# Impacts of Nuclear Reaction Rate Uncertainties on Sub-Chandrasekhar-Mass
White Dwarf Detonations

Thomas Fitzpatrick  Department of Astronomy and Theoretical Astrophysics
Center, University of California, Berkeley, CA, USA  Ken J. Shen  Department
of Astronomy and Theoretical Astrophysics Center, University of California,
Berkeley, CA, USA Thomas Fitzpatrick<EMAIL_ADDRESS>
###### Abstract

The precise nature of Type Ia supernova (SN Ia) progenitors remains a mystery,
but the detonation of a sub-Chandrasekhar-mass white dwarf (WD) has become a
promising candidate. There is a growing body of work suggesting that the
carbon core detonation of a sub-Chandrasekhar-mass WD can be triggered by the
detonation of a helium shell accreted from a companion WD, through either
inward shock convergence near the center or direct edge-lit detonation. This
“double-detonation” SN Ia can be triggered by a small helium shell and is
therefore well approximated by the detonation of a bare carbon-oxygen white
dwarf (C/O WD). The impacts of uncertainties in experimentally and
theoretically determined nuclear reaction rates on nucleosynthesis in the
detonations of sub-Chandrasekhar-mass WDs have not yet been fully explored. We
investigate the sensitivity of this model to nuclear reaction rate
uncertainties to better constrain the nucleosynthetic yields resulting from
these phenomena and identify the nuclear reaction rates whose uncertainties
have the most significant impacts on nucleosynthesis. We find that the
chemical abundances, and in particular those of the iron-group elements, are
relatively insensitive to these nuclear reaction rate uncertainties.

nucleosynthesis, nuclear reactions, white dwarf binaries, Type Ia supernovae

††software: MESA version 8845.; Paxton et al. (2011, 2013, 2015, 2018), FLASH
version 4.2.2; Fryxell et al. (2000); Dubey et al. (2009)

##  1 Introduction

Type Ia supernovae are useful cosmological tools as standardizable candles,
and this feature was essential in discovering the accelerated expansion of the
Universe (Riess et al., 1998; Perlmutter et al., 1999). The role of SNe Ia in
galactic nucleosynthesis has been thoroughly studied and they are known to
contribute significantly to the production of iron-group and intermediate-mass
elements crucial to the chemical evolution of the Galaxy (Timmes et al.,
1995). However, many fundamental questions regarding SNe Ia persist, including
the precise nature of the progenitor scenario leading to their explosions.

There is a consensus that SNe Ia occur when a WD in a close binary system
undergoes explosive burning initiated by mass transfer from either a non-
degenerate or degenerate companion star (Maoz et al., 2014). The WD mass
distribution produces a typical mass for a single non-rotating white dwarf of
$\approx 0.6M_{\odot}$, which alone, is not vulnerable to nuclear ignition
(Homeier et al., 1998). In the historically favored Chandrasekhar-mass
($M_{\text{Ch}}$) WD scenario, a WD must be accompanied by a companion star
from which to accrete mass; the accumulation of this mass leads to increased
temperature and density in the core, eventually resulting in nuclear ignition
and thermonuclear explosion when the WD nears the Chandrasekhar mass limit. In
the single-degenerate case, a C/O WD approaches the Chandrasekhar limit
through stable mass accretion from a non-degenerate hydrogen or helium burning
companion star (Whelan & Iben, 1973). In the double-degenerate case, the
unstable coalescence of two C/O WDs results in the combined mass of the system
exceeding the Chandrasekhar limit (Webbink, 1984). For all SNe Ia progenitor
scenarios, it has been both theoretically and observationally determined that
the light curves are dominated by the radioactive decay of newly synthesized
56Ni in the 56Ni $\rightarrow$ 56Co $\rightarrow$ 56Fe reaction chain (Pankey,
1962; Truran et al., 1967; Colgate & McKee, 1969).

Alternative to these $M_{\rm Ch}$ scenarios, a class of “double-detonation”
scenarios involving a sub-Chandrasekhar-mass C/O WD has become a promising SN
Ia progenitor scenario. The “double-detonation” scenario involves the carbon-
core detonation of a sub-Chandrasekhar-mass (sub-$M_{\text{Ch}}$) C/O WD
ignited by the detonation of an accreted helium shell acquired from a
companion star, either through inward shock propagation leading to shock
convergence near the center of the WD (Livne, 1990; Woosley & Weaver, 1994;
Shen & Bildsten, 2014), or through direct edge-lit detonation (Nomoto, 1982a,
b). The earliest models of this scenario included a thick helium shell ($\sim
0.1M_{\odot}$) accreted from a non-degenerate companion star. The detonation
of the thick helium shells in these early models yielded an overproduction of
iron-group elements including 56Ni (Hoeflich & Khokhlov, 1996; Nugent et al.,
1997) and yielded redder spectra than those typically associated to SNe Ia due
to Fe-group line blanketing from the ashes of the nuclear burning of these
shells111The recent discovery of SN 2018byg, a thermonuclear transient with
observational properties well explained by the detonation of a massive He
shell on a sub-$M_{\text{Ch}}$ WD, supports the findings of these earlier
models (De et al., 2019). (Nugent et al., 1997; Kromer et al., 2010; Woosley &
Kasen, 2011).

Recent work has resolved this issue, revealing that accretion from degenerate
companion WDs yield significantly smaller helium shells, and that the minimum
mass helium shell required to trigger a double detonation is much smaller than
previously thought (Bildsten et al., 2007; Fink et al., 2007, 2010; Shen &
Moore, 2014). A recent study analyzing _Gaia_ ’s second data release has
uncovered hypervelocity WDs that may be the surviving degenerate companions
shot out following such a double-degenerate double-detonation SN Ia at extreme
velocities equal to their pre-SN orbital velocities (Shen et al., 2018b). In
addition, recent radiative transfer calculations have shown that the
observational signatures from the bulk of observed SNe Ia can be reproduced by
the double detonation of sub-$M_{\text{Ch}}$ WDs when non-local thermodynamic
equilibrium and multi-dimensional effects are taken into account (Shen et al.,
2021a, b).

The impacts of nuclear reaction rate uncertainties have yet to be thoroughly
studied in the context of sub-Chandrasekhar-mass progenitor scenarios. The
bulk of previous work studying the impacts of nuclear reaction rate
uncertainties on the nucleosynthesis of SNe Ia has focused on the W-7 model
(Nomoto et al., 1984), and other near-Chandrasekhar-mass models (Bravo &
Martínez-Pinedo, 2012; Parikh et al., 2013). Recent studies that have included
sub-$M_{\text{Ch}}$ models in their investigations of reaction rate
uncertainties have been limited in their scope; focusing on either one isotope
(Kushnir et al., 2020), a set of four reactions involving 12C and 16O (Bravo
et al., 2019), or on the rates of electron capture reactions (Bravo, 2019).

