Determination of electron production rates caused by cosmic ray particles in ionospheres of terrestrial planets

) Pergamon www.elsevier.com/locate/asr

Adv. SpaceRes. Vol.27, No. 11, pp. 1901-1908,2001 © 2001 COSPAR.Publishedby ElsevierScienceLtd.All rightsreserved Printedin GreatBritain 0273-1177/01 $20.00+ 0.00 PII: S0273-1177(01)00323-4

DETERMINATION OF ELECTRON PRODUCTION RATES CAUSED BY COSMIC RAY PARTICLES IN IONOSPHERES OF TERRESTRIAL PLANETS P. I. Y. Velinov ~, M. B. Buchvarova 1, L. Mateev ~, and H. Ruder 2

ICentral Solar-Terrestrial Influences Laboratory, Bulgarian Academy of Sciences, 3ofia 1113. Bulgaria :InstHut fiir Astronomic und Astrophysik, Eberhard-Karls-Universitdt Tfibingen, D -72076, Germany

ABSTRACT Cosmic rays (CR) create the lower parts of~lanetary ionospheres. The observed CR spectrum can be distributed into the following five intervals: I ( E = 3.10 - 10 H GeV/n ), II ( E = 3. l 0 2 - 3 . 1 0 6 GeV/n ), III ( E = 30 MeV/n 3.102GeV/n ), IV ( E = 1 - 30 MeV/n ) and V ( E = 10 KeV/n - 1 MeV/n ), where E is the kinetic energy of the particles (Dorman, 1977; Velinov, 2000). Some methods exist for calculating ionization by relativistic particles in CR intervals I, II and III. For the high latitude and polar ionosphere, however, intervals III, IV and V are also significant since they contain solar cosmic ray and anomalous cosmic ray components. Formulas for the electron production rate q ( cm3s -t ) at height h in the planetary ionosphere as a result of penetration of energetic particles from intervals III, 1V and V are deduced in this paper. For this purpose the law of particle energy transformation by penetration through the ionosphere - atmosphere system is obtained. A model for the calculation of the cosmic ray spectrum on the basis of satellite measurements is created. This computed analytical model gives a practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component. © 2001 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION Describing particle ionization, particularly cosmic ray(CR) ionization in planetary ionospheres and atmospheres, is one of the most important problems in solar-terrestrial physics (Akasofu and Chapman, 1972; Whitten and Poppoff, 1971). Until now, attention has been focused on interval III, which includes the galactic CR with energies from 300 GeV per nucleon to 30 MeV per nucleon, i.e., 3.102 GeV/n > E > 30 MeV/n (Velinov et al., 1974). For the polar ionosphere, however, intervals IV ( 30 MeV/n > E > 1 MeV/n ) and V ( 1 MeV/n > E > 10 KeV/n ) are also significant since they contain solar cosmic ray (SCR) and anomalous cosmic ray (ACR) components (Dorman, 1977; Velinov, 2000). The CR classification into the above mentioned I - V intervals is based on some physical considerations and observation data. The ACR component represents interstellar neutrals drifting into the heliosphere, which after ionization by solar UV radiation, are accelerated in interplanetary space (Velinov, 1991). Formulas for the law of particle energy transformation E(h) due to penetration through the ionosphere and atmosphere will be derived in this paper. In addition the electron production rate profiles q(h) during SCR events will be calculated. An analytical presentation of the differential spectrum of galactic cosmic rays (with account of the ACR component) will be obtained. This is important for evaluation of the ionization state, caused by galactic CR in the ionosphere and middle atmosphere. IONIZATION LOSSES IN T H E A T M O S P H E R E Formulas for the electron production rate q (cm-3sl ) at height h in a planetary ionosphere as a result of penetration of high energy particles have been deduced for galactic cosmic rays (Velinov, 1966) and for solar cosmic rays (Velinov, 1968; Velinov et al., 1974). A similar theory was developed and applied for the galactic CR influence in the atmosphere and ionosphere of Mars (Velinov and Mateev, 1991). The expression for ionization losses (MeV/gcm 2) of subrelativistic particles (kinetic energy E<600 MeV/n), which actually produce a maximal ionospheric effect, is given by Velinov and Georgieva (1970): 1901

1902

R I. Y.

