A&A 383, L27-L30 (2002)
DOI: 10.1051/0004-6361:20020088
S. Goriely1 - J. José2 - M. Hernanz3 - M. Rayet1 - M. Arnould1
1 - Institut d'Astronomie et d'Astrophysique, Université
Libre de Bruxelles, CP 226, 1050 Brussels, Belgium
2 -
Departament de Fisica i Enginyeria Nuclear, Universitat
Politecnica de Catalunya, Av. Víctor Balaguer s/n,
08800 Vilanova i la Geltrú (Barcelona), Spain,
and Institut d'Estudis Espacials de Catalunya,
Ed. Nexus-201, C/ Gran Capità 2-4, 08034 Barcelona, Spain
3 -
Institut de Ciències de l'Espai, CSIC, Barcelona, Spain,
and Institut d'Estudis Espacials de Catalunya,
Ed. Nexus-201, C/ Gran Capità 2-4, 08034 Barcelona, Spain
Received 13 December 2001 / Accepted 13 January 2002
Abstract
He-accreting white dwarfs with sub-Chandrasekhar mass
are revisited. The impact of the use of an extended reaction network on the
predicted energy production and characteristics of the detonating layers is studied.
It is shown that the
considered scenario can be the site of an -process combined with a
p-process and with a variant of the rp-process we refer to as the pn-process. We define
the conditions under which the derived distribution of the abundances of the
p-nuclides in the ejecta, including the puzzling light Mo and Ru isotopes, mimics the
solar-system one.
Key words: hydrodynamics - nuclear reactions - nucleosynthesis - shock waves - stars: white dwarfs
The outcome of He-accreting sub-Chandrasekhar white dwarfs (WD) has deserved a special attention since the early 80's (e.g. Nomoto 1982; Woosley et al. 1986). Iben & Tutukov (1991) have investigated the evolution of a close binary system leading to the formation of a compact CO WD accreting He from a nondegenerate low-mass companion. Limongi & Tornambe (1991) concluded that such systems could in some conditions lead to explosive phenomena. Their relatively high estimated frequency, around 0.01 y-1(Iben & Tutukov 1991), have drawn attention to their possible connection with the progenitors of type Ia supernovae.
He-accreting CO WDs are not viewed today as the most likely candidates for such explosions (e.g. Höflich & Khokhlov 1996; Hillebrandt & Niemeyer 2000; Branch 2001), but they might well be responsible for some special types of events. In fact, some one-dimensional calculations (e.g. Woosley & Weaver 1994 and references therein) have concluded that He-detonations on the considered WDs could well be identified as peculiar supernovae, characterized by rapidly declining light curves with lower maximum luminosities than those reached by C-deflagration Chandrasekhar-mass WDs. These properties are reminiscent of subluminous supernovae like SN 1991bg. Multidimensional simulations have confirmed the onset of the He-detonation, but have revealed significant differences in the central C-ignition which may be triggered by the He-detonation (Livne & Arnett 1995; Garcia-Senz et al. 1999).
This Letter limits its focus to some aspects of the
surface He detonation which have not deserved much attention up to now. More
precisely, we want to test the classical practice of calculating the energy production
and associated nucleosynthesis through a nuclear reaction network made of
captures. This approach is
obviously unable to treat the production or captures of protons and neutrons
in the detonating layers as well as their impact on the energetics and the
nucleosynthesis of the He detonation. Concomitantly, we present the first detailed
calculation of the synthesis of the nuclides heavier than the iron peak in the considered
He detonation. These problems are tackled in the framework of a 1-D model of
the He detonation, the details of which are presented in
Sect. 2. Section 3 discusses the impact of the use of an extended reaction network on the
predicted energy production and characteristics of the detonating layers. The composition
of the ejected material is analyzed in Sect. 4. We demonstrate that the considered scenario
can be the site of an
-process combined with a p-process and
with a variant of the rp-process we refer to as the pn-process. We define the
conditions under which the derived distribution of the abundances of the
p-nuclides mimics the solar-system one.
Conclusions are drawn in Sect. 5.
We consider a non-rotating 0.8
CO-WD made of 30% C and 70% O by mass (Salaris et al. 1997). It is stabilized and cooled to an initial luminosity
,
the central density and temperature being
g cm-3, and
K. The accreted matter is He-rich (X(4He) = 0.98), and is
assumed to contain traces of other nuclides:
,
and
[X(i) is the mass fraction of
nuclide i]. As pointed out by
Woosley & Weaver (1994), the consideration of an initial non-zero
14N amount is critical.
The
mass fraction adopted here
results from the burning of H in the companion assumed to be of typical Pop I
composition, but its precise value is considered by Woosley & Weaver
(1994) not to be critical for the He detonation outcome. The accretion rate on the
CO-WD is adopted equal to
,
in agreement with the values
reported by Limongi & Tornambè (1991). The classical assumption
is also made that the accreted material has the same specific entropy as the outermost WD
shells. In these conditions, a thick He-rich envelope forms on the WD surface.
