Table Of ContentNuclear and Gamma-ray Production by Supernova Ejecta
Brian D. Fields,1,2 Michel Cass´e,3 Elisabeth Vangioni-Flam,1 and Ken’ichi Nomoto4
1Institut d’Astrophysique
98 bis, boulevard Arago, Paris 75014, France
6 1Department of Physics, University of Notre Dame
9
Notre Dame, IN 46556 USA
9
1
2CE-Saclay, DSM/DAPNIA/Service d’Astrophysique
n
91191 Gif sur Yvette cedex, France
a
J 3Department of Astronomy and Research Center for the Early Universe
9
University of Tokyo, Tokyo, Japan
1
v
2
3
0
1
0 ABSTRACT
6
9 The fastest ejecta of supernova explosions propagate as a precursor to the main
/
h supernova shock wave, and can be quite energetic. The spectrum of such fast ejecta is
p estimated based on recent analytic and numerical supernova models, and found to be a
-
o power law having a cutoff at an energy of order 10 MeV/nucl, the precise value of which
r depends on the supernova mass and energetics. With cutoffs in this range there can be
t
s
significant flux with energies above the thresholds for γ-ray and Li, Be, and B produc-
a
: tion. These nuclear interactions should inevitably accompany the passage of prompt
v
i supernova ejecta through the surrounding medium. The fast particle composition is
X
that of the outermost layers of the progenitor; if the progenitor experienced significant
r
a loss of its envelope to a companion or by mass loss, then the composition is nonso-
lar, and in particular, metal-rich. Such a composition and spectrum of fast particles
is required to explain the recent COMPTEL observations of γ-ray emission in Orion.
Supernova ejecta from one progenitor having lost a large amount of mass are shown to
quantitatively account for the Orion γ rays, and to imply the presence of other, weaker
lines and of a supernova explosion in Orion in the last < 104 years. Implications for
∼
this mechanism as a mode of nucleosynthesis, and as a potential supernova diagnostic,
are discussed. Model dependences and uncertainties are noted, and the need is shown
for accurate measurements of γ-ray and spallation production cross sections at energies
near threshold.
Subject headings: acceleration of particles—gamma rays:theory—nuclear reactions, nu-
cleosynthesis, abundances—supernovae:general
1
1. Introduction 2. Composition and spectrum of ener-
getic massive star ejecta
An exploding supernova is one of the most
powerful engines in the Galaxy. Modern super- Considerasupernovaexplodinginsomemedium,
nova models predict that the ejecta should have e.g. the ISM or, in the case of Orion, a molecular
adistributioninvelocity, withtheoutermostlay- cloud. Theejecta willinteract withthismedium,
ers being ejected at great speed. Indeed, it was which may have been altered locally by the su-
originally hoped (e.g., Colgate & Johnson 1960) pernova progenitor. For example, if there was a
that these energetic particles might be the cos- strong wind, it will have cleared out a cavity in
mic rays, and thus supernovae would be the di- the local medium in which the local material is
rect agents of cosmic ray acceleration. This has replaced by that of the wind. Moreover, a typi-
been shown to be incorrect (e.g., Cass´e & Goret cal progenitor begins life as an O star whose UV
1978; Meyer 1985a, 1985b), and instead it is now radiation partially clears out the region near the
believedthatthesupernovablastleadsindirectly star. Infact,itisonlyimportantforourpurposes
to cosmic ray production via shock acceleration that the explosion be in some medium, and we
(as reviewed, e.g., in Blanford & Eichler 1987, willseethattheparticlesweareinterestedinwill
and Jones & Ellison 1991). travel much further than the lengthscale of local
Nevertheless, very fast ejecta are indeed cre- inhomogeneities.
ated by supernova explosions. Indeed, some After the explosion the bulk of the material
have energies above thresholds for nuclear in- will form a shock and pass through the usual
teractions, in particular for γ-ray and Li, Be, phases (free-coasting, Sedov, etc.). But the pre-
& B (LiBeB) production. These interactions cursors to the blast, the fastest particles ejected,
should inevitably accompany the passage of fast are dilute and will not participate in the shock.
ejecta through the medium surrounding the su- Theywillinsteadpropagateoutandbegintolose
pernova. Given the presence of these interac- energy predominantly through ionization losses,
tions, the crucial question is whether they are eventually to bestopped. These arethe particles
numerous enough to be detectable. Indeed, if in which we are interested. Specifically, we want
the flux of the fast particles is sufficiently high, tocalculatetheintensity, spectrum,composition,
the γ-rays could offer a new and unique window and duration of the precursor nuclei.
