#  A discovery of a low-energy excess in cosmic-ray iron: an evidence of the
past supernova activity in the Local Bubble

M. J. Boschini INFN, Milano-Bicocca, Milano, Italy  CINECA, Segrate, Milano,
Italy  S. Della Torre INFN, Milano-Bicocca, Milano, Italy  M. Gervasi INFN,
Milano-Bicocca, Milano, Italy  Physics Department, University of Milano-
Bicocca, Milano, Italy  D. Grandi INFN, Milano-Bicocca, Milano, Italy  Physics
Department, University of Milano-Bicocca, Milano, Italy  G. Jóhannesson
Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
NORDITA, Roslagstullsbacken 23, 106 91 Stockholm, Sweden  G. La Vacca INFN,
Milano-Bicocca, Milano, Italy  Physics Department, University of Milano-
Bicocca, Milano, Italy  N. Masi INFN, Bologna, Italy  Physics Department,
University of Bologna, Bologna, Italy  I. V. Moskalenko Hansen Experimental
Physics Laboratory, Stanford University, Stanford, CA 94305  Kavli Institute
for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA
94305  S. Pensotti  INFN, Milano-Bicocca, Milano, Italy  Physics Department,
University of Milano-Bicocca, Milano, Italy  T. A. Porter Hansen Experimental
Physics Laboratory, Stanford University, Stanford, CA 94305  Kavli Institute
for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA
94305  L. Quadrani  INFN, Bologna, Italy  Physics Department, University of
Bologna, Bologna, Italy  P. G. Rancoita INFN, Milano-Bicocca, Milano, Italy
D. Rozza INFN, Milano-Bicocca, Milano, Italy  Physics Department, University
of Milano-Bicocca, Milano, Italy  M. Tacconi INFN, Milano-Bicocca, Milano,
Italy  Physics Department, University of Milano-Bicocca, Milano, Italy

###### Abstract

Since its launch, the Alpha Magnetic Spectrometer – 02 (AMS-02) has delivered
outstanding quality measurements of the spectra of cosmic-ray (CR) species,
$\bar{p}$, $e^{\pm}$, and nuclei, 1H– 8O, 10Ne, 12Mg, 14Si, which resulted in
a number of breakthroughs. One of the latest long awaited surprises is the
spectrum of 26Fe just published by AMS-02. Because of the large fragmentation
cross section and large ionization energy losses, most of CR iron at low
energies is local, and may harbor some features associated with relatively
recent supernova (SN) activity in the solar neighborhood. Our analysis of new
iron spectrum together with Voyager 1 and ACE-CRIS data reveals an unexpected
bump in the iron spectrum and in the Fe/He, Fe/O, and Fe/Si ratios at 1–2 GV,
while a similar feature in the spectra of He, O, Si, and in their ratios is
absent, hinting at a local source of low-energy CRs. The found excess fits
well with recent discoveries of radioactive 60Fe deposits in terrestrial and
lunar samples, and in CRs. We provide an updated local interstellar spectrum
(LIS) of iron in the energy range from 1 MeV nucleon-1 to $\sim$10 TeV
nucleon-1. Our calculations employ the GalProp–HelMod framework that is proved
to be a reliable tool in deriving the LIS of CR $\bar{p}$, $e^{-}$, and nuclei
$Z\leq 28$.

cosmic rays — diffusion — elementary particles — interplanetary medium — ISM:
general — Sun: heliosphere

100

##  1 Introduction

New era of precise astrophysical measurements has started about a decade ago
with the launch of the Payload for Antimatter Matter Exploration and Light-
nuclei Astrophysics (PAMELA, Picozza et al., 2007; Adriani et al., 2014). It
was followed by a continuing series of launches of unique instrumentation,
such as the Fermi Large Area Telescope (_Fermi_ -LAT, Atwood et al., 2009),
the Alpha Magnetic Spectrometer – 02 (AMS-02, Aguilar et al., 2013), NUCLEON
experiment (Grebenyuk et al., 2019a, b), CALorimetric Electron Telescope –
(CALET, Adriani et al., 2019; Torii et al., 2019; Maestro et al., 2020), DArk
Matter Particle Explorer mission – (DAMPE, Chang et al., 2017; DAMPE
Collaboration et al., 2017; An et al., 2019), and Cosmic-Ray Energetics and
Mass investigation – (ISS-CREAM, Seo et al., 2014). These experiments are
operating in the high-energy and very-high-energy domains.

Meanwhile, understanding the origin of cosmic rays (CRs) and our interstellar
environment is impossible without connecting high energy measurements with
data from low-energy experiments, such as the Cosmic Ray Isotope Spectrometer
onboard of the Advanced Composition Explorer (ACE-CRIS, Israel et al., 2018;
Binns et al., 2016) operating at the L1 Lagrange point for more than two
decades, and Voyager 1, 2 spacecraft (Stone et al., 1977), the grandparents of
the current instrumentation. The latter are providing unique data on the
elemental spectra and composition at the interstellar reaches of the solar
system (Stone et al., 2013; Cummings et al., 2016; Stone et al., 2019),
currently at 149 AU and 124 AU from the sun, correspondingly.

These instruments and their experimental teams deliver CR data with unmatched
precision and have not tired to surprise us with new-found features in the
energy range that is deemed well-studied. One of the latest long awaited
surprises is the spectrum of iron published by AMS-02 (Aguilar et al., 2021).
This is an expected surprise because CR iron is quite different from lighter
species whose spectra have been recently published: 1H– 8O, 10Ne, 12Mg, 14Si
(Aguilar et al., 2014, 2015a, 2015b, 2016a, 2016b, 2017, 2018a, 2018b, 2019a,
2019b, 2020). Because of the large fragmentation cross section of iron and
large ionization energy losses at low energies, most of low-energy CR iron is
local, coming from relatively recent supernova (SN) activity in the solar
neighborhood, apart from lighter species that may come from more distant
sources. The injection of iron is quite different from the injection of
lighter species—it is injected into the interstellar space only during the SN
explosion, while lighter elements are abundant in pre-supernova winds of
massive stars. Besides, it has lower charge to mass ratio $(Z/A)_{\rm
Fe}\approx 0.46$ compared to $(Z/A)_{\rm He,C,O,Si}\approx 1/2$ for lighter
species and $(Z/A)_{p}=1$ for protons, and thus its acceleration in SN shock
should be somewhat different from other nuclei. It is, therefore, natural to
expect that the spectrum of CR iron should be somewhat different from other
species, and we emphasized that numerous times (e.g., Boschini et al., 2020a).

