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Spiral patterns in geophysics
Journalof Atmosphericand TerrestrialPhysics, 1!)60,Vol. 10, pp. 136 to 140.Per@~nonPress Ltd. Printed in KorthornIreland
Spiral patterns in geophysics V. AC;P National Bureau of Standards,
Boulder, Colorado
Ab&&-Recent analyses of magnetic and ionospheric data., notably by A. P. Nikolski, have resulted in spiral “precipitation” patterns which lead the aut.hors to c&m support for Stijrmor’s theor,y of the auro~‘~t. Although it may be possible to argue agsinst t~hess cla,ims by &tacking the methods of analysis and /or the StGrmer theory itself. an entirety diEwent approach is used in the paper presented here: an examination of pertinent points of St86nner’s t~hcory shows that the anal~tioal spirals mentioned cannot be SMrmer spirals and this conclusion holds regwdlesa of the soundness of the arialysos tend, indeed, of the validity of Stiirmer’s theory.
A ~-UMBER of papers have appeared in the literature during t’he past few years purporting to give support to StGrmer’s theory of the aurora. Most of these claims of support are based on acceptable methods of data analysis combined with apparent similarities between spiral patterns arising in the analysis and Stiirmer’s “line of precipitation”. In view of the increasingly apparent electromagnetic complexities of interpla,netary space (e.g. the Van Allen radiation belts) and t,he unresolved logical di~cult,ies faced by the Stihmer theory, confirl~a~,io?~ of t,he sort offered in the papers mentioned is surprising, to say the least. It WBStherefore thought useful to examine t,hese claims of confirmation and some of the pertinent points of the theory in order to determine whether t’he claims are well based. It is found that, in fact, they are not. First, consider the spiral lines of precipitation as derived by ST~~RNER (I%%). Figs. 1 and 2 (STSRMER, 1955, Figs. 158a and b) are a copy of one of Birkeland’s photographs showing the spiral pattern of fluorescence produced by elect,rons impinging on the surface of his tcrrella (Fig. 1) and the spiral derived by StEirmer by application of his theory of electron motion in a dipole magnetic field (Fig. 2). It is clear (ST~~~~ER, 1955, C‘h. VII) that in this case St,ijrmer’s com~?ut,at,ions were based on Birkeland’s experimental values for electron velocity, tcrrella dipole moment, etc. The spiral, then, is strictly a. “laboratory” spiral and cannot properi~ be used for comparison with the results of geophysical data analysis unless the laboratory experiment is an accurately scaled model of the cosmic reality. Nevertheless, this spiral is so used by HACG Pt trl. (I M!t) and by P\‘IKOI,WI (l!L!Xi)~ although Nikolski has extrapolat,ed the spiral into the geomagnetic pole. Another precipitat,ion spiral given by S?‘~RiYIEK (1956, Fig. 177) is bas(4 on &e strength of t,he geomagnetic dipole and on an assumed relocity of the particles (l~rot,~~ns)emit,ted by the sun. Stiirmt~r was able to show by the use of this spiral, shown in Fig. 3, that for certain values of the iutcgration constant 1~there may be tremendous east-west elongat,ion of the region of precipitation, explaining, according to StGrmer, the Ion g rayed arcs actually observed extending hundreds of times farther east-west than they do north-south. In attempting to relate this spiral to aurora1 observations as summarized by Fritz, ST&MER (1955, Fig. 16) assumed that the inside (poleward) t~lgr of thr
Spiral p&terns
in geophysics
aurora1 “belt” was limited by the natural limitation in possible values of solar declination and that the outside edge corresponded more-or-less to the lower latitude boundary of the spiral, i.e. that the whole latitude range of the spiral was included in the aurora1 belt. In order to move the theoretical aurora1 belt to t,he 23” ~olat,it,~lde required for agreement with aurora1 observations, he postulated the existence of a ring current, having a magnetic field strong enough to deflect. the
Fig. 2. The line of precipit&ion
on the sphere from the t,heory.