on the explosion, and the LiBeB could provide a Before making detailed calculations, let us fix
record of such events, integrated over the history the order of magnitude of the effect. Typical su-
of the Galaxy. pernova velocity spectra have maximum veloci-
In this paper we estimate the flux of the fast tiesoftheorderof40,000km/s,i.e., withparticle
supernova ejecta and find that it is in fact suffi- energies (per nucleon) up to 8 MeV/nucl. Typi-
cientlyenergeticandintensetoleadtosignificant cal γ-ray thresholds (for reactions between an α
γ-ray production,and less significant LiBeB pro- particle and a heavy nucleus) are ∼2 MeV/nucl,
duction. It is thus plausible that this mechanism andspallationthresholdsafewtimeshigher;pro-
is of great interest as a diagnostic of supernovae ton thresholds are higher still. A threshold en-
in general. More particularly, it is interesting in ergy of E = 2 MeV/nucl corresponds to a
th
light of recent Orion γ-ray observations, which velocity of v = 20 000 km/s; the amount of
th
can be accounted for by prompt ejecta a single mass ejected above this energy is roughly M(v >
type Ic supernova (if it indeed arises from a CO vth) ∼ 0.001M⊙, i.e., a tenth of a percent of the
core progenitor as recently suggested by Nomoto totalejecta. Thismaterialhasakineticenergyof
et al. 1994). order 4×1048 erg, i.e., about 0.4% of the super-
2
nova energy. This is to be compared with a typi- of LiBeB or γ-ray production by this flux. For-
cal efficiency of ∼ 1% for acceleration of galactic mally, the rate is given by
cosmic ray supernovashocks (e.g., Gaisser 1990).
dN ∞ ∂N
Since prompt ejecta have comparable energetics, l = n dE σl i v (5)
dt j ij ∂E
it is plausible that their effects could be impor- ij ZEi
X
tant. 1 ∞ dM
= n dE σl X
We are thus interested in calculating the ini- j A m2 ij i dv
ij i p ZEi
tial spectrum of particles and determining their X
nuclearinteractions astheypropagateaway from Note that the spectrum ∂N /∂E will be out of
i
the explosion. The initial spectrum is calculated equilibrium and so time dependent (in contrast
as follows. Imagine as well that the star emits at to the steady state of galactic cosmic rays). Be-
total number N of isotopes i. The spectrum is cause of the energy losses, the fast particle flux
i
obtainedfromthecalculationsofthemass,veloc- will be continuously degraded in intensity and
ity, and composition of supernova shells. Specif- energy over time. For the purposes of a first ap-
ically, we know the velocity v(M) and mass frac- proximation, however, imagine a constant flux
tion X (M) as a function of mass coordinate M. lasting for a duration ∆t. The appropriateness
i
We want the number spectrum ∂N /∂E for each of this approximation will be discussed in §5.
i
species i of interest. We have, for the total num- From eq. (5) it is clear that what is crucial
ber of particles, to our calculation is the nature of the fastest
ejecta, i.e., the composition X and the veloc-
Mh dM Mh X i
i i
N = = dM (1) ity spectrum dM/dv of the outermost supernova
i
A m A m
ZMℓ i p ZMℓ i p shells. Both of these will be sensitive to the pro-
genitor mass and history. Specifically, the outer-
integrated over the ejected shells mass between
most composition (and indeed the pre-explosion
the inner M and outer M mass coordinates of
ℓ h
mass) will depend on the amount of mass loss
the ejecta. But by definition we also have
the progenitor has suffered. Although the out-
Eh ∂N ermost layers will be born with the composition
i
N ≡ dE
i
∂E of the ISM at the time, with sufficient mass loss
ZEℓ
vh dE ∂N this could be shed and the inner nucleosynthetic
i
= dv
dv ∂E shells can be exposed. Thus mass loss considera-
Zvℓ
tions are crucial for determining the fast particle
Mh dv dE ∂N
i
= dM (2) composition.
