Astron. Astrophys. 351, 759-765 (1999)

3. Attenuation of X-rays and -rays

The absorption of the GRB energy by the gas and dust in the nebula would have occurred through the processes of photoelectric absorption and Compton scattering. The combined cross-sections due to these processes for the elements from H to Fe are plotted in Fig. 2. Solar abundance values were adopted for the nebula (Anders & Grevesse, 1989) and the photoelectric and Compton cross-sections for the elements have been used (Veigele, 1973) with the exception of molecular hydrogen (H₂) where a value of 1.25 times the elemental photoelectric cross-section was adopted (Morrison & McCammon, 1983). The photoelectric effect absorbs the photon completely but in Compton scattering only a fraction of the energy is removed per scattering and this fraction varies from 0.14 at 100 keV to 0.45 at 1 MeV. The product of the Compton cross-section by the fraction of the energy absorbed in the first scattering was used for the Compton cross-section and many scatterings may occur before the degraded photon is finally absorbed by the photoelectric effect. Decreasing the abundance of H and He by a factor of 10 relative to the solar value significantly reduces the cross-section below 1 keV and above 20 keV (Fig. 2b). The cross-section of Fe (Fig. 2d) is dominant between the K edge at 7.1 keV and 30 keV but the upper bound of 30 keV extends to above 50 keV for low abundance of H and He. Fe makes the major contribution to the absorption by the dust and is the key to chondrule formation.

Fig. 2. The combined photoelectric and Compton cross-sections relative to H as a function of energy, scaled by E/10 keV for clarity of presentation. (a) The elements H to Fe that are at least as abundant as Fe (H, He, C, N, O, Ne, Mg, Si, Fe) (b) the same elements as in (a) with solar abundance of H and He reduced by 10 (c) The precursor dust combination and (d) the element Fe.

The elements O, Si, Mg and Fe dominate the composition of the chondrules but the composition of the precursor grains has been the subject of much study and speculation (Hewins, 1997). A number of chondrule classification systems have been adopted and early approaches depended mainly on either bulk composition or texture or both. McSween (1977) recognised two main types, type I or FeO poor and type II or FeO rich. However in comparison with chondrules, the fine-ground matrix in chondritic meteorites is more FeO rich than even type II chondrules and it has been proposed that this matrix may be close to the composition of the chondrule precursor (Huang et al., 1996). In this scenario, the precursors of type I chondrules were enriched in Fe and more efficiently heated by x-ray and -ray absorption, resulting in the loss of Fe and other volatile elements that ended in the enriched matrix. Type II chondrules appear not to have lost significant amounts of volatiles in the melting process. The composition of the precursor grains may be resolved by new x-ray and -ray heating experiments. A composition consisting of solar abundance of oxides of Fe, Si and Mg or was assumed for the precursor grains and the product of the cross-section of this combination by abundance relative to H is plotted in Fig. 2c. The x-ray and -ray absorption efficiencies of different thicknesses of precursor grains, assuming a density of one, are given in Fig. 3 and grains in the range 10 µm to 1 cm are very efficient absorbers in the region where dust dominates the absorption (Fig. 2). This range agrees quite well with the measured Weibull and lognormal distributions of chondrule sizes (Martin & Hughes, 1980; Rubin & Keil, 1984). The deficiency of small grains is caused by low absorption efficiency and substantial radiation losses from grains with large surface to volume ratios.

Fig. 3. The absorption efficiency of different thickness of as a function of energy: (a) 10 µm, (b) 100 µm, (c) 1000 µm, (d) 1 cm, and (e) 5 cm.

The thickness of the dust layer converted to chondrules depends on the GRB spectrum which must have significant emission below 30 keV where dust absorption dominates (Fig. 2) and also on the mixture and distribution of gas and dust in the nebula. For a GRB with 10⁵³ ergs and an assumed spectrum = -1, = - 2 and = 15 keV (Fig. 1), the fraction of GRB energy photoelectrically absorbed by the dust is 20%, increasing to 27% for a factor 10 reduction in H and He. In the simplified case of solar abundance and a uniform mix of gas and dust, the thickness of the chondrule layer created is 0.18 g cm^-2 corresponding to one optical depth for 30 keV x-rays. The layer thickness increases to about 0.8 g cm^-2 and 2.0 g cm^-2 for optical depths to 40 keV and 55 keV x-rays with H and He abundances reduced by factors of 3 and 10 respectively. The thickness of the chondrule layer is therefore controlled by the degree of gas depletion from the nebula. The minimum GRB fluence required to produce chondrule layers of 0.18, 0.8 and 2.0 g cm^-2 is 1.8 10¹⁰, 7.0 10¹⁰ and 1.5 10¹¹ ergs cm^-2, adopting 20%, 23% and 27% absorption by the chondrule precursors and 2 10¹⁰ erg g^-1 for heating and melting. A fluence of 10¹¹ erg cm^-2 implies a distance of about 100 pc to the source for an output of 10⁵³ ergs radiated isotropically. The GRB would also form a layer of chondrules over a large area (10³ - 10⁴ pc²) in a nearby molecular cloud provided large precursor grains had already formed (Weidenschilling & Ruzmaikina, 1994). The process of chondrule amalgamation might be sufficient to trigger star formation over this region. In this case chondrule formation precedes cloud collapse and star formation. The existence of pre-solar grains in meteorites is well established (Zinner, 1996) but there is no evidence for pre-solar chondrules.

The chondrules cooled at a much slower rate than if they were isolated (Hewins, 1997). They may have been warmed by a fading source or by forming a thermal blanket or a combination of both effects. BeppoSAX discovered x-ray afterglow from GRB sources and the limited measurements show considerable variability between the various GRBs (Costa et al., 1997; Piro et al., 1998). The afterglow typically decreases by at least a factor of 20 in 10³ s which yields more than a factor of two drop in temperature. This decrease of 3800 K hr^-1 is too rapid to account for the chemical and textural properties of chondrules (Yu & Hewins, 1998). The chondrules on the far side of the layer from the GRB source cool even more rapidly because of shielding by foreground chondrules and spectral softening of the afterglow. The optical depth of the chondrules to their infrared radiation at a peak of about 1.5 µm is about 0.25 g cm^-2 assuming all the chondrules have size 0.1 cm (Hood & Horanyi, 1991; Wood, 1988). The x-ray and infrared optical depths are comparable and the cooling rate was further reduced by this thermal blanket.

There are several indicators that the dust was concentrated and/or gas depleted in the nebula when chondrules formed. These include: (1) the increased rate of collisions between plastic and molten chondrules to form adhering pairs (Wasson, 1993), (2) the seeding of melted chondrules with dust grains (Connolly & Hewins, 1995), (3) the O/H ratio well above the solar value (Fegley & Palme, 1985), and (4) the improved absorption efficiency of x-rays and -rays by the precursor dust balls. The rims on chondrules indicate time spent in dusty regions.

© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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