Velinovet al.

- ( d E / dh)= 220p(h)Z 2 E - b ,

(l)

where/9 is the atmospheric density (g.cm -3) and Z is the charge of the particle. The parameter b was determined in each of 4 intervals of kinetic energy. It can be calculated empirically on the basis of the results summarized by Sternheimer (1961), and Johnson (1990). In fact (1) has the following form in different cosmic ray intervals (Velinov, 2000): 2

E > 600 MeV

I11oo4

E = 0.15 - 600 MeV

[ 3 . 6 x 1 0 3 E 3/7

E = 0.01 - 0.05 MeV

1 dE = 2 4 2 E ' 3 ' 4

E = 0.05- 0.15 MeV

(2)

The interval III can be divided into two subintervals: III-1: III-2:

3xl02GeV/n >_E>_3xlO2MeV/n 3 x l 0 2 M e V / n > E > _ 3 x l 0 lMeV/n

(3)

in connection with solar modulation of cosmic rays by interplanetary magnetic fields. The energy E ~ 300 MeV/n corresponds to the maximum in the differential spectrum of galactic CR. From (2) it is clear that interval V also must be divided, but not from the point of view of solar-terrestrial physics, rather because of processes in nuclear physics (Johnson, 1990): W-l V-2: V-3:

1 MeV/n > E > 0.15 MeV/n 0.15 MeV/n > E > 0.05 MeV/n 0.05 MeV/n > E > 0.01 MeV/n

(4)

In this paper, particles of the ambient solar wind are not taken into account; this is the interval VI with energies E _< 10 KeV. They will be included in a future investigation. The energy of particles in the atmosphere at a depth h (gcm -2) can be determined by the equation (Velinov and Georgieva, 1970):

K ( h ) = ( E l+b _El+b)l/(l+b)

where

E A = [220(1 + b)'hCh(O,h)Z 2/.4 + A] l/(l+b)

(5)

is the atmospheric cut-off energy for the penetration angle 0; Ch is the Chapman function of the Earth's sphericity: A is related to the lowest energy boundary 10 KeV of the considered particles and the corresponding ionization losses (2) and (4). Formula (5) follows directly from expression (1) for ionization losses of charged particles. The law of energy transformation in different energy intervals (3, 4) resulting from particle penetration through the ionosphere-upper atmosphere-middle atmosphere system is obtained from formulas (5, 2): interval III - 1, E >_600 MeWn

E - EA, E7/4

7/4 4/7

EA

~j

'

interval III - 1, III - 2, IV, V - 1

E(h) =

interval V - 2

E -EA , E4/7

4/7 x,7/4 - EA

)

'

(6)

interval V - 3

For the composition of this expression the values of parameter b are used in different intervals and subintervals according to the data presented by Sternheimer (1961). These values are shown in Table 1.

1903

CosmicRay Ionizationat TerrrestrialPlanets Table 1. Values of Parameter b in Different EnerL,v Intervals b 0 3/4 0 -3/7

1+b 1 7/4 1 4/7

b/(l+b)

1/(1 +b) 1 4/7 1 7/4

E , MeV _>600 0.15 - 600 0 . 0 5 - 0.15 0 . 0 1 - 0.05

0 3/7 0 -3/4

Intervals III - 1 V - l , IV, III-1, III-2 V-2 V-3

ELECTRON PRODUCTION RATE PROFILES For the quantitative analysis of the ionization profiles in different CR energy intervals we use the expression (Velinov, 1966; 1968): n EM (7) q ( h ) : 1.8×105 Z J" ~ D,(E,O) ( ~ h l i sin0 dOdE

i=lOE,,, where D,(E) is the differential spectrum of particles from type i (protons: i=1, alpha-particles:i=2; L-, M-, H-, VHand SH - groups of nuclei: i=3+7), Em and EM are respectively, the minimal and maximal energies of the intervals III. IV and V , and the corresponding subintervals I I I - 1, I I I - 2, V - 1, V - 2 and V - 3. Let us examine the electron production rate of monoenergetic protons, which penetrate vertically downwards. In this case in (7) the sum and the two integrals over E and 0 are no longer necessary and the following expression is obtained: q(h) = 1.8× 10 5 p (h) 220Z2D(E)( E l+b - E l+b )-b/(l+b) (8) After accounting for the coefficient values in Table 1, formula (8) becomes:

1 (E7/4

q(h)

= 1.8 x 105 p (h) 220

Z2D(E) x

_ E7A/4)-3/7 (9)

1 ( E 4/7

_E4/7) 3/4

corresponding to 7 energetic intervals and subintervals. If we introduce the dimensionless parameter fl = EA / E , formula (9) takes the form:

1 q(h) = 1.8 x 105 p(h)

220

Z2D(E) x

E-3/4( l_ flT / 4) -3/7 1 ( l _ f14/7 ) 3/ 4E3/7

(lO)

Because of the complexity of the double integral (7) it has no analytical solution and it is necessary to use adequate methods from computational physics to obtain acceptable results.

Computations and Results In order to evaluate our theoretical results a computation will be made. Our model is evaluated using Turbo Pascal algorithmic language for PC. If we want to make a possible comparison with calculations of other authors we shall use data they have used. Reid (1961) has considered one of the first SCR events using the differential spectrum D(E) = 2.4 × 10 I° E -5 proton / emz s MeV (11) The corresPonding integral spectrum is D(> E) = 6 x 1 0 9 E - 4 proton / em2s.

1904

P.I.Y. Velinov et al.

The laws of particle energy decrease in the ionosphere in the intervals E _>600 MeV and E > 0.15 MeV are: E k (h) = E k - 2h, E k >_600 MeV, E k (h) >_600 MeV 4 +6007/4 - 4 2 4 h ) 4 / 7 ,

Ek(h)=(212Ek-12.72xlO

El. > - 6 0 0 M e V , E k ( h ) < 6 O O M e V

These equations are essential for our theoretical model. Data from CIRA (1986) are used for the distribution of p(h) and h. The scale height is calculated for every altitude, which makes our model rather realistic. Figure 1 presents the electron production rate profiles by monoenergetic protons with energies 10, 20, 40 and 60 MeV. The maximum' of the q(h) - profiles are connected with particle absorption. Figure 2 presents the ionization profiles by protons from solar particle flux with spectrum (11) for energy cut-offs 10, 20, 30 and 40 MeV, which correspond to geomagnetic cut-off rigidities R = 150, 200, 275 and 350 MV, respectively. . . . . . .

100 .... 90

\\

80

\

\

\

"~

100

\

\

\\\

~

~

-

90

,

\

\

', \,

\\\

\,

\

\\

\

\\

"\

" 6 ~ ~ ~\ 2 0 4 0 ~ ~ 1 0 MeV -~:-'~7080 ~-

\\

\\

70 (D

\\\

60

..x:~ 60 -

,

\

\,

\,

~

4o ~v

50

....

'\ \ \

k\\

< 50

"\,,

\'\\

,

\\ ,,

/ /

4O 30

30 ~,, ,.,,,I i i,,,,,,I

1E-2 0.1

.....

1

,,,I

.....

.,I

, ,,,,,,,I

........

I

,,,,,,I

1E+I IE+2 IE+3 1E+4 IE+5 1E+6

Electron Production Rate (cm-3. s- 1) Fig. 1. q(h) - profiles by monoenergetic SCR protons with energies 10, 20, 40 and 60 MeV.

//

, ,,,,,,,I

IE-20.1 1 1E+I 1E+2 IE+3 IE+4 IE+51E+6 Electron Production Rate (cm-3. s-1 ) Fig.2. q(h)- profiles by SCR protons with spectrum (11) for energy cut-offs 10, 20, 40 and 60 MeV.