In a recent paper (Boschini et al., 2020a) we put forward a set of predicted
spectra for all CR nuclei 1H– 28Ni, including those that are not yet published
by AMS-02. Our predicted spectra for those species were based on Voyager 1
(Cummings et al., 2016) and ACE-CRIS data at low energies, while at high
energies we used ATIC-2 (Panov et al., 2009), CREAM (Ahn et al., 2008),
NUCLEON (Grebenyuk et al., 2019a, b), CALET (Adriani et al., 2019), and DAMPE
(An et al., 2019). In the intermediate range we used the HEAO-3-C2 data
(Engelmann et al., 1990) that correspond to the aerogel counter of HEAO-3-C2
experiment. Our comparison with the published AMS-02 spectra of 1H– 8O, 10Ne,
12Mg, 14Si has shown that the HEAO-3-C2 data in the middle range from
2.65–10.6 GeV nucleon-1, the so-called “plateau” corresponding to the aerogel
counter, agree with the AMS-02 data quite well while at lower and higher
energies the systematic deviations are large (see a detailed discussion in
Boschini et al., 2020a). However, the newly measured precise spectrum of iron
just published by AMS-02 (Aguilar et al., 2021) is indeed harboring a surprise
that provides an exciting opportunity to gain insight into the origin and
evolution of the local interstellar medium.

In this paper we discuss the particularity of the measured spectrum of iron.
Our calculations and interpretation employ the GalProp111Available from
http://galprop.stanford.edu –HelMod222http://www.helmod.org/  framework that
is proved to be a reliable tool in deriving the LIS of CR species (Boschini et
al., 2019, 2020a).

##  2 Calculations

Table 1: Best-fit propagation parameters for I\- and P-scenarios Parameter | Units | Best Value | Error
---|---|---|---
$z_{h}$ | kpc | 4.0 | 0.6
$D_{0}(R=4\ {\rm GV})$ | cm2 s-1 | $4.3\times 10^{28}$ | 0.7
$\delta$aaThe P-scenario assumes a break in the diffusion coefficient with index $\delta_{1}=\delta$ below the break and index $\delta_{2}=0.15\pm 0.03$ above the break at $R=370\pm 25$ GV (for details see Boschini et al., 2020b). |  | 0.415 | 0.025
$V_{\rm Alf}$ | km s-1 | 30 | 3
$dV_{\rm conv}/dz$ | km s-1 kpc-1 | 9.8 | 0.8
Table 2: The injection spectrum of iron

| Spectral parameters
---|---
Nucleus |  $\gamma_{0}$ |  $R_{0}$ (GV) | $s_{0}$ | $\gamma^{\prime}$ |  $R^{\prime}$ (GV) | $s^{\prime}$ | $\gamma_{1}$ |  $R_{1}$ (GV) | $s_{1}$ | $\gamma_{2}$ |  $R_{2}$ (GV) | $s_{2}$ | $\gamma_{3}$
Old 26 | Fe | 0.27 | 1.04 | 0.18 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.99 | 7.00 | 0.20 | 2.51 | 355 | 0.17 | 2.19
New 26 | Fe | 0.95 | 2.00 | 0.20 | 3.62 | 2.94 | 0.10 | 2.05 | 17.0 | 0.18 | 2.452 | 355 | 0.17 | 2.23

Note. — The primary abundance of 56Fe is increased from 515 to 577 (c.f.
Tables 2, 3 in Boschini et al., 2020a), with relative abundances of isotopes
of Fe after propagation tuned to ACE-CRIS data.

In this work we are using the same CR propagation model with distributed
reacceleration and convection that was used in our previous analyses (for more
details see Boschini et al., 2017, 2018a, 2018b, 2020a, 2020b). The latest
versions of the GalProp code for Galactic propagation of CRs and the HelMod
code for heliospheric propagation are described in detail in a recent paper by
Boschini et al. (2020a), see also references therein.

The values of propagation parameters along with their confidence limits are
derived from the best available CR data using the Markov Chain Monte Carlo
(MCMC) routine. Five main propagation parameters, that affect the overall
shape of CR spectra, were left free in the scan using GalProp running in the
2D mode: the Galactic halo half-width $z_{h}$, the normalization of the
diffusion coefficient $D_{0}$ at the reference rigidity $R=4$ GV and the index
of its rigidity dependence $\delta$, the Alfvén velocity $V_{\rm Alf}$, and
the gradient of the convection velocity $dV_{\rm conv}/dz$ ($V_{\rm conv}=0$
in the plane, $z=0$). Their best-fit values tuned to the AMS-02 data are
listed in Table 1 and are the same as obtained in Boschini et al. (2020a). The
radial size of the Galaxy does not significantly affect the values of
propagation parameters and was set to 20 kpc. Besides, we introduced a factor
$\beta^{\eta}$ in the diffusion coefficient, where $\beta=v/c$, and $\eta$ was
left free. The best fit value of $\eta=0.70$ improves the agreement at low
energies, and slightly affects the choice of injection indices ${\gamma}_{0}$
an ${\gamma}_{1}$. A detailed discussion of the injection (I) and propagation
(P) scenarios of the 350 GV break can be found in Vladimirov et al. (2012) and
Boschini et al. (2020a).

