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Astron. Astrophys. 337, 591-602 (1998)

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2. The model

In general, the flow pattern around a meteoroid penetrating through the atmosphere or around aerodynamically interacting fragments should be modeled using three-dimensional radiation hydrodynamic codes. However, to obtain the detailed spectral and angular dependencies of the radiation field in the 3D geometry is a formidable task. Moreover, observations do not give us the necessary input data on the sizes of fragments, their relative position, and shape. In case of the Beneov bolide, only a few fragments were resolved spatially (see Paper I). To predict the spectra we will therefore analyze only two limiting cases - individual motion and radiation of one or several fragments and a liquid-like cloud of fragments and vapor with a common shock wave. In both cases we will use the one-dimensional ablating-piston single-body model (Golub' et al. 1996a).

The emerging spectra are determined by conducting radiation-hydrodynamic simulations taking into account ablation and radiation transfer in the air and the meteoric vapor. The local thermodynamic equilibrium is assumed for the gas. In the following we review the spectral opacities used and give examples of the resulting thermodynamic configuration and the emerging spectra. In Paper I, the spectra were integrated over the wavelength providing theoretical luminous efficiencies for meteoroids of various sizes.

2.1. Spectral opacities

The model assumes a strict boundary between the atmosphere and the vapor layer. The opacities of the air and the vapors are therefore taken separately. The air opacities were taken from Avilova et al. (1970) and Romanov et al. (1993). Detailed tables of spectral opacities of chondritic material at different temperatures and densities were computed in Kosarev et al. (1996). The opacity tables were further improved for this work taking into account more chemical elements and increasing the number of wavelength points to describe better the line shapes. The methods of calculation were in general the same as in Kosarev et al. (1996). The main new features are the following:

a) The chemical composition of the chondrite vapor was modeled by 166 chemical compounds arising from a mixture of 10 elements: Fe-O-Mg-Si-C-H-S-Al-Ca-Na. In Kosarev et al. (1996) only the first four elements were taken into consideration. The lines of calcium and sodium proved particularly important in the resulting spectra.

b) Besides O2, FeO, MgO and SiO the absorption in bands and the continuous spectrum of diatomic molecules CO, CO+, H2, MgH, OH, FeH, SiH, SiH+, CS, SiS, S2, SO, SH, AlO, AlH, CaO, CaH, NaH, Na2 was taken into consideration. The data for these molecules have been obtained from different published works, e.g. for the important molecule CaO the work of Hedderich & Blum (1989) was used. Absorption in the infrared bands of MgO was also added (Diffenderfer et al. 1983).

c) The absorption by triatomics H2O, CO2, SO2 was also considered. The cross sections for the water vapor were compiled up to 8000 cm-1 from the data found in Young (1977), Soufiani et al. (1985), Hartmann et al. (1984), Phillips (1990). Beyond 8000 cm-1 the absorption by the overtone bands was calculated by means of the HITRAN 92 total band intensities (Rothman et al. 1992). The parameters for CO2 and SO2 were taken from HITRAN 92 as well.

d) The absorption in the fundamental bands and overtones of the added diatomic molecules was calculated by using the slightly modified just overlapping line approximation (Penner 1959; Sulzmann 1973).

e) The broadening due to the interaction with hydrogen atoms was added in the calculation for the width of the atomic lines (Deridder & Van Rensbergen 1976).

f) The spectroscopic constants for some additional lines of Fe I observed in the Beneov spectra were taken from Nave et al. (1994).

g) The number of points for the photon energy grid was increased up to almost 20,000 (in the "old" tables there were about 10,000 spectral intervals). This allowed us to describe the line emission with better resolution.

The average chemical composition of several types of meteorites was given in Jarosewich (1990). For the modeling of the Beneov radiation we used the H-chondrite composition which is sufficiently close to the composition of other chondrites for our purposes. The H-chondrite abundances (by weight) are: SiO2 - 36.6%, FeO - 10.3%, MgO - 23.26%, Fe(metallic) - 15.98%, FeS - 5.43%, C - 0.11%, H2O+ and H2O- - 0.44%, Al2O3 - 2.14%, CaO - 1.74%, Na2O - 0.86%. In addition H-chondrites typically consist of TiO2 (about 0.12%), CrO3 (0.5%), MnO (0.3%) and Ni (about 1.6-1.75%). However, Ti, Cr, Mn and Ni have not been included in the calculations of the composition and opacities of the vapor.

Conserving the proportionality in number of atomic nuclei we obtain the corresponding element fractions in particle number: Fe - 11.484%, O - 51.836%, Mg - 15.428%, Si - 16.287%, S - 1.651%, Al - 0.561%, Ca - 0.830%, Na - 0.371%, C - 0.245%, H - 1.306%. The analysis of the composition of vapor shows that the number fraction of Fe I and Mg I is rather stable at temperatures 4000-6000 K and is close to the above mentioned fractions of these elements. The fraction of Na I , Ca I and Al I substantially decreases at temperatures of about 5000 K due to ionization.

As an example of the dependencies of the absorption coefficients on the photon energy, the results for pressure [FORMULA] bar and several temperatures of the H-chondrite vapor are presented in Fig. 1.

[FIGURE] Fig. 1. Spectral opacities for H-chondrite vapor at different temperatures under pressure [FORMULA] bar.

2.2. Thermodynamic configuration

The thermodynamic configuration of the vapor and the atmosphere around the ablating body is a result of the radiation-hydrodynamic simulations. As a typical example we present here the simulations for the H-chondrite body with radius [FORMULA] m, velocity [FORMULA] km s-1 and altitude of flight [FORMULA] km.