(STGRMER,
1055, Fig.
1.5%).
incoming particles sufficiently and weak enough to affect the surface values of the terrestrial magnetic field only slightly. It should be emphasized that the ring current was hypothesized for this purpose although perhaps suggested by certain of ~irkeland~s experiments (and Stiirmer’s t,heoretical studies of them) in which circular equatorial electron orbits were discerned. Unfortunately t’he addition of even this relativeIy simple hypothesis greatly complicates the theory. The spiral as such has not been derived for the “new” conditions, i.e. dipole field plus ring current field. It is likely, however, that the addition of a ring current t,o the theory will result in decreasing the latit,ude of the inside edge of the aurora1 belt as well as t,he outside edge and the spiral would probably be contained in a latitude range only slightly greater than that found for the dipole field alone, i.e. little more than about 5’. ST~RMER (1965, p. 345) st’ates, moreover, that such a ring current will tend to concentrate corpuscles with very different values of Hp (stiffness) in the aurora1 belt. In any case, the complet,e theory has not been developed. In Fig. 3 it is seen that a parameter y, not heretofore mentioned, varies along ,>
137
t,he spiral. From Stormer’s derivation, it is seen that- ~1 is t,he [le~Ii?lat‘io~ of the source and, t)herefore, that the spiral as shown (if SGrmer’s theory is correct.) could result experimentally from, say. a year’s observations (during which t,he solar declination will vary through it’s ent’ire range). In ot’her vvords, only discrete points on the spiral would be ‘~illuminated” at a given instant; and this is oontJrary t’o t’he suggest’ion of HAKURA rt al. (105~) basctl on n study of specific periods of To the
emanation
point
Fig. 3. Line of precipitation of positive corpuscles coming down round ‘I%a spreading out, corresponding to rturoral arcs, is ween nez~r maxima (STGRMER , 19.X , Fig . 175) .
the msgnet,ir and minima.
axis. of y’.
world-wide blackout activity, during which instantaneous spiral pat’terns seem to occur. The elongation of the precipitation region discussed by Stijrmer (t’o explain the long rayed arcs) is less by an order of magnitude or so than that required for an instantaneous display of a substantial portion of the spiral. NLKOLSKI ( I !hW) t,oo> has apparently misint#erpreted the Stiirmer spiral since he speaks of his observational spirals as lines of ‘~simLlltaneous occurrence of magnetic dist~urbance.” These argun~e~~ts ca*nnot be offered as opposing MEEK'S (I%%) sLI~~~st,iol~ of a “modified” Stiirmer theory since, in fact, if the modifications ca,n be carried out, the t,heory will be so different from Stiirmer’s as to be essentially new. In a more recent paper in the series suggesting confirmation of Stormer’s theory, NIKOLSKT (19.56) has pointed out the bunching of points at various locations along the spiral in Fig. 3. These point,s correspond to discrete values of y), the declination of the source. Nikolski suggests that as the earth rotates cliwnally I38
Spmal patterns in geophysics