The corresponding B/C ratio also remains the same (see Fig. 4 in Boschini et
al., 2020a), and compares well with all available measurements: Voyager 1
(Cummings et al., 2016), ACE-
CRIS333http://www.srl.caltech.edu/ACE/ASC/level2/cris_l2desc.html, AMS-02
(Aguilar et al., 2018a), ATIC-2 (Panov et al., 2009), CREAM (Ahn et al., 2008,
2009), and NUCLEON (Grebenyuk et al., 2019b).

In this calculation we are tuning only the injection spectrum of iron to match
the new data from AMS-02 at high energies and ACE-CRIS and Voyager 1 at low
energies, the old and new injection parameters are shown in Table 2. Compared
to the old injection spectrum we have to add another break at low rigidities
at $R^{\prime}=2.94$ GV and a very steep spectrum with index
$\gamma^{\prime}=3.62$ between $R_{0}=2.00$ GV and $R^{\prime}=2.94$ GV. The
obtained agreement with data is good, but the new Fe spectrum is quite
different from what was expected based on the fit that employs the HEAO-3-C2
data (Boschini et al., 2020a).

##  3 Results

Figure 1:  A fit to the new spectrum of iron by AMS-02 (Aguilar et al., 2021).
In the top panel, only AMS-02 data are shown. The middle panel shows the
quality of the fit, the relative difference between the calculations and the
data set. The bottom panel shows two fits as compared to the data sets by
HEAO-3-C2 (Engelmann et al., 1990) or by AMS-02 (Aguilar et al., 2021) in the
intermediate range, while at low and very-high energies we use Voyager 1
(Cummings et al., 2016), ACE-CRIS, CREAM (Ahn et al., 2008), and NUCLEON
(Grebenyuk et al., 2019a, b) data. The gray lines show the LIS tuned to AMS-02
data (solid line) and the old LIS tuned to the “plateau” middle range of the
HEAO-3-C2 data (dashed line). The red line shows the LIS modulated
appropriately to the solar activity during the AMS-02 data taking, while solid
blue line is the LIS derived from the AMS-02 data and modulated appropriately
to the HEAO-3 flight. The two green lines correspond to two ACE-CRIS data
taking periods, where the modulated spectra are almost independent on which
data are used at high energies, AMS-02 or HEAO-3-C2, dashed and solid lines
are overlapping.  Figure 2:  The LIS of He, O, Si, and Fe compared to Voyager
1 data (Cummings et al., 2016). The solid black line shows the updated Fe LIS
tuned to AMS-02 data, while dashed line shows the previous LIS (Boschini et
al., 2020a) based on the “plateau” middle range of the HEAO-3-C2 data.

Figure 3:  The calculated ratios of primary species, Fe/He, Fe/O, Fe/Si, are
compared with Voyager 1 (Cummings et al., 2016), ACE-CRIS, and AMS-02 data
(Aguilar et al., 2017, 2021, 2020). Also shown are HEAO-3-C2 data (Engelmann
et al., 1990). The gray line shows the LIS ratios tuned to AMS-02 data, and
the red line shows the modulated LIS ratios. The dashed gray line shows the
LIS ratios tuned to HEAO-3-C2 data (Boschini et al., 2020a) based on the
“plateau” middle range of the HEAO-3-C2 data. For the Fe/He ratio, only Fe was
tuned to the HEAO-3-C2 data. In all plots, the Voyager 1, ACE-CRIS, and
HEAO-3-C2 data are converted from kinetic energy per nucleon to rigidity
assuming $A/Z=2$. The shaded area shows the ratios modulated to the
appropriate level (ACE-CRIS, HEAO-3-C2) with the width corresponding to
1$\sigma$ error.

Figure 4:  The calculated ratios of primary species, He/O and Si/O, are
compared with Voyager 1 (Cummings et al., 2016), ACE-CRIS, HEAO-3-C2, and
AMS-02 data (Aguilar et al., 2015b, 2017, 2020). The Voyager 1, ACE-CRIS, and
HEAO-3-C2 data are converted from kinetic energy per nucleon to rigidity
assuming $A/Z=2$.

Fig. 1 shows the fit to the iron spectrum by AMS-02 (Aguilar et al., 2021). In
the top panel, only AMS-02 data are shown. The quality of the fit is good with
the residuals being $\lesssim$5% in the whole range (middle panel). The bottom
panel shows two fits as compared to the data sets by HEAO-3-C2 (Engelmann et
al., 1990) or by AMS-02 (Aguilar et al., 2021) in the intermediate range,
while at low and very-high energies we use Voyager 1 (Cummings et al., 2016),
ACE-CRIS, CREAM (Ahn et al., 2008), and NUCLEON (Grebenyuk et al., 2019a, b)
data. The gray lines show the LIS tuned to AMS-02 data (solid line) and the
previous LIS tuned to the “plateau” middle range of the HEAO-3-C2 data (dashed
line), while colored lines show the LIS modulated appropriately to the periods
of ACE-CRIS, AMS-02, and HEAO-3 data taking. The solid blue line in Fig. 1
shows where the correct spectrum of HEAO-3-C2 should be if we assume the iron
LIS based on AMS-02 data. One can see that matching the Voyager 1 and
modulated ACE-CRIS data, on one hand, and modulated AMS-02 data, on the other
hand, requires a sharp spectral steepening in the transition region of the LIS
between $\sim$2 GV and $\sim$3 GV and a similar feature in the injection
spectrum as well (see Table 2).

Obvious is also the difference in the spectral shapes of He, O, Si, on one
hand, and Fe, on the other hand (Fig. 2). This difference becomes more obvious
when one looks at the ratios. A comparison of the ratios of iron to lighter
primary species, Fe/He, Fe/O, Fe/Si, with AMS-02 data shows excellent
agreement in the rigidity range from 2 GV – 2 TV (Fig. 3). If the ratios are
extended to lower energies where they compare with Voyager 1 and ACE-CRIS
data, one can see a clear bump at $\sim$1–2 GV. The middle plot of the ratio
Fe/O, where we use Voyager 1, ACE-CRIS, and AMS-02 data plotted vs. kinetic
energy per nucleon without converting to rigidity, proves that fitting all
data simultaneously is impossible without a bump. Therefore, the bumps appear
in every ratio, Fe/He, Fe/O, Fe/Si, while a similar bump in the He/O and Si/O
ratios is absent, see Fig. 4.

