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

## 4. Comparison of the theoretical and observed spectra

Before making the comparison we must set the theoretical spectra to the same resolution as the observed spectra. This was done by the convolution of the theoretical spectra with the Gaussian profile:

where is the theoretical spectrum, is the convoluted spectrum and is the width of the Gaussian profile.

The spectra were computed for altitudes of 60 km, 40 km and 25 km. They are compared with the observed spectra in Figs. 8 - 10. The instrumental width was 3 Å at 60 and 40 km and 5 Å at 25 km. Since the velocity of the bolide at all altitudes is well known (approximately 20 km s-1 at 60 and 40 km and 15 km s-1 at 25 km) and the meteoroid composition was very probably not far from that of an H-chondrite, the only free parameter of the model is the meteoroid radius. We computed the spectra for fixed radii of 1.4 m, 0.42 m, and, at 25 km, also 0.14 m. The observed luminosity can be attained either by one large body or by a number of smaller bodies. We first evaluate the possible meteoroid radii from the total radiated intensity and then we will discuss the details of the spectra.

### 4.1. Total intensities, scaling laws

The assessment of the meteoroid radius from the bolide luminosity is a process analogous to the radiative radius approach used in Paper I. However, here we compare calibrated spectra in a well defined wavelength range and no doubts therefore arise because of the transformations of different magnitude systems.

In Table 1, the integral intensity (erg s-1 ster-1) in the wavelength range 4500-6600 Å, where the observed spectra were in good focus, and in a wider passband are given for three altitudes. The theoretical integral intensity increases between the altitude of 60 and 40 km by a factor of about 15, while the air density increases by a factor of 13.4. With the increase in the radius of the body from 0.42 to 1.4 m ( changes by a factor of 11.1) the intensity of the emitted radiation increases by a factor of about 12. Similar relations exist at altitudes 40 and 25 km. We will assume in the next simple estimates that the radiation intensity is proportional to the air density and to the square of the radius.

Table 1. Direct comparison of the modeled and observed intensities in a given passband at various altitudes and for different meteoroid sizes.

When comparing the observed intensity at 63.5 km with the theoretical data for 60 km (a factor of 1.5 in the air density), we see that the observed intensity corresponds to the body radius of about 0.7 m. For a density of 2 g cm-3 this gives a mass of 3000 kg, which is at the lower limit of our estimate of the initial mass from the progressive fragmentation model (see Paper I).

At altitude 40 km, the radius needed to explain the luminosity is 1.2 m (15,000 kg of mass). However, the meteoroid was already fragmented at this altitude. The luminosity can alternatively be explained by 8-10 individual fragments with a radius of 0.42 m (see Table 1), giving a total mass of 5000-6200 kg. The dynamic mass of the leading fragment at this altitude (Paper I) is, however, only 300 kg (radius of 0.33 m), so a larger number of smaller fragments probably existed.

The situation is even more complicated at 24.5 km. This is just before the main flare at 24.3 km and the bolide is very bright here. The luminosity could be formally explained by a single body of 1.3 m radius, 13 fragments of 0.42 m radius or about 180 fragments of 0.14 m radius (23 kg). In all cases, however, the total mass is too large, ranging from 18,000 kg to 4000 kg. The mass participating in the main flare was estimated to be no more than 1500 kg in Paper I. The explanation may be that catastrophic fragmentation had already begun at 24.5 km and so we are dealing with one or more clouds of fragments with an average density much lower than the bulk density of the meteoroid.

Therefore, by comparing the radiated energy in wide passbands, we conclude that meteoroid fragmentation severely affected the Beneov bolide radiation at an altitude of 25 km and also at 40 km. This is in accordance with our progressive fragmentation modeling performed in Paper I. Next we compare the shape of the spectra.

### 4.2. The shape of the spectra

In Figs. 8, 9, and 10, the theoretical and observed spectra at the altitudes of 60 km, 40 km, and 25 km, respectively, are given. Only the wavelength range where the observed first order spectrum is in sufficiently good focus is shown. Two computed spectra are given for each altitude, one for a single body with a radius of 1.4 m and one for a number of smaller bodies.

 Fig. 8. Comparison of the observed spectrum at altitude 63.5 km and the modeled spectra for meteoroid radii 0.42 m and 1.4 m at altitude 60 km and velocity 20 km s-1. Note the different scale for 1.4 m.

 Fig. 9. Comparison of the observed spectrum at altitude 40 km and the modeled spectra for 10 independent fragments with radii 0.42 m and one single body with radius 1.4 m at the same altitude. The velocity is 20 km s-1.

 Fig. 10. Comparison of the observed spectrum at altitude 24.5 km and the modeled spectra for 180 independent fragments with radii 0.14 m and one single body with radius 1.4 m at altitude 25 km. The velocity is 15 km s-1.

Both theoretical and observed spectra consist of a superposition of continuum radiation and atomic line radiation with an additional component from molecular bands. There are, however, differences in the number of lines and their strength relative to the continuum level. When comparing the computed spectra for the 1.4 m body we see a clear tendency for the decreasing of the role of lines and an increasing role for the continuum with decreasing altitude. The same tendency is present in the observed spectra where the continuum level is much higher at 24.5 km than at larger altitudes. However, the role of the lines is significantly higher at all altitudes in the observed spectra than in the 1.4 m spectra.

