Production of the Upper Atmospheric Sodium from Impinging Meteors

J. Geomag. Geoelectr., 36, 305-316, 1984

Nobuo MARUYAMA

The 1st Research Center of Technical Research and Development Institute, Defense Agency, Nakameguro, Meguro-ku, Tokyo, Japan

(Received January 29, 1983; Revised April 26, 1984)

The temperature dependent vaporization rate for meteoric particles is applied to estimate the production profile of the upper atmospheric sodium. It is shown that the earlier result estimated using a constant temperature that controls the vaporization process for meteoric particles leads to an underestimation of the thickness of the production profile. A typical production profile of sodium calculated by taking account of a mass distribution of the meteoric particles shows the peak height of about 93km and a thickness (10-1) of about 26km. This thickness is significantly wider than that of a usually observed sodium layer, so that effective removal process of sodium is required for shaping the sodium layer.

1. Introduction

The maintenance mechanism of the upper atmospheric sodium layer discovered about half a century ago has not yet been established.The sodium layer is usually observed in the height region of about 90km with a peak number density ranging from 103cm-3to 104cm-30f atomic sodium and a layer thickness(10-1) Of about 20km(GIBBON and SANDFORD,1971;MEGIE and BLAMONT,1977; SIMoNICH et al., 1979). The topside scale height of the layer is usually 1/2～1/3 of the atmospheric scale height in the same region, and a sharp cutoff of the bottomside is observed. The production source and the loss sink of atomic sodium are required to exist inside or near the sodium layer to maintain such a sharp profile. If this production source and loss sink were absent, the sodium layer would disperse within an order of several days due to diffusion. Atmospheric dust was suggested to be one of the important sources of atomic sodium (HUNTEN and WALLACE, 1967; DONAHUE and MEIER, 1967; Flocco and VISCONTI, 1973). It was formerly suggested that atomic sodium would be sublimated from the dust surface being warmed by the sunlight in the upper atmosphere. FIOCCO et al. (1974) estimated the dust temperature to be about 400K, and concluded that the dust distributing in an adequate height region might create the sodium layer. However, they adopted vaporization parameters for solid sodium which are not valid for the estimation of the dust sublimation. Apart from the dust-source hypothesis, some piece of evidence for upward transport

305 306 N. MARUYAMA of sea salt particles during the wintertime have been presented by HUNTENand GODSON(1967) and MEGIE et al. (1978). From the early stage of the investigation, the meteor ablation process has been proposed frequently as the source of atomic sodium (CHAPMAN,1939; JUNGE et al., 1962; GADSDEN,1968). This hypothesis is based on the fact that the meteor height ranges from about 80km to 100km, and that the sodium layer is enhanced during meteor showers (HAKEet al., 1972; ARUGAet a!., 1974; MEGIE and BLA- MONT,1977). In addition to the above, Na + , Si + and Fe + found in the upper atmosphere are considered of meteoric origin, and this makes the meteor hypothesis more plausible (ZBINDENet al., 1975). GADSDEN(1968) showed that the ablation profile of the meteoric particles having an initial radius ranging from 10-3cm to 3×10-2cm and entering into the atmosphere with an initial velocity of 25km Sec-1 were consistent with the required production profile of atomic sodium. In his estimation, however, he neglected the temperature dependence of vaporization for meteoric particles, so that the ablation profile was narrowed due to suppressing the commencement of vaporization in result. In the present paper, the meteor ablation as the production source of atomic sodium is calculated using the temperature dependent vaporization rate for meteoric particles. And the production profile of atomic sodium to evaluate more realistic features is estimated by taking account of a mass distribution of meteoric particles. The material constants required in the calculation for meteor ablation are estimated for the composition of chondrite as it is a representative of meteoric particles. An effect of atmospheric dust in the sodium layer is also discussed from the viewpoint of atomic sodium adsorption to the dust surface.

2. Vaporization Rate

Vaporization rate for various materials is known as temperature dependent (DUSHMAN, 1962). Accordingly, meteor ablation is considered to be controlled by such temperature dependence. However, the parameters characterizing the temperature dependence of meteoric particles are not consistent among authors due to the difference of meteoric materials assumed. In this paper, chondrite is assumed as a representative meteoric material that produces the atmospheric sodium, and the material constants including the above parameters to calculate the meteor ablation are tried to estimate as follows. In thermal equilibrium between the gas and other phases, the following Clausius-Clapevron's equation is established.

