Sudden Fmin Enhancements and Sudden Cosmic Noise Absorptions

J. Geomag. Geoelectr., 27, 95-112, 1975

Sudden fminEnhancements and Sudden Cosmic Noise Absorptions Associated with Solar X-Ray Flares

Teruo SATo Physics Department, Hyogo College of Medicine, Mukogawa-cho, Nishinomiya, Hyogo, Japan

(Received November 28, 1974; Revised May 23, 1975)

Sudden fmin enhancements (SFmE's) and sudden cosmic noise absorptions (SCNA's) associated with increments of X-ray fluxes during solar flares are studied on the basis of X-ray flux data measured by SOLRAD 9 and 10 satellites. Some statistical analyses on SFmE's observed at five observatories in Japan, corresponding to increased X-ray fluxes in the 1-8 A band are made for 50 solar flare events during the period January 1972 to December 1973, and value of fmin is expressed as functions of cos x(x; solar zenith angle) and 1-8 A band X-ray flux. Similar study is also made for SCNA's observed by 30 MHz riometer at Hiraiso for 15 great solar flare events during the same period, together with 27.6 MHz riometer data reported by SCHWENTEK(1973) and 18 MHz data published by DESHPANDEand MITRA (1972b). It is found that fm, value (MHz) and SCNA value (L, dB) of a radio wave with frequency f(MHz) are related to X-ray flux (F0, ergcm-2 sec-1) in the 1-8A band and to cos x, by following approximate expressions, fmin(MHz)=l0Fo4cos1/2x, L(dB)=4.37X103f-2Fo2cosx, respectively. Blackout seems to occur for Fo values causing fmin's greater than about 5 MHz. It is shown that these expressions can be derived from a brief theoretical calculation of radio wave absorption in the lower ionosphere. Also it is suggested that threshold X-ray fluxes in the 1-8 A band which may produce a minimum SFME(2MHz), blackout and minimum SCNA (0.27-0.36dB for 30 MHz noise) are 1.6x10-3, 6.2x10-2 and (3-8)x10-3erg cm-2 sec-1, respectively, for cos x=1.

1. Introduction

It has been well established that enhanced X-ray emissions associated with solar flares produce excess ionizations at various heights of the ionosphere and cause sudden ionospheric disturbances (SID's). Especially, X-ray emissions with wavelengths less than 10 A produce intense ionizations at levels below A about 100km (KREPLINet al., 1962; ALLEN, 1965) and they are responsible for

95 96 T. SATO sudden fmin enhancement (abbreviated as SFmE), or blackout (BO) in the vertical incidence sounding, as well as sudden fieldstrength anomaly (SFA), sudden enhancement of atmospherics (SEA), sudden phase anomaly (SPA) and sudden cosmic noise absorption (SCNA). In recent years X-ray emissions mainly with wavelengths less than 20 A have been monitored continuously by satellites, and using these data a number of authors have studied various X-ray flare effects in the lower ionosphere and propagation of radio waves. For example, KREPLIN et al. (1970) reported a relationship between flare X-ray and radio wave emission. SENGUPTA (1971) treated X-ray effects on VLF and HF wave propagations and electron concentration profiles. In a series of papers DESHPANDE et al. (1972a, b), DESHPANDE and MITRA (1972a, b, c) and MITRA and ROWE (1972) made an extensive analysis on various kinds of the SID effects including variations of wave field intensity, phase height, ionization profile and cosmic noise absorption. Recently, OHLE et al. (1974) pointed out that flare X-ray effects in the lower ionosphere depend strongly on season and solar zenith angle, and TAUBENHEIM et al. (1974) analysed phase-height variations in SFA effects. In spite of the comprehensive studies mentioned above, SFmE's during solar flares have been studied very little up to date. Also quantitative relationship between X-ray fluxes and SCNA values seems to be not yet established. The aim of this paper is to examine statistically fmin,and SCNA values corresponding to X-ray fluxes during solar flares and to try to derive expressions showing dependence of fmin and SCNA on X-ray flux and solar zenith angle. A brief theory is presented to endorse the two derived expressions. Also threshold X-ray fluxes which will produce, respectively, minimum fmin blackout and minimum SCNA are estimated.