under this spiral, the high point-density sections of the spiral will trace out “amoral zones” or regions of increased magnetie activity. In Fig. 3 there are four such according to Kikolski, four aurora1 high point-density sections and therefore, %ones mill occur: the inner one corresponds to the zone of ‘“polar activity”, i.e. t,he and the second and third front the pole region of Nikolski’s “morning maximum” a are responsible for the “usual” amoral zone. He arbitrarily assumes, apparently. change in shape of the Stiirmer spiral to suggest that’ the fourt,h is much farther south, perhaps passing through Homba,y! Nikolski does not account for t,he great’ latitude discrepancy found between the StGrmer spiral shown in Fig. 3 and the hypot~hetical Nikolski spira,l reaching int,o equatorial regions. It, has been pointed out that the assumption of a ring current is not sufficient and it can easily be shown t,hat, particles of greater stiffness (higher velocit,y) cannot8 produce the desired effect. It. is of interest, to not2e &at the Stiirmer spiral can be extended beyond tOhepoint, at which ~t~rIller stopped plot~t,illg so it would be just as reasonable to insist., say, on six amoral zones. It is at first, suggestive that the wctions of high point-densit,y occur around the points for which y -= 0. i.e. at the equinoxes. However, &Y.IV I> ( l!ibti) t’irne of greater magnetic activity. the ~‘traditional” has shown that t)he morning maximum is also a summertime maximum ~(1 further doubt’ is cast’ on Nikolski’s conclusions. Although it is easy to believe in large scale distortions of the Stiirmer sljiral from its regular theoretical shepe in t,he dipole field to something far different, in the actual geomagnetic field, it is improper to accept wholly arbitrary distortions on this basis, i.e. without some specific theoret,ical arguments. Merely t-o stat,e, for example: that the earth’s field is quit,e different from the dipole field assumed byStijrmer is insu~~ien~ argL~nlent, for claiming that “any old” spiral can bc called a Stiirmer spiral. There is no point in suggesting that while the da,ta spirals are not ~~~~~~~ Stiirmer spirals, they are ‘Stiirmer-like”
made a careful study of polar magnetic activity in which he presents cogent arguments for the use of the “field at an altitude” and local magnetic time. Although, at one point, he presents a spiral precipitation pattern, he uses it only as an aid in presentation of his data rather than as “proof” of Stiirmer’s theory. The above comments are not meant as an indictment either of spiral presentations of the results of data analysis or Stiirmer’s theory. They are intended, however, to suggest that, in spite of first appearances, the spiral presentations appearing recently in the literature are incompatible with the Stkrner theory and that, in any case, the theory must be greatly extended before comparisons of thta sort recently made have any meaning at, all. REFEREKCES Haac:
L.,
E.
MULDREWD.
ant1
WARRENE. Ha~mta
Y., TAKENOSHITA
OTSUKI MAYAIJD MEEK
Y.
arltl
T. P. x.
.J.H.
NIKOLSKI
PI. r’.
?\TIKOLSKI
A. P.
ST~~KNIRR (1.
19.77
1965
140
Spiral patterns in geophysics V. AC;P National Bureau of Standards,
Boulder, Colorado
Ab&&-Recent analyses of magnetic and ionospheric data., notably by A. P. Nikolski, have resulted in spiral “precipitation” patterns which lead the aut.hors to c&m support for Stijrmor’s theor,y of the auro~‘~t. Although it may be possible to argue agsinst t~hess cla,ims by &tacking the methods of analysis and /or the StGrmer theory itself. an entirety diEwent approach is used in the paper presented here: an examination of pertinent points of St86nner’s t~hcory shows that the anal~tioal spirals mentioned cannot be SMrmer spirals and this conclusion holds regwdlesa of the soundness of the arialysos tend, indeed, of the validity of Stiirmer’s theory.