Motivated by recent observational evidence supporting the sub-$M_{\text{Ch}}$
double detonation model and the need for more detailed nucleosynthetic data,
we explore the impacts of nuclear reaction rate uncertainties on the
nucleosynthetic yields in the detonations of bare $1.0\,M_{\odot}$ C/O WDs.

##  2 Numerical Methods

Here we describe our methods for post-processing the one-dimensional
hydrodynamic simulation of the detonation of a $1.0\,M_{\odot}$ C/O WD
described in Shen et al. (2018a) used for our study. The explosion of a bare
$1.0\,M_{\odot}$ C/O WD and the calculation of the nucleosynthetic yield is
done in multiple steps. Our choice of WD mass is motivated by the results of
Shen et al. (2018a), who find that sufficient 56Ni is produced in the
detonation of a $1.0\,M_{\odot}$ C/O WD to power a median brightness Type Ia
light curve through the 56Ni $\rightarrow$ 56Co $\rightarrow$ 56Fe decay
chain.

###  2.1 Detonation Model and Post-Processing

We use the explosion model for a $1.0\,M_{\odot}$ C/O WD described in Shen et
al. (2018a). The initial conditions for a bare $1.0\,M_{\odot}$ C/O WD were
calculated using the stellar evolution code MESA, which solves the fully
coupled equations of stellar structure and composition simultaneously (Paxton
et al., 2011, 2013, 2015, 2018). The density profile generated in MESA is used
as the initial condition for a FLASH simulation where the detonation is
ignited and evolved (Fryxell et al., 2000; Dubey et al., 2009). We adopt a WD
composition of equal parts 12C and 16O by mass and approximate a solar
metallicity ($Z_{\odot}$) by including 22Ne and 56Fe at mass fractions of
$X_{22\text{Ne}}=0.01$ and $X_{56\text{Fe}}=0.1X_{\text{22Ne}}$, respectively.
The 41-isotope nuclear physics network employed in the hydrodynamic
simulation, consisting of 190 interlinking reactions from JINA’s REACLIB
(Cyburt et al., 2010), is sufficient to accurately calculate energy release
but is not adequate for calculations of isotopic abundances (Miles et al.,
2018). To accurately determine isotopic abundances, tracer particles tracking
the radius, velocity, density, and temperature were included in the explosion
model for post-processing, separated uniformly throughout the WD every
$5\times 10^{6}$cm for a total of 120 zones. We post-process the thermodynamic
histories captured by the inner $107$ zones of the explosion model. We ignore
nucleosynthetic contributions from the remaining zones as the thermodynamic
trajectories are untrustworthy due to the reverse shockwave that travels back
through them, but the nucleosynthetic contributions to final isotopic
abundances from these zones are negligible. Further details about the
numerical setup of the hydrodynamic simulation we use for our study including
the detonation procedure and detonation broadening scheme are explained in
Shen et al. (2018a).

The hydrodynamic simulation is evolved for $10\,$s, and we then perform all
nucleosynthetic calculations by post-processing the tracer particles’
thermodynamic histories using MESA’s one zone burner. To accurately determine
nucleosynthetic yields, we couple an extended 205-isotope nuclear reaction
network to the density and temperature histories of our tracer particles
composed of neutrons, 1-2H, 3-4He, 6-7Li, 7,9-10Be, 8,10-11B, 12-13C, 13-16N,
15-19O, 17-20F, 19-23Ne, 21-24Na, 23-27Mg, 25-28Al, 27-33Si, 30-34P, 31-37S,
35-38Cl, 35-41Ar, 39-44K, 39-49Ca, 43-51Sc, 43-54Ti, 47-56V, 47-58Cr, 51-56Mn,
51-62Fe, 54-62Co, 54-62Ni, 58-66Cu, 59-66Zn, 59-66Ga, and 59-66Ge. We include
942 interlinking nuclear reactions, along with their corresponding reverse
processes, including $(p,\gamma)$, $(\alpha,\gamma)$ $(n,\gamma)$ $(p,n)$,
$(\alpha,n)$, and $(\alpha,p)$ reactions. Nuclear reaction rates are
determined from JINA’s REACLIB (Cyburt et al., 2010).

###  2.2 Nuclear Reaction Rate Variation

Here we describe our procedure for investigating the extent to which
uncertainties in experimentally and theoretically determined nuclear reaction
rates impact the nucleosynthetic yields of our sub-$M_{\text{Ch}}$ explosion
model. Analogous calculations have been performed by Bravo & Martínez-Pinedo
(2012) and Parikh et al. (2013), who studied the impacts of nuclear reaction
rate uncertainties in the context of the standard $M_{\text{Ch}}$ WD Type Ia
supernova models including the delayed detonation model and the carbon
deflagration W7 model of Nomoto et al. (1984) and Thielemann et al. (1986). We
employ a similar approach including the individual normalization of all input
nuclear reaction rates by constant factors.

We post-process the thermodynamic history of the simulation by coupling the
extended nuclear network described above to the density and temperature
histories of our tracer particles, individually normalizing the rate of each
nuclear reaction in our standard network by two constant factors ($10.0$ and
$0.1$ times the standard rate). Note that in order to maintain a detailed
balance, for each normalization factor we apply to a reaction rate we apply
the same factor to its corresponding reverse process. For each normalization
of an individual nuclear reaction rate and its corresponding reverse process,
we repeat all nucleosynthetic calculations and determine the final yields of
all isotopes in our network $10\,$s after explosion. To determine the final
isotopic abundances we sum the mass-weighted contributions from each of the
107 post-processed zones of our simulation. Performing all nucleosynthetic
calculations for all normalizations of the reaction rates, we obtain 1884 sets
of post-processed nucleosynthetic results.

We compare the nuclear yields produced in the individual normalization of
reaction rates by a factor of ten up and down to the nuclear yields generated
using standard rates by calculating the relative change between the yields of
each isotope in our network for each variation of a reaction rate. The
relative change in isotopic abundances is calculated as

$\text{RelativeChange}=\frac{X_{\text{normalized}}-X_{\text{standard}}}{X_{\text{standard}}}$
(1)

where $X_{\text{normalized}}$ is the mass fraction of an isotope generated by
the normalization of an individual reaction rate, and $X_{\text{standard}}$ is
the mass fraction of that same isotope produced using the default rates of our
standard nuclear network.

In our analysis, we focus our attention on nuclear reaction rates whose
uncertainties have the most pronounced effects on nuclear yields. To identify
individual reaction rates which have the most significant impact on nuclear
abundances, we present only isotopes that achieve an initial abundance of at
least $10^{-4}M_{\odot}$ in the baseline model, and only reaction rates that
impact the abundance of an isotope in our network by at least $20\%$ when
normalized.