(1) where Q is the heat of vaporization of the meteoric material in cal mol-1, R the gas constant of 1.978ca1 mol-1 K-1, P the gas pressure in dyne cm-2, and T the temperature in Kelvin. When the heat of vaporization Q is assumed as Production of the Upper Atmospheric Sodium 307 a material constant, then the following equation is obtained.

(2) where C is an integral constant. The rate, W, of vaporization on the surface is obtained by employing the above pressure P as follows;

(3) where W is in g cm-2. sec-1, M the mean atomic weight of the gas, and R the gas constant expressd in 8.31×107 erg mol-1 K-1. The heat of vaporization Q tends to increase in the material with higher boiling temperature Tb (Fig. 1). When Q is assumed proportional to Tb with a proportional constant A, then both Q and C in Eq. (2) are estimated as follows;

Q=ATb, (4)

Fig. 1. The heats of vaporization for various materials tend to be proportional to their boiling temperatures with the proportional constant of 22.5cal mol-1 K-1 (solid line) Referred data; BUTsuRI-JOSUHYO (1978). 308 N. MARUYAMA

C=lnPb+A/R, (5)

where Pb is the gas pressure at the boiling temperature Tb and is equal to 1 atm of 1.02 × 106 dyne cm-2. If chondrite is assumed to be the typical material for meteoric particles, it is expected to be composed of much Si, Fe and other metallic elements. The boiling temperatures of these elements are near 3000K, so that this value is adopted to estimate C=25.2 and Q=67.5kcal mol-1, using A=22.3cal mol-1 K-1(Fig. 1). And the other material constant to calculate the meteor ablation are estimated on the basis of the chemical composition of chondrite (Table 1)as the mass density ρm=3.54 g cm-3 and the mean atomic weight M=24.3, respectively. The latent heat and the specific heat are estimated as Lm=Q/M=1.16×1011 erg g-1 and Cm=3R/M=1.03×107 erg g-1 K-1, respectively. Equation (3) can be expressed by using the above constants as follows:

(6)

where C1=1.90×107g cm-2 sec-1 K-1/2, C2=3.41×104K. These parameters are comparable to those adopted by KORNBLUM (1969) for "Opik stone" with C1=123×107g cm-2 sec-1 K-1/2, C2=3.11×104K, and are different from those adopted by LEBEDINEC and SUSKOVA (1968) for "Stone meteoroid" with

Table 1. Chemical composition of chondrite.

Composition ratio has been referred from RIKA-NENPYO (1971), and mass densities from BUTSURI-JOSUHYO(1978) and RIKAGAKU-JITEN(1975). Production of the Upper Atmospheric Sodium 309

C1=6.92×1010g cm-2 sec-1 K-1/2, C2=5.78×104K. The latter is more difficult to vaporize than the former or "chondrite" estimated here, and is similar to "Tektite" in Kornblum's Table where some of experimentally determined values are listed. On the other hand, the estimated specific heat Cm and the mass density pm are almost the same as those used by other authors (GADSDEN, 1968; LEBEDINEC and SUSKOVA, 1968; KORNBLUM, 1969). The estimated latent heat Lm is about twice a large as that for other authors, however, it plays a role in the energy equation for meteoric particle as Lm W which is not so different from "Opik stone" . The material constants estimated here seem natural for the composition of chondrite, so that these values are adopted to calculate the sodium production profile from meteor ablation. Apart from the vaporization of meteoric particles itself, FIOCCO et al. (1974) proposed the atmospheric dust being warmed by the sunlight to be the production source of the sodium layer. They adopted the temperature dependent sublimation rate applicable to solid sodium. However, the dust cannot be considered to be composed of pure sodium, and atomic sodium on the dust surface seems in chemical bond with neighboring atoms different from sodium. Generally, the heats of chemical bond are larger than that of the vaporization for solid sodium. For example, the heats of chemical bond analogized with the dissociation energies for Na-O2, Na-O, and Na-Cl (MURAD and SWIDER, 1979) are 55.8, 60.1, 97.2kcal mol-1, respectively; therefore, they are more than twice as large as that of the vaporization being 25.8kcal mol-1 (BUTSURI-JOSUHYO,1978). If such large heats are applied to evaluate the role of the dust, no possibility as to the production source of the sodium is obtained, i.e., the sodium sublimation from the dust surface is remarkably exceeded in number by the sodium adsorption to the surface in the sodium layer.