The evolution of this envelope is followed with a modified version of the code SHIVA
described by José & Hernanz (1998). It is a spherically symmetric, implicit,
hydrodynamic code in Lagrangian formulation which has been used extensively for the
modeling of classical nova outbursts. For the simulation reported here, a fine Lagrangian
mass grid of 400 shells is adopted. Shell masses range from
for the innermost shells to
for the outer layers.
The adopted nuclear reaction network is discussed in Sect. 3.
A thermonuclear runaway develops near the base of the He envelope when about
0.18
has been accreted. At this point, the density reaches a critical value
of about
allowing the transformation
.
When the temperature gets high enough, the resulting
transforms into
through
,
this
-particle consumption channel competing successfully with the
-reaction in the relevant temperature and density regimes (Hashimoto et al.
1986; also Piersanti et al. 2001). The associated energy release triggers the detonation of He. More precisely, two shock waves propagate inward and outward from
the He-ignition shell. The outward-moving He-detonation wave heats the matter to
temperatures around
.
The expansion velocities range from
in the vicinity of the He-ignition shell to more than
20000
when the front reaches the WD surface, which is achieved in only
.
The whole envelope is ejected into the interstellar medium.
The ingoing compressional wave pushes the inner WD material to velocities of nearly
.
Its temperature, however does not exceed
,
which does not allow to trigger the burning of carbon. The WD centre
is reached by the compressional wave after 0.7 s. As a result, carbon ignites, and
a second detonation develops near the centre.
The high temperatures encountered during the C-deflagration (
), as well as the
initial composition of the CO WD lead mainly to the production of iron-peak nuclei
and are not expected to affect the nucleosynthesis of the p-nuclei. For this reason, the
calculations do not follow the evolution of the inner part after C-ignition, so that only
the fate of the He-detonating envelope is modeled here.
The estimate of the energy released by the He detonation is generally derived from the use
of a limited network of some 50 nuclear reactions and 26 nuclides. In addition to the
-chains from He to Ni, it is made of the
14N(
C(
O and the C+C, C+O and O+O
reactions. Reverse photodisintegrations are also included.
Post-processing calculations based on a full network to be described
in Sect. 4 demonstrate that the detonation produces substantial amounts of neutrons and
protons through
and
reactions. They induce
nucleon capture reactions that modify substantially the nuclear flow predicted by the
limited network, and concomitantly the energetics of the detonation and the associated
nucleosynthesis. For these reasons, an extended nuclear reaction network inspired by the
post-processing calculations has been implemented in the hydrodynamic simulations. It
includes 188 nuclides up to 68Zn linked through a net of 571 nuclear reactions. These
reactions are selected on grounds of the fact that they contribute to more than one
per mil of the total energy generated at any timestep. They comprise neutron, proton and
-captures, as well as photodisintegrations and
-decays. Although the new
calculations are extremely time consuming, they are considered to be essential for a
reliable determination of the energetics of the He detonation and of the thermodynamics of
the He shells. In fact, the pre-explosion evolution at T<108 K is not affected by the
network extension. Differences are found at temperatures in excess of 109 K, where
a large number of reactions neglected in the reduced networks are responsible for an
increase of the energy deposited in the envelope. In our simulations, the reduced
network leads to a peak temperature of the He-burning shell of
K,
with a maximum rate of energy production of
erg/g/s,
while a peak temperature of
K and
erg/g/s are obtained with the extended network. The He-detonation wave hits the WD
surface a bit earlier (0.166 s) than with the reduced network (0.176 s). As an example,
we display in Fig. 1 the quite significant differences in the evolution of Tand
predicted with the two networks for a layer located about
above the base of the He-burning shell. In fact, the considered
layer is seen to experience a unique energy burst due to the
-chain of the
reduced network (involving solely
N=Z nuclei), and in particular to
20Ne
Mg
Si. The extended network leads
to an initial double energy burst, the first one being due to
14C
O, the second one resulting from radiative neutron
captures on the most abundant species. The reactions 18O
Ne,
followed by
22Ne
Mg and 26Mg
Si are indeed responsible
for a neutron density as high as
.
At later times,
the major energy burst results from the main
-chain burning. It develops
earlier than the peak obtained with the reduced network, this time shift being due to the
faster temperature increase predicted with the extended network. It is followed by a
secondary
peak resulting from the capture of protons produced by
reactions on
nuclei, and in particular on 44Ti, the mass fraction of which
reaches about
.
At the peak temperature of
reached in
this
layer, the proton mass fraction amounts to
.