2. Data

Data on solar X-ray flux analysed in this work are those in the 1-8 A band for 50 solar X-ray flare events during the period January 1972 to December 1973 measured by SOLRAD 9 and 10 satellites which were reported in SOLAR- GEOPHYSICAL DATA (1972-1974). The corresponding fmin data are taken from f-plots at Wakkanai (45.4N, 141.7E), Akita (39.7N, 140.1E), Kokubunji (35.7N, 139.5E), Yamagawa (31.2N, 130.6E) and Okinawa (26.3N, 127.8E), published in IONOSPHERICDATA IN JAPAN (1972, 1973). Values of f minmeasured at observatories in other countries are not used because capa- bilities of instruments might be different from those in Japan. Performances of instruments used for ionospheric vertical sounding at Japanese observatories are approximately the same, therefore, in this study they are assumed to be all the same. Some details of them are shown in Table 1. Analysed data for SCNA fmin Enhancements and SCNA's during Solar X-ray Flares 97

Table 1. Typical performance specifications of instruments for ionospheric vertical sounding in Japanese observatories.

events are 30 MHz riometer data for 15 large flares observed at Hiraiso (36.4N, 140.6E), Japan, which are available from the data in 1972 and 1973, and in addition to this, 27.6 MHz riometer data observed at Lindau (51.7N, 10.1 E) during the period July 28 to August 12 1972, reported by SCHWENTEK (1973), and 18 MHz data published by DESHPANDEand MITRA (1972b), which were recorded at Delhi (28.6N, 77.2E) and other stations during 1967-1969, are used for comparison with Japanese data.

3. Results

3.1 Sudden fmin enhancement (SFmE) 3.1.1 Statistical results Figure 1 shows some examples of fmin enhancements associated with increased solar X-ray fluxes (i.e. SFmE's) observed at Yamagawa in Japan and Rostov in USSR. The figure indicates a clear one-to-one correspondence between X-ray flux and fmin enhancement. Figure 2 demonstrates seasonal and local time distributions of occurrence number of distinct SFmE's (including blackout) such as are shown in Fig. 1, who have peak fmin values larger than 3 MHz for the 1-8 A band fluxes exceeding 1 X 10-2ergcm-2 sec-1, observed at five observatories in Japan during the period January 1972 to October 1974. (The X-ray data measured from SOLRAD satellites were presented until April 1974. After May fmin enhancements which are regarded obviously as flare- associated enhancements are counted as SFmEevents.) Each SFmEis numbered when fmin enhancements are observed simultaneously at least at three observatories. The peak fmin, 3 MHz, is tentatively determined to be the threshold value, 98 T. SATO

Fig. 1. An example of correspondence between solar X-ray flux enhancements in the 0-3 and 1-8 A bands and sudden fmin enhancements (SFmE's) which were observed during the period April 30 to May 3 Values of fmin are taken from f -plots at Yamagawa (31.2N, 130.6E) and Rostov (47.2N, 39.7E).

1972 1973 1974

Fig. 2. Occurrence number of sudden fmin enhancements (SFmE's, above 3 MHz) for 1-8 A fluxes greater than 1 x 10-2erg cm-2 sec-1, observed at five observatories in Japan during the period January 1972 to October 1974. The enhancement is numbered when the event occurred simultaneously at least at three observatories. fmin Enhancements and SCNA's during Solar X-ray Flares 99 because normal f minexceeds usually 2 MHz in the daytime in summer. Thin lines in Fig. 2 represent that fmin is between 3 and 5 MHz, whereas thick lines represent that fmin.is greater than 5 MHz or blackout occurs. It is recognized from this figure that there is a tendency that SFmE's occur mainly in equinoxes and summer in a wide range of local time, whereas in winter they take place in a narrow time range centered on local noon. These results, which seem to indicate an seasonal and local time dependence of SFmE, is presumed from a viewpoint that SFmE's are caused due to excess absorption of radio waves pass- ing through flare-associated ionization layers, whose magnitudes and locations depend on both X-ray flux and cos x (x; solar zenith angle) (CHAPMAN,1931). Since solar flares occur irregularly in time, we cannot exclude a possibility that SFmE's in any other year occur more often in winter than in summer or equinoxes. But this possibility seems to be low because X-ray flares responsible for SFmE's in winter are comparatively great flares. In fact, SFmE's in winter i Fig. 2 occur for the 1-8 A fluxes exceeding about 1 X 10-1erg cm-2 sec-1, whereas other SFmE's occur for the fluxes larger than about 1 x 10-2erg cm-2 sec-1. The relation of SFmEoccurrence to cos x is also expected from results demonstrated by OBAYASHI (1970), showing a dependence of fmin ion cos x. In order to examine the relationship among fmin, X-ray flux (F0)and cos x, fmin values (fmin'S)for 30 great X-ray events during the period January 1972 to December 1973 are plotted in Fig. 3 against X-ray flux in the 1-8 A band and cos X value. In this case fmin's themselves are not shown in the figure, but the values between two fixed frequencies (1 MHz width) are all indicated by the same mark (for instance, open circles for fmin's between 2 and 3 MHz). Blackouts are also marked by filled circles. For a comparatively small-scale X-ray event, only peak fmin value is plotted, whereas for an extraordinarily large X-ray event, fmin's are plotted every 15 or 30 minutes near the time of the peak X-ray flux and every one hour in the gradual decay phase of the flux. This is the reason why low fmin's below 2 MHz which is close to normal value exist in the figure. Similar analyses are made for both the 0-3 and 8-20 A band fluxes. For the 0-3 A band, however, the flux values corresponding to certain fm11ivalue scatter in a wide range of 1 X 10 to 1 X 10-1erg cm-2 sec-1, on the contrary, for the 8-20 A band the flux values are in a narrow range of 1 X 10-2 to 1 X 10-1 erg cm-2 sec-1. Therefore, no further analyses are made for these two bands. The same treatment is made in the analysis of SCNA which will be shown below. Solid lines in Fig. 3 indicates possible locations of fmin=2, 3, 4 and 5MHz for various values of cos x. Individual line is at first drawn arbitrarily as a most probable line representing a boundary between two different groups of marks. But after some examinations it is found that these solid lines are parallel to each 100 T. SATO