3. Ablation Equation for Meteoric Particles

The ablation equation for meteoric particles applied by GADSDEN (1968) to estimate the sodium production is improved by the use of the temperature dependent vaporization rate. As will be shown later, the ablation profiles calculated using the temperature dependent vaporization rate differ significantly from those calculated assuming a constant temperature that controls the vaporization process. The kinetic equation for spherical particle with a radius r and a velocity V in the atmosphere is expressed by;

(7) where pa is the mass density of the atmosphere. When the kinetic energy lost due to atmospheric friction is assumed to be converted to the temperature increase of the particle, to the latent heat of vaporization and to the thermal radiation from the surface, the energy equation is expressed by; 310 N. MARUYAMA

(g)

where, T and Ta are the temperatures of the particle and the atmosphere, respectively, and σ the Stefan-Boltzmann constant of 5.67 × 10-5 erg cm-2 sec-1 K-4. In this equation, the thermal radiation is assumed as black body. Strictly speak- ing, this assumption is not adequate for those particles with a radii smaller than about 10-4cm as discussed by FIOCCO et al. (1974). This assumption makes cool- ing efficiency for small particles somewhat overestimated, therefore, it makes the vaporization rate for them somewhat underestimated. However, the sodium is mainly produced by particles with an initial radii of 10-3cm～10-1cm, as described later, so that the thermal radiation as black body is assumed for simplicity. In the initial stage of the particle incident into the atmosphere, the energy input expressed in the left side of Eq. (8) is mainly dispensed for the temperature increase of the particle, and then, the energy dispensation for thermal radiation and vaporization from the surface becomes dominant. For simplicity, T>1500K, dT/dt<1000K sec-1 and r<10-2cm are assumed, then, the temperature increase of the particle can be neglected in contrast to the thermal radiation from the surface. In this case, almost all energy input is dispensed for the thermal radiation and the vaporization in which the ratio for the vaporization to energy input increases as shown by a solid line in Fig. 2. If the constant temperature of 2100K that controls the commencement of the vaporization, and that remains constant during the vaporization process is assumed, as GADSDEN(1968) adopted, the ratio

Fig. 2. Energy ratio dispensed for vaporization. Abscissa means total energy dispensed for vaporization and thermal radiation, and ordinate for vaporization divided by the total. Solid line is calculated using the temperature dependent vaporization rate and broken line assuming the constant temperature of 2100K that controls the commencement of vaporization and that remains constant during the vaporization. Production of the Upper Atmospheric Sodium 311 dispensed for the vaporization increases rapidly as shown by a broken line. It is clear that Gadsden's assumption suppresses the commencement of the vaporization and results in an underestimation of the height of sodium production. The decreasing radius of the particle is obtained from the following equation.

(9)

And, the vaporized mass E per unit height interval along the meteor flight-path is expressed as follows;

(10) where, θ is the incident angle of the particle measured from the zenith which isa ssumed as a constant during the flight. Above Eqs. (7), (8) and (9) are numerically integrated by putting dz/dt=-V cosθ to obtain the ablation profile by Eq. (10). The mass density ρa and the temperature Ta for the atmosphere are taken from Mean Atmosphere (LIRA, 1965). This model atmosphere is somewhat old, however, recalculations using later atmospheric models (CIRA, 1972; U.S. Stan- dard Atmosphere, 1976) will make little modification to the results presented in this paper. For example, the differences of atmospheric densities in the 100km height region are about 5 °lo. This corresponds to height' differences of about 0.3km of the same atmospheric density which is small in contrast to the size of the ablation profile of meteoric particles. Atomic sodium is assumed to be contained in particles homogeneously in the weight ratio of 0.7% (Table 1).