![]() |
Figure 1:
Comparison of the evolution of the rate of nuclear energy production and of
temperature predicted with the reduced (dashed lines) and with the extended network
(solid lines) in a layer located about
![]() |
Open with DEXTER |
The composition of the
of ejected envelope is evaluated by a post-processing
nucleosynthesis calculation based on the temperature and density profiles derived from the
extended-network simulation described in Sect. 3. A full network including
some 50000 reactions on about 4000 nuclides up to Po and lying between the proton and
neutron drip lines is solved for each of the 100 envelope layers. All experimental and
theoretical reaction and
-decay rates are taken from the Nuclear Network Generator
of the Brussels Library (Jorissen & Goriely 2001). This network is also the one used
to define the minimum network that had to be implemented in the hydrodynamic simulations to
calculate the nuclear energy production in each layer of the model (Sect. 3). The
initial envelope composition is described in Sect. 2 for the light nuclei and assumed to
be solar above Ne.
As already explained in Sect. 3, the pattern of nuclear reactions developing
during the explosion is rather complex. Initially, a high neutron irradiation
(neutron densities
)
originating from
18O
Ne, and later from 22Ne
Mg and
26Mg
Si, drives most of the flow to the neutron-rich side of the
nuclear chart. A weak r-process ensues. However, the increase of temperature above
induces fast photodisintegrations driving the
matter back to the valley of
-stability, and even to its neutron-deficient side.
From this point on, two major nucleosynthesis processes take place.
In the layers with peak
temperatures
,
a typical p-process is found reponsible for the production
of the stable p-nuclides (Rayet et al. 1995). In these conditions, the nuclear flow is
dominated by (
), (
,p) or (
,
)
photodisintegrations,
complemented with mainly some neutron captures. For layers with peak temperatures
,
large amounts of 40Ca and 44Ti are produced by radiative
-captures.
Further
-captures proceed through (
,p) reactions, so that a so-called
-process develops, the resulting proton mass fraction reaches about
.
In the considered hot environment, these protons are rapidly captured
to produce heavier and heavier neutron-deficient species, making up a kind of
"proton-poor rp-process'', in view of the much lower proton concentrations than in the
"classical'' rp-process. In this process, some nuclei are produced with proton separation
energies that are small enough to experience
photodisintegrations which
slow down the nuclear flow. However,
reactions made possible by the high neutron density (at this stage,
)
revive the flow towards higher-mass nuclei by new p-captures. One
might thus talk about a "proton-poor neutron-boosted rp-process'', which we coin the
pn-process. The nuclear flow associated with this variant of the rp-process lies much
further away from the proton-drip line than in the classical rp-process. This results from
the lower proton and non-zero neutron concentrations encountered in the He detonation. A
detailed discussion of this pn-process nuclear flow and of the associated nuclear physics
uncertainties will be presented elsewhere.
![]() |
Figure 2: a) Final composition of the ejected envelope as a function of the mass number A. Full symbols denote the p-nuclides. b) Same as a), but the initial abundances of the s-nuclides is assumed to be 100 times solar. |
Open with DEXTER |
The final envelope composition is displayed in Fig. 2a. As a new nucleosynthesis
prediction associated with the He detonation, we note that almost all the p-nuclei are
overproduced in solar proportions within a factor of 3 as a combined result of the
p- and pn-processes.
This includes the puzzling Mo and Ru p-isotopes (Rayet
et al. 1995; Costa et al. 2000) which are efficiently produced at peak temperatures
.
The lighter Se, Kr and Sr p-isotopes are synthesized in layers heated to
,
being the most abundantly produced in these conditions.
The high sensitivity to temperature of the production of the A < 100 p-nuclei makes the
correct description of the corresponding layers (and thus the use of a suitably extended
reaction network) mandatory.
Figure 2a also makes evident that the Ca-to-Fe nuclei are overabundant
with respect to the p-nuclei but
by a factor of about 100, which implies that
the considered He detonation is not an efficient scenario for the production of the bulk
solar-system p-nuclides. In order to cure this problem, one may envision enhancing the
initial abundance of the s-nuclides, which are the seeds for the p-process.
Figure 2b shows that an increase by a factor 100 of the s-nuclide abundances
over their solar values makes the overproduction of a substantial variety of p-nuclides
comparable to the one of
and of the Ca-to-Fe nuclei. The factor 100
enhancement would have to be increased somewhat if the material processed in the core of
the CO-WD by C-detonation were ejected along with the envelope. At this point, one
essential question concerns the plausibility of the required s-nuclide enhancement. We do
not have any definite answer to this key question. The required s-process enrichment of
the accreting WD might result from its past AGB history if indeed some of its outer
s-process enriched layers could be mixed convectively (or due to rotationnal effects)
with part at least of the accreted He-rich layers before the detonation. Alternatively, the
He-rich matter accreted by the CO-WD could be (or become) enriched in s-process elements.
Such speculations (e.g. Iben & Tutukov 1991) need to be confirmed by detailed simulations.
In spite of this problem, we consider that the results presented here are encouraging
enough for justifying an extension of our calculations to other situations involving
CO-WD of different masses and accretion rates. These additional simulations will be
presented elsewhere, along with a detailed discussion of the characteristics and nuclear
physics uncertainties of the associated ,
pn- and p-process flows.
Acknowledgements
S.G. and M.R. are FNRS research associates. Work partially supported by the Spanish MCYT (J.J. and M.H.).