Decreasing the size of the body leads to an increase of the line radiation in the computed spectra, especially at lower altitudes. In this sense, the computed spectra of a large number of independent small bodies are closer to the observations at 40 km and 25 km than the spectrum of a single large body. This is in agreement with our conclusions from the total radiated intensity. However, significant differences in the theoretical and observed line radiation still remain. They are discussed in detail in the next section.

The shape of the continuum is similar in the observed and computed spectra. The observations show a very flat continuum at all altitudes in the given wavelength range. The theoretical spectrum for a 1.4 m body at 25 km shows a blue continuum but a 0.14 m body at the same altitude has flat continuum. At higher altitudes all computed spectra exhibit flat continua.

The continuum bears little information regarding its origin and it is difficult to say whether it is produced mostly by the vapor or by the air. In this respect the line radiation offers more possibilities for an analysis.

### 4.3. The line and band radiation

The number of lines included in the theoretical computations is large. For Fe I as many as 1717 lines were taken into account, even though some of them have rather low oscillator strength. On the other hand, such elements as Mn, Ti, Cr and Ni and molecular bands of oxides such as MnO and TiO2 have not been taken into account as yet.

If we ignore the above elements Mn-Ni, the comparison of the atomic lines in the observed and computed spectra shows that, despite of different intensities, the same lines are generally present in both spectra. All predicted atomic lines are present in the observed spectrum. Some of them are identified in Figs. 8 - 10.

Of the lines present in the observed spectrum but not in the theoretical spectrum, the most important are the Si II lines (6347 and 6371 Å). They belong to the second, high temperature spectral component and are visible at 63.5 km and weakly at 40 km. The theoretical spectra do not contain this line though temperatures of about 10,000 K are predicted to be present in the model (Fig. 3). Also, no atmospheric lines (i.e. lines of nitrogen or oxygen) are present in the computed spectra. In particular, the oxygen triplet at 6156-6158 Å, which is observed in fast meteors, is not present. This is in accordance with the observations (except of the peculiar N II lines) but somewhat surprising owing to the importance of the shocked air radiation in the model. The absence of Si II and of the air lines in the theoretical spectrum is explained by the presence of a dense vapor layer in the model. The cooler vapors are supposed to absorb the hot radiation originating from the vicinity of the bolide nose.

The intensities of the lines which are both observed and predicted are often different. The theoretical spectra are dominated by the lines of Mg I , Ca I and Na I , while the lines of Fe I are much fainter than in the observed spectra. Since the Fe I lines are very numerous this causes the different appearance of the line spectra.

To go deeper into the problem, both the observed and the theoretical spectra at 40 km have been analyzed (after subtracting the continuum and the band emissions) by the method of Borovicka (1993). The method computes the effective excitation temperature and the column densities of individual atomic species from the line intensities. Of course, neither the theoretical nor the real spectrum are produced at a single temperature. But Borovicka (1993) has shown that the single-temperature assumption can describe a meteor spectrum relatively well for not very fast bolides.

The results for the Beneov bolide at 40 km are given in Table 2. The effective excitation temperature of 5100 K was obtained for the observed spectrum. The theoretical spectra gave a temperature 1000 K higher but we do not consider this as a significant difference. More important is the difference in the column density of Fe I atoms. The observed spectrum yields more Fe I atoms along the line of sight by an order of magnitude. The presence of a large number of Fe I lines in the observed spectrum is a demonstration of this fact. On the other hand, the theoretical spectra give larger ratios of Ca I and Na I to Fe I by an order of magnitude. This is the reason why the lines of Ca I and Na I are so conspicuous in the theoretical spectra, although the intensity of Na I lines is in fact not significantly larger than their observed intensity.

Table 2. The analysis of the theoretical and observed spectra of the Beneov bolide at altitude 40 km. The precision of the effective temperature is about  K, other parameters have been determined within a factor of 2-3.

The situation at other altitudes is similar but there are also some differences. At 63.5 km, the wake was very strong and many of the bright lines in the observed spectrum originate in the non-equilibrium wake. The theoretical model, however, assumes local thermal equilibrium and cannot reproduce the wake spectrum. At 25 km, on the other hand, the agreement between the observation and the theoretical model is the best, though the Fe I lines are still underestimated. We included the computed spectrum for a 0.14 m body in Fig. 10. The 0.42 m spectrum is something between the 0.14 and 1.4 m spectra and is comparably good in comparison with the observations as the 0.14 m spectrum.

There are also molecular bands in the spectra. The MgO band near 5000 Å is one of the brightest features in the theoretical spectra. In the observed spectra, though present, it is much fainter. The MgO radiation is predicted to originate in the wake. Other molecules identified in the observed spectrum, FeO, CaO, and AlO, have extended band systems and do not form bright features neither in the observed nor in the computed spectra.

The theoretical spectra exhibit an apparent band radiation near 6504 Å which is not observed. It seems that the feature is produced by an interpolation error in the opacity tables but we were unable to identify the source of the error.

© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998