Fig. 3. Values of fmin in SFmE events as functions of cos x and X-ray fluxes in the 1-8 A band observed at five observatories in Japan during the period January 1972 to December 1973. BO meanslackout. other and indicate following relations among F0, fmin and cos x. That is, for a fixed fmin, F0 can be approximately expressed in term of sec x as follows,

F0=Clsect2x, (1) and for a fixed cos x, F0=Ctijmin)4, (2) fmin Enhancements and SCNA's during Solar X-ray Flares 101 where C1 and C2 are constants differing for different fmin and sec x, respectively. Strictly speaking, the exponents for sec x and fmin the above expressions may not be integers such as 2 and 4, but the values seem to be close to these integers. Therefore the above expressions could be regarded as to be reasonable as a first approximation. Combining (1) and (2) and giving numerical value derived from Fig. 3 as a proportional constant, following expressions are conclusively obtained, Fo(ergcm-2sec-1)=10-4(fmin)4sectx, (3) and inversely, fmin(MHz)=10F4cosv2x. (4) These expressions (3) and (4) can be derived, as will be shown below, from a theory of radio wave absorptions, in which the radio wave frequency is equal to fmin. Further, it will be realized that according to that theory, magnitudes of absorption of radio waves with frequencies fmin'S which satisfy the condition (4) are all the same, in other words, calculated absorption values are all the same for F0 and cos x values corresponding to points on every solid line (fixed fmin lines) in Fig. 3. Figure 4 is another type of figure indicating relationships among F0, fmin and cos x, making use of the solid lines in Fig. 3. The X-ray fluxes in the 1-8 A band necessary to produce certain fmin seem to be estimated more easily.

Fig. 4. Relationship between fmin values in SFmE events and X-ray fluxes in the 1-8 A band as a function of cos x. 102 T. SATO

3.1.2 Threshold X-ray flux for SFmE Threshold X-ray flux that will produce a minimum SFmE can be inferred from Figs. 3 and 4. It is clear that the threshold value depends on solar zenith angle. If we assume that a minimum fmin value admittable as X-ray-associated enhancement is 2 MHz, then the threshold X-ray flux in the 1-8 A band is 1.6 x 10-3, 6.4x 103 and 4 x 10-2 erg cm-2 sec-1 for cos x=1, 0.5 and 0.2, respectively. 3.1.3 Threshold X-ray flux for blackout Threshold X-ray flux for blackout phenomena also can be estimated from Fig. 3. Blackouts seem to occur for X-ray fluxes in the 1-8 A band larger than those necessary to cause SFmE's of about 5 MHz. The threshold flux is approximately 6.2 x 10-2 erg cm-2 sec-1 for cos x -1. The cause for blackout occurrence will be commented briefly in the discussions.

3.2 Sudden cosmic noise absorption (SCNA) 3.2.1 Statistical results Relationship between flare X-ray fluxes and ionospheric absorption values in SCNA events have been studied by MITRA (1966), JAYARAM and CHIN (1967), BURGESSand JONES (1967), DESHPANDEet al. (1972b), and DESHPANDEand MITRA (1972c). The aim of this section is to derive an expression indicating dependence of SCNA value on X-ray flux, cos x and wave frequency, which seems to be not yet established. A statistical analysis is made at first for this purpose. SCNA values measured by 30 MHz riometer at Hiraiso, Japan are plotted against corresponding X-ray fluxes in the 1-8 A band for 15 great SCNA events which occurred during the period January 1972 to December 1973. Following normalization, however, is made for plotting of these data. Since absorption of radio waves in the ionosphere is proportional to f-2 where f is a wave frequency, as is well known (for example, RATCLIFFE and WEEKS, 1960), and since the absorption is reported to be proportional to coshx where n is a constant by LAUTER(1966), LAUTER and NITZSCHE (1967) and HIGASHIMURA et al. (1969), the absorption is eventually expected to be proportional to f-2coshx. LAUTER (1966) showed that n=0.9 for 1.178 MHz wave for the most time of the year from measurements of steep incidence of the wave into the ionosphere, and LAUTERand NITZSCHE (1967), from A-3 absorption measurements, reported that n=1.28, 1.0 and 0.9 for 2.614 MHz wave and n=1.2, 0.9 and 0.9 for 1.178 MHz wave in equinox (April), summer and winter, respectively. Also HIGASHIMURA et al. (1969), from routine absorption measurements for 2.4 MHz wave, demonstrated that n=1.02, 0.94 and 0.83, respectively, in equinox, summer and winter. These results seem to show that n is approximately unity on average. fmin Enhancements and SCNA's during Solar X-ray Flares 103