4. Production Profile of the Sodium

Here the ablation profile is defined as a quantity of atomic sodium ablated per unit height interval along the flight-path of an individual particle. An example of a particle with an initial radius of 10 - 2cm, an initial entering velocity of 20km sec - 1 and an incident angle of 45 deg is shown by a solid line in Fig. 3. As can be seen, the peak ablation occurs at a height of about 87km, and the thickness (10 - 1) of the profile is about 17km. For this particle, if a constant temperature of 2100K that controls the vaporization process, as mentioned previously, is assumed, the ablation profile will be narrowed as shown by a broken line. This assumption makes a thickness of about 11 km which is significantly narrow in contrast to the result calculated using the temperature dependent vaporization rate. Various heights of observed meteors are considered to be caused by the differences in various factors, such as their mass and the entering velocity into the upper atmosphere. The effects due to the mass and the entering velocity of the meteoric particle on the ablation profile were examined by using the 312 N. MARUYAMA

Fig. 3. Quantities of atomic sodium ablated per unit height interval along the flight path of the meteoric particle with the initial radius of 10-2cm, the incident velocity of 20km sec-1 and the incident angle of 45°. Solid line is calculated using the temperature dependent vaporization rate, and broken line assuming the constant temperature of 2100K that controls the vaporication process for meteoric particle.

temperature dependent vaporization rate, and the similar tendencies shown by GADSDEN(1968) were obtained, i.e., a particle with a smaller radius and/or a higher entering velocity ablates in a higher altitude region, and the effect due to the incident angle is little compared with them. The observed geocentric velocity distribution of visual meteors and that of radio meteors differ greatly. The former has a double humped velocity distribution with a maximum at 18km sec-1 and a secondary maximum at 65km sec-1, however, the latter has a single maximum at 36km sec-1 (HUGHES, 1978). Generally, the visual meteors correspond to larger particles compared with the radio meteors, so that the discrepancy of the velocity distribution between them implies that the mass distribution and the velocity distribution for meteoric particles are not independent. Their relation is not precisely known, therefore, a mass distribution of meteoric particles and a constant velocity as a parameter are assumed to calculate the production profile of the sodium. According to MILLMAN(1970), the mass distribution of interplanetary particles estimated from a number of oservational data such as meteors and interplanetary dust is given by;

dN∞m-(s+1)dm (11)

where, dN is the number of interplanetary particles with the mass ranging from m to m+dm, and s the distribution index of 0.6 for m<10-5g and 1.3 for 10-5g

Fig. 4. Production profiles of atomic sodium calculated by taking into account a mass distribution of the meteoric particles, and assuming the initial velocity of 30 km sec-1 (solid line) and 15km sec-1 (broken line). The incident angle of 45° is assumed in both cases. mass ranging from 10-8g to 10-2g, corresponding to particle radii ranging from 10-3cm to 10-1cm, and these particles in this range are vaporized almost completely. The production profile of the sodium is obtained by superposing individual ablation profiles by referring to the mass distribution. An example of the result calculated for an initial velocity of 30km sec - 1 and an incident angle of 45 deg as typical values is shown by a solid line in Fig. 4. The peak production occurs at a height of about 93km and the thickness of the production profile is about 26km which is significantly wider than that of the usually observed sodium layer. If an effective mechanism for shaping the sodium layer is absent, its thickness will be remarkably widened by eddy diffusion and also by the spread of velocities of meteoric particles. This mechanism appears to have a rapid response to the sodium production when compared with the characteristic time estimated of about 100 hours using the eddy diffusion coefficient of 106cm2sec - 1 and atmospheric scale height of 6km as a characteristic length. The rapid response to the sodium production and the stability of the sodium layer accord with the fact that an atomic sodium enhancement during a meteor shower returns to its normal level within 20 hours (MEGIE and BLAMONT,1977). A second example, covering initial velocity of 15km sec-1 and an incident angle of 45 deg, is shown by a broken line in order to compare the results with those obtained by HUNTENet al. (1980). They assumed a constant temperature of 2100K that controlled the vaporization process of meteoric particles and calculated the production profile of the sodium by referring to a mass distribution somewhat different from that adopted here and an independent velocity distribution having the mean velocity of 14.5km sec-1. They obtained a produc- 314 N. MARUYAMA tion profile showing a peak height of about 83km and a thickness of about 17km. This thickness is narrower than that of the usually observed sodium layer, and that shown by a broken line in Fig. 4 which has a large thickness of about 24km without velocity distribution. The above difference between the result obtained by Hunten et al. and that shown in Fig. 4 is mainly due to the temperature dependent vaporization rate adopted in this paper. The characteristic shape of the sodium layer is principally due to the height profile of the production source and that of the loss sink of sodium. Their relative intensity controls the basic shape of the sodium layer. A wider height profile off the sodium production source in contrast to that of the sodium layer requires an effective loss sink for sodium as mentioned previously. The loss sink or removal process for sodium is an important problem to be studied for understanding the sodium layer as an atmospheric phenomenon.