dM dv ∂E
ZMℓ
Since mass loss can change the progenitor
and so by equations (1) and (2) we have mass considerably, it also affects the velocity of
the ejecta, and thus influences the normalization
∂N X dv dE −1
i i of the velocity spectrum. However, it appears
= m (3)
p
∂E Ai (cid:18) dM dv(cid:19) that the shape of the velocity spectrum is gener-
ically a power law to a reasonable approxima-
and in the nonrelativistic case which holds here,
tion. In a beautiful analytic treatment, Nady-
we may simplify further to
ozhin (1994) has examined the passage of the
∂N 1 X 1 dM type II supernova shock through the outermost
i i
= (4)
∂E m2 A v dv layers. He shows that in this a self-similar solu-
p i
tion holds, and calculates the velocity spectrum
Now wemay defineandthenestimate therate of the fastest layers. He finds the spectrum to
3
have the form of a power law with a cutoff at a (1992) whose numerical model of SN 1987A was
maximum velocity v . Specifically, he finds specifically designed to calculate shock breakout.
max
The slope s of the velocity spectrum (eq. 6)
B(v−s−v −s)+∆M , v < v
M(v) = max max is related to the hydrodynamic properties of the
0 , v ≥ v
( max self-similar shock solution. In particular, s =
(6)
(n+1)/γ, where n is a power law index for the
whereB isaconstantthatdependsonthedetails
density dependence on the distance to the sur-
of the hydrodynamics, while v scales roughly
max face, and λ is a similar index for the velocity
as vmax ∝ U/Mej with the supernova mechan- (related to n and the adiabatic index). At any
ical energyqU and the ejected mass M .1 For rate, the universality of the power law solution is
ej
SN 1987A, Nadyozhin calculates v = (26 − very fortuitous, as it allows us to make general
max
40)×108 cm/s, corresponding to an energy (per remarks about all SNe.
nucleon) cutoff of Emax = 6−8 MeV/nucl. The other major feature of the velocity spec-
As we will see in detail below, the presence trum which is equally crucial for our purposes is
of the cutoff velocity v is crucial in determin- theexistence of thecutoff invelocity, andthusin
max
ing the nuclear interactions of the fast particles. energy. The cutoff is quite near to the γ-ray and
Physically,thecutoffarisesfromthequenchingof spallation thresholds, and so will greatly empha-
the shock’s acceleration of the outer layers of the size the differences among the different thresh-
supernova. As the shock moves through the de- olds. To be sure, there is the above-mentioned
creasingdensityoftheouteratmosphere,thema- scaling with supernova mass and energy, so a
terial is accelerated progressively faster in reac- lighter pre-supernova star could perhaps achieve
tion to the large radiation pressure of the shock. higher energies. Regardlessly, the low energy be-
Thisprocessceases, however, whentheshockap- havior of the cross sections will be crucial. In
proachesthesurfaceandtheopticaldepthforthe particular, protons reactions are disallowed be-
shock radiation becomes comparable to the opti- low ∼ 20 MeV/nucl for C and O reactions, but
caldepthtoreach thephotosphere. Atthispoint sinceαthresholdsarelowerbyafactor∼ 4inen-
the radiation escapes from the putative super- ergy per nucleon, thecomponents of theejecta in
nova as an ultraviolet flash, and theshock causes αparticles, andheavier nucleiwhichcaninteract
no further direct acceleration (for further discus- with interstellar He, will be crucial.
sion see Nadyozhin 1994). The smallness of the cutoff energy means that
AverynicefeatureoftheNadyozhinspectrum the numerical calculations are difficult to do cor-
is that it takes the exceedingly simple form of a rectly. Results are very sensitive to the gener-
power law. Thus one can immediately deduce ally unmeasured threshold behavior of the cross
that the effective particle spectrum (cf. eq. 5) is sections. Semianalytic fits to experimental data
also a power law dM/dv ∝ v−(s+1), or (Read & Viola 1984) do extrapolate down to
threshold, but clearly there is a need to under-
dM
(E) ∝ E−(s+1)/2 , E < E (7) stand this low-energy physics exceedingly well,
max
dv
and we urge experimentalists to consider these
For SN 1987A, Nadyozhin estimates that s = measurements. Indeed if accurate cross sec-
7.2, which gives an energy dependence of E−4.1. tions were available, one could turn the problem
This result is supported by Ensman & Burrows around, and use the γ-ray and spallation yields
as apowerfuldiagnostic onthefastejecta’s spec-
1 Note there is an additional shell ejected at the highest trum and composition.
velocity, but its mass is so small (∆M ≃ 10−6M⊙) that
Another word of caution: Nadyozhin’s calcu-
we ignore it.
