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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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