##  3 Nucleosynthetic Results

In this section, we show the nucleosynthetic yields for a selection of
isotopes in our network and analyze the impact of nuclear reaction rate
uncertainties on the yields of these isotopes and the important isotopic
ratios 57Ni/56Ni and 55Co/57Ni. The nucleosynthetic yields of all isotopes in
our study are calculated $10\,$s after the start of the explosion, and are not
the final stable isotopic yields unless otherwise specified. The value of
these ratios can be inferred through observations of late-time SN Ia light
curves, and at these late times nucleosynthetic effects of
near-$M_{\text{Ch}}$ and sub-$M_{\text{Ch}}$ progenitor scenarios result in
differences in the photometric evolution of the light curves. The values of
these ratios are therefore useful diagnostic tools in breaking the degeneracy
between near-$M_{\text{Ch}}$ and sub-$M_{\text{Ch}}$ progenitor models (Röpke
et al., 2012; Kerzendorf et al., 2014; Graur et al., 2016; Shappee et al.,
2017). We also discuss the impact of reaction rate uncertainties on the value
of the Mn to Fe ratio, the value of which can also be used to discriminate
between these two scenarios (Seitenzahl et al., 2013).

###  3.1 Isotopic Yields

To determine the final nucleosynthetic yields we sum over the mass-weighted
contributions from each of the 107 post-processed zones of the simulation. The
final isotopic yields of the 32 isotopes selected for our analysis generated
using standard nuclear reaction rates are shown in Table 1.

Again, we restrict our analysis to only isotopes that achieved an abundance of
at least $10^{-4}M_{\odot}$ in our reference model using standard nuclear
reaction rates and reactions which impact the abundance of any of these
isotopes by at least $20\%$. 27Al and 31P do not meet the $10^{-4}M_{\odot}$
mass criterion for our analysis using standard nuclear reaction rates, but do
exceed this criterion in certain cases of a reaction rate variation and we
have included both of these isotopes in our analysis: when the rates of
23Na($p$, $\gamma$)24Mg, 20Ne($\alpha$, $\gamma$)24Mg, and 23Na($\alpha$, $p$)
26Mg were normalized by a factor of 10.0, and when the rates of 27Al($p$,
$\gamma$)28Si, 28Si($\alpha$, $\gamma$)32S, and 28Si($\alpha$, $p$)31P were
normalized by a factor of 0.1, the yields of 27Al and 31P were increased past
our $10^{-4}M_{\odot}$ criterion. Note that the nucleosynthetic yields of the
highest mass elements at the end of our nuclear network are uncertain because
elements with $Z\geq 31$ are neglected.

Isotope |  | Ejected Mass
---
($M_{\odot}$)
Isotope |  | Ejected Mass
---
($M_{\odot}$)
4He | $5.01\times 10^{-3}$ |  40Ca | $1.96\times 10^{-2}$
12C | $7.74\times 10^{-4}$ |  48Cr | $4.14\times 10^{-4}$
16O | $4.92\times 10^{-2}$ |  50Cr | $1.07\times 10^{-4}$
20Ne | $4.89\times 10^{-4}$ |  52Fe | $8.89\times 10^{-3}$
24Mg | $1.11\times 10^{-3}$ |  53Fe | $5.52\times 10^{-4}$
27Al | $6.46\times 10^{-5}$ |  54Fe | $1.12\times 10^{-2}$
28Si | $1.89\times 10^{-1}$ |  55Co | $2.72\times 10^{-3}$
29Si | $1.29\times 10^{-4}$ |  56Ni | $5.55\times 10^{-1}$
30Si | $1.21\times 10^{-4}$ |  57Ni | $8.63\times 10^{-3}$
31P | $8.62\times 10^{-5}$ |  58Ni | $6.64\times 10^{-3}$
32S | $1.07\times 10^{-1}$ |  59Cu | $2.61\times 10^{-4}$
33S | $1.27\times 10^{-4}$ |  60Cu | $1.67\times 10^{-4}$
34S | $7.01\times 10^{-4}$ |  60Zn | $8.37\times 10^{-3}$
36Ar | $2.09\times 10^{-2}$ |  61Zn | $2.33\times 10^{-4}$
38Ar | $4.66\times 10^{-4}$ |  62Zn | $1.23\times 10^{-3}$
Table 1: Nucleosynthetic yields generated by the $1.0\,M_{\odot}$ WD
detonation model using standard nuclear reaction rates. We present the results
for a selection of 32 important isotopes from our 205-isotope nuclear reaction
network that achieve an abundance of at least $10^{-4}M_{\odot}$.

###  3.2 Sensitivity to Reaction Rate Normalization

(a)

(b)

Figure 1: (a) The relative change in the nucleosynthetic yields generated with
standard nuclear reaction rates normalized by a factor of 10.0 compared
against the yields generated using standard nuclear reaction rates. The
colorbar indicates the value of the relative change in logarithmic scale, and
a small range of $\pm 0.1$ around zero is mapped linearly to avoid ln(0). We
present isotopes ($y$-axis) that achieve an initial abundance greater than
$10^{-4}M_{\odot}$ and nuclear reactions ($x$-axis) which affected the yields
of at least one species by $\geq 20\%$. We also include 27Al and 31P. (b) Same
as Figure 1a, but with standard reaction rates normalized by a factor of 0.1.
The magnitude of the relative change is lower when nuclear reaction rates are
normalized by a uniform factor of 0.1 as compared to using a factor of 10.0
normalization.

In Figure 1a we show the relative change in isotopic abundances generated when
each nuclear reaction rate in our network is individually normalized by a
uniform factor of 10.0. Figure 1b shows the results of an analogous
calculation, but for the individual normalization of each nuclear reaction
rate in our network by a uniform factor of 0.1. We apply these two
normalizations to the rates of all nuclear reactions in our network, each time
repeating all nucleosynthetic calculations, to identify those reactions whose
uncertainty in the rate has the largest influence on the final chemical
composition of the ejecta produced by the model. The normalization of all
rates by a uniform factor of ten is an approximation to the actual
temperature-dependent uncertainties of these reaction rates provided by
STARLIB (Sallaska et al., 2013) shown in Figures 3a and 3b. Most
experimentally determined reaction rates follow a lognormal probability
density, and the factor uncertainty of the rate is defined as
$f.u.=e^{\sigma}$, where $\sigma$ is the lognormal spread parameter
corresponding to the lognormal approximation of the rate. Only a select number
of these reaction rates have been derived from Monte Carlo sampling of
experimental data, and the remaining rates and uncertainties have been
determined theoretically using Hauser-Feshbach model calculations (Goriely et
al., 2008). These theoretically determined rates are assigned a constant
factor uncertainty $f.u.=10$ at all temperatures. For a more detailed
discussion of the calculation of nuclear reaction rate uncertainties see
Sallaska et al. (2013). For the purposes of our study, the normalization of
all rates by a uniform factor of 10 is a sufficient approximation to explore
the extent to which nucleosynthesis in the detonations of sub-$M_{\text{Ch}}$
WDs is sensitive to nuclear reaction rate uncertainties. For analogous studies
employing a similar approach to investigate near-$M_{\text{Ch}}$ WD Type Ia
explosion models, see Martínez-Rodríguez et al. (2017), Parikh et al. (2013),
and Bravo & Martínez-Pinedo (2012).