4
lation was plainly not intended for the use we Lingenfelter (1995a, 1995b).
make of it. In particular, it is doubtful that the The COMPTEL experiment also set limits to
real cutoff behavior is as sharp as he calculates the flux outside of the 3−7 MeV band; in par-
it to be (eq. 6). In actual supernovae it is likely ticular, the flux in the 1−3 MeV range was con-
that the quenching of the shock is a continuous strainedtobe<∼ 1/7 thatofthe3−7MeVrange.
process and so while the cutoff scale may be cor- Thelack of such lines is a crucial indicator of the
rect, the details of the spectrum at these highest lack of fast protons or α particles, which would
energies may be quite complicated. One should exciteambientFe,Si,andNe,leadingtoemission
thusregardnumericalresultsobtainedviaeq.(6) in this range.
asroughindicatorsoftheyieldsoneexpectsfrom
It is assumed that these lines have their ori-
these fast ejecta. Nevertheless, we forge ahead in
gin in energetic particle interactions with ambi-
applying our method to the recent γ-ray obser-
ent matter in the Orion complex, but it is clear
vations of Orion.
that any explanation of the γ emission will have
to be unconventional. No lines are observed be-
3. Gamma-ray Observations of Orion
low the 3−7 MeV band,and noexcess π0 decays
havebeenobservedathigherenergies(i.e.,noex-
The γ-ray production in the Orion complex
cess over the level expected from galactic cosmic
is huge, as Bloemen et al. (1993) recently deter-
rays; see Digel, Hunter, & Mukherjee1995). The
mined with the COMPTEL experiment on the
if galactic cosmic rays produced the 3−7 MeV
Compton Gamma Ray Observatory. The most
lines, they would also produce 1–3 MeV γ-ray
surprising feature of the γ emission from Orion
lineswhicharenotobserved;alsotheGCRinten-
is that thelarge fluxis confinedto the3−7 MeV
sity would have to be much larger, which would
range. Bloemen et al. (1993) measured the flux
give a high excess of π0 decay photons, again un-
in the 3-7 MeV band to be
observed. Moreover, theenergeticdemandwould
Φ (3−7MeV) = (1.0±0.15)×10−4 cm−2 s−1 . be enormous. This process is therefore excluded.
γ
(8) The most economic way to obtain the ob-
In this range, the spectrum shows features con- served γ-ray flux is through accelerated C and
sistent with de-excitation emission from the 4.44 O nuclei, and above all, a suppression of pro-
MeVexcitedstateof12C∗andthe6.13MeVstate tons (Ramaty, Kozlovsky, & Lingenfelter 1995a,
of16O∗;thesefeatureshaveroughlythesameam- 1995b;Vangioni-Flametal.1996; Cass´e,Lehoucq,
plitude. & Vangioni-Flam 1995; and Cass´e et al. 1994).
The features at 4 and 6 MeV appear wide, Indeed, if one assumes merely that the Orion
which would have implications for the nature of γ-rays arise from energetic particle interactions,
theaccelerated particles dueto thekinematics of then one may deduce in a model-independent
the nuclear excitations. Fast C and O nuclei give way the particles must be a large flux with low
rise to fast 12C∗ and 16O∗ which have Doppler- energy, predominantly composed of C and O
broadened decay lines, whereas fast protons and rather than protons and α particles.
α nuclei lead to slow 12C∗ and 16O∗ having nar- A low energy CO flux was suggested by the
row lines. However, Bloemen et al. (1993) cau- Bloemen et al. (1993) paper itself, and the low
tion that their lineshapes are not corrected for energy character was assumed in all subsequent
broadening due to finite detector response, and efforts at explaining the γ-ray emission. Bykov
to the widths are artificial, a point also noted by & Bloemen (1994) and Nath & Biermann (1994)
Reeves & Prantzos (1995) and emphasized via connect the observation to theories of cosmic ray
detailed calculations by Ramaty, Kozlovsky, & origin. Bykov & Bloemen (1994) propose a spe-
5
cific spectrum arising from collisions between su- in a molecular cloud.
pernova shocks and stellar winds. They use pure Ourmechanismnaturallyhasalloftheneeded
supernovacompositionsintheircalculations, but features, provided only that the supernova ex-
it remains unclear how much of an admixture of ploding within Orion be sufficiently massive to
normal material will be present in the hot re- have undergone significant mass loss. Then the
gions they consider. Nath & Biermann (1994) progenitorwouldbestrippedtoaCOcore,which
favor acceleration in shocks of winds of hot O would be ejected at high speeds (for a fixed ex-
and B stars; they argue that this naturally gives plosion energy, a smaller core mass has less grav-
the desired composition. Ramaty, Kozlovsky, & itational binding energy and so leads to higher
Lingenfelter (1995a) pointed out that while the kinetic energy for the ejecta). Furthermore, nei-
observed γ-ray features appear broad, there is therthefastparticlespectrumnorthenumberof
insufficient experimental resolution to exclude a particles is arbitrary, but rather these are given
narrowlinecomponent. Parameterizingalowen- by the supernova model. Thus the predictions of
ergy spectrum, they tried different source com- this process are specific and so the mechanism is
positions,showingthatacompositionlikethatof testable.