Discussion

The electron production rate maxima of the q(h) - profiles (Figure 2) are a factor of 2-3 higher than in Reid (1961) for several reasons. Our model takes into account also the lowest energy interval V, which increases the ionization losses of the particles according (2) and (9,10). In addition Reid (1961) used isotropic solar particle flux (11). Our results concern vertically penetrating SCR. Because of that the altitudes of the q(h) - maxima in our case are lower than q(h) - maxima by isotropic penetration. For example, the q(h) - maximum for 10 MeV on Figure 2 is situated at 65 km, but in Reid (1961) the same maximum is at 70 km. In the beginning of the particle penetration in the ionosphere the solar protons arrive in polar cap zones from a small space angle, i.e., almost unidirectionally (Velinov et al., 1974). A few hours after the beginning of a polar cap absorption event a certain isotropy of the solar CR sets in. During the next several days the space angle distribution of the protons becomes practically an isotropic one (Reid, 1961: Velinov, 1968). It must be noted that the spectrum (11) represents one of the most powerful solar proton events. The case considered here is an extreme one. A MODEL FOR COSMIC RAY DIFFERENTIAL SPECTRUM DURING CR INFLUENCE ON PLANETARY IONOSPHERES In almost all models until now the differential energy spectrum of galactic cosmic rays ( which takes part in the basic ionospheric expression (7)) was presented as a power function: D ( E ) : K E -~ (12) where ? ~ 2.6 is constant (Ginzburg and Syrovatskii, 1964; Hillas, 1972: Berezinsky et al., 1984). The simple equation (12) used up to now was not complete and caused some limits on the model. The energy spectrum of

Cosmic Ray Ionization at Terrrestrial Planets

1905

protons and other groups of cosmic ray nuclei only in range III is described by Velinov (1991). This spectrum has the following form: -,

where K, a andfl are constants, which are determined by Velinov et al. (1997). Comparison between (12) and (13) shows that (12) describes the spectrum only in the subinterval III-1, but the more generalized expression (13) describes well the whole region III, i. e., III-1 and III-2. It is clear that in the relativistic case, E >> 1, formula (13) becomes the expression (12). Spectrum with Account of Anomalous Cosmic Rays In the present work the primary differential energy spectrum of protons and other groups of cosmic ray nuclei will be obtained analytically not only in region III, but also in the entire region IV. These particles are anomalous cosmic ray ( hereinafter ACR ) component. Anomalous cosmic rays ( ACRs ), which include the elements H, He, C, N, O, Ne, and Ar, originate from interstellar neutral particles that have been swept into the heliosphere and ionized to form pickup ions, which are then convected into the outer heliosphere and accelerated to = 5 to 50 MeV/nucl. The bulk of ACR acceleration occurs at the solar wind termination shock (e.g., Jokipii, 1999), which would also be expected to accelerate (or re- accelerate) other species (Mewaldt, 1999). The improved generalized CR spectrum will be shown in the following form (Velinov, 1991: Zellhuber, 1999: Velinov et al., 2001) :

I)(1~): K ( I + E l - f l (1 + E)-~(arctan[s~ E - E l ) ] + 0.51+ x ( l + ~ z z ) (

arctan[S2~r(E-E2 )]+ 051

(14)

In the spectrum formula (14) the parameters K, a,/7, 7, x, y and z take part. The value of y which varies between 2.5 and 2.7 is set to 2.6. The calculation of the other parameters is done in the following way. By inserting six experimentally measured points (El, D~), one will get six unknowns K, a, /7, x, y, z. Such nonlinear systems are treated by Newton iteration (Press et al., 1991). For that purpose they are given in the following form: f(xl .......... x n ) = 0 , / = 1....... n. In the neighbourhood of x, each of the functions F~ can be expanded in Taylor series:

:,ix + <,x):

:,ix)+j=l ±

)<,.<,+o(<,..)

By neglecting terms of higher order and by setting f(x + dx) = 0, we obtain a set of linear equations for the correction vector dx 1 ?/ -

-

-

.

-

,:1

.......

