meridian may conceal the true luminosity-altitude distribution. Jt is the purpose of t,he present note to investigate this effect. 4 2.’ For convenience we shall consider a two-dimensional model aurora throughout which t,he emission per unit volume is simply

L(z,z)=Zzexp

(a-F2)

=o

(z,+ve) (2, -

ve)

(1)

Jr-here z is measured vertically from the base which is at an altitude h,, 2 is measured horizontally from a line making an angle tl with the Earth’s surface, tc and ,$ are parameters defining the vertical and horizontal spread of the aurora and2 is a proportionality constant (see Fig. 1). Clearly the true luminosity-altitude distribution is given by

(2) To an observer at a point 0 it would appear that the luminosity vector s making an angle $ with the horizontal is

in the direction

of’ a

L(4) = J L(z, 2) dx (3) 339

Reeemoh

notes

This expression may readily be evaluated with the aid of any of the standard tables of the probability integral. In order to convert the luminosity-angle curves thus obtained into luminosity-altitude curves it is of course necessary to associate with each angle a definite fact that has not been altitude. Unfortunately the association is rather ill-defined-a taken properly into account in the presentation of the observational data in the literature. It is, however, convenient and natural to take the altitude h corresponding to a given angle CENTRE LINE OF, AURORA

Fig. 1. 4 to be that of S, the point of intersection of the observing line and the central line of the aurora. Adopting this convention calculations were carried out for the following cases. (see Fig. 1.) Angle of central line 8 75” Altitude of base h, 100 km Vertical extent parameter a 1 to 20 km Horizontal extent parameter /3 0.5 to 200 km Observation distance D 200 km and 600 km 5 3. The luminosity-altitude curves may be characterized (HARANG 1944) by the distances tln(a, 8) and &“(a, fi) between the level of maximum intensity and the two levels at which the intensity is a fraction, n, of the maximum, the subscript 1 referring to the level in the lower part of the aurora and the subscript u to the level in the upper part. For aurorae with bases near the 100 km level HARANG(1944) reports that t,0.5 and tU0.5average about 6.8 km and 13-5 km respectively. The observed luminosity curves of such aurorae may be represented by equation (2) if a is taken to be about 8 km. From the computations which were carried out it was found that the observed and true values of tln(a, /I) and tUn(a,j3) are almost the same except when #l/ais appreciably greater than unity. Consequently the apparent luminosity-altitude distribution of HARANG,with a as indicated above, may be accepted as the actual luminosity-altitude curve unless @ is some 10 km or greater (which seems unlikely to be common). It was found also that if the emission were confined to a vertical interval of 1 or 2 km (cf. 4 1) it would be necessary for /? to be extremely large to yield apparent luminosityaltitude curves such as are observed, the required value, which of course depends on the observing distance, being some 50 km when D is 200 km and some 100-200 km a-hen I) is 340

Research notes

600 km; moreover the apparent luminosity-altitude curve would then be controlled almost entirely by the value of ,!?and would presumably be very variable. In view of these results it may be concluded that the finite horizontal extent of aurorae cannot be invoked to explain the discrepancy between the measurements and the predictions based on the assumption that the incoming protons are mono-energetic. Acknowkdgements-We wish to thank Professor D. R. BATES for suggesting this problem and for many helpful discussions. Department of Applied

G. W. GRIFFING*

Mathematics,

The Queen’s University of Belfast

A. L. STEWART

References BATES, D. R. and DALOARNO, A. BATES,D. R. and GRIFFINC,G.

RERKEY,D. K. and GARTLEIN, C. W. GARTLEIN, C. W. HARANG,L. MEINEL,A. B. MEI~EL,A. B. \‘E~~RD,L.

1953 1952 1952 1950

1944 1950 1952 1939

Proc. Phys. Sot. A. 66, 972 J. Atmosph. Terr. Phys. 3, 212 Mem. Sot. Roy. Sci., LBige 12,

199 Trans. Amer. Geophys. Union 31, 7 Geof. Publ. 10, No. 6 Astrophys. J. 111, 555 Mem. Sot. Roy. Sci. Liege 12, 203 Nature ,114, 1089

A note on solar-terrestrial relationships This note suggests a possible explanation for some of the deviations obtained when correlating particular solar events with geophysical disturbances presumably caused by corpuscles ejected from the sun. It is generally agreed that aurorae, geomagnetic variations, etc., are caused by the impingement of solar particles upon the earth’s atmosphere. The particle stream is essentially neutral and consists of approximately equal numbers of electrons and positive ions. Neutral particles also exist in equilibrium with the radiation field, but their number is relatively small. The approximate charge equality may occur on emission from the sun, by acquisition of the deficient charges from the ions of interplanetary space, or by other means. Several theories have evolved to explain the acceleration of the solar particles towards the earth’s dark hemisphere. ST~RMER mathematically described the trajectory of a single charge as it approaches a magnetic dipole. Depending upon their velocity vectors, charges approaching the earth could strike the sunlit hemisphere, the dark side, or could be entirely deflected from the earth. CHAPMANand FERRAROobjected to the application of ST~RMER’S results to aurora1 theory, mainly on the basis that the treatment of only isolated charges moving in a magnetic dipole field did not represent the probable conditions involved in aurora1 formation and geomagnetic changes. Their model envisages a neutral stream (or plasma) of charged particles which after leaving the sun engulfs the earth. Some aspects of the geomagnetic changes appear to be clarified by their model. However, it is not quite clear how particles in the “hollow” behind the earth leave the stream to invest the dark hemisphere. No consideration is given to the possibility that charged particles may strike and cause aurorae in the sunlit hemisphere. Of the two theories, the former is considered to apply to cosmic rays and the latter to aurorae and magnetic dist’urbances. * Affiliated to the Geophysics Research Directorate of the U.S. Air Force, Cambridge, YKassachusetts 341