Interestingly, the bump appears in the energy gap between ACE-CRIS and AMS-02,
and is the result of tuning the Fe spectrum to all three data sets, Voyager 1,
ACE-CRIS, AMS-02, each with an appropriate heliospheric modulation level. The
anomaly would be unnoticed if the data of each instrument is taken separately.

##  4 Discussion

The first ever accurate measurement of Fe spectrum in the rigidity range from
2 GV – 2 TV (Aguilar et al., 2021) is a giant milestone. For the first time it
allows us to analyze the spectra of primary species, He, O, Fe, whose atomic
and mass numbers, fragmentation cross sections, and ionization energy losses
are considerably different. The appearance of the bump in the Fe/He, Fe/O, and
Fe/Si ratios, while lacking a similar feature in the He/O and Si/O ratios,
implies a local source of low-energy CRs. Because of the fast ionization
losses of iron nuclei in the ISM, CR iron from distant sources is suppressed
and this gives the local source such a prominence. In the case of lighter CR
nuclei, whose ionization losses are not that fast, the local component is
mixed up with old Galactic CRs coming from distant sources and thus a
prominent excess does not form.

The likely source of the excess CR iron are the old SN remnants. In fact, the
evidence of the past SN activity in the local ISM is abundant. The Local
Bubble is a low density region of the size of $\sim$200 pc around the Sun
filled with hot H i gas that itself was formed in a series of SN explosions
(e.g., Sfeir et al., 1999; Frisch et al., 2011). There are multiple reports of
an excess of radioactive 60Fe found in the deep ocean sediments (Knie et al.,
1999, 2004; Ludwig et al., 2016; Wallner et al., 2016), in lunar regolith
samples (Cook et al., 2009; Fimiani et al., 2012, 2014), and more recently in
the Antarctic snow (Koll et al., 2019). Such deposits can be made by SN
explosions in the solar neighborhood. Recent observation of 60Fe (the half-
life $\tau_{1/2}\sim 2.6$ Myr, Rugel et al., 2009) in CRs by ACE-CRIS
spacecraft (Binns et al., 2016) implies that the low-energy CRs from the most
recent SN are still around.

It is hard to establish the number of SNe events and their exact timing, but
it is clear that there could be several events during the last $\sim$10 Myr at
distances of up to 100 parsecs (Wallner et al., 2016). The most recent SN
events in the solar neighborhood were 1.5–3.2 Myr and 6.5–8.7 Myr ago (Fry et
al., 2015; Wallner et al., 2016). The measured spread (width) of the signal is
$\sim$1.5 Myr (Fry et al., 2015), which is too long for a single event. Each
of these events could, in principle, consist of several consequent SN
explosions separated by some 100 kyr, as an estimated time spread for a single
SN, located at $\sim$100 pc from the Earth, is just $\sim$100–400 kyr and the
travel time is $\sim$200 kyr. A detailed modeling by Breitschwerdt et al.
(2016) indicates two SNe at distances 90–100 pc with the closest occurred 2.3
Myr ago and the second-closest exploded about 1.5 Myr ago, both with stellar
masses of $\sim$9$M_{\odot}$.

The new-found excess in the Fe spectrum below $\sim$2 GV is therefore falling
in line with other excesses in 60Fe. However, this is the first time when the
excess is found in the spectrum of the element that is dominated by stable
species, most notably 56Fe. Such an excess has implications for the spectra of
fragmentation products of iron. However, it is too early to make predictions
for them as we have to await for a confirmation of similar features in the
spectra of sub-Fe species.

##  5 HEAO-3-C2 data

In the previous paper we relied on the HEAO-3-C2 data (Engelmann et al., 1990)
in the middle range, a so-called “plateau” region, to substitute the missing
AMS-02 data. While it worked well for light and middle-range nuclei, it does
not work so good for Fe – as we have learned after AMS-02 data were published
(Aguilar et al., 2021). Surprisingly all HEAO-3-C2 data points for Fe overlap
with AMS-02 data (Fig. 1), but the solar modulation levels during the HEAO-3
flight and AMS-02 data taking are dramatically different. The former was
launched on September 20, 1979 and ended on May 29, 1981, and took the data
during the solar maximum conditions, while the AMS-02 data were taken from
2011–2019, i.e., through almost entire Cycle 24 where the solar activity was
moderate even during the polarity reversal of the solar magnetic field.
Therefore, the LIS derived from these two datasets are also quite different.
The solid blue line in Fig. 1 shows where the correct spectrum of HEAO-3-C2
should be if we assume the iron LIS based on AMS-02 data. Here we discuss a
possible reason for such a discrepancy.

The AMS-02 experiment uses modern technology, its response was thoroughly
simulated and tested, it also has several independent systems that allow for
data cross checks. Therefore, it is rather unlikely to have a serious flaw. On
the other hand, the HEAO-3-C2 experiment was built in 1970s, at the same time
that Voyager 1, 2 were built. There was no prelaunch detector response
simulations. Many systems went untested and the calibrations were done after
the launch. In particular, the rigidity calibration was done using the
geomagnetic field; the latter was lacking the detailed knowledge at that time
(for a discussion see Boschini et al., 2020a). Meanwhile, our analysis has
shown that the middle range of the HEAO-3-C2 data, a so-called “plateau,”
agrees well with AMS-02 data for light and medium nuclei. There must be some
reason why the situation with iron is different.