A ~-UMBER of papers have appeared in the literature during t’he past few years purporting to give support to StGrmer’s theory of the aurora. Most of these claims of support are based on acceptable methods of data analysis combined with apparent similarities between spiral patterns arising in the analysis and Stiirmer’s “line of precipitation”. In view of the increasingly apparent electromagnetic complexities of interpla,netary space (e.g. the Van Allen radiation belts) and t,he unresolved logical di~cult,ies faced by the Stihmer theory, confirl~a~,io?~ of t,he sort offered in the papers mentioned is surprising, to say the least. It WBStherefore thought useful to examine t,hese claims of confirmation and some of the pertinent points of the theory in order to determine whether t’he claims are well based. It is found that, in fact, they are not. First, consider the spiral lines of precipitation as derived by ST~~RNER (I%%). Figs. 1 and 2 (STSRMER, 1955, Figs. 158a and b) are a copy of one of Birkeland’s photographs showing the spiral pattern of fluorescence produced by elect,rons impinging on the surface of his tcrrella (Fig. 1) and the spiral derived by StEirmer by application of his theory of electron motion in a dipole magnetic field (Fig. 2). It is clear (ST~~~~ER, 1955, C‘h. VII) that in this case St,ijrmer’s com~?ut,at,ions were based on Birkeland’s experimental values for electron velocity, tcrrella dipole moment, etc. The spiral, then, is strictly a. “laboratory” spiral and cannot properi~ be used for comparison with the results of geophysical data analysis unless the laboratory experiment is an accurately scaled model of the cosmic reality. Nevertheless, this spiral is so used by HACG Pt trl. (I M!t) and by P\‘IKOI,WI (l!L!Xi)~ although Nikolski has extrapolat,ed the spiral into the geomagnetic pole. Another precipitat,ion spiral given by S?‘~RiYIEK (1956, Fig. 177) is bas(4 on &e strength of t,he geomagnetic dipole and on an assumed relocity of the particles (l~rot,~~ns)emit,ted by the sun. Stiirmt~r was able to show by the use of this spiral, shown in Fig. 3, that for certain values of the iutcgration constant 1~there may be tremendous east-west elongat,ion of the region of precipitation, explaining, according to StGrmer, the Ion g rayed arcs actually observed extending hundreds of times farther east-west than they do north-south. In attempting to relate this spiral to aurora1 observations as summarized by Fritz, ST&MER (1955, Fig. 16) assumed that the inside (poleward) t~lgr of thr
Spiral p&terns
in geophysics
aurora1 “belt” was limited by the natural limitation in possible values of solar declination and that the outside edge corresponded more-or-less to the lower latitude boundary of the spiral, i.e. that the whole latitude range of the spiral was included in the aurora1 belt. In order to move the theoretical aurora1 belt to t,he 23” ~olat,it,~lde required for agreement with aurora1 observations, he postulated the existence of a ring current, having a magnetic field strong enough to deflect. the
Fig. 2. The line of precipit&ion
on the sphere from the t,heory.
(STGRMER,
1055, Fig.
1.5%).
incoming particles sufficiently and weak enough to affect the surface values of the terrestrial magnetic field only slightly. It should be emphasized that the ring current was hypothesized for this purpose although perhaps suggested by certain of ~irkeland~s experiments (and Stiirmer’s t,heoretical studies of them) in which circular equatorial electron orbits were discerned. Unfortunately t’he addition of even this relativeIy simple hypothesis greatly complicates the theory. The spiral as such has not been derived for the “new” conditions, i.e. dipole field plus ring current field. It is likely, however, that the addition of a ring current t,o the theory will result in decreasing the latit,ude of the inside edge of the aurora1 belt as well as t,he outside edge and the spiral would probably be contained in a latitude range only slightly greater than that found for the dipole field alone, i.e. little more than about 5’. ST~RMER (1965, p. 345) st’ates, moreover, that such a ring current will tend to concentrate corpuscles with very different values of Hp (stiffness) in the aurora1 belt. In any case, the complet,e theory has not been developed. In Fig. 3 it is seen that a parameter y, not heretofore mentioned, varies along ,>
137
t,he spiral. From Stormer’s derivation, it is seen that- ~1 is t,he [le~Ii?lat‘io~ of the source and, t)herefore, that the spiral as shown (if SGrmer’s theory is correct.) could result experimentally from, say. a year’s observations (during which t,he solar declination will vary through it’s ent’ire range). In ot’her vvords, only discrete points on the spiral would be ‘~illuminated” at a given instant; and this is oontJrary t’o t’he suggest’ion of HAKURA rt al. (105~) basctl on n study of specific periods of To the
emanation
point
Fig. 3. Line of precipitation of positive corpuscles coming down round ‘I%a spreading out, corresponding to rturoral arcs, is ween nez~r maxima (STGRMER , 19.X , Fig . 175) .
the msgnet,ir and minima.
axis. of y’.