Figure 2: The temperature-dependent factor uncertainty of the rate provided by
STARLIB for the triple-$\alpha$ process, 20Ne($\alpha$, $\gamma$)24Mg,
23Na($p$, $\gamma$)24Mg, 16O($\alpha$, $\gamma$)20Ne, and 30Si($p$,
$\gamma$)31P, plotted over the temperatures reached during detonation.

From our nuclear reaction network of 942 nuclear reactions and 205 isotopes,
we find that 50 reactions induce a change of at least $20\%$ on the final
nucleosynthetic yield of at least one isotope. Uncertainties in the rates of
20Ne($\alpha$, $\gamma$)24Mg, 23Na($p$, $\gamma$)24Mg, 23Na($\alpha$,
$p$)26Mg, 16O(16O, $p$)31P, 16O($\alpha$, $\gamma$)20Ne, 30Si($p$,
$\gamma$)31P, and the triple-$\alpha$ process are the reactions which
consistently have the most pronounced effects on nuclear yields. Figure 2
shows the temperature-dependent factor uncertainty for those reactions for
which there is sufficient experimental data available for Monte Carlo based
reaction rates and uncertainties, plotted over the temperatures reached during
the detonation.

###  3.3 Isotopic Ratios

In this section, we analyze the impact of nuclear reaction rate variation on
the model’s predictions of important isotopic ratios. It is of interest to
investigate the extent to which the results summarized in Figures 1a and 1b
impact the model’s predictions of 57Ni/56Ni, 55Co/57Ni, and the final mass
ratio of Mn/Fe after all radioactive decays have taken place. To account for
decays, the masses of Mn and Fe are calculated as 55Mn + 55Co + 55Fe and 54Fe
+ 56Fe + 56Co + 56Ni + 57Fe + 57Co + 57Ni, respectively. The values of these
ratios can serve as a useful tool for breaking the degeneracy between
competing SN Ia progenitor models. Note that we calculate all isotopic ratios
$10\,$s after the start of explosion.

Reaction & Normalization | Isotopic Ratio
---|---
|  57Ni/56Ni |  55Co/57Ni | Mn/Fe
| triple-$\alpha$ $\times 10.0$
---
$\times 0.1$
| 12%
---
-15%
| -38%
---
53%
| -30%
---
31%
|  55Co($p$, $\gamma$)56Ni $\times 10.0$
---
$\times 0.1$
|  $<$-1%
---
$<$1%
| -23%
---
30%
| -23%
---
30%
|  57Co($p$, $n$)57Ni $\times 10.0$
---
$\times 0.1$
| -15%
---
19%
| 19%
---
-16%
|  $<$1%
---
$<$-1%

Table 2: The relative change in the ratios of 57Ni/56Ni, 55Co/57Ni, and Mn/Fe
generated by applying two normalization factors (10.0$\times$ and 0.1$\times$)
to the standard nuclear reaction rates.

The effects that our nuclear reaction rate normalizations have on the values
of these isotopic ratios are summarized in Table 2. In the standard case using
default nuclear reaction rates, we obtain a value of 0.0155 for the ratio of
57Ni to 56Ni. In general, the value of this ratio was relatively robust to
variations in nuclear reaction rates throughout our study. The ratio of 55Co
to 57Ni achieves a value of 0.135 using standard nuclear reaction rates, and
is affected by at most $53\%$ due to normalization of the triple-$\alpha$
process. The ratio of Mn/Fe achieves a value of $4.76\times 10^{-3}$ using
standard reaction rates, and changes by at most $31\%$ due to the
normalization of the rate of the triple-$\alpha$ process.

Of these ratios, the value of 57Ni to 56Ni is the least sensitive to reaction
rate normalizations. The final nucleosynthetic yields of these two isotopes
are particularly robust to normalizations of nuclear reaction rates by a
factor of 10.

(a)

(b)

Figure 3: (a) The factor uncertainty of the rate as a function of temperature
as provided by STARLIB for the first set of reactions, and their corresponding
reverse processes, that induce a relative change of at least 20% in the yield
of at least one isotope in our nuclear network when normalized. (b) Same as
Figure 3a, but for the remaining reactions that induce a relative change of at
least 20% in the yield of at least one isotope in our nuclear network when
normalized.

##  4 Conclusions

Following up the work of Shen et al. (2018a) who suggested the detonations of
sub-$M_{\text{Ch}}$ WDs as promising candidates to explain most SNe Ia, but
found enduring tensions in the neutron-rich nucleosynthesis generated in
simulations of these explosions compared to SNe Ia observations, we have
investigated the extent to which nuclear reaction rate uncertainties impact
the nucleosynthetic yields of a one dimensional simulation of the detonation
of a bare $1.0\,M_{\odot}$ C/O WD.

To calculate nucleosynthetic yields, we post-process the results of the
41-isotope hydrodynamical simulation described in Shen et al. (2018a) using a
205-isotope nuclear reaction network including all 942 interlinking reactions.
To examine the impacts of nuclear reaction rate uncertainties we individually
normalize the rates of all input nuclear reaction rates by two constant
factors (10.0 and 0.1 times the standard rate), repeating all post-processing
calculations for each individual normalization to a reaction rate and its
corresponding reverse process.

Of the 942 nuclear reactions in our network, the individual normalization of
50 nuclear reaction rates impacts the nucleosynthetic yield of at least one
isotope in our network by at least $20\%$ from the fiducial model. The rates
of 20Ne($\alpha$, $\gamma$)24Mg, 23Na($p$, $\gamma$)24Mg, 23Na($\alpha$,
$p$)26Mg, 16O(16O, $p$)31P, 16O($\alpha$, $\gamma$)20Ne, 30Si($p$,
$\gamma$)31P, and the triple-$\alpha$ process have the greatest impact on
supernova nucleosynthesis over all isotopes included in our nuclear network
when normalized by a factor of 10.0 and 0.1. Individually increasing reaction
rates by a factor of 10.0 has a more pronounced impact on nucleosynthetic
yields than reducing these rates by the same factor. Individual normalizations
to the rates of these reactions has the largest impact on the final abundances
of isotopes in the range of 10 $\lesssim Z\lesssim$ 20\. In general, we find
that the abundances of the Fe-group elements are relatively robust to
individual normalizations of nuclear reaction rates in our network by constant
factors of 10.

Our results are in general agreement with the previous studies of Bravo &
Martínez-Pinedo (2012) and Parikh et al. (2013), who investigated the impacts
of nuclear reaction rate uncertainties in simulations of near-$M_{\text{Ch}}$
WD SNe Ia scenarios including the W7 pure deflagration and the delayed
detonation models. Both of these studies also found that the Fe-group elements
were particularly robust to individual variations in the rates of nuclear
reactions. This result can be explained by the fact that during explosion many
of the Fe-group elements are produced in nuclear statistical equilibrium
(NSE), which is insensitive to reaction rate variations. The nucleosynthetic
yields in the explosions of WDs less massive than $1.0\,M_{\odot}$ may be more
sensitive to reaction rate uncertainties because more of the burning takes
place outside of NSE. Future work is required to quantify the impact of
nuclear reaction rate uncertainties on nucleosynthesis in lower-mass WD
detonations.

