Heating Energy Input Rate for Chondrule Forming Region and Its Evolution

Introduction: Chondrules are believed to have formed through some sort of heating events in the early solar system. Although several heating mechanisms have been proposed to date, no one has been widely accepted. In this work, we attempt to reveal the gross feature of the heating events, especially the heating energy input rate, which is a product of the energy given to the chondrule-forming system by every heating event and the frequency of the chondrule-forming heating events, and its time variation. The energy input rate can be deduced without specifying any particular heating mechanism by using the fraction of chondrules in chon-drites and the age distribution of chondrules as constraints. Since the age distribution of chondrules is not well-determined, we estimate it first. Then, we make a simple model for chondrule formation and obtain the heaing energy input rate as a function of time by comparing model results with observations. Age Distribution: We compiled the 26 Al-26 Mg ages of twenty UOC chondrules from type 3.0-3.1 ordinary chondrites [1-4]. We do not include data from UOCs with petrologic sub-types higher than 3.3 because there is a possibility of age resetting by the mild thermal metamorphism [2, 5]. From this data set, we obtain age variation somewhere between 1 m.y. and 3 m.y. (the origin of the time is set to be the formation time of CAI) with a peak near 1.8 m.y., though many data show a large age error of > 0.5 m.y., making it difficult to estimate detailed age distribution. We consider the age distribution, showing a peak at ~2 m.y., well represents the general trend among chondrules from LL chondrites, although detail distributions should not be considered seriously. Mostefaoui and co-workers first indicated that there is a correlation between 26 Al-ages of LL3.0-3.1 chon-drules and their olivine and pyroxene contents [4]. This is further recognized as a correlation between 26 Al-ages and bulk volatile (Si, Mn, Na)/Mg ratios by Tachibana et al. [6], indicating that chondrule bulk chemical compositions changed with time. If we assume this correlation to the whole population of chondrules, we can estimate age distribution by applying bulk Si/Mg distribution of chondrules. Unfortunately, bulk analyses of Si/Mg ratios of LL3.0-3.1 chondrules are limited [e.g., 6, 7]. For this reason, we estimated the range of Si/Mg ratios among six types of chondrules (IA, IAB, IB, IIA,