Fig. 5. Relationship between X-ray fluxes in the 1-8 A band and SCNA values normalized to the values at 18 MHz and cos x=1. Analysed data (filled circle) are observed at Hiraiso (36.4N, 140.6E). Data at Lindau (51.7N, 10.1E) reported by SCHWENTEK(1973) and data at Delhi (28.6N, 77.2E) and other observatories published by DESHPANDE and MITRA (1972b) are also plotted for comparison. +mark represents the normalized value of 2.4 MHz wave in measurements of absorptions on the ground reported by HIGASHIMURAet al. (1969).

Referring to this, we assume in this analysis that the same n value (n=1) could be applied to absorptions for higher frequency radio waves and that SCNA value, L, is proportional to f-2 cos x. On the basis of these assumptions, each L value observed at Hiraiso is normalized to the value for f=18 MHz and cos x=1, and this normalized value, 4, is plotted against the 1-8 A band flux. For some SCNA events, absorption values are scaled every 15 or 30 minutes, as same as the procedure in fmin plotting. The results are shown in Fig. 5 by filled circles. Additionally, SCNA's for 27.6 MHz wave observed at Lindau during the period July 31 to August 12 1972 (SCHWENTEK,1973), and SCNA's for 18 MHz wave observed at Delhi and other stations for 25 events in 1967- 1969 (DESHPANDE and MITRA 1972b) are, after the same normalization, plotted in Fig. 5 for comparison. It is clear from Fig. 5 that absorption value (in log scale) seems to increase linearly with increasing X-ray flux (in log scale) for the X-ray fluxes greater 104 T. SATO than about 5 X 10-2erg cm-2sec-1. This result indicates that the assumption mentioned above concerning dependence of L on f and cos x seems to be valid, at least, in the high absorption range. The calculation using the least square method, based on distinct SCNA values in Fig. 5, indicates that relationship between X-ray flux (F0) and absorption value (L0) is expressed by

F0=C3L95 (5) where C3 is a constant. This exponent value for L0, however, is close to 2.0 which is derived from a simple theoretical calculation of cosmic noise absorption in the later section. Therefore, it may be considered that the relationship between F0 and L0 is approximately expressed by F0=C3L0. The solid line in Fig. 5 represents this expression and seems to fit to the F0-L0 distribution fairly well. Inserting numerical value into C3, the relation between F0 and L0 is conclusively given by F0(ergcm-2sec-1)=5.5X103L, (6) and inversely, L0(dB)=13.5F2. (7) The absorption values at Delhi for X-ray fluxes less than about 5 X 10-2 erg cm-2sec-1 deviate significantly from the solid line. The data at Hiraiso shows somewhat similar trend. The reason for this is not clear. One of reasons to be considered, however, is that signal levels of received cosmic noises are generally recorded to be higher than the actual ones, owing to superposition of solar radio bursts or other noise signals during flares. This effect (error) is larger for lower absorptions, therefore, low absorptions are apparently recorded to be lower than they would be. The solid line, when it is extended to the low absorption region as dotted line, passes approximately over cross mark. This cross mark indicates normalized absorption value of 2.4 MHz wave incident vertically in the lower ionosphere, reported by HIGASHIMURA et al. (1969). Since the absorption value for 2.4 MHz wave is much larger than that for 18 MHz wave, effects of solar radio bursts and other noise signals on this wave are very little. From this point of view, the cross mark seems to be situated at a comparatively correct point in the figure. Therefore, it may be considered that the scattered points in the figure should be on or close to the solid line. Since the absorption values in Fig. 5 are normalized values for 18 MHz and cos x=1 under the assumption that L is proportional to f-2 cos x, following expression holds, L(dB)=Lo(18/f)2cosx, (8) where f is expressed in unit of MHz. Using (7), expression (8) can be written as, fmin Enhancements and SCNA's during Solar X-ray Flares 105