We conclude that uncertainties in the rates of input nuclear reactions in the
simulation of a bare $1.0\,M_{{\odot}}$ C/O WD detonation have a small
influence on the final chemical composition of the ejecta. Our results suggest
that individual nuclear reaction rate uncertainties alone cannot account for
current tensions between the isotopic ratios of Fe-group elements produced in
simulations of sub-$M_{\text{Ch}}$ WD detonations and their values inferred
through observations of late-time SNe Ia light curves, the Solar abundance of
Mn, and SN remnant observations. Future work will be required to alleviate
these tensions.

##  5 Acknowledgements

We thank Patrick J. Fitzpatrick, Alison Miller, and Dan Kasen for helpful
discussions and advice. K.J.S. received support for this work from NASA
through the Astrophysics Theory Program (NNX17AG28G). Calculations in this
work were made using the Savio cluster provided by UCB.

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[a,b]Mario Bertaina

# Implications of Mini-EUSO measurements for a space-based observation of
UHECRs

Matteo Battisti  Marta Bianciotto  Karl Bolmgren  Francesco Fenu

###### Abstract

Mini-EUSO is the first mission of the JEM-EUSO program on board the
International Space Station. It was launched in August 2019 and it is
operating since October 2019 being located in the Russian section (Zvezda
module) of the station and viewing our planet from a nadir-facing UV-
transparent window. The instrument is based on the concept of the original
JEM-EUSO mission and consists of an optical system employing two Fresnel
lenses of 25 cm each and a focal surface composed of 36 Multi-Anode
Photomultiplier tubes, 64 channels each, for a total of 2304 channels with
single photon counting sensitivity and an overall field of view of
44$\times$44∘. Mini-EUSO can map the night-time Earth in the near UV range
(predominantly between 290 nm and 430 nm), with a spatial resolution of about
6.3 km and different temporal resolutions of 2.5 $\mu$s, 320 $\mu$s and 41 ms.
Mini-EUSO observations are extremely important to better assess the potential
of a space-based detector in studying Ultra-High Energy Cosmic Rays (UHECRs)
such as K-EUSO and POEMMA. In this contribution we focus the attention on the
results of the UV measurements and we place them in the context of UHECR
observations from space, namely the estimation of exposure.

##  1 Introduction

The current main goal in the field of UHECR (Ultra-High Energy Cosmic Ray)
science is to identify their astrophysical sources and composition [1]. For
this, increased statistics is one of the essential requirements. A space-based
detector for UHECR research has the advantage of a very large exposure and a
uniform coverage of the celestial sphere. The aim of the JEM-EUSO program [2]
is to bring the study of UHECRs to space. The principle of observation is
based on the detection of UV light emitted by isotropic fluorescence of
atmospheric nitrogen excited by Extensive Air Showers (EASs) in Earth’s
atmosphere and forward-beamed Cherenkov radiation reflected at the Earth’s
surface or at dense cloud tops. The JEM-EUSO program includes missions on
ground (EUSO-TA [3]), on stratospheric balloons (EUSO-Balloon [4], EUSO-SPB1
[5], EUSO-SPB2 [6]), and from space (TUS [7], Mini-EUSO [8, 9]) employing
fluorescence detectors to demonstrate the feasibility of the UHECR observation
from space and prepare for the large size missions K-EUSO [10] and POEMMA
[11]. Mini-EUSO is the first detector of the JEM-EUSO program to observe the
Earth from the International Space Station (ISS) and to validate from there
the observational principle of a space-based detector for UHECR measurements.

##  2 The Mini-EUSO space telescope

Mini–EUSO (Multiwavelength Imaging New Instrument for the Extreme Universe
Space Observatory, known as _UV atmosphere_ in the Russian Space Program) [8]
is operating on the ISS since October 7th, 2019, and till June 2023, more than
80 sessions have been performed lasting 12 hours each. The pouches containing
all stored data are then returned to Earth every $\sim$12 months by the Soyuz
spacecraft.

The optics are based on two 25 cm diameter Fresnel lenses in Polymethyl
methacrylate (PMMA). The Mini–EUSO focal surface, or Photo Detector Module
(PDM), consists of a grid of 36 Multi-Anode Photomultiplier Tubes (MAPMTs,
Hamamatsu Photonics R11265-M64). Each MAPMT consists of $8\times 8$ pixels,
resulting in a total of 2304 channels. The MAPMTs are grouped in Elementary
Cells (ECs) of $2\times 2$ MAPMTs. MAPMTs are separated by 2 – 3 mm spacing to
avoid vibration damage at launch. Consequently, gaps exist between MAPMTs in
the collected images. Each EC has an independent high voltage power supply
(HVPS) and board connecting the dynodes and anodes of the four
photomultipliers. The HVPS system is based on a Cockroft-Walton circuit. The
system has an internal safety mechanism which operates either reducing the
collection efficiency of the four MAPMTs or reducing the MAPMT gain when
particularly bright signals occur (i.e. lightning or large cities) [8]. The
recovery to the nominal mode takes place only few ms after the light level has
decreased to a sufficiently low value. In the following we will refer to
Cathode3 for the nominal mode and Cathode2 for the reduced efficiency/gain
mode.

The system has a single photon-counting capability with a double pulse
resolution of $\sim$6 ns. Photon counts are summed in Gate Time Units (GTUs)
of 2.5 $\mu$s. The PDM Data Processor (PDM-DP) stores the 2.5 $\mu$s GTU data
stream (D1) in a running buffer on which the trigger code is executed. A
detailed description of the trigger algorithm is reported in [12], which
represents an adaptation of the trigger logic conceived for JEM-EUSO [13],
while the on-board performance of the trigger system is summarized in [14].
The algorithm searches for a signal integrated over 8 consecutive GTUs above
16 standard deviations from the average in any pixel of the focal surface. The
choice to operate on 8 GTUs integration and to act on each pixel independently
is based on the time needed by a light signal to cross the FoV of a pixel and
the fact that 20 $\mu$s represent a significant portion of an EAS light-track
in atmosphere (see Fig. 1 left).