world-wide blackout activity, during which instantaneous spiral pat’terns seem to occur. The elongation of the precipitation region discussed by Stijrmer (t’o explain the long rayed arcs) is less by an order of magnitude or so than that required for an instantaneous display of a substantial portion of the spiral. NLKOLSKI ( I !hW) t,oo> has apparently misint#erpreted the Stiirmer spiral since he speaks of his observational spirals as lines of ‘~simLlltaneous occurrence of magnetic dist~urbance.” These argun~e~~ts ca*nnot be offered as opposing MEEK'S (I%%) sLI~~~st,iol~ of a “modified” Stiirmer theory since, in fact, if the modifications ca,n be carried out, the t,heory will be so different from Stiirmer’s as to be essentially new. In a more recent paper in the series suggesting confirmation of Stormer’s theory, NIKOLSKT (19.56) has pointed out the bunching of points at various locations along the spiral in Fig. 3. These point,s correspond to discrete values of y), the declination of the source. Nikolski suggests that as the earth rotates cliwnally I38
Spmal patterns in geophysics
under this spiral, the high point-density sections of the spiral will trace out “amoral zones” or regions of increased magnetie activity. In Fig. 3 there are four such according to Kikolski, four aurora1 high point-density sections and therefore, %ones mill occur: the inner one corresponds to the zone of ‘“polar activity”, i.e. t,he and the second and third front the pole region of Nikolski’s “morning maximum” a are responsible for the “usual” amoral zone. He arbitrarily assumes, apparently. change in shape of the Stiirmer spiral to suggest that’ the fourt,h is much farther south, perhaps passing through Homba,y! Nikolski does not account for t,he great’ latitude discrepancy found between the StGrmer spiral shown in Fig. 3 and the hypot~hetical Nikolski spira,l reaching int,o equatorial regions. It, has been pointed out that the assumption of a ring current is not sufficient and it can easily be shown t,hat, particles of greater stiffness (higher velocit,y) cannot8 produce the desired effect. It. is of interest, to not2e &at the Stiirmer spiral can be extended beyond tOhepoint, at which ~t~rIller stopped plot~t,illg so it would be just as reasonable to insist., say, on six amoral zones. It is at first, suggestive that the wctions of high point-densit,y occur around the points for which y -= 0. i.e. at the equinoxes. However, &Y.IV I> ( l!ibti) t’irne of greater magnetic activity. the ~‘traditional” has shown that t)he morning maximum is also a summertime maximum ~(1 further doubt’ is cast’ on Nikolski’s conclusions. Although it is easy to believe in large scale distortions of the Stiirmer sljiral from its regular theoretical shepe in t,he dipole field to something far different, in the actual geomagnetic field, it is improper to accept wholly arbitrary distortions on this basis, i.e. without some specific theoret,ical arguments. Merely t-o stat,e, for example: that the earth’s field is quit,e different from the dipole field assumed byStijrmer is insu~~ien~ argL~nlent, for claiming that “any old” spiral can bc called a Stiirmer spiral. There is no point in suggesting that while the da,ta spirals are not ~~~~~~~ Stiirmer spirals, they are ‘Stiirmer-like”
made a careful study of polar magnetic activity in which he presents cogent arguments for the use of the “field at an altitude” and local magnetic time. Although, at one point, he presents a spiral precipitation pattern, he uses it only as an aid in presentation of his data rather than as “proof” of Stiirmer’s theory. The above comments are not meant as an indictment either of spiral presentations of the results of data analysis or Stiirmer’s theory. They are intended, however, to suggest that, in spite of first appearances, the spiral presentations appearing recently in the literature are incompatible with the Stkrner theory and that, in any case, the theory must be greatly extended before comparisons of thta sort recently made have any meaning at, all. REFEREKCES Haac:
L.,
E.
MULDREWD.
ant1
WARRENE. Ha~mta
Y., TAKENOSHITA
OTSUKI MAYAIJD MEEK
Y.
arltl
T. P. x.
.J.H.
NIKOLSKI
PI. r’.
?\TIKOLSKI
A. P.
ST~~KNIRR (1.
19.77
1965
140