While it is difficult to point to a single specific reason for such a
difference, we think that the incorrect evaluation of the probability of
nuclear fragmentation is the most likely. In the data analysis, the charge
changing cross section was assumed to be energy-independent (Engelmann et al.,
1990),

$\sigma=57.3(A_{t}^{1/3}+A_{p}^{1/3}-0.83)^{2},$ (1)

with parameters tuned to the measurements of charge changing reactions of 12C,
16O, and 56Fe beams with He target in the energy range from 540 MeV nucleon-1
to 1600 MeV nucleon-1 (Ferrando et al., 1988). Here $A_{p}$ and $A_{t}$ are
the mass numbers of the projectile and target nuclei, correspondingly.
Meanwhile, the average grammage for particles passing the instrument is 16 g
cm2 and the “mean atomic number is $Z_{t}=30$.” The mean atomic number of the
material $Z_{t}$ is likely a typo and perhaps more correct would be to assume
that it is the mean mass number $A_{t}=30$ rather than the atomic number.

In any case, the instrumental grammage is significant and the loss of heavy CR
nuclei due to the fragmentation was considerable. Therefore, the accuracy of a
charge changing cross section is crucial for heavy species while it is less
essential for light nuclei. The adopted scaling formula Eq. (1) was tuned to a
rather light He target and extrapolated for $A_{t}=30$ target. We believe it
is this correction for nuclear fragmentation for Fe that makes it different
from lighter species and is the most likely reason for the disagreement with
the AMS-02 data in the HEAO-3-C2 “plateau” energy range 2.65–10.6 GeV
nucleon-1. If our conclusion is correct, we should see a gradual increase in
the discrepancy between the HEAO-3-C2 “plateau” data and AMS-02 data as the
mass number increases from 14Si to 26Fe even though the agreement is good for
all species from 4Be to 14Si.

##  6 Conclusion

Using a combined data of AMS-02 (Aguilar et al., 2021), ACE-CRIS, and Voyager
1 (Cummings et al., 2016), we found an unexpected bump in the spectrum of CR
iron and the Fe/He, Fe/O, and Fe/Si ratios, which is revealed as a sharp
steepening in the range 2–3 GV necessary to connect ACE-CRIS and AMS-02 data.
Meanwhile, a similar feature in the spectra of He, O, and Si and their ratios
is absent. Taken independently, the data of each instrument do not show any
feature.

The new-found excess in the Fe spectrum below $\sim$2 GV is therefore falling
in line with other excesses in 60Fe, which is likely connected to the past SN
activity in the Local Bubble. However, this is the first time when the excess
is found in the spectrum of the element that is dominated by stable species,
most notably 56Fe. Such an excess has implications for the spectra of
fragmentation products of iron. It is also important to measure the spectra of
other heavy CR species, specifically in the middle rigidity domain
$\lesssim$10 GV, to see if a similar spectral feature is present.

We are also discussing the reason for the discrepancy between AMS-02 and
HEAO-3-C2 data. We argue that the likely reason is the incorrect estimate of
fragmentation of CR iron nuclei inside the instrument. Given a significant
instrumental grammage $\sim$16 g cm-2 and its high mean mass number, the loss
of heavy nuclei due to the fragmentation was considerable. Therefore, the
accuracy of a charge changing cross section is crucial for heavy species while
it is not so essential for light nuclei. If our conclusion is correct, we
should see a gradual increase in the discrepancy between the HEAO-3-C2
“plateau” data and AMS-02 data as the mass number increases from 14Si to 26Fe
even though the agreement is good for all species from 4Be to 14Si.

Special thanks to Pavol Bobik, Giuliano Boella, Karel Kudela, Marian Putis,
and Mario Zannoni for their continuous support of the HelMod project and many
useful suggestions. This work is supported by ASI (Agenzia Spaziale Italiana)
through a contract ASI-INFN No. 2019-19-HH.0 and by ESA (European Space
Agency) through a contract 4000116146/16/NL/HK. Igor V. Moskalenko and Troy A.
Porter acknowledge support from NASA Grant No. NNX17AB48G. We thank the ACE
CRIS instrument team and the ACE Science Center for providing the ACE data.
This research has made use of the SSDC Cosmic rays database (Di Felice et al.,
2017) and LPSC Database of Charged Cosmic Rays (Maurin et al., 2014).

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##  Appendix A Analytical parameterization and numerical tables of the iron
LIS

Here we provide an analytical parameterization of the iron LIS:

$\displaystyle F_{\rm Fe}$ $\displaystyle(R)=$ (A1)
$\displaystyle\begin{cases}\displaystyle
R^{-2.7}\left[a-bR+cR^{2}-dR^{3}+f\tanh\left(\tanh\left(RG(-gR)\right)\right)-hG(iR^{2})\right],&R\leq
2.8\,{\rm GV},\vskip 3.0pt plus 1.0pt minus 1.0pt\\\ \displaystyle
R^{-2.7}\left[l-mR-n\tilde{R}+o\frac{\tilde{R}}{R^{2}}-\frac{p}{\tilde{R}}+\frac{q}{R^{2}\tilde{R}}+r\log\left(s+R\right)+\frac{t}{\tilde{R}\log\left(s+R\right)}\right],&R>2.8\,{\rm
GV},\end{cases}$

where $R$ is the particle rigidity in GV, the values of the fitting parameters
from $a$ to $t$ are given in Table 3, and the $\tilde{R}$, and $G(x)$
functions are defined as:

$\displaystyle\tilde{R}$ $\displaystyle=\log{R},$ $\displaystyle G(x)$
$\displaystyle=e^{-x^{2}}.$

The analytical representation, Eq. (A1), is also complemented by numerical
tables calculated for the I-scenario, which tabulate the LIS in rigidity $R$
(Table 4) and in kinetic energy $E_{\rm kin}$ per nucleon (Table 5).

