Astron. Astrophys. 346, 831-842 (1999)

1. Introduction

Exploding massive stars, and supernovae in particular, are known to be major sites for the production of a large variety of elements heavier than carbon. One of the few available ways to study the physics in the deep interior of such stars is the determination of the abundances of stable nuclides freshly produced and ejected by the explosion. Infrared, optical, and X-ray spectroscopic measurements are capable of determining elemental abundances in the photosphere during different phases of the outburst. But the results from such observations are, in general, sensitive to the models of line excitations in the photosphere, resulting in large correction factors to be applied before deducing the isotopic yields at the time of the explosion. In addition, results are hampered by the uncertainty of the optical depth, and by the possibility of heavy element condensation into dust shortly after the explosion, as was witnessed in SN 1987A.

A more direct probe of massive-star interior physics is, in principle, to investigate unstable nuclides and to measure the -rays associated with their decays after they have been ejected by the supernova explosion. For an optimum probe, the mean lifetime of such a radioactive isotope should range from around a few weeks up to about 10⁶ years. The lower limit is set by the requirement that the ejecta should become optically thin to -rays in a few decay times, and the upper limit by instrumental sensitivities of -ray telescopes (the -ray flux from a trace isotope must exceed the instrumental noise level, presently in the range of 10^-5 photons cm^-2s^-1, which corresponds, for instance, to (several times) of an intermediate-mass isotope with a lifetime of y at the Galactic center or to of the isotope in a supernova at a distance of a few hundreds of pc).

Furthermore, whereas short-lived isotopes will clearly trace individual events, long-lived ones with mean lifetimes of the order of 10⁶ y or longer will reflect a superposition of different supernovae at different times, mixed with interstellar matter. Consequently clues to abundances in an individual object are only very indirect.

Only a few isotopes fulfill those constraints (see e.g. Diehl and Timmes 1998). Most promising cases are found among the Fe group elements, primarily because of their expected large abundances. The 0.847 and 1.238 MeV -ray lines from the ⁵⁶Co Fe decay (half-life: = 77 d) were detected from SN 1987A (Matz et al. 1988; Sandie et al. 1988; Mahoney et al. 1988; Rester et al. 1988; Teegarden et al. 1989). There is also evidence for these decay lines from the unusually fast and bright Type Ia supernova 1991T (Morris et al. 1995, 1997). The ⁵⁷Co Fe decay ( = 272 d) is another probe: the 122 and 136 keV lines were detected from SN 1987A (Kurfess et al. 1992; Clayton et al. 1992). Cases at the upper end of the favored radioactive lifetime range are ²⁶Al ( = 7.4 y) and ⁶⁰Fe ( = 1.5 y). The 1.809 MeV line from the ²⁶Al decay has been detected and mapped along the entire plane of the Galaxy (see review by Prantzos & Diehl 1996). If supernovae, rather than Wolf Rayet stars, were responsible for this ²⁶Al, the lines from the ⁶⁰Fe decay would be expected simultaneously with the ²⁶Al decay, identifying a supernova origin (review by Diehl and Timmes 1998). Instrumental sensitivity appears just at the borderline for this test.

In this paper, we focus our discussion on ⁴⁴Ti, which decays with = 60 y (Ahmad et al. 1998; Görres et al. 1998; Norman et al. 1998; Wietfeldt et al. 1999), making it ideal for a study of inner-supernova physics within young supernova remnants. ⁴⁴Ti decays almost uniquely to the 2nd excited state of ⁴⁴Sc, followed immediately by the almost unique decay of ⁴⁴Sc ( = 4 h) to the 1.156 MeV excited state of ⁴⁴Ca. The 1.156 MeV de-excitation line has indeed been observed by the COMPTEL telescope on the Compton Observatory from Cas A, a young supernova remnant with an estimated age of 320 y (Iyudin et al. 1994, 1997; Dupraz et al. 1997). The measured -ray flux is photons /cm²/s (Iyudin et al. 1997) concordant with an upper limit obtained by the OSSE instrument (The et al. 1996). With an adopted distance to Cas A of 3.4 kpc (Reed et al. 1995) and the laboratory decay rate, the inferred initial mass of ⁴⁴Ti is (Iyudin et al. 1997; Woosley & Diehl 1998).

The current model predictions of the ⁴⁴Ti initial mass lie in an approximate range of for Type-II SNe (Woosley & Weaver 1995; Thielemann et al. 1996), and of for Type-Ib SNe (Woosley et al. 1995), more or less strongly depending on the progenitor masses. Higher values up to were obtained in some of the Type-II SN models, when progenitor masses above 30 combine with high explosion energies (Woosley & Weaver 1995), and for a 20 (SN1987A) model star (Thielemann et al. 1996). Barring the possibility that the progenitor of Cas A happened to be such a star, one may conclude that COMPTEL observed significantly more ⁴⁴Ti than expected (see, e.g., Fesen & Becker 1991; Hurford & Fesen 1996 for discussions on the progenitor characteristics).

As far as its -decay properties are concerned, ⁴⁴Ti is a very interesting trace isotope, because its decay mode is pure orbital electron capture, which means that fully ionized ⁴⁴Ti is stable. Even partial ionization of the innermost electrons should lead to a considerably longer effective half-life (Mochizuki 1999). Therefore, the question arises whether in supernova remnants ⁴⁴Ti could be highly ionized and thus more stable for a considerable period of time during the evolution. In this case, it would be incorrect to use the half-life measured in the laboratory, and initial abundances of ⁴⁴Ti as deduced from -ray intensities could be too high.

However, there is no simple answer to this question and, as we shall emphasize below, the thermodynamic history of a remnant has to be known in detail before firm predictions can be made. On the other hand, it is interesting to speculate whether the COMPTEL observations, which indicate an amount of ⁴⁴Ti in Cas A that appears higher than expected, reflect the effects of an increased lifetime of the explosively-produced ⁴⁴Ti because of temporary and partial ionization.

The primary aim of the present paper is to outline possible implications of (partial) ionization on the observable -ray line flux from the decay of ⁴⁴Ti. We shall present results obtained for a variety of different conditions, based on a simple model for young supernova remnants which, nonetheless, accounts for the features most relevant to this question. Of course, our main focus will be on Cas A, the best studied case, and the parameters of the model are chosen accordingly.

Sect. 2 contains an overview of observational aspects of SN explosions and remnants which are of relevance in the context of this work. In Sect. 3, we describe the employed model for young supernova remnants, i.e., the analytic model of McKee & Truelove (1995), augmented by a description of the reverse shock interacting with denser cloudlets (Sgro 1975; Miyata 1996). In addition, we describe the microphysics used in the model on which the calculation of the "effective" decay rate of ⁴⁴Ti is based. In Sect. 4, we present our results for the time variation of the ⁴⁴Ti decay rate, the ⁴⁴Ti abundance in young supernova remnants and the associated -ray activities that can be measured. As a specific example, we will preferentially use the case of Cas A. Summary and conclusions are given in Sect. 5.

© European Southern Observatory (ESO) 1999

Online publication: June 17, 1999
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