5. Discussion

Removal process for atmospheric sodium seems to play an important role in shaping the sodium layer. Although many chemical models including vertical diffusion were proposed (for example, GADSDEN, 1970; FIOCCO et al., 1974; RICHTER and SECHRIST, 1979; LIU and REID, 1979), they are insufficient to explain the behavior of the sodium layer after its sporadic enhancement. According to a quite recent observation of the time variation of the sodium layer, a tem- poral enhancement in the total content of atomic sodium is usually followed by a rapid decrease in the sodium density in the lower part of the layer which is difficult to explain by chemical processes (KAMIYAMA, 1982). SZE et al. (1982) adopted a new rate coefficient found 103 times faster than that previously reported for the reaction Na+02+M→NaO2+M, and examined its effect on the height distribution of atomic sodium by their photochemical diffusive model. A somewhat unrealistic production source for atomic sodium at the height of 100km is assumed, however, they showed that the nominal sodium layer could be created by using the rate coefficients variable in the range of uncertainties for proper chemical reactions, and concluded the need for signifi- cant revision of earlier aeronomic models for sodium. This examination implies fast conversion of the sodium between the atomic and molecular state, so that the chemical process seems to control principally the ratio of the sodium between them. In this case, another problem is likely to appear concerning what process removes the sodium from the upper atmosphere. Eddy diffusion is considered as one of the removal processes of the sodium, and its typical characteristic time is estimated to be several days. On the other hand, MEGIE and BLAMONT (1978) observed the decaytime for an enhancement of the sodium layer after a meteor shower to be less than 20 hours. If the lifetime of the sodium for removal from the sodium layer is assumed to be of this order, the above eivdence cannot be explained by the eddy diffusion only. HUNTEN et al. (1980) proposed the meteoric dust produced from reconden- Production of the Upper Atmospheric Sodium 315 sation of meteor vapor to be the sink for mesospheric sodium. Their calculation showed that the dust surface area makes the lifetime about 2 days for atomic sodium at the height of 90km. HUNTEN (1981) obtained the result that the basic character of the sodium layer could be explained by the source of meteor ablation with dust of meteoric origin as the sink. This idea seems quantitatively possible because of the role of the dust as evaluated previously, however, the chemical problems examined by SZE et al. (1982) are not included, and the production profile of atomic sodium and the dust particle is calculated on the same assumption as adopted by GADSDEN (1968) that leads to an underestimation of the thickness of the production profile as described previously.. Recent studies indicate that some of the time varying features of the sodium layer are caused by atmospheric waves (ROWLETT et al., 1978; SHELTON et al., 1980; CLEMESHA et al., 1981). A meteor shower also makes sodium layer time variable, and it is one of the natural tests for the sodium layer where physical and chemical processes are not precisely known. Continuous observations of the time varying layer during and after a meteor shower are desired for understanding the removal process of sodium in addition to the laboratory experiments of sodium chemistry.

6. Summary

Meteor ablation as a production source of the upper atmospheric sodium is evaluated using the temperature dependent vaporization rate for meteoric particles, which is estimated for a composition of chondrite as it is a representative. The ablation profile of the meteoric particle is significantly wider than earlier results estimated using a constant temperature that controls the vaporization process of the particle. A typical production profile of atomic sodium showing the peak height of about 93km and the thickness (10-1) of about 26km is obtained by taking account of a mass distribution of the meteoric particles, and by assuming the incident velocity of 30km sec-1 into the upper atmosphere.

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