Table 3: Parameters of the analytical fit to the iron LIS  Param |  26Fe | Param |  26Fe | Param |  26Fe | Param |  26Fe
---|---|---|---|---|---|---|---
a | 2.8224e+0 | g | 2.3448e+0 | m | 5.9700e-8 | q | 1.6412e+2
b | 3.3660e-1 | h | 2.8171e+0 | n | 5.6550e+0 | r | 6.5309e+0
c | 6.1955e-1 | i | 3.8226e-1 | o | 2.4807e+2 | s | 2.0316e+2
d | 1.2735e-1 | l | 2.6334e+1 | p | 1.3610e+2 | t | 1.5300e+2
f | 2.3980e-1 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
Table 4: $Z=26$ – Iron LIS

Rigidity | Differential | Rigidity | Differential | Rigidity | Differential | Rigidity | Differential | Rigidity | Differential
---|---|---|---|---|---|---|---|---|---
GV | intensity | GV | intensity | GV | intensity | GV | intensity | GV | intensity
9.299e-02 | 5.252e-03 | 7.508e-01 | 3.968e-01 | 1.039e+01 | 1.475e-02 | 5.430e+02 | 6.616e-07 | 3.413e+04 | 1.376e-11
9.758e-02 | 5.891e-03 | 7.892e-01 | 4.239e-01 | 1.127e+01 | 1.234e-02 | 5.977e+02 | 5.152e-07 | 3.759e+04 | 1.069e-11
1.024e-01 | 6.587e-03 | 8.297e-01 | 4.510e-01 | 1.224e+01 | 1.029e-02 | 6.580e+02 | 4.013e-07 | 4.139e+04 | 8.297e-12
1.075e-01 | 7.365e-03 | 8.724e-01 | 4.780e-01 | 1.330e+01 | 8.542e-03 | 7.243e+02 | 3.126e-07 | 4.558e+04 | 6.441e-12
1.128e-01 | 8.233e-03 | 9.175e-01 | 5.043e-01 | 1.448e+01 | 7.060e-03 | 7.974e+02 | 2.436e-07 | 5.019e+04 | 4.999e-12
1.183e-01 | 9.204e-03 | 9.651e-01 | 5.300e-01 | 1.576e+01 | 5.812e-03 | 8.779e+02 | 1.898e-07 | 5.527e+04 | 3.880e-12
1.242e-01 | 1.029e-02 | 1.015e+00 | 5.547e-01 | 1.718e+01 | 4.766e-03 | 9.665e+02 | 1.479e-07 | 6.086e+04 | 3.012e-12
1.303e-01 | 1.150e-02 | 1.069e+00 | 5.778e-01 | 1.873e+01 | 3.889e-03 | 1.064e+03 | 1.152e-07 | 6.702e+04 | 2.337e-12
1.368e-01 | 1.285e-02 | 1.125e+00 | 5.987e-01 | 2.045e+01 | 3.162e-03 | 1.172e+03 | 8.974e-08 | 7.380e+04 | 1.813e-12
1.435e-01 | 1.435e-02 | 1.184e+00 | 6.164e-01 | 2.233e+01 | 2.561e-03 | 1.290e+03 | 6.989e-08 | 8.126e+04 | 1.407e-12
1.506e-01 | 1.603e-02 | 1.248e+00 | 6.309e-01 | 2.440e+01 | 2.065e-03 | 1.420e+03 | 5.443e-08 | 8.948e+04 | 1.092e-12
1.581e-01 | 1.790e-02 | 1.315e+00 | 6.415e-01 | 2.668e+01 | 1.657e-03 | 1.564e+03 | 4.238e-08 | 9.854e+04 | 8.468e-13
1.659e-01 | 1.998e-02 | 1.386e+00 | 6.476e-01 | 2.920e+01 | 1.325e-03 | 1.722e+03 | 3.300e-08 | 1.085e+05 | 6.569e-13
1.741e-01 | 2.230e-02 | 1.461e+00 | 6.486e-01 | 3.196e+01 | 1.057e-03 | 1.896e+03 | 2.570e-08 | 1.195e+05 | 5.095e-13
1.827e-01 | 2.488e-02 | 1.542e+00 | 6.436e-01 | 3.500e+01 | 8.402e-04 | 2.087e+03 | 2.001e-08 | 1.316e+05 | 3.952e-13
1.918e-01 | 2.775e-02 | 1.627e+00 | 6.317e-01 | 3.835e+01 | 6.665e-04 | 2.298e+03 | 1.559e-08 | 1.449e+05 | 3.065e-13