L(dB)-4.37X103f-2Fa/2cosx, (9) and inversely, Fo(ergcm-2sec-1)=5.24x10-8L2f4sectx. (10) 3.2.2 Threshold X-ray flux for SCNA Threshold X-ray flux for SCNA events is difficult to determine because magnitudes of SCNA's depend not only on X-ray flux, but also on wave frequency and solar zenith angle as shown in (9). Therefore, it is only possible to determine a threshold flux under a limited condition. In the present case the results obtained in Fig. 5 give a clue to rough estimation of the threshold flux. That is, the threshold flux in the 1-8 A band for 18 MHz wave and cos x-1 is about 8 x 10-3 erg cm-2 sec-1. The low absorption values for 30 and 27.6 MHz riometers we have analysed in Fig. 5 are, however, those close to threshold absorptions but not threshold values themselves, since we have calculated absorption values only for comparatively clear absorption data to avoid inclusion of errors. As a matter of fact, Fo 2 cos x values (it seems to be better to include cos x rather than Fo itself) in SCNA events at the beginning time are 0.06-0.09 and 0.05 (erg cm-2 sec-1)12 for 30 and 27.6 MHz data, respectively. This implies that the threshold Fo values in the 1-8 A band for detectable SCNA events are in the range of (3-8) X 10-3 erg cm-2 sec-1 at cos x=1 for 30 MHz cosmic noise. Threshold values for certain cos x are, therefore, in the range of (3-8)X10-3/costx, because L should be constant in expression (9).

4. Theoretical Considerations

The expressions (4) and (9) in the previous sections can be derived from a brief theoretical treatment. For an isothermal atmosphere electron production rate, p, at a height h due to a monochromatic X-ray emission with a flux F0 at the top of the atmosphere is given by

p=ijAF00poeXp(Ap0Heh/h1secx), (11)

(CHAPMAN,1931), where n denotes the number of electrons produced by unit quantity of absorbed energy in unit volume, A, the average absorption cross section of the X-ray for atmospheric constituents, po, the datum level value of atmospheric particle number density which varies as e-h/H, the constant scale height, and x, the solar zenith angle. A is assumed to be constant throughout the heights. For a band of X-ray emissions, (11) holds for each X-ray emission with different wavelength, and total production rate is a sum of those production rates. In the present study, however, we assume that ionizations produced 106 T. SATO by a monochromatic X-ray emission with a wavelength Aeff (which we call effective wavelength) contribute to most absorptions of radio waves. Therefore, (11) may be used conveniently for calculation of wave absorptions. Since absorptions of radio waves occur at altitudes below about 100 km, effective electron recombination coefficient, a, may be expressed by

α=α0e-h/H, (12) where a0 is the datum level value of a. Then electron concentration, N, in the steady state is given by

N=1Poexp(Ap0He1/lsecX (13)

Total absorption, LT, of radio wave with a frequency f in the ionosphere may be calculated from the following expression (RATCLIFFE and WEEKS, 1960), assuming that the absorption is of non-deviative and that permitivity in the ionosphere is unity,

LT=2ue2/mcSNvdh/v2+(w+wL)2, (14)

where w=2uf, WLis the component of electron gyrofrequency along the earth's magnetic field, v, the effective electron collision frequency and e, m, and c, the conventional physical constants. Assuming that w>WL, v in the altitudinal range where main absorption takes place, and that v may be expressed by

v=v0e-h/H, (15) where v0 is the datum level value of v, the total absorption is as follows,

Li4rceilo1/5vcOS/(1e(1/2)Ap6Hsecx) (16)

If we assume that the datum level (h=0) is 50 km height, the possible values for po and H are 3 X 1016cm-3 and 8 X 105cm, respectively (U.S. STANDARDATMOS- PHERE1962) at that height. According to results obtained by SATO(1973) maximum absorption in the lower ionosphere occurs at a height between 60 and 90 km, and X-ray wavelength responsible for the absorption is between 1.5 and 5A. Therefore, value A for the effective wavelength in the 1-8 A band is greater than 4.3 X 10-22cm2, which is mean absorption cross section for 1.5 A (FRIEDMAN, 1960; OHSHIOet al., 1966). For these numerical values, 1/2 sec x Ap0H>1. Thus (16) can be written approximately as

LT(dB)=2.33X10-14vof2F/2cosx, (17)

where units of LT and f are dB and MHz, respectively. fmin Enhancements and SCNA's during Solar X-ray Flares 107

Expression (17) can be applied to calculations of cosmic radio noise absorptions. Also the expression may be applied to absorptions of waves with various frequencies, fmin's, which are reflected from the ionosphere in the vertical direction, if we assume that most of absorptions of reflected waves occur at lower heights than the reflection levels, that is, in the lower ionosphere. For the latter case LT should be 2LT because the received waves pass through the same ab- sorbing region twice. It is very clear that expression (17) is quite the same as the expression (9), if we put F0=Fo,

2.33X10-14(i)0=4.37x103. (18)

Therefore, (9) can be regarded as the expression endorsed theoretically as a first approximation, if we consider that some portion of the observed 1-8 A band fluxes, corresponding to certain wavelength, contributes practically to most of observed wave absorption. If the value LT in (17) is kept constant for various combinations of cos x, f and Fo, then cosxf-2F2=constant, (19) which is the same expression as (3) and (4), when fmin is used instead of f, and Fo instead of Fem. Also from (19) the expressions (1) and (2) can be derived. Therefore, magnitude of absorption in the lower ionosphere of reflected radio wave with a frequency fmin is the same for every combination of Fo and cos x, corresponding to every point on fixed fminiline in Fig. 3. This absorption value (that is, constant in expression (19)) is a maximum absorption value for waves in the frequency range concerned, in the meaning that radio waves which sub- ject to higher absorption than this value cannot be detected by receiver, owing to reduction of signal strengths of the waves to a level below signal noise of receiver.