a WC supernova wind would be needed to meet
the γ spectrum and energetic constraints. These 4. Confrontation with the Orion Obser-
authorshavealsosuggested(Ramaty, Kozlovsky, vation
&Lingenfelter1995b)thatthelowenergycosmic
rays could have an origin akin to that of the so- Wehaveseenthattheoryallowsustocompute
called anomalous component of the cosmic rays N˙γ, while the Orion observation report the flux
observed at earth (a suggestion also made by Jin Φγ at Earth. These quantities are simply related
& Clayton 1995). by
A low energy cosmic ray flux has implica-
dN
tions for the nucleosynthesis of Li, Be, and B γ = 4π R2 Φγ
dt
(LiBeB), as first pointed out by Meneguzzi & = (3.0±0.45)×1039 s−1 (9)
Reeves (1975b). Cass´e, Lehoucq, & Vangioni-
Flam(1995)investigated theimplicationsofsuch using R ≃ 500 pc as the distance to Orion,
Orion
a process for LiBeB chemical evolution. They and assuming the flux to be emitted isotropi-
show that the LiBeB synthesis can be significant cally so that the total subtended solid angle is
(for an exposure time of 105 yr), comparable to 4π. Of course it is conceivable that the emission
that of galactic cosmic rays (e.g. Walker, Math- is anisotropic due to, e.g., magnetic fields hav-
ews, & Viola 1985). ing somehow focussed (or defocussed) the beam
Much of the work on the Orion γ-rays thus in our direction. In the lack of clear evidence for
far has either: (1) assumed arbitrary flux shape, sucheffects,wewillhenceforthmakethesimplest
or (2) assumed SN composition. These first ap- assumption regarding the angular distribution of
proaches adopt a spectrum of the form ∝ E−s, the radiation and consider it to be isotropic.
with s = 0 below an energy Ec, and n = 5−10 To get a feel for the numerical results, let us
above Ec (a form chosen for exploratory pur- make an order of magnitude estimate of the γ-
poses,followingMeneguzzi&Reeves(1975b)and ray emissivity. The particles of interest are the
Ramaty, Kozlovsky, & Lingenfelter (1979)) and ejecta having a velocity larger than the reaction
try different supernova compositions, as Bykov thresholds; these particles have mass M (v >
ej
& Bloemen (1994). We propose a more specific v ). Taking an energy (E = 2 MeV/nucl)
th min
scenario related to a type Ic supernova explosion slightly above the threshold for gamma rays (∼
6
1.5 MeV for α+C), we have result of an explosion of a CO core supernova,
similar to that observed recently in the type
N˙ ∼ n vσγ N (v > v )
γ Orion pC CO min Ic supernova 1994I (Schmidt, Challis, & Kirch-
XCO M (v > v ) ner 1994; Clocchiatti, Brotherton, Harkness, &
= n vσγ i ej min
Orion pC A m Wheeler1994). Nomotoetal.(1994)arguedthat
i p
= 1.0×1039 s−1 X (10) theobserved characteristics ofthisevent arebest
C
understood in the context of a CO model arising
γ
n σ M (v > v )
× Orion pC ej min from envelope loss to a companion (as opposed
20 cm−3 10 mb 0.03 M⊙ to mass loss of a single star). While such events
are not the most common fates of massive stars,
where we have taken the cross section to be a
they are not so unlikely: Nomoto et al. estimate
typical one in the low energy range, about 10%
a ratio of type Ic to type II explosions of ∼ 10%.
of the maximum, and have allowed for an aver-
agedensityinOrionthatismoderatelyenhanced We now apply our formalism in more detail
over that of the ISM. to the particular case of a CO core explosion.
We use the results from the supernova model
Note that eq. (10) shows that for the fiducial
of Nomoto et al. (1994) (specifically the v(M)
values we have chosen, the emissivity is just at
and X (M) relations) to generate the spectrum
the observed levels for the C lines (which con- i
shownin Figure 1. As expected, most of thepar-
tribute about half of the total emissivity) but
ticles indeed lie at low energies, and the compo-
only if X (and similarly X ) is close to unity.