,,.

j=O These equations can be solved by LU decomposition (Press et al., 1991). The corrections are then added to the solution vector xt: x2 = x ~ + dx ~ and the process is iterated to convergence. Iteration stops if either the sum of the magnitudes of the functions f is less than 104 , or the sum of the absolute values of the corrections to dx is less than 10 -7. The initial guess x (1: n ) is determined by the globally convergent Newton's method in the following way: We minimize f : F = ½ (f×f) and check at each iteration that the proposed step dx reduces F. If not, we backtrack along the Newton direction until we have an acceptable step. Because the Newton step is a descent direction for F, we are guaranteed to find an acceptable step by backtracking. The backtracking algorithm is discussed in more detail by Press et al. (1991). Results The recent cosmic ray data concern the beginning and the ascending part of solar cycle 23. In 1996 minimal solar activity - sunspot number (or Wolf number) W=8.6, was observed (Solar-Geophysical Data, 2000). In the next years the W number increases to 21.5 in 1997 and 64.3 in 1998, which is considered as near the average level of the solar activity (http://www.ngdc.noaa.gov/STP/SOLAR/SSN). It must be noted that the observed sunspot numbers W in the present solar cycle 23 are smaller than the predicted W (Mininni et al., 2000). We considered the recent solar cycles, 19 - 23, interval 1954 - 2000, to establish in a more reliable way the W values for minimal and average solar activity. In the Table 2 are shown the years of the beginning, the maximum and the end of solar cycles 19-23 as well as the corresponding minimal Wm and maximal WM. The value WM* for the 23 cycle is not

1906

P.I.Y. Velinovet al.

final, because W values are preliminary after September 2000. From Table 2 we calculate the average level of solar activity Wa for cycles 19 - 23: Wa = 77.8.

Table 2. Extremal Sunspot Numbers W for Solar Cycles 19 - 23 Solar Cycle 19 20 21 22 23 Mean of cycles 19-23

Beginning 1954 1964 1976 1986 1996

Maximum 1957 1968 1979 1989 2000*

End 1963 1975 1985 1995

Wm

WM

4.4 10.2 12.6 13.4 8.6 9.8

190.2 105.9 155.4 157.6 119.6" 145.7

Table 3. Cosmic Ray Data for Six Energies and Four Levels of Solar Activity E, GeV 0.18000 0.23000 0.10000 0.39000 0.10000 0.10000

E -2 E-I E +0 E +0 E +1 E +2

1 0.70250 0.13900 0.50000 0.90000 0.60839 0.12884

E +1 E +0 E +0 E +0 E +0 E -1

D~, particles / ( m2.sec.str.MeV/nucleon ) 2 3 4 0.56200 E +1 0.42150 E +1 0.28100 E +l 0.11120E+0 0.83400 E - I 0.55600 E - I 0.42098 E +0 0.34196 E +0 0.26294 E +0 0.90000 E +0 0.90000 E +0 0.90000 E +0 0.62928 E +0 0.64854 E +0 0.66743 E +0 0.12884 E -1 0.12884 E -1 0.12884 E -1

Table 3 contains a summary of the experimental data (E~, DO for six different levels of energy (Hillas, 1972: Jokipii, 1999: Moraal et al., 1999). For energies < 390 MeV, a strong modulation of cosmic ray intensity is observed. For each energy in the interval between the energies 1.8 MeV + 10 GeV, values for four solar activity levels are given in columns 1, 2, 3 and 4. Column 1 corresponds to Wm=9.8, the column 4 to average value Wa = 77.8, and columns 2 and 3 to intermediate values W=32.5 and W=55.1. They divide to equal parts the interval

[Wm,W ] Table 4. Computed Coefficients of Cosmic Ray Differential Spectrum (14) Coefficients K a Xfl Y Z

1 0.71481E+l 0.10324 E +1 0.92313 E +0 0.11887E +0 0.26244 E -5 0.26966 E +1

Values of coefficients 2 3 0.70615 E +l 0.70100 E +l 0.68728 E +0 0.46275 E +0 0.16313 E +1 0.15001E +1 0.99590 E - 1 0.65300 E - 1 0.57732 E -5 0.63916 E -5 0.25644 E +1 0.21209 E +1

4 0.69594 E +l 0.29146 E +0 0.20894 E +1 0.56167 E - I 0.69668 E -5 0.25154 E +1

In Table 4 the computed values of the coefficients K, a, fl, x, y and z in formula (14) for the four values of the experimental data are shown. In the Figure 3 are presented the first results from the computation of the differential energy spectrum (14) of primary protons - the predominant component in the composition of the galactic cosmic rays. In fact this Figure is based on the results in the Tables 3 and 4. In the Figure 3 are shown D(E) during different levels of the solar activity: curve 1 is for solar minimum. The other curves correspond to a slight increase of the solar activity. Curve 4 relates to an average level of solar activity. In such a way we have spectra for four W numbers between minimal and average solar activity.