5. Discussions 1) It is noted that the present analysis on the relationship between flare X-ray fluxes and SFmE's is made on the basis of the data at five observatories in Japan. Since fmin'S depend on performances of transmitter and receiver, they would become higher for lower output transmitter, or lower gain receiver, if other conditions are the same, and vice versa. Therefore, numerical values in expressions (3) and (4) should be modified more or less for fmin data measured by instruments with different performances from those in Japan. It is noted, 108 T. SATO however, that more than 60 percent of f min's observed at various locations over the world during large solar flares on 4 and 7 August 1972 are approximately the same as those predicted from expression (4). As for SCNA events, observed SCNA's in other countries are approximately coincident with values at Hiraiso in a comparatively high X-ray flux region, implying that expression (9) seems to be useful at least in this flux region. The results of the present study are conclusively demonstrated by expressions (4) and (9), and it is shown that these expressions are derived from the simple theoretical calculation on ionospheric absorption of radio wave under some assumed conditions. If we make similar analyses using much more data, the exponents for Fo and cos x and proportional constants in their expressions would vary more or less and these exponents could be estimated from a more strict theoretical calculation, which takes into account ionizations due to a band of X-ray emissions. In spite of these situations, we consider that the expressions (4) and (9) demonstrate approximately exact quantitative relations of X-ray flux to SFmE and SCNA. 2) It is suggested that the threshold X-ray fluxes in the 1-8 A band re- quired to produce a minimum fmin (2MHz for cos x=1) in SFmE,blackout and minimum SCNA (0.27-0.36dB at 30MHz and cos x=1) are 1.6 x 10-3, 6.2 x 10-2 and (3-8)x 10-3erg cm-2 sec-1, respectively. These values may be com- pared with values reported by other authors. KREPLINet al. (1962) reported a threshold flux of 2 x 10-3 erg cm-2 sec-1 in the 0-8 A band for occurrence of shortwave fadeouts or the ionospheric effects, based on data measured by SR-1 satellite. SENGUPTAand VAN ALLEN (1968) suggested a threshold value of 1 x 103 erg cm-2sec-1 in the 2-12 A band from measurements in Explorer 33 satellite. DESHPANDEet al. (1972b) reported that a threshold value of (1-2) x 10-3erg cm-2sec-1 in the 0-8 A band from data taken by SOLRAD 8 and OGO I-III satellites is sufficient to produce a detectable SID effect. Deshpande et al. suggested, however, that all X-ray flares producing SCNA events have very high flux levels in the 0-8 A band in the range of 2 x 10-2-5 x 10-1 ergcm-2sec-1. Thus the threshold values presented here are not much apart from those reported by other authors. 3) The fact that a blackout occurs suddenly for X-ray flux slightly exceeding the flux responsible for SFmE of 5 MHz, irrespective of cos x value, seems to imply that wave field strength is lost, not due to absorption, but due to other causes. One of causes to be considered is scattering of radio waves by ionospheric irregularities in the lower ionosphere. BOOKER(1950) and BOOKERand GoRDON (1950) studied this problem, originally, in relation to disappearance of E3 echoes. Their theory showed that for waves with wavelengths shorter than 4rl, where 1 is a size of irregularity, the scattering is predominantly in the fmin Enhancements and SCNA's during Solar X-ray Flares 109 forward direction and the field strength of the backward scatter echo decreases inversely as the square of the wavelength. Therefore, there is sudden decrease in the field strength of the backward scatter echo around the wavelength 4rl. If this theory could be applied to the present study, the wavelength of the 5 MHz wave is the critical wavelength for scattering and this is equal to 4rl, that is, 6 X 103=4rl. Thus the size of irregularities is 4.77m. 4) The expressions (4) and (9), especially the latter, are considered to be useful for an estimation of solar X-ray flux in the 1-8 A band when the flux data is missing. For instance, peak X-ray flux during a large solar flare is frequently not recorded because detector is saturated with a flux greater than certain magnitude. In such a case the X-ray flux in the 1-8 A band can be estimated from expression (10), using SCNA data. The August 1972 event is one of such examples. Very large solar flares occurred on 2, 4 and 7 August, but the peak fluxes in any X-ray band were not measured by detectors on both SOLRAD 9 and 10 satellites (DERE et al., 1973). OHsHIo (1973), using a method based on extrapolation in temporal variation of fluxes and maximum phase deviation SPA, estimated the peak fluxes in the 1-8 A band to be (3-7) X 10-1, (1-2) x 10 A and (1-4) x 10 erg cm sec-1 for the flares on 2, 4 and 7 August, respectively. According to present method corresponding values for the latter two flares are 1.8 x 10 and 2.2 X 10 erg cm-2sec-1, respectively. 5) Recently, an analysis similar with that presented here is made by WAKAI et al. (1973) on SFA effects, on the basis of data of the Loran-C waves propagated over more than 500 km. In their study, however, magnitudes in SFA events were plotted against enhancement ratios of X-ray fluxes in the 1-8 A band during flares (that is, ratio of peak enhanced flux to quiet level flux just before the commencement of flare), and not against enhanced X-ray fluxes themselves. The results show a comparatively large scatter of points.. One of reasons for this would be that effects of solar zenith angle are not taken into account.