Figure 1: Left: Comparison between JEM-EUSO and Mini-EUSO FoVs. The image
shows the detected light track of three simulated EAS with ESAF [15] of energy
1020 eV with different zenith angles ($\theta$ = 30∘, 60∘, and 75∘) as imaged
by JEM-EUSO detector. Each little colored dot represents the pixel FoV of JEM-
EUSO projected on ground, each grey square indicates the MAPMT FoV and the
large black squares show the FoV of JEM-EUSO PDMs. The green and red squares
represent Mini-EUSO pixel’s and MAPMT’s FoV, respectively. Mini-EUSO pixel’s
FoV is larger than the FoV of a JEM-EUSO MAPMT and Mini-EUSO MAPMT’s FoV is
larger than the FoV of one JEM-EUSO PDM. Right: Trigger efficiency curves of
Mini-EUSO for ESAF simulated proton-generated EASs of different energies on
different background levels. The red and violet points assume a fixed
nightglow background of 1 and 2 counts/pix/GTU, respectively. The continuous
black (green) line represents the convolved trigger efficiency curve in which
each background level below 2 (5) counts/pix/GTU is weighted for the relative
fraction of time in which it was measured by Mini-EUSO. The dotted black
(green) line provides the fractional increase in exposure [relative to the
black (green) line] if the accepted nightglow background is increased from 2
(5) counts/pix/GTU to 30 counts/pix/GTU. A significant increase in exposure is
obtained only at the highest energies. See text for details. Image adapted
from [16].

Independently from the trigger, sums of 128 frames (320 µs, D2) are
continuously calculated and stored in another buffer where a similar trigger
algorithm, but at this time scale, is running. Similarly, sums of 128 D2
frames (40.96 ms, D3) are calculated in real time and continuously stored.
Every 5.24 s, 128 GTUs of D3 data, up to 4 D2 packets and up to 4 D1 packets
(if triggers were present) are sent to the CPU for storage. In this way
various classes of phenomena with different duration can be detected with an
appropriate time scale (see sec. 3 for details).

Prior to the launch, the instrument underwent a series of integration and
acceptance tests in Rome, Moscow, and Baikonur, where it was placed in the
uncrewed Soyuz capsule. A systematic test of the acquisition logic was
performed at the TurLab facility [17] of the University and at the
Astrophysical Observatory (INAF-OATo) [18] in Turin. After launch, an end-to-
end in-flight calibration of the Mini-EUSO detector has been performed by
assembling different UV-flasher systems on ground in Japan, Italy, and France
and by firing them in various observational campaigns. A detailed description
of the methodology and of the observational results is reported in [19].

##  3 Mini-EUSO design, expected performance and exposure studies

Mini-EUSO has been designed to detect a photon rate per pixel from diffuse
sources (nightglow, clouds, cities, etc.) in the range of values expected from
a large mission in space such as the original JEM-EUSO mission [20] or the
future detectors K-EUSO or POEMMA. The pixel FoV is, therefore, $\sim$100
times larger in area with respect to the FoV of a JEM-EUSO pixel ($\sim$0.5
$\times$ 0.5 km2), to compensate for the optical system $\sim$100 times
smaller, constrained by the dimension of the UV transparent window (see Fig. 1
left).

In order to have a precise ratio of the photon rate per pixel from diffuse
sources between JEM-EUSO and Mini-EUSO, a full simulation of JEM-EUSO and
Mini-EUSO detectors was performed with ESAF simulation software [15]. In case
of Mini-EUSO the overall efficiency of the detector was fine-tuned with ESAF,
mainly acting at the level of MAPMT response, to match the measured one
$\epsilon_{ME}$ = 0.080 $\pm$ 0.015 (see the end-to-end in-flight calibration
of Mini-EUSO reported in [19]) for a point-like source on ground. A flat
diffused UV emission in the range $\lambda$ = 300 - 400 nm was simulated at
the detector’s aperture either with a range of zenith directions much larger
than the FoV of the instrument ($\pm$60∘ for both detectors) or just within
the FoV of the detectors ($\pm$30∘ for JEM-EUSO and $\pm$22∘ for Mini-EUSO).
The estimated background ratio ($R(ME/JE)$) between Mini–EUSO and JEM–EUSO at
FS level is $R(ME/JE)$ = 0.98 – 1.04 slightly depending on the range of zenith
angles. This result confirms that the expected photon rate from diffuse
sources is similar in JEM-EUSO and Mini-EUSO instruments.

The energy threshold of Mini-EUSO for point-like sources like UHECRs is
roughly 2 orders of magnitude higher than the original JEM-EUSO one. The right
side of Fig. 1 shows the trigger efficiency of Mini-EUSO for ESAF simulated
proton-generated EASs of different energies. Events have been simulated
according to a $\sin(2\cdot\theta)$ dependence on a larger area than the FoV
of the instrument on ground to take into account border effects. The
efficiency ($\epsilon$) as a function of the energy $(E)$ has then been
calculated as:

$\epsilon(E)=\frac{N_{trig}}{N_{simu}}\cdot\frac{A_{simu}}{A_{FoV}},$ (1)

where $N_{trig}$ and $N_{simu}$ represent the number of triggered events over
the simulated ones for a specific energy bin, while $A_{simu}$ and $A_{FoV}$
indicate the area on which EAS have been injected and the area on ground in
the FoV of Mini-EUSO, respectively. The red and violet points assume a fixed
nightglow background of 1 and 2 counts/pix/GTU, respectively. The 50% trigger
efficiency is located between 3 - 5 $\times$ 1021 eV depending on the UV
nightglow level.

The D3 data taken by Mini-EUSO allow a first comparison with the assumed
background levels in JEM-EUSO, K-EUSO and POEMMA to verify that the estimated
performance is based on justified assumptions. The analysis presented in the
following is preliminary as it is based on part of the data collected in 25
sessions between session 20 and 44. A more refined analysis will be performed
when all the data collected by Mini-EUSO is available. The left side of Fig. 2
displays the typical number of minutes in which Mini-EUSO was in operation
during all data taking sessions between Session 5 and Session 44. The
different time of operation in each orbit reflects several aspects such as the
different duration of the night in that specific orbit or the moon condition
or the switch on and off by the astronauts among others. The right side of
Fig. 2 displays in brown colour the fraction of time from session 20 to
session 44 in which Mini-EUSO operated in a specific Moon Bin (MB). This is
compared to the monthly averaged fraction of time in which the Moon appears in
the sky with a specific MB (blue colour). Mini-EUSO operated in all the
possible Moon conditions with a preference for low Moon phases. This is done
on purpose to maximize the scientific potential of Mini-EUSO for atmospheric
science (i.e. meteors, elves).

Figure 2: Left: Time in minutes in which Mini-EUSO was operational during the
various orbits between session 05 and session 44. Right: Brown histogram
displays the fraction of time in which Mini-EUSO was operational between
sessions 20 and 44 with a specific MB while blue histogram shows the monthly
averaged fraction of time in which the Moon appears in the sky in a specific
MB.