2.013e-01 | 3.093e-02 | 1.718e+00 | 6.120e-01 | 4.204e+01 | 5.275e-04 | 2.531e+03 | 1.215e-08 | 1.596e+05 | 2.377e-13
2.112e-01 | 3.447e-02 | 1.816e+00 | 5.839e-01 | 4.610e+01 | 4.166e-04 | 2.787e+03 | 9.464e-09 | 1.757e+05 | 1.843e-13
2.217e-01 | 3.839e-02 | 1.919e+00 | 5.472e-01 | 5.057e+01 | 3.283e-04 | 3.068e+03 | 7.374e-09 | 1.935e+05 | 1.429e-13
2.327e-01 | 4.273e-02 | 2.031e+00 | 5.031e-01 | 5.549e+01 | 2.583e-04 | 3.379e+03 | 5.744e-09 | 2.131e+05 | 1.108e-13
2.442e-01 | 4.754e-02 | 2.150e+00 | 4.539e-01 | 6.091e+01 | 2.029e-04 | 3.720e+03 | 4.474e-09 |  $\cdots$ |  $\cdots$
2.563e-01 | 5.286e-02 | 2.277e+00 | 4.025e-01 | 6.688e+01 | 1.592e-04 | 4.097e+03 | 3.485e-09 |  $\cdots$ |  $\cdots$
2.690e-01 | 5.873e-02 | 2.414e+00 | 3.521e-01 | 7.344e+01 | 1.247e-04 | 4.511e+03 | 2.713e-09 |  $\cdots$ |  $\cdots$
2.823e-01 | 6.521e-02 | 2.561e+00 | 3.051e-01 | 8.068e+01 | 9.766e-05 | 4.967e+03 | 2.113e-09 |  $\cdots$ |  $\cdots$
2.964e-01 | 7.234e-02 | 2.720e+00 | 2.633e-01 | 8.864e+01 | 7.640e-05 | 5.470e+03 | 1.645e-09 |  $\cdots$ |  $\cdots$
3.111e-01 | 8.019e-02 | 2.891e+00 | 2.274e-01 | 9.741e+01 | 5.972e-05 | 6.023e+03 | 1.280e-09 |  $\cdots$ |  $\cdots$
3.265e-01 | 8.881e-02 | 3.075e+00 | 1.974e-01 | 1.071e+02 | 4.665e-05 | 6.632e+03 | 9.964e-10 |  $\cdots$ |  $\cdots$
3.428e-01 | 9.826e-02 | 3.275e+00 | 1.723e-01 | 1.177e+02 | 3.639e-05 | 7.303e+03 | 7.754e-10 |  $\cdots$ |  $\cdots$
3.598e-01 | 1.086e-01 | 3.490e+00 | 1.508e-01 | 1.294e+02 | 2.836e-05 | 8.042e+03 | 6.033e-10 |  $\cdots$ |  $\cdots$
3.777e-01 | 1.199e-01 | 3.724e+00 | 1.319e-01 | 1.423e+02 | 2.209e-05 | 8.855e+03 | 4.693e-10 |  $\cdots$ |  $\cdots$
3.966e-01 | 1.322e-01 | 3.978e+00 | 1.151e-01 | 1.565e+02 | 1.720e-05 | 9.751e+03 | 3.651e-10 |  $\cdots$ |  $\cdots$
4.163e-01 | 1.456e-01 | 4.254e+00 | 1.002e-01 | 1.721e+02 | 1.339e-05 | 1.074e+04 | 2.839e-10 |  $\cdots$ |  $\cdots$
4.371e-01 | 1.600e-01 | 4.554e+00 | 8.683e-02 | 1.894e+02 | 1.042e-05 | 1.182e+04 | 2.208e-10 |  $\cdots$ |  $\cdots$
4.590e-01 | 1.756e-01 | 4.880e+00 | 7.502e-02 | 2.083e+02 | 8.110e-06 | 1.302e+04 | 1.717e-10 |  $\cdots$ |  $\cdots$
4.820e-01 | 1.925e-01 | 5.236e+00 | 6.465e-02 | 2.292e+02 | 6.311e-06 | 1.434e+04 | 1.335e-10 |  $\cdots$ |  $\cdots$
5.061e-01 | 2.105e-01 | 5.625e+00 | 5.552e-02 | 2.522e+02 | 4.911e-06 | 1.579e+04 | 1.037e-10 |  $\cdots$ |  $\cdots$
5.315e-01 | 2.299e-01 | 6.049e+00 | 4.752e-02 | 2.775e+02 | 3.821e-06 | 1.738e+04 | 8.062e-11 |  $\cdots$ |  $\cdots$
5.582e-01 | 2.505e-01 | 6.513e+00 | 4.056e-02 | 3.054e+02 | 2.973e-06 | 1.914e+04 | 6.265e-11 |  $\cdots$ |  $\cdots$