6. Conclusions The results of the present study can be summarized as follows: (1) SFmE events with fmin's greater than 3 MHz associated with solar X- ray flares seem to occur mainly in summer and equinoxes. (2) Relationship between fmin value in SFmE event and X-ray flux (F) in the 1-8 A band is approximately expressed by

fmin(MHz)=10Fp4cos2, where unit of F0 is erg cm sec-1. 110 T. SATO

(3) Threshold Fo values causing a minimum fmin(2 MHz) and blackout are 1.6 x 10-3 and 6.2 X 10-2erg cm-2sec-1, respectively, in the 1-8 A band for cosx=1. (4) Relationship between SCNA (L) for a wave with frequency f and X- ray flux in the 1-8 A band is approximately expressed by L(dB)=4.37X103E2f-2cosx, where units of Fo and f are erg cm-2sec-1 and MHz, respectively. (5) Threshold Fo value causing a minimum SCNA is (3-8)x10-3 erg cm-2sec-1 in the 1-8 A band for 30 MHz wave and cos x-1. It is shown that expressions mentioned above can be derived from a simple theoretical calculation of radio wave absorption in the lower ionosphere under some assumed conditions.

The author would like to express his sincere thanks to Dr. N. Wakai and Mr. F. Yamashita of the Hiraiso Observatory, Radio Research Laboratories, who kindly arranged for him to be provided with the 30 MHz riometer data and gave him valuable suggestions. The author also wishes to thank Drs. Y. Nakata, K. Sinno, M. Ohshio, Y. Hakura and N. Matsuura of the Radio Research Laboratories for their continuous encouragement and useful comments for this study.

REFERENCES

ALLEN, C.W., The interpretation of the XUV solar spectrum, Space Sci. Rev., 4, 91-122, 1965. BOOKER, HG., The theory of the scattering of radio waves in the troposphere and ionosphere, Paper, read before the Symposium on the Theory of Electromagnetic Waves held at New York University, 1950. BOOKER, H.G. and W.E. GoRDON, A theory of radio scattering in the troposphere, Proc. IRE, 38, 401-412, 1950. BURGESS, B. and T.B. JoNEs, Solar flare effects and VLF radio wave observations of the lower ionosphere, Radio Sci., 2, 619-626, 1967. CHAPMAN, S., The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth, Proc. Phys. Soc., 43, 26-45, 1931. DERE, K.P., D.M. HoRAN, and R.W. KREPLIN, Solar X-ray emission measured by SOLRAD 9 and 10 during the period July 26-August 14, 1972, in Collected Data Reports on August 1972 Solar-Terrestrial Events, World Data Center A for Solar-Terrestrial Physics, Report UAG- 28 Part II, 298-318, 1973. DESHPANDE, S.D., S. GANGULY, V.C. JAIN, and A.P. MITRA, Ionospheric effects of solar flares- V. The flare event of 30 January 1968 and its implications, J. Atmos. Terr. Phys., 34, 267- 281, 1972a. DESHPANDE, S.D. and A.P. MITRA, Ionospheric effects of solar flares-II. The flare spectrum below 10 A deduced from satellite observations, J. Atmos. Terr. Ploys., 34, 229-242, 1972a. DESHPANDE, S.D. and A.P. MITRA, Ionospheric effects of solar flares-III. The quantitative relationship of flare X-rays to SID'S, J. Atmos. Terr. Phys, 34, 243-253, 1972b. DESHPANDE, S.D. and A.P. MITRA, Ionospheric effects of solar flares-IV. Electron density profiles deduced from measurements of SCNA's and VLF phase and amplitude, J. Atmos. Terr. Phys., 34, 255-266, 1972c. fmin Enhancements and SCNA's during Solar X-ray Flares 111