According to Mini-EUSO results in low MB conditions, in $\sim$90% of the time
of clear sea conditions the count rate is below 2.0 counts/pix/GTU, the median
being $\sim$0.8 counts/pix/GTU (see Fig. 3). In clear land conditions there is
a higher probability of very low counts. These are associated with deserts and
forests (see [21] for details). Under the reasonable assumption that
conditions above 2 counts/pix/GTU on land are due to the presence of
anthropogenic lights ($\sim$20% of the time) and taking into account $\sim$30%
land coverage on Earth, this result corresponds to $\sim$6% of the total
fraction of time, which is close to the 7% estimation performed for JEM-EUSO
in [20]. Moreover, cloudy conditions typically shift curves by a factor 1.5 -
2 towards higher count rates as already measured in JEM-EUSO balloon flights
[4]. Taking into account the fact that JEM-EUSO and Mini-EUSO are expected to
measure similar count rates from diffuse sources, these results are consistent
with the assumption done in [20] for JEM-EUSO where the exposure was
calculated under the nominal condition of $\sim$1.1 count/pix/GTU.

In order to have a proper estimation of Mini-EUSO exposure at different
energies it is necessary to compute an efficiency curve for the various
background levels and convolve each efficiency curve with the fraction of time
in which such background level is measured. The methodology is described in
detail in [16] and we report here only the essential points. As it is not
possible to simulate the efficiency curves for infinite background levels, as
a first step the efficiency curves are estimated by simulated proton-generated
EASs of various energies only for a limited set of background levels in the
range [0.2;4.0] counts/pix/GTU and the obtained efficiency curves are fitted
with a function of the form:

$\epsilon(E)=0.5\cdot[1+erf(\frac{log_{10}(E/eV)-P_{0}}{P_{1}})],$ (2)

where the parameter $P_{0}$ indicates the energy ($E$) at which the efficiency
reaches 50% and $P_{1}$ measures the slope of the efficiency curve
($\epsilon(E)$). Subsequently, the obtained parameter values at different
background levels have been fitted with appropriate functions (logarithmic and
exponential functions for $P_{0}$ and $P_{1}$, respectively) and the
dependencies of $P_{0}$ and $P_{1}$ as function of the background level have
been obtained. Finally, the trigger efficiency curves are modelled at all
background levels by equation (2) using as $P_{0}$ and $P_{1}$ derived by
means of the two functions.

Next, the convolved exposure curve ($\mathcal{E}(E)$) has been calculated
according to equation:

$\mathcal{E}(E)=\sum_{i}(\epsilon_{i}(E)\cdot t_{i}\cdot
A_{i})\cdot\Omega\cdot t_{tot}\cdot k,$ (3)

where $i$ denotes the UV background level, $t_{i}$ represents the relative
fraction of time in which the measured background is in the interval $i$ (each
interval having a width of 0.01 counts/pix/GTU), $A_{i}$ accounts for the
cumulative area on ground with background $i$, $\Omega$ measures the UHECR
observational solid angle (which assumes the value of $\pi$), and $t_{tot}$ =
69.16 hours is the total accumulated time in Cathode3 mode. The parameter $k$
represents the efficiency factor for detecting the EAS maximum in presence of
clouds. This value depends on the type of clouds, their optical depth and
height. A detailed analysis was performed at the time of JEM-EUSO and adopted
in this calculation ($k$ = 72%).

In order to have a more realistic estimation of the exposure curve, a
renormalization has been applied to the fraction of time in which Mini-EUSO
has measured a specific UV background level during a specific MB (see left
panel of Fig. 3) by rescaling it for the ratio between the fraction of time in
which Mini-EUSO operated with a specific MB and the expected monthly average
fraction of time according to the Moon cycle (see right panel of Fig. 2). This
is summarized in equation:

$t_{i}=\sum_{MB}\frac{T_{i}(MB)}{F(MB)},$ (4)

where $T_{i}(MB)$ is the fraction of time in which Mini-EUSO measured the
background $i$ in MB and $F(MB)$ is the conversion factor for each MB in order
to get the expected monthly averaged fraction of time in a specific MB
according to the Moon cycle.

At the same time the duty cycle of Mini-EUSO as a function of the tolerated
background level ($\eta_{i}$) can be estimated by the following equation:

$\eta_{i}=\frac{1}{\Delta T_{orbit}\cdot N_{orbit}}\cdot\sum_{j=0}^{i}t_{j},$
(5)

and it is displayed in the right panel of Fig. 3. As an example it corresponds
to $\eta\sim$ 15 (18)% if up to 2 (5) counts/pix/GTU are tolerated to estimate
the duty cycle. Finally, the exposure curve obtained by integrating all
background levels below 2 (5) counts/pix/GTU has been renormalized using the
exposure obtained at the plateau level of 1022 eV. The result, which
represents the convolved trigger efficiency curve, is shown as black (green)
line in Fig. 1. The green curve is very close to the efficiency curve obtained
at the fixed background level of 1 count/pix/GTU, indicating that such a curve
provides a reasonable approximation of the integrated performance in the
various UV background conditions. Moreover, by convolving $\eta$ =18% with $k$
= 72% an effective conversion factor between aperture and exposure of 13% is
derived which is consistent with the value obtained in JEM-EUSO computations,
confirming the assumptions made in those estimations. Similarly, these
conclusions can be extended also to the estimation of K-EUSO and POEMMA
trigger efficiency curves as they have been derived adopting the very same
methodology used for JEM-EUSO.

Figure 3: Left: Cumulative fraction of time in which Mini-EUSO measured a UV
intensity higher than a specific value reported on the X-axis. Different
colours refer to the different MB. Each phase has its own normalization.
Right: Same as above but summing up all above distribution each weighted for
the expected monthly average fraction of time with a specific MB (see text for
details).

The accumulated exposure of Mini-EUSO in this analysis amounts to $\sim$1400
Linsley. A very preliminary extrapolation of this result to all good so far
recorded data indicates that Mini-EUSO has potentially accumulated till now an
exposure equivalent to $\sim$3600 Linsley. This value is already about 4%
percent of the exposure collected so far by ground-based detectors, and
equivalent to the one accumulated in the case of hybrid data [22, 23].

##  4 Acknowledgements

This work was supported by the Italian Space Agency through the agreement n.
2020-26-Hh.0, by the French space agency CNES, and by the National Science
Centre in Poland grants 2017/27/B/ST9/02162 and 2020/37/B/ST9/01821. This
research has been supported by the Interdisciplinary Scientific and
Educational School of Moscow University “Fundamental and Applied Space
Research” and by Russian State Space Corporation Roscosmos. The article has
been prepared based on research materials collected in the space experiment
“UV atmosphere”. We thank the Altea-Lidal collaboration for providing the
orbital data of the ISS.