Analysis The ratio of differential intensities of protons and helium nuclei (on an energy / nucleon basis) increases from 4 in the region IV, to 17.6 + 1.2 in the subinterval I I I - 1. The contribution of the other groups of nuclei (L, M, H, VH and SH) in the total spectrum is about 1 per cent (Webber, 1967). In the energy interval E > 1 GeV the main contribution of the generalized spectrum (14) is the term:

Cosmic Ray Ionization at Terrrestrial Planets

1907

0+E)-' In the interval between the energies 30 MeV - IGeV the first term gives the main contribution, i.e., formula (13). The differential spectrum D (E) in the energy range 1.8 MeV + 30 MeV is determined by the second term: x(l÷-~-z)(

arctan[s2(E-E2)]~c t-0.5]

The members with arctan are smoothing functions (Zellhuber, 1999). The values of the coefficients s,, s2, E1 and E2 are: sl = s2 = 40 and Ej = E2 = 65 MeV.

O Fig.3. The modeled differential spectrum D(E) of galactic CR protons and ACR for four levels of solar activity: curve 1 represents D(E) for solar minimum Wm = 9.8, Curve 2 for W =325, curve 3 for W =55.1 and curve 4 for average solar activity Wa =77.8.

"-

100

10

,':'~. '~:(..

1

d

.

• "."

~:~;~'

. ";4"

0.1

.~

0.01

1E-3 IE-3

,

,

,

i

0.01

,

,

,

i

,

,

i

0.1

i

1

,

,

,

i

10

,

,

,

i

100

E, GeV In this way the obtained improved spectrum (14) represents well the 1 l-year variations of galactic cosmic rays and ACRs which are one of the most important ionization sources in terrestrial and planetary atmospheres. The differential spectrum (14) can be used for computation of the electron production rate profiles (7) in the middle atmosphere and ionospheric CR layer (situated in the lower part of the D - region) for all latitudes including the polar regions, at which the ACR component is also taken into account. CONCLUSION An improved model for energetic particle ionization from CR intervals III, 1V and V ( i. e. galactic and solar CR and ACR particles) in a planetary ionosphere was presented in this paper. This model can be applied to terrestrial planets(Venus, Earth and Mars), which are almost spheres - see eqs. (5-10). For the Jovian planets oblateness effects must be included in the modified Chapman function. The electron production rate, together with the chemical and transport (winds, waves, drifts, electric and magnetic fields, etc.) processes in the upper atmosphere, determines the ionization - neutralization balance in the ionosphere and the parameters of the global electric circuit. In periods of high solar activity the role of the solar particle fluxes increases as a factor in the Earth's environment (Akasofu and Chapman, 1972, Velinov et aL, 1974; Whitten and Popoff, 1971), affecting the conductivities, currents, electric fields and energetic processes in the whole ionosphere and middle atmosphere. The effects of high-energetic solar particles in the terrestrial atmosphere (especially the stratosphere and ozonosphere) were recently investigated by Tassev et al.(1999) during the major proton flare from October 1989 in the maximum of the previous solar cycle 22. The solar proton event contributions to odd nitrogen concentrations in the polar middle atmosphere are found to be asymmetric with respect to hemispheres (Vitt et al., 2000a). The computed SCR contributions to odd nitrogen concentrations at 30 km are significant more often over the South Pole than the North Pole. The thermospheric contributions to odd nitrogen concentrations in the polar middle atmosphere are also asymmetric with respect to hemispheres. A stronger thermospheric influence in the stratosphere is computed over the South Pole than the North Pole. The evaluation of the sources and concentrations of odd nitrogen chemical species in the Earth's middle atmosphere is important for climate studies such as stratospheric ozone balance (Vitt et al., 2000a, b).

1908

E 1. Y. Velinov et al.

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