DESHPANDE, S.D., C.V. SUBRAHMANYAM, and A.P. MITRA, Ionospheric effects of solar flares- I. The statistical relationship between X-ray flares and SID's, J. Atmos. Terr. Phys., 34, 211- 227, 1972b. FRIEDMAN, H., The sun's ionizing radiations, in Physics of the Upper Atmosphere, edited by J.A. Ratcliffe, pp. 133-218, Academic Press, New York, 1960. HIGASHIMURA, M., K. SINNO, and Y. HIRUKAWA, Analysis of long-term observations of ionospheric absorption measurement (I), Observations at Kokubunji, J. Radio Res. Labs, 16, 131- 138, 1969. IONOSPHERIC DATA IN JAPAN, Published by the Radio Research Laboratories, Ministry of Posts and Telecommunications, Japan, 1972, 1973. JAYARAM, R. and C.Y. CHIN, Analytical study of the D-region response to solar flares monitored by Anal satellite (UK-1), J. Geophys.Res., 72, 1889-1899,1967. KREPLIN, R.W., T.A. CHUBB, and H. FRIEDMAN, X-ray and Lyman-Alpha from the sun as measured from the NRL SR-1 satellite, J. Geophys. Res., 67, 2231-2253, 1962. KREPLIN, R.W., P.J. MOSER, and J.P. CASTELLI, Flare X-ray and radio emission, Space Res., X, 920-927, 1970. LAUTER,E.A., A survey of A-3 absorption measurements at low and medium frequencies, Ann. Geophys., 22, 289-299, 1966. LAUTER,E.A. and P. NITZSCHE,Seasonal variations of ionospheric absorption deduced from A3-measurements in the frequency range 100-2000kc/s, J. Atmos. Terr. Phys., 29, 533-544, 1967. MITRA,A.P., A comparative study of solar X-ray measurements from satellite and sudden Iono- spheric disturbances, Space Res., VI, 558-578, 1966. MITRA,A.P. and J.N. RoWE, Ionospheric effects of solar flares-VI. Changes in D-region ion chemistry during solar flares, J. Atmos. Terr. Phys., 34, 795-806, 1972. OBAYASHI, T., Space Physics, (in Japanese), Syokabo Pub. Co., Tokyo, 1970. OHLE, K.H., R. KNUTH, G. ENTZIAN, and J. TAUBENHEIM, On the information content of ionospheric solar flare effect observations-I. Experimental evidence of solar and atmospheric control of the flare effects, J. Atmos. Terr. Phys., 36, 513-524, 1974. OHSHIO,M., Solar-terrestrial disturbances of August 1972, 4. Solar X-ray flares and their corresponding sudden ionospheric disturbances, Quart. J. Radio Res. Labs., 19, 261-280, 1973 (in Japanese). OHSHIO, M., R. MAEDA, and H. SAKAGAMI, Height distribution of local photoionization ef- ficiency, J. Radio Res. Labs., 13, 245-277, 1966. RATCLIFFE, J.A. and K. WEEKS, The ionosphere, in Physics o f the Upper Atmosphere, edited by J.A. Ratcliffe, pp. 379-470, Academic Press, New York, 1960. SATO,T., The response of the lower ionosphere to the great solar flare of August 7, 1972, J. Geomag. Geoelectr., 27, 1975 (in press). SCHWENTEK, H., Shortwave fadeouts and Ionospheric absorption measured at Lindau (N51.2, E8.7) in the period 15 July to 15 August 1972, in Collected Data Reports on August 1972 Solar-Terrestrial Events, published by World Data Center A for Solar-Terrestrial Physics, Report UAG 28 Part II, 579-583, 1973. SENGUPTA, P.R., A study of two flares on 8 July 1968 in the light of their Ionospheric effects, J. Atmos. Terr. Phys., 33, 1953-1971,1971. SENGUPTA, P.R. and J.A VAN ALLEN, Scientific Report, Department of Physics and Astronomy, University of Iowa, Iowa, 1968. SOLAR-GEOPHYSICAL DATA, COMPREHENSIVE REPORTS, Published by National Geophysical and Solar-Terrestrial Data Center, National Oceanic and Atmospheric Administration, U.S Department of Commerce, 1972-1974. 112 T. SATO

TAUBENHEIM, J., G. ENTZIAN, R. KNUTH, and K.H. OHLE, On the information content of ionospheric solar flare effect observations-II. Some model considerations on the interpretation of solar flare effects in the ionosphere, J. Atmos. Terr. Phys., 36, 525-535, 1974. U.S. STANDARD ATMOSPHERE 1962, Prepared under the sponsorship of NASA, U.S. Air Force and U.S. Weather Bureau, 1962. WAKAI, N., S. FUJII, and C. OucHI, SID effects as observed in intensities of LF radio waves, J. Radio Res. Labs., 20, 67-78, 1973.