C O
sition varies over energies reflecting the variation
That this, the fast ejecta must be predominantly
of the composition with mass shell. Since the
composed of C and O. But the fastest ejecta
reaction thresholds are all ≥ 2 MeV/nucl, the
arises from material at the outermost layers of
only part of the flux relevant to our problem is
the supernova progenitor. One expects a “nor-
that at and above this scale. At these energies,
mal” supernova progenitor, one not having sig-
thecomposition doesnotvarywithradius(being
nificant mass loss, to have a composition similar
that of the outmost shells). Moreover, the spec-
to that of the local ISM at the time of the pro-
trum has, fortunately, settled down to a fairly
genitor’s birth. This would give C and O mass
fractions < 10−2, which leads, via eq. (10), to smooth shape close to a power law, with a slope
a significant underproduction of 12C∗ and 16O∗ of approximately ∼ 4, in reasonable agreement
with the Nadyozhin analytical calculation. Pre-
lines.
liminary calculations using the velocity profiles
However, if the progenitor has suffered signifi-
for Wolf-Rayet supernovae (Woosley, Langer, &
cant mass loss, or has lost its outer envelope to a
Weaver 1993) giveasimilarslopeandsogivefur-
companion star, then it is possiblethat the inner
ther credence to the analytic solutions.
nucleosynthetic shells could be left at the outer
To investigate the effect of the flux, it is cru-
layers of the progenitor. In this case the fastest
cial to know its behavior for energies above those
ejecta would have a very nonsolar composition.
specified in the Nomoto calculation. We have
In particular, if the progenitor is reduced to a
chosen to extrapolate the flux to higher energies
CO core, then it would have X ≃ X ≃ 0.5;
C O
by taking a power law with the slope of the last
this is just the composition required to explain
points. Specifically, if we write φ ∼ E−α, we
the Orion observations. While these nuclei dom-
find α ∼ 3.5 around 1 MeV, steepening to α ∼ 4
inate, there remain some α particles and also a
small amout of Ne (having the form 22Ne rather around 2 MeV; it is this last slope we used in the
than 20Ne). extrapolation.
Following Nadyozhin, we wish to introduce a
We thus suggest that the Orion γ-rays are the
7
maximum energy E to the flux. The self- below (§5.) the timescale for significant loss is
max
similar solution provides the scaling mentioned energy-dependent but at least of order 1 kyr.
above, Emax ∝ (U/Mej)1/2, which Nadyozhin Figure 2(a) shows calculated the emissivity
normalizes to SN1987A hydrodynamic models. from excited 12C, 16O, as well as 22Ne, plot-
Scaling his result to our CO core explosion, and ted as a function of E . The normalization
max
assuming a total energy U = 1051 erg, gives is fixed by requiring the total 12C∗ +16O∗ emis-
Emax ∼ 40 MeV/nucl. However, sincethe details sivity to match theOrion observations (eq. 9); as
of determining Emax are difficult, the supernova discussed in the previous paragraph, this fixes a
energy is uncertain as well, we will take Emaxto value of nH for each Emax, which appears in Fig-
be a parameter and we will investigate values in ure 2(b). We see that over the preferred range of
the range 8 MeV/nucl ≤ Emax ≤ 50 MeV/nucl. Emax, the γ-line ratios, and the required density,
Usingthisextrapolatedfluxwehaveevaluated show almost no variation, and what little change
numerically the 12C∗, 16O∗, 22Ne∗, and LiBeB there is has settled down by 10 MeV/nucl. We
production. We assume that the escape length find C∗/O∗ = 2.7, consistent with the Bloemen
Λ is large and so the LiBeB produced are all et al. (1993) observations.
esc
either thermalized through ionization losses (the It is insufficient to show that the flux can pro-
dominant process), or lost through inelastic col- duce the observed 3−7 MeV lines; we must also
lisions. In fact, since the ionization losses dom- show there will not be lines outside this range.
inate, the results are insensitive to the escape In particular, we must show that the 1−3 MeV
length. Further we assume that the medium has lines are below the COMPTEL limits (c.f. §3.).