Note. — Differential Intensity units: (m2 s sr GV)-1.

Table 5: $Z=26$ – Iron LIS

$E_{\rm kin}$ | Differential | $E_{\rm kin}$ | Differential | $E_{\rm kin}$ | Differential | $E_{\rm kin}$ | Differential | $E_{\rm kin}$ | Differential
---|---|---|---|---|---|---|---|---|---
GeV/n | intensity | GeV/n | intensity | GeV/n | intensity | GeV/n | intensity | GeV/n | intensity
1.000e-03 | 2.434e-01 | 6.309e-02 | 2.428e+00 | 3.981e+00 | 3.246e-02 | 2.512e+02 | 1.428e-06 | 1.585e+04 | 2.969e-11
1.101e-03 | 2.602e-01 | 6.948e-02 | 2.483e+00 | 4.384e+00 | 2.708e-02 | 2.766e+02 | 1.112e-06 | 1.745e+04 | 2.305e-11
1.213e-03 | 2.773e-01 | 7.651e-02 | 2.531e+00 | 4.827e+00 | 2.253e-02 | 3.046e+02 | 8.663e-07 | 1.922e+04 | 1.790e-11
1.335e-03 | 2.954e-01 | 8.425e-02 | 2.571e+00 | 5.315e+00 | 1.866e-02 | 3.354e+02 | 6.748e-07 | 2.116e+04 | 1.389e-11
1.470e-03 | 3.148e-01 | 9.277e-02 | 2.602e+00 | 5.853e+00 | 1.540e-02 | 3.693e+02 | 5.257e-07 | 2.330e+04 | 1.079e-11
1.619e-03 | 3.353e-01 | 1.022e-01 | 2.623e+00 | 6.446e+00 | 1.266e-02 | 4.067e+02 | 4.096e-07 | 2.566e+04 | 8.371e-12
1.783e-03 | 3.572e-01 | 1.125e-01 | 2.635e+00 | 7.098e+00 | 1.036e-02 | 4.478e+02 | 3.192e-07 | 2.825e+04 | 6.497e-12
1.963e-03 | 3.805e-01 | 1.239e-01 | 2.637e+00 | 7.816e+00 | 8.450e-03 | 4.931e+02 | 2.487e-07 | 3.111e+04 | 5.042e-12
2.162e-03 | 4.052e-01 | 1.364e-01 | 2.627e+00 | 8.607e+00 | 6.864e-03 | 5.430e+02 | 1.937e-07 | 3.426e+04 | 3.912e-12
2.381e-03 | 4.315e-01 | 1.502e-01 | 2.602e+00 | 9.478e+00 | 5.555e-03 | 5.980e+02 | 1.508e-07 | 3.773e+04 | 3.035e-12
2.622e-03 | 4.593e-01 | 1.654e-01 | 2.564e+00 | 1.044e+01 | 4.476e-03 | 6.585e+02 | 1.175e-07 | 4.155e+04 | 2.355e-12
2.887e-03 | 4.889e-01 | 1.822e-01 | 2.513e+00 | 1.149e+01 | 3.590e-03 | 7.251e+02 | 9.147e-08 | 4.575e+04 | 1.827e-12
3.179e-03 | 5.202e-01 | 2.006e-01 | 2.447e+00 | 1.266e+01 | 2.870e-03 | 7.985e+02 | 7.122e-08 | 5.038e+04 | 1.417e-12
3.501e-03 | 5.533e-01 | 2.209e-01 | 2.367e+00 | 1.394e+01 | 2.287e-03 | 8.793e+02 | 5.546e-08 | 5.548e+04 | 1.099e-12
3.855e-03 | 5.884e-01 | 2.432e-01 | 2.270e+00 | 1.535e+01 | 1.818e-03 | 9.682e+02 | 4.318e-08 | 6.109e+04 | 8.524e-13
4.245e-03 | 6.256e-01 | 2.678e-01 | 2.156e+00 | 1.690e+01 | 1.442e-03 | 1.066e+03 | 3.364e-08 | 6.727e+04 | 6.611e-13
4.675e-03 | 6.648e-01 | 2.949e-01 | 2.024e+00 | 1.861e+01 | 1.141e-03 | 1.174e+03 | 2.621e-08 | 7.408e+04 | 5.127e-13
5.148e-03 | 7.061e-01 | 3.248e-01 | 1.873e+00 | 2.049e+01 | 9.009e-04 | 1.293e+03 | 2.042e-08 | 8.157e+04 | 3.975e-13
5.669e-03 | 7.498e-01 | 3.577e-01 | 1.705e+00 | 2.257e+01 | 7.098e-04 | 1.424e+03 | 1.591e-08 | 8.983e+04 | 3.082e-13
6.242e-03 | 7.957e-01 | 3.938e-01 | 1.525e+00 | 2.485e+01 | 5.583e-04 | 1.568e+03 | 1.239e-08 | 9.892e+04 | 2.390e-13
6.874e-03 | 8.440e-01 | 4.337e-01 | 1.339e+00 | 2.736e+01 | 4.385e-04 | 1.726e+03 | 9.654e-09 |  $\cdots$ |  $\cdots$
7.569e-03 | 8.947e-01 | 4.776e-01 | 1.158e+00 | 3.013e+01 | 3.440e-04 | 1.901e+03 | 7.519e-09 |  $\cdots$ |  $\cdots$
8.335e-03 | 9.479e-01 | 5.259e-01 | 9.886e-01 | 3.318e+01 | 2.695e-04 | 2.093e+03 | 5.855e-09 |  $\cdots$ |  $\cdots$
9.179e-03 | 1.004e+00 | 5.791e-01 | 8.372e-01 | 3.654e+01 | 2.110e-04 | 2.305e+03 | 4.559e-09 |  $\cdots$ |  $\cdots$
1.011e-02 | 1.062e+00 | 6.377e-01 | 7.069e-01 | 4.023e+01 | 1.650e-04 | 2.539e+03 | 3.549e-09 |  $\cdots$ |  $\cdots$
1.113e-02 | 1.122e+00 | 7.022e-01 | 5.982e-01 | 4.431e+01 | 1.290e-04 | 2.795e+03 | 2.762e-09 |  $\cdots$ |  $\cdots$
1.226e-02 | 1.186e+00 | 7.733e-01 | 5.092e-01 | 4.879e+01 | 1.008e-04 | 3.078e+03 | 2.150e-09 |  $\cdots$ |  $\cdots$
1.350e-02 | 1.251e+00 | 8.515e-01 | 4.365e-01 | 5.373e+01 | 7.859e-05 | 3.390e+03 | 1.673e-09 |  $\cdots$ |  $\cdots$
1.486e-02 | 1.319e+00 | 9.377e-01 | 3.757e-01 | 5.916e+01 | 6.124e-05 | 3.733e+03 | 1.302e-09 |  $\cdots$ |  $\cdots$
1.637e-02 | 1.389e+00 | 1.033e+00 | 3.236e-01 | 6.515e+01 | 4.770e-05 | 4.110e+03 | 1.013e-09 |  $\cdots$ |  $\cdots$
1.802e-02 | 1.462e+00 | 1.137e+00 | 2.785e-01 | 7.174e+01 | 3.714e-05 | 4.526e+03 | 7.877e-10 |  $\cdots$ |  $\cdots$
1.985e-02 | 1.536e+00 | 1.252e+00 | 2.393e-01 | 7.900e+01 | 2.891e-05 | 4.984e+03 | 6.126e-10 |  $\cdots$ |  $\cdots$
2.185e-02 | 1.612e+00 | 1.379e+00 | 2.050e-01 | 8.699e+01 | 2.250e-05 | 5.489e+03 | 4.764e-10 |  $\cdots$ |  $\cdots$
2.406e-02 | 1.689e+00 | 1.518e+00 | 1.753e-01 | 9.580e+01 | 1.751e-05 | 6.044e+03 | 3.704e-10 |  $\cdots$ |  $\cdots$
2.650e-02 | 1.767e+00 | 1.672e+00 | 1.496e-01 | 1.055e+02 | 1.363e-05 | 6.656e+03 | 2.879e-10 |  $\cdots$ |  $\cdots$
2.918e-02 | 1.846e+00 | 1.841e+00 | 1.274e-01 | 1.162e+02 | 1.060e-05 | 7.329e+03 | 2.238e-10 |  $\cdots$ |  $\cdots$
3.213e-02 | 1.925e+00 | 2.027e+00 | 1.082e-01 | 1.279e+02 | 8.250e-06 | 8.071e+03 | 1.739e-10 |  $\cdots$ |  $\cdots$
3.539e-02 | 2.003e+00 | 2.233e+00 | 9.171e-02 | 1.409e+02 | 6.419e-06 | 8.887e+03 | 1.352e-10 |  $\cdots$ |  $\cdots$

Note. — Differential Intensity units: (m2 s sr GeV/n)-1.