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Full Authors list: The JEM-EUSO Collaboration

S. Abeff, J.H. Adams Jr.ld, D. Allardcb, P. Alldredgeld, R. Aloisioep, L.
Anchordoquile, A. Anzaloneed,eh, E. Arnoneek,el, M. Bagherilh, B. Baretcb, D.
Barghiniek,el,em, M. Battisticb,ek,el, R. Bellottiea,eb, A.A. Belovib, M.
Bertainaek,el, P.F. Bertonelf, M. Bianciottoek,el, F. Biscontiei, C.
Blaksleyfg, S. Blin-Bondilcb, K. Bolmgrenja, S. Brizlb, J. Burtonld, F.
Cafagnaea.eb, G. Cambiéei,ej, D. Campanaef, F. Capeldb, R. Carusoec,ed, M.
Casolinoei,ej,fg, C. Cassardoek,el, A. Castellinaek,em, K. Černýba, M.J.
Christllf, R. Colalilloef,eg, L. Contiei,en, G. Cottoek,el, H.J. Crawfordla,
R. Cremoniniel, A. Creusotcb, A. Cummingslm, A. de Castro Gónzalezlb, C. de la
Tailleca, R. Diesinglb, P. Dinaucourtca, A. Di Nolaeg, T. Ebisuzakifg, J.
Eserlb, F. Fenueo, S. Ferrareseek,el, G. Filippatoslc, W.W. Finchlc, F.
Flaminioeg, C. Fornaroei,en, D. Fuehnelc, C. Fuglesangja, M. Fukushimafa, S.
Gadamsettylh, D. Gardiolek,em, G.K. Garipovib, E. Gazdalh, A. Golzioel, F.
Guarinoef,eg, C. Guépinlb, A. Haungsda, T. Heibgeslc, F. Isgròef,eg, E.G.
Juddla, F. Kajinofb, I. Kanekofg, S.-W. Kimga, P.A. Klimovib, J.F.
Krizmaniclj, V. Kungellc, E. Kuznetsovld, F. López Martínezlb, D. Mandátbb, M.
Manfrinek,el, A. Marcelliej, L. Marcelliei, W. Marszałha, J.N. Matthewslg, M.
Meseef,eg, S.S. Meyerlb, J. Mimouniab, H. Miyamotoek,el,ep, Y. Mizumotofd, A.
Monacoea,eb, S. Nagatakifg, J.M. Nachtmanli, D. Naumovia, A. Neronovcb, T.
Nonakafa, T. Ogawafg, S. Ogiofa, H. Ohmorifg, A.V. Olintolb, Y. Onelli, G.
Osteriaef, A.N. Ottelh, A. Pagliaroed,eh, B. Panicoef,eg, E. Parizotcb,cc,
I.H. Parkgb, T. Paulle, M. Pechbb, F. Perfettoef, P. Picozzaei,ej, L.W.
Piotrowskihb, Z. Plebaniakei,ej, J. Posliguali, M. Pottslh, R. Preveteef,eg,
G. Prévôtcb, M. Przybylakha, E. Realiei,ej, P. Reardonld, M.H. Renoli, M.
Ricciee, O.F. Romero Matamalalh, G. Romoliei,ej, H. Sagawafa, N. Sakakifg,
O.A. Saprykinic, F. Sarazinlc, M. Satofe, P. Schovánekbb, V. Scottief,eg, S.
Selmanecb, S.A. Sharakinib, K. Shinozakiha, S. Stepanofflh, J.F. Sorianole, J.
Szabelskiha, N. Tajimafg, T. Tajimafg, Y. Takahashife, M. Takedafa, Y.
Takizawafg, S.B. Thomaslg, L.G. Tkachevia, T. Tomidafc, S. Toscanoka, M.
Traïcheaa, D. Trofimovcb,ib, K. Tsunofg, P. Vallaniaek,em, L. Valoreef,eg,
T.M. Venterslj, C. Vigoritoek,el, M. Vrabelha, S. Wadafg, J. Watts Jr.ld, L.
Wienckelc, D. Winnlk, H. Wistrandlc, I.V. Yashinib, R. Younglf, M.Yu. Zotovib.

aa Centre for Development of Advanced Technologies (CDTA), Algiers, Algeria
ab Lab. of Math. and Sub-Atomic Phys. (LPMPS), Univ. Constantine I,
Constantine, Algeria
ba Joint Laboratory of Optics, Faculty of Science, Palacký University,
Olomouc, Czech Republic
bb Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
ca Omega, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France
cb Université de Paris, CNRS, AstroParticule et Cosmologie, F-75013 Paris,
France
cc Institut Universitaire de France (IUF), France
da Karlsruhe Institute of Technology (KIT), Germany
db Max Planck Institute for Physics, Munich, Germany
ea Istituto Nazionale di Fisica Nucleare - Sezione di Bari, Italy
eb Università degli Studi di Bari Aldo Moro, Italy
ec Dipartimento di Fisica e Astronomia "Ettore Majorana", Università di
Catania, Italy
ed Istituto Nazionale di Fisica Nucleare - Sezione di Catania, Italy
ee Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati,
Italy
ef Istituto Nazionale di Fisica Nucleare - Sezione di Napoli, Italy
eg Università di Napoli Federico II - Dipartimento di Fisica "Ettore Pancini",
Italy
eh INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Italy
ei Istituto Nazionale di Fisica Nucleare - Sezione di Roma Tor Vergata, Italy
ej Università di Roma Tor Vergata - Dipartimento di Fisica, Roma, Italy
ek Istituto Nazionale di Fisica Nucleare - Sezione di Torino, Italy
el Dipartimento di Fisica, Università di Torino, Italy
em Osservatorio Astrofisico di Torino, Istituto Nazionale di Astrofisica,
Italy
en Uninettuno University, Rome, Italy
eo Agenzia Spaziale Italiana, Via del Politecnico, 00133, Roma, Italy
ep Gran Sasso Science Institute, L’Aquila, Italy
fa Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Japan
fb Konan University, Kobe, Japan
fc Shinshu University, Nagano, Japan
fd National Astronomical Observatory, Mitaka, Japan
fe Hokkaido University, Sapporo, Japan
ff Nihon University Chiyoda, Tokyo, Japan
fg RIKEN, Wako, Japan
ga Korea Astronomy and Space Science Institute
gb Sungkyunkwan University, Seoul, Republic of Korea
ha National Centre for Nuclear Research, Otwock, Poland
hb Faculty of Physics, University of Warsaw, Poland
ia Joint Institute for Nuclear Research, Dubna, Russia
ib Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,
Russia
ic Space Regatta Consortium, Korolev, Russia
ja KTH Royal Institute of Technology, Stockholm, Sweden
ka ISDC Data Centre for Astrophysics, Versoix, Switzerland
la Space Science Laboratory, University of California, Berkeley, CA, USA
lb University of Chicago, IL, USA
lc Colorado School of Mines, Golden, CO, USA
ld University of Alabama in Huntsville, Huntsville, AL, USA
le Lehman College, City University of New York (CUNY), NY, USA
lf NASA Marshall Space Flight Center, Huntsville, AL, USA
lg University of Utah, Salt Lake City, UT, USA
lh Georgia Institute of Technology, USA
li University of Iowa, Iowa City, IA, USA
lj NASA Goddard Space Flight Center, Greenbelt, MD, USA
lk Fairfield University, Fairfield, CT, USA
ll Department of Physics and Astronomy, University of California, Irvine, USA
lm Pennsylvania State University, PA, USA