a solar system composition as given by Anders& Here again, the composition of the stripped su-
Grevesse (1989). pernova core proves advantageous. In particular,
Given these parameters, the ratios among the notonlyarethefastejecta dominantinCandO,
γ andspallation ratesarefixed;however, tocom- as discussed above, but they also have relatively
pute absolute rates requires specification of the small abundances of heavier elements. In partic-
Orion H density n . Specifically, we find, for the ular,thenextmostabundantelement,afterC,O,
H
total γ production from 12C∗+16O∗, we have and He, is 22Ne. Although its abundance is not
large, it is much larger than its solar proportion,
dN n
γ = 2.4×1038 H photons s−1 (11) indeed much larger than the solar proportion of
dt 1 cm−3
heavy elements. Thus this will be the most im-
with very little variation over the chosen range portant contributor of heavy element lines, even
of E . Comparing this to the measured value more than those caused by the α reactions in the
max
(eq. 9), we see that our mechanism can account ISM.
for the observed Orion γ-ray flux if the ejecta Indeed, we find (C∗ + O∗)/Ne∗ > 13 for all
∼
encounter an average density values of E , which falls safely below the ob-
max
servationallimits, whichareoforder7. However,
n ≃ 12 cm−3 . (12)
H if ours is the mechanism for making the C and O
γ-rays, then there should be 22Ne lines present
This is to be compared with to the estimated av-
erage density of Orion, nOrion ≃ 5 cm−3 (Goudis at a level just below the current limits. While
H
COMPTEL may not have a good chance to see
1982), the uncertainty in which is large enough
them, INTEGRAL will see them in detail. This
so that it is in good agreement with eq. (12). We
will then provide a clean discrimination between
note, however, that thedensity requirement rises
our idea and others, as our prediction of 22Ne
withthetimesincetheexplosion,sincethefluxis
lines (at 1.3 MeV), rather than 20Ne lines (at 1.6
constantly decreasing in intensity. As discussed
8
MeV), is likely to be unique. with progenitor mass (for a fixed explosion en-
Given the roughness of our estimate, and its ergy), we compare the spectrum from the 2.1M⊙
closeness to the observational limit, it is clear CO core we have considered so far with that of
that the 1−3 MeV window offers an important CO cores with masses 1.8 (Iwamoto et al. 1994)
constraint. Moredetailedmodelingisneededand and 2.9M⊙ (Nomoto et al. 1995a). The results
is under way (Ramaty, Vangioni-Flam, Fields, & appear in figure 4. Here we find the agreement
Cass´e 1996). Indeed, we see thatthe generic sen- is not as good; indeed it appears that the parti-
sitivity of the γ-ray emission to the supernova cle fluxes are more similar without the scaling.2
composition and velocity structure makes the γ While for our calculations we have used the nu-
spectrum a powerful diagnostic tool. Since all merical results anyway, it would be interesting
supernovae should have fast ejecta, one could in if the results were less sensitive to ejecta mass
generalturntheproblemaroundandusethecon- than expected, as this would lead to larger fluxes
straint as a probe of supernova ejecta. (above threshold) than expected. At any rate
we find that as a whole, the slope, the energy
Although a full study of fast particle inter-
cutoff, and the intensity is well-described by the
actions from all possible supernovae is beyond
very simple Nadyozhin model itself coming from
the scope of this paper, nevertheless some dis-
well-understood physics.
cussion of model dependence is in order. We are
interested in the sensitivity to progenitor mass We now turn to the composition, which de-
and mass loss, as manifested in the flux inten- pends strongly on the mass loss, and so is tied
sity, spectrum, and composition. To begin to to much less certain physics. Indeed, mass loss is
address this question we have studied variants to poorly understood and simply treated paramet-
the supernova model we have used thus far. rically. We have tried using different mass loss
rates; results appear in Table 7. At any rate, it
The hydrodynamics of the explosion deter-
is apparent from figure 1, the composition of the
minestheintensity andspectrum,andtheNady-
fastest shells is fairly homogeneous. Thus one
ozhin (1994) model suggests (eq. 6) that the
need only determine the (uncertain) outermost
spectral slope is fairly independent of the ini-
composition without having to get the full pro-
tial mass, but the velocity scaling and energy
file and convolving it with the hydrodynamics.
cutoff depends on v ∝ U/M . The scal-
max ej
ing with mass means that sqignificant mass loss
5. Propagation and Energetics
can be important since, for a fixed explosion en-
ergy, it reduces the gravitational potential to be Recall that in calculating the rates for nuclear
overcome and so increases the final kinetic en- interactions ofthefastparticles wehaveassumed
ergy. To test the accuracy of the expected scal- the flux to be present at full strength for some
ing with the explosion energy (at a fixed mass), time interval ∆t, during which the spectrum is
we compare the spectrum for a 2.1M⊙ core at constant. While this is adequate for estimates of
energies of (0.6,0.8,1)×1051 erg (Nomoto et al. emissivity, it is too simplistic. At the energies of
1995a, 1995b). Results appear in figure 3; we see interest the particles are stopped predominantly
that while the scaling is not exact, it is a good by ionization energy losses. As these losses are a
approximation. Notethatchangesinenergyscal- strongfunctionofenergyandofAandZ (scaling
ing do not affect the intensity of the scaled flux,
but the shifts in the velocity scale change the in- 2Note,however,thattheplotonlydemonstratesthescaling
of the overall intensity; the models on which the calcula-
tensity of the relevant, highest energy flux.
tions are based do not include the physics of the shock
To test the accuracy of the expected scaling breakout and so cannot show theenergy cutoff.
9
asZ2/A), theparticle spectrumandcomposition M44 = 5×10−5M⊙ −2×10−4M⊙ (Nomoto et
will change with time. al. 1991; Kumagai et al. 1991; Thielemann et al.
The calculation is done in detail in Fields 1996), a value close to the 10−4M⊙ inferred from
(1996). Thebasiceffectisthatthespectrumcon- observations in Cas A (Iyudin et al. 1994). If the
tinuallybecomeslessintense,butalsoharder. To time since the explosion is ∆t, there will be a
see this, imagine an (unphysical) spectrum that 44Ti emissivity of
is a δ-function in energy. It would degrade from 1 M
N˙ = 44 e−∆t/τ (13)
its initial energy according to the usual Bethe- 44 τ 44 m
p
Bloch ∂E/∂t formula. Thus for a continuous
at an energy E = 1.16 MeV. The observa-
spectrum, one expects the entire flux to degrade γ
tional limit on such lines in Orion is L < 3 ×
in energy. But since ∂E/∂t ∝ E−1, lower en- ∼
1038 photons s−1 (namely the limit for the 1–3
ergyparticlesloseenergyfaster,sothespectrum,
MeV band), which gives
though less intense. has an increasing average
energy per particle. ∆t > τ ln M44 = 570 yr . (14)
∼
44m τL
An important related point is that the stop- p
ping ranges are larger than size of Orion. This This is a strong constraint, being only a factor
means that if the fast particles are still in Orion of 4 shorter than the minimum particle stopping
then the supernova is young. More quantita- time. Taking this result at face value, we are led
tively, the range of a 2 MeV/nucl oxygen nucleus to infer a possible age range of 0.6–10 kyr for the
in Orion is about 50 pc; it traverses this distance supernova.
in about 2 kyr; this is about a factor 3 smaller However, caution is merited in using the 44Ti
than the crossing time, but it is also a lower lower bound on the age. The 44Ti yield is very
bound; for particles above about 5 MeV/nucl
uncertain, as it requires an accurate knowledge
the range is larger than Orion. Thus we can use
of which of the deepest layers of the star are
the crossing time to put an approximate upper
ejected, andwhichfallback intotheneutronstar
limit to the supernova date of ∼ 104 yr ago. Of
(i.e., the mass cut). Different mass cut choices
course, an accurate calculation must include the are allowed and can lead to smaller 44Ti yields
fact that the exposure time is not the total stop-
(although the age limit depends only logarith-
ping time but rather the time it takes the fast
mically on the mass yield). Also, we note that
particles to pass below the threshold for γ-ray
the observational limit we have used is that of
production. Since the stopping time is a strong
COMPTEL and is more suited for broad lines;
function of energy (t ∝ E2) this difference will
Bloemen et al. (1993) caution that narrow lines
only be important for the particles very close to
may be left undetected. And in any case, if the
the threshold energy. This effect is discussed in age is closer to the ∼ 104 yr crossing time, then
Fields (1996). there is no 44Ti to be seen by either COMP-
Thepossibilityofarelativelyrecentsupernova TEL or INTEGRAL. On the other hand, to take
is constrained by observations of short-lived ra- more optimistic viewpoint and turn the problem
dioactivities. In particular, the lack of observed around: iftherehasbeenaveryrecentsupernova
44Ti (τ = 78.2 yr) sets a lower limit to the in Orion, the 44Ti lines (or lack thereof) can give
supernova age of order τ, assuming that there important information about the mass cut.
is significant 44Ti production in the supernova
Finally, we turn to the question of energy re-
in question. In fact, we can make this point
quirements. As pointed out by Ramaty, Ko-
morequantitative. TheCOcore supernovamod-
zlovsky, & Lingenfelter (1995a, 1995b), the sig-
els we have been using give 44Ti yields of order
nificant low-energy flux in Orion is a challenge
10