The distribution of the brightness temperature in the panchromatic passband (left side) and the real temperature (right side) versus the radius R and the distance Z from the blunt nose of the meteoroid is given in Fig. 2. In Fig. 3 (upper panel) the maximal temperature of the air ([FORMULA]) and of the vapor ([FORMULA]) and the maximal brightness temperature ([FORMULA]) in each cross-section are given versus the distance Z. In the lower panel of Fig. 3 the ratio [FORMULA] of the density at the point of maximum brightness to the undisturbed atmospheric density [FORMULA] ([FORMULA] g cm-3 at altitude 40 km) is given. At the distances Z of 2-20 m, where the temperature of the vapor falls down to 0.35-0.55 eV (4000-6000 K) and the radiation is emitted mainly in the visible range, the typical density is about [FORMULA] g cm-3. It is interesting to note that the brightness temperature [FORMULA] closely follows the vapor temperature [FORMULA] and is lower by a factor of two than the air temperature [FORMULA].

[FIGURE] Fig. 2. Distribution of the brightness temperature in the panchromatic passband (left side) and the real temperature distribution (right side) computed in the framework of the ablation model for the body radius 0.42 m, velocity 20 km s-1, and altitude 40 km.

[FIGURE] Fig. 3. a Maximal temperature of the air ([FORMULA]), of the vapor ([FORMULA]) and the brightness temperature in the panchromatic passband ([FORMULA]) in the cross-section of the bolide versus the distance along the axis Z. b The ratio of the density [FORMULA] at the point of maximum brightness to the undisturbed atmospheric density [FORMULA] g cm3.

In Fig. 4 the radius [FORMULA] corresponding to the maximum brightness temperature [FORMULA] in the cross-section is shown. The maximum radius of the volume with the brightness temperature of about 0.4 eV and a density of (1-5)[FORMULA] g cm-3 is about 0.8 m, i.e. twice the radius of the body. The length of this bright part of the luminous volume is about 2-6 m. The size of the luminous volume in the first approximation is proportional to the size of the body.

[FIGURE] Fig. 4. Radius [FORMULA], corresponding to the maximum of brightness temperature in the panchromatic passband in the cross-section of the bolide, versus distance along the axis Z.

2.3. Theoretical spectra of radiation

Theoretical spectra represent the sum of radiation of all regions up to a distance of 200 m behind the body. The radiation is averaged over all directions. The theoretical spectrum for altitude 40 km, meteoroid velocity 20 km s-1 and radius 0.42 m is given in Fig. 5a and b. The spectrum in the whole spectral range is shown as a function of photon energy [FORMULA] (Fig. 5a). It should be noted that large part of the emitted energy is out of the registration passband of photographic networks. The part of the spectrum corresponding to the panchromatic passband is presented in Fig. 5b as a function of wavelength.

[FIGURE] Fig. 5a and b. The theoretical spectrum at altitude 40 km for body radius 0.42 m and velocity 20 km s-1: a in whole spectral range, b and in the panchromatic passband. The length of the luminous volume was limited by [FORMULA] m.

The computed spectrum is formed by a superposition of a continuum radiation and emission lines and bands. The maximum of the intensity is reached by several narrow atomic lines in the 1.9-2.6 eV region. However, large amount of energy is emitted by a high continuum level and relatively broad band emissions in the region 0.9-1.7 eV. This region (7000-14,000 Å) is out of the photographic panchromatic passband, but is partly covered by the satellite-based infrared detectors which are sensitive up to 10,500 Å (Tagliaferri et al. 1994). We should underline that the spectrum in the wavelength range of the Satellite Network (SN) sensors, i.e. 1.1-3.1 eV, is substantially different from the spectrum in the panchromatic band and in the visible range. This means that it would be erroneous to use observational data from the ground based photographic systems directly for the calibration of the Satellite Network data and vice versa.

The contribution of different parts of the luminous volume to the total spectrum is demonstrated in Fig. 6. Spectral radiation cut off at some distances Z from the bolide nose is shown. The maximum of the spectra gradually moves from the UV range, i.e. 4.5-5.5 eV at Z = 0.1 m, into the visible and IR range, i.e. 1.5-3.5 eV at Z = 6 m. The role of lines in the spectra increases with the distance Z when new, colder and colder regions are taken into account. The region of the nearby wake at a distance of several diameters of the body, is mainly responsible for the emission in the panchromatic wavelength range, while the bolide's head is mainly responsible for the UV emission, and the far wake for the emission in the IR.

[FIGURE] Fig. 6. The theoretical spectra at altitude 40 km for [FORMULA] m, [FORMULA] km s-1, and different lengths Z of the luminous volume.

The dependence of the total energy loss radiated in the whole spectrum ([FORMULA]), in the wavelength range of the SN sensors ([FORMULA]), and in the panchromatic passband ([FORMULA]), on the distance Z is given in Fig. 7. The value of [FORMULA] shows virtually no change for Z larger than about 20-50 m, while the total losses ([FORMULA]) and the output in the SN sensor wavelength range ([FORMULA]) continue to grow, since a large amount of energy, mainly in the IR, is emitted by the rather cold part of the bolide. The total energy losses exceed the output in the panchromatic wavelength range by a factor of three.

[FIGURE] Fig. 7. The fractions of the kinetic energy loss radiated in the whole spectrum ([FORMULA]), in the satellite sensor wavelength range ([FORMULA]) and in the panchromatic passband ([FORMULA]) as functions of the distance Z from the meteoroid nose for [FORMULA] km, [FORMULA] m, [FORMULA] km s-1.

The dependence of the theoretical spectra on altitude and meteoroid size will be discussed in Sect. 4.2in connection with a comparison to